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data.txt
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connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: =>p1 / NOT p1 =>
rule: p1 => / =>NOT p1
rule: / =>TOP
analyticity:
sequent: (p1 OR p2) AND ((p1 IMPLIES p3) AND (p2 IMPLIES p3))=>p3
provable: true
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
nextOperators: BOX
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: =>p1 / NOT p1 =>
rule: p1 => / =>NOT p1
rule: / =>TOP
analyticity:
sequent: =>(NOT BOX (p1 AND NOT p1))
provable: true
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
nextOperators: BOX
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: =>p1 / NOT p1 =>
rule: p1 => / =>NOT p1
rule: / =>TOP
analyticity:
sequent: BOX p1 => NOT BOX NOT p1
provable: true
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
nextOperators: BOX
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: =>p1 / NOT p1 =>
rule: p1 => / =>NOT p1
rule: / =>TOP
analyticity:
sequent: NOT BOX NOT p1 => BOX p1
provable: true
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
nextOperators: BOX
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: =>p1 / NOT p1 =>
rule: p1 => / =>NOT p1
rule: / =>TOP
analyticity:
sequent: p1 => BOX p1
provable: false
connectives: AND:2,OR:2,IMPLIES:2,TOP:0
nextOperators: q1 said, q2 said, q3 said, q4 said
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: / =>TOP
analyticity:
inputSequent: => q1 said (p1 IMPLIES p1)
sequent: q1 said ((p1 OR p2) AND ((p1 IMPLIES p3) AND (p2 IMPLIES p3)))=>q1 said p3
provable: false
connectives: AND:2,OR:2,IMPLIES:2,NOT:1, TOP:0, BOT:0
nextOperators: q1 said, q2 said, q3 said, q4 said
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: / =>TOP
rule: /=>BOT IMPLIES p1
rule: /BOT OR p1=>p1
rule: /p1 OR BOT=> p1
rule: /(p1 AND p2) OR p1 => p1
rule: /p1 OR (p1 AND p2) => p1
rule: /p1 OR p1 => p1
rule: /p1,NOT p1=>
rule: /=>p2 IMPLIES (p1 IMPLIES p2)
rule: /=>p1 IMPLIES p1
rule: /=>(p1 AND p2) IMPLIES p1
rule: /=>(p1 AND p2) IMPLIES p2
analyticity:
sequent: q1 said ((p1 OR p2) AND ((p1 IMPLIES p3) AND (p2 IMPLIES p3)))=>q1 said p3
provable: false
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: p1=>/NOTNOTp1=>
rule: p1=>/=>NOTp1
rule: =>p1;=>NOTp1/NOT(p1 AND NOTp1)=>
rule: NOTp1=>;NOTp2=>/NOT(p1 AND p2)=>
rule: NOTp1=>; p2,NOTp2=>/NOT(p1 OR p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 OR p2)=>
rule: p1=>; p2,NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: / =>TOP
analyticity: NOT
sequent: (p1 OR p2) AND ((p1 IMPLIES p3) AND (p2 IMPLIES p3))=>p3
provable: true
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: p1=>/NOTNOTp1=>
rule: p1=>/=>NOTp1
rule: =>p1;=>NOTp1/NOT(p1 AND NOTp1)=>
rule: NOTp1=>;NOTp2=>/NOT(p1 AND p2)=>
rule: NOTp1=>; p2,NOTp2=>/NOT(p1 OR p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 OR p2)=>
rule: p1=>; p2,NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: / =>TOP
analyticity: NOT
sequent: => NOT ((A OR NOT A) AND NOT (A OR NOT A))
provable: false
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: p1=>/NOTNOTp1=>
rule: p1=>/=>NOTp1
rule: =>p1;=>NOTp1/NOT(p1 AND NOTp1)=>
rule: NOTp1=>;NOTp2=>/NOT(p1 AND p2)=>
rule: NOTp1=>; p2,NOTp2=>/NOT(p1 OR p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 OR p2)=>
rule: p1=>; p2,NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: / =>TOP
analyticity: NOT
sequent: A AND B=> NOT ( NOT A OR NOT B)
provable: false
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: p1=>/NOTNOTp1=>
rule: p1=>/=>NOTp1
rule: =>p1;=>NOTp1/NOT(p1 AND NOTp1)=>
rule: NOTp1=>;NOTp2=>/NOT(p1 AND p2)=>
rule: NOTp1=>; p2,NOTp2=>/NOT(p1 OR p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 OR p2)=>
rule: p1=>; p2,NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: / =>TOP
analyticity: NOT
sequent: NOT (A AND NOT B)=> A IMPLIES B
provable: false
connectives: AND:2,OR:2,IMPLIES:2,NOT:1,TOP:0
rule: =>p1; =>p2 / => p1 AND p2
rule: p1,p2=> / p1 AND p2
rule: =>p1,p2 / => p1 OR p2
rule: p1=> p2=> / p1 OR p2 =>
rule: p1 => p2 / =>p1 IMPLIES p2
rule: =>p1; p2=> / p1 IMPLIES p2 =>
rule: p1=>/NOTNOTp1=>
rule: p1=>/=>NOTp1
rule: =>p1;=>NOTp1/NOT(p1 AND NOTp1)=>
rule: NOTp1=>;NOTp2=>/NOT(p1 AND p2)=>
rule: NOTp1=>; p2,NOTp2=>/NOT(p1 OR p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 OR p2)=>
rule: p1=>; p2,NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: p1,NOTp1=>;NOTp2=>/NOT(p1 IMPLIES p2)=>
rule: / =>TOP
analyticity: NOT
sequent: => NOT (A AND NOT A AND NOT (A AND NOT A))
provable: true