TSTP Solution File: LCL116-2 by Toma---0.4
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% File : Toma---0.4
% Problem : LCL116-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:13:51 EDT 2023
% Result : Unsatisfiable 33.28s 33.50s
% Output : CNFRefutation 33.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL116-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 04:47:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 33.28/33.50 % SZS status Unsatisfiable
% 33.28/33.50 % SZS output start Proof
% 33.28/33.50 original problem:
% 33.28/33.50 axioms:
% 33.28/33.50 implies(truth(), X) = X
% 33.28/33.50 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth()
% 33.28/33.50 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 33.28/33.50 implies(implies(not(X), not(Y)), implies(Y, X)) = truth()
% 33.28/33.50 goal:
% 33.28/33.50 implies(not(a()), implies(b(), not(implies(b(), a())))) != truth()
% 33.28/33.50 To show the unsatisfiability of the original goal,
% 33.28/33.50 it suffices to show that implies(not(a()), implies(b(), not(implies(b(), a())))) = truth() (skolemized goal) is valid under the axioms.
% 33.28/33.50 Here is an equational proof:
% 33.28/33.50 0: implies(truth(), X0) = X0.
% 33.28/33.50 Proof: Axiom.
% 33.28/33.50
% 33.28/33.50 1: implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))) = truth().
% 33.28/33.50 Proof: Axiom.
% 33.28/33.50
% 33.28/33.50 2: implies(implies(X0, X1), X1) = implies(implies(X1, X0), X0).
% 33.28/33.50 Proof: Axiom.
% 33.28/33.50
% 33.28/33.50 3: implies(implies(not(X0), not(X1)), implies(X1, X0)) = truth().
% 33.28/33.50 Proof: Axiom.
% 33.28/33.50
% 33.28/33.50 4: implies(implies(X2, truth()), truth()) = implies(X2, X2).
% 33.28/33.50 Proof: A critical pair between equations 2 and 0.
% 33.28/33.50
% 33.28/33.50 6: truth() = implies(implies(not(X2), not(truth())), X2).
% 33.28/33.50 Proof: A critical pair between equations 3 and 0.
% 33.28/33.50
% 33.28/33.50 8: truth() = implies(implies(X0, truth()), implies(X3, implies(X0, X3))).
% 33.28/33.50 Proof: A critical pair between equations 1 and 0.
% 33.28/33.50
% 33.28/33.50 9: truth() = implies(X3, implies(implies(X3, X2), implies(truth(), X2))).
% 33.28/33.50 Proof: A critical pair between equations 1 and 0.
% 33.28/33.50
% 33.28/33.50 10: truth() = implies(implies(implies(implies(X3, X5), X5), X3), truth()).
% 33.28/33.50 Proof: A critical pair between equations 1 and 1.
% 33.28/33.50
% 33.28/33.50 13: implies(implies(X3, implies(X2, X3)), implies(X2, X3)) = implies(implies(implies(X3, X2), X2), X3).
% 33.28/33.50 Proof: A critical pair between equations 2 and 2.
% 33.28/33.50
% 33.28/33.50 16: truth() = implies(implies(implies(X3, implies(X5, X3)), implies(X5, X3)), truth()).
% 33.28/33.50 Proof: Rewrite equation 10,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [13].
% 33.28/33.50
% 33.28/33.50 17: truth() = implies(X3, implies(implies(X3, X2), X2)).
% 33.28/33.50 Proof: Rewrite equation 9,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 27: truth() = implies(implies(truth(), implies(implies(X7, X7), X7)), truth()).
% 33.28/33.50 Proof: A critical pair between equations 16 and 17.
% 33.28/33.50
% 33.28/33.50 28: truth() = implies(implies(truth(), implies(truth(), implies(X6, truth()))), truth()).
% 33.28/33.50 Proof: A critical pair between equations 16 and 8.
% 33.28/33.50
% 33.28/33.50 31: truth() = implies(X6, X6).
% 33.28/33.50 Proof: Rewrite equation 28,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0,0,4].
% 33.28/33.50
% 33.28/33.50 32: truth() = implies(X7, truth()).
% 33.28/33.50 Proof: Rewrite equation 27,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [31,0,0].
% 33.28/33.50
% 33.28/33.50 33: truth() = implies(X3, implies(X0, X3)).
% 33.28/33.50 Proof: Rewrite equation 8,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [32,0].
% 33.28/33.50
% 33.28/33.50 37: truth() = implies(implies(X0, X4), implies(truth(), implies(X0, implies(X5, X4)))).
% 33.28/33.50 Proof: A critical pair between equations 1 and 33.
% 33.28/33.50
% 33.28/33.50 38: truth() = implies(truth(), implies(implies(implies(X5, X4), X2), implies(X4, X2))).
% 33.28/33.50 Proof: A critical pair between equations 1 and 33.
% 33.28/33.50
% 33.28/33.50 42: truth() = implies(implies(X0, implies(not(X3), not(truth()))), implies(truth(), implies(X0, X3))).
% 33.28/33.50 Proof: A critical pair between equations 1 and 6.
% 33.28/33.50
% 33.28/33.50 45: truth() = implies(truth(), implies(implies(implies(implies(X4, X5), X5), X2), implies(X4, X2))).
% 33.28/33.50 Proof: A critical pair between equations 1 and 17.
% 33.28/33.50
% 33.28/33.50 47: truth() = implies(implies(implies(implies(X4, X5), X5), X2), implies(X4, X2)).
% 33.28/33.50 Proof: Rewrite equation 45,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 50: truth() = implies(implies(X0, implies(not(X3), not(truth()))), implies(X0, X3)).
% 33.28/33.50 Proof: Rewrite equation 42,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 52: truth() = implies(implies(implies(X5, X4), X2), implies(X4, X2)).
% 33.28/33.50 Proof: Rewrite equation 38,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 53: truth() = implies(implies(X0, X4), implies(X0, implies(X5, X4))).
% 33.28/33.50 Proof: Rewrite equation 37,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 57: truth() = implies(truth(), implies(X7, implies(X6, implies(X8, X7)))).
% 33.28/33.50 Proof: A critical pair between equations 52 and 53.
% 33.28/33.50
% 33.28/33.50 59: truth() = implies(truth(), implies(X4, implies(X7, implies(implies(X4, X5), X5)))).
% 33.28/33.50 Proof: A critical pair between equations 47 and 33.
% 33.28/33.50
% 33.28/33.50 63: truth() = implies(truth(), implies(implies(not(not(truth())), not(not(X3))), X3)).
% 33.28/33.50 Proof: A critical pair between equations 50 and 3.
% 33.28/33.50
% 33.28/33.50 69: truth() = implies(implies(not(not(truth())), not(not(X3))), X3).
% 33.28/33.50 Proof: Rewrite equation 63,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 73: truth() = implies(X4, implies(X7, implies(implies(X4, X5), X5))).
% 33.28/33.50 Proof: Rewrite equation 59,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 75: truth() = implies(X7, implies(X6, implies(X8, X7))).
% 33.28/33.50 Proof: Rewrite equation 57,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 81: truth() = implies(truth(), implies(not(not(X6)), X6)).
% 33.28/33.50 Proof: A critical pair between equations 52 and 69.
% 33.28/33.50
% 33.28/33.50 94: truth() = implies(not(not(X6)), X6).
% 33.28/33.50 Proof: Rewrite equation 81,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 96: truth() = implies(truth(), implies(X1, not(not(X1)))).
% 33.28/33.50 Proof: A critical pair between equations 3 and 94.
% 33.28/33.50
% 33.28/33.50 109: truth() = implies(X1, not(not(X1))).
% 33.28/33.50 Proof: Rewrite equation 96,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 173: implies(implies(X7, not(not(X7))), not(not(X7))) = implies(truth(), X7).
% 33.28/33.50 Proof: A critical pair between equations 2 and 94.
% 33.28/33.50
% 33.28/33.50 180: not(not(X7)) = X7.
% 33.28/33.50 Proof: Rewrite equation 173,
% 33.28/33.50 lhs with equations [109,0]
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 185: truth() = implies(implies(X8, not(X1)), implies(X1, not(X8))).
% 33.28/33.50 Proof: A critical pair between equations 3 and 180.
% 33.28/33.50
% 33.28/33.50 198: truth() = implies(implies(X8, X9), implies(not(X9), not(X8))).
% 33.28/33.50 Proof: A critical pair between equations 185 and 180.
% 33.28/33.50
% 33.28/33.50 221: truth() = implies(X9, implies(X7, implies(truth(), implies(X10, implies(X11, X9))))).
% 33.28/33.50 Proof: A critical pair between equations 73 and 75.
% 33.28/33.50
% 33.28/33.50 226: truth() = implies(X9, implies(X7, implies(X10, implies(X11, X9)))).
% 33.28/33.50 Proof: Rewrite equation 221,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 232: truth() = implies(X9, implies(X7, implies(implies(implies(X11, X9), X12), X12))).
% 33.28/33.50 Proof: A critical pair between equations 226 and 2.
% 33.28/33.50
% 33.28/33.50 434: truth() = implies(X14, implies(X7, implies(implies(implies(implies(X14, X13), X13), X12), X12))).
% 33.28/33.50 Proof: A critical pair between equations 232 and 2.
% 33.28/33.50
% 33.28/33.50 447: truth() = implies(X14, implies(X7, implies(truth(), implies(X16, not(implies(X14, not(X16))))))).
% 33.28/33.50 Proof: A critical pair between equations 434 and 185.
% 33.28/33.50
% 33.28/33.50 455: truth() = implies(X14, implies(X7, implies(X16, not(implies(X14, not(X16)))))).
% 33.28/33.50 Proof: Rewrite equation 447,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 462: truth() = implies(X14, implies(implies(implies(X16, not(implies(X14, not(X16)))), X17), X17)).
% 33.28/33.50 Proof: A critical pair between equations 455 and 2.
% 33.28/33.50
% 33.28/33.50 480: truth() = implies(X14, implies(truth(), implies(X18, implies(X20, not(implies(X14, not(X18))))))).
% 33.28/33.50 Proof: A critical pair between equations 462 and 53.
% 33.28/33.50
% 33.28/33.50 485: truth() = implies(X14, implies(X18, implies(X20, not(implies(X14, not(X18)))))).
% 33.28/33.50 Proof: Rewrite equation 480,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 494: truth() = implies(X14, implies(X18, implies(implies(not(implies(X14, not(X18))), X21), X21))).
% 33.28/33.50 Proof: A critical pair between equations 485 and 2.
% 33.28/33.50
% 33.28/33.50 527: truth() = implies(truth(), implies(not(implies(not(X11), not(X10))), not(implies(X10, X11)))).
% 33.28/33.50 Proof: A critical pair between equations 198 and 198.
% 33.28/33.50
% 33.28/33.50 533: truth() = implies(not(implies(not(X11), not(X10))), not(implies(X10, X11))).
% 33.28/33.50 Proof: Rewrite equation 527,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 540: truth() = implies(not(X22), implies(X23, implies(truth(), not(implies(X23, X22))))).
% 33.28/33.50 Proof: A critical pair between equations 494 and 533.
% 33.28/33.50
% 33.28/33.50 550: truth() = implies(not(X22), implies(X23, not(implies(X23, X22)))).
% 33.28/33.50 Proof: Rewrite equation 540,
% 33.28/33.50 lhs with equations []
% 33.28/33.50 rhs with equations [0].
% 33.28/33.50
% 33.28/33.50 551: implies(not(a()), implies(b(), not(implies(b(), a())))) = truth().
% 33.28/33.50 Proof: Rewrite lhs with equations [550]
% 33.28/33.50 rhs with equations [].
% 33.28/33.50
% 33.28/33.50 % SZS output end Proof
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