TSTP Solution File: LCL115-2 by Toma---0.4
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% File : Toma---0.4
% Problem : LCL115-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n016.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 08:13:50 EDT 2023
% Result : Unsatisfiable 1.32s 1.70s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL115-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.13/0.36 % Computer : n016.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 24 23:35:09 EDT 2023
% 0.13/0.36 % CPUTime :
% 1.32/1.70 % SZS status Unsatisfiable
% 1.32/1.70 % SZS output start Proof
% 1.32/1.70 original problem:
% 1.32/1.70 axioms:
% 1.32/1.70 implies(truth(), X) = X
% 1.32/1.70 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth()
% 1.32/1.70 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 1.32/1.70 implies(implies(not(X), not(Y)), implies(Y, X)) = truth()
% 1.32/1.70 goal:
% 1.32/1.70 implies(not(implies(a(), b())), not(b())) != truth()
% 1.32/1.70 To show the unsatisfiability of the original goal,
% 1.32/1.70 it suffices to show that implies(not(implies(a(), b())), not(b())) = truth() (skolemized goal) is valid under the axioms.
% 1.32/1.70 Here is an equational proof:
% 1.32/1.70 0: implies(truth(), X0) = X0.
% 1.32/1.70 Proof: Axiom.
% 1.32/1.70
% 1.32/1.70 1: implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))) = truth().
% 1.32/1.70 Proof: Axiom.
% 1.32/1.70
% 1.32/1.70 2: implies(implies(X0, X1), X1) = implies(implies(X1, X0), X0).
% 1.32/1.70 Proof: Axiom.
% 1.32/1.70
% 1.32/1.70 3: implies(implies(not(X0), not(X1)), implies(X1, X0)) = truth().
% 1.32/1.70 Proof: Axiom.
% 1.32/1.70
% 1.32/1.70 4: implies(implies(X2, truth()), truth()) = implies(X2, X2).
% 1.32/1.70 Proof: A critical pair between equations 2 and 0.
% 1.32/1.70
% 1.32/1.70 6: truth() = implies(implies(not(X2), not(truth())), X2).
% 1.32/1.70 Proof: A critical pair between equations 3 and 0.
% 1.32/1.70
% 1.32/1.70 8: truth() = implies(implies(X0, truth()), implies(X3, implies(X0, X3))).
% 1.32/1.70 Proof: A critical pair between equations 1 and 0.
% 1.32/1.70
% 1.32/1.70 9: truth() = implies(X3, implies(implies(X3, X2), implies(truth(), X2))).
% 1.32/1.70 Proof: A critical pair between equations 1 and 0.
% 1.32/1.70
% 1.32/1.70 10: truth() = implies(implies(implies(implies(X3, X5), X5), X3), truth()).
% 1.32/1.70 Proof: A critical pair between equations 1 and 1.
% 1.32/1.70
% 1.32/1.70 13: implies(implies(X3, implies(X2, X3)), implies(X2, X3)) = implies(implies(implies(X3, X2), X2), X3).
% 1.32/1.70 Proof: A critical pair between equations 2 and 2.
% 1.32/1.70
% 1.32/1.70 16: truth() = implies(implies(implies(X3, implies(X5, X3)), implies(X5, X3)), truth()).
% 1.32/1.70 Proof: Rewrite equation 10,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [13].
% 1.32/1.70
% 1.32/1.70 17: truth() = implies(X3, implies(implies(X3, X2), X2)).
% 1.32/1.70 Proof: Rewrite equation 9,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 27: truth() = implies(implies(truth(), implies(implies(X7, X7), X7)), truth()).
% 1.32/1.70 Proof: A critical pair between equations 16 and 17.
% 1.32/1.70
% 1.32/1.70 28: truth() = implies(implies(truth(), implies(truth(), implies(X6, truth()))), truth()).
% 1.32/1.70 Proof: A critical pair between equations 16 and 8.
% 1.32/1.70
% 1.32/1.70 31: truth() = implies(X6, X6).
% 1.32/1.70 Proof: Rewrite equation 28,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0,0,4].
% 1.32/1.70
% 1.32/1.70 32: truth() = implies(X7, truth()).
% 1.32/1.70 Proof: Rewrite equation 27,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [31,0,0].
% 1.32/1.70
% 1.32/1.70 33: truth() = implies(X3, implies(X0, X3)).
% 1.32/1.70 Proof: Rewrite equation 8,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [32,0].
% 1.32/1.70
% 1.32/1.70 37: truth() = implies(implies(X0, X4), implies(truth(), implies(X0, implies(X5, X4)))).
% 1.32/1.70 Proof: A critical pair between equations 1 and 33.
% 1.32/1.70
% 1.32/1.70 38: truth() = implies(truth(), implies(implies(implies(X5, X4), X2), implies(X4, X2))).
% 1.32/1.70 Proof: A critical pair between equations 1 and 33.
% 1.32/1.70
% 1.32/1.70 42: truth() = implies(implies(X0, implies(not(X3), not(truth()))), implies(truth(), implies(X0, X3))).
% 1.32/1.70 Proof: A critical pair between equations 1 and 6.
% 1.32/1.70
% 1.32/1.70 45: truth() = implies(truth(), implies(implies(implies(implies(X4, X5), X5), X2), implies(X4, X2))).
% 1.32/1.70 Proof: A critical pair between equations 1 and 17.
% 1.32/1.70
% 1.32/1.70 47: truth() = implies(implies(implies(implies(X4, X5), X5), X2), implies(X4, X2)).
% 1.32/1.70 Proof: Rewrite equation 45,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 50: truth() = implies(implies(X0, implies(not(X3), not(truth()))), implies(X0, X3)).
% 1.32/1.70 Proof: Rewrite equation 42,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 52: truth() = implies(implies(implies(X5, X4), X2), implies(X4, X2)).
% 1.32/1.70 Proof: Rewrite equation 38,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 53: truth() = implies(implies(X0, X4), implies(X0, implies(X5, X4))).
% 1.32/1.70 Proof: Rewrite equation 37,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 56: truth() = implies(truth(), implies(not(X7), implies(X7, X6))).
% 1.32/1.70 Proof: A critical pair between equations 52 and 3.
% 1.32/1.70
% 1.32/1.70 59: truth() = implies(truth(), implies(X4, implies(X7, implies(implies(X4, X5), X5)))).
% 1.32/1.70 Proof: A critical pair between equations 47 and 33.
% 1.32/1.70
% 1.32/1.70 62: truth() = implies(truth(), implies(implies(implies(X6, not(X3)), not(truth())), X3)).
% 1.32/1.70 Proof: A critical pair between equations 50 and 52.
% 1.32/1.70
% 1.32/1.70 63: truth() = implies(truth(), implies(implies(not(not(truth())), not(not(X3))), X3)).
% 1.32/1.70 Proof: A critical pair between equations 50 and 3.
% 1.32/1.70
% 1.32/1.70 69: truth() = implies(implies(not(not(truth())), not(not(X3))), X3).
% 1.32/1.70 Proof: Rewrite equation 63,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 70: truth() = implies(implies(implies(X6, not(X3)), not(truth())), X3).
% 1.32/1.70 Proof: Rewrite equation 62,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 73: truth() = implies(X4, implies(X7, implies(implies(X4, X5), X5))).
% 1.32/1.70 Proof: Rewrite equation 59,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 76: truth() = implies(not(X7), implies(X7, X6)).
% 1.32/1.70 Proof: Rewrite equation 56,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 81: truth() = implies(truth(), implies(not(not(X6)), X6)).
% 1.32/1.70 Proof: A critical pair between equations 52 and 69.
% 1.32/1.70
% 1.32/1.70 88: truth() = implies(truth(), implies(not(X8), implies(X5, implies(X8, X9)))).
% 1.32/1.70 Proof: A critical pair between equations 53 and 76.
% 1.32/1.70
% 1.32/1.70 92: truth() = implies(not(X8), implies(X5, implies(X8, X9))).
% 1.32/1.70 Proof: Rewrite equation 88,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 94: truth() = implies(not(not(X6)), X6).
% 1.32/1.70 Proof: Rewrite equation 81,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 104: truth() = implies(not(not(X8)), implies(X7, implies(truth(), X8))).
% 1.32/1.70 Proof: A critical pair between equations 73 and 94.
% 1.32/1.70
% 1.32/1.70 106: truth() = implies(not(X8), implies(implies(implies(X8, X9), X10), X10)).
% 1.32/1.70 Proof: A critical pair between equations 92 and 2.
% 1.32/1.70
% 1.32/1.70 108: truth() = implies(not(not(X8)), implies(X7, X8)).
% 1.32/1.70 Proof: Rewrite equation 104,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 112: truth() = implies(not(implies(X11, not(X12))), implies(truth(), X12)).
% 1.32/1.70 Proof: A critical pair between equations 106 and 70.
% 1.32/1.70
% 1.32/1.70 126: truth() = implies(not(implies(X11, not(X12))), X12).
% 1.32/1.70 Proof: Rewrite equation 112,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 133: truth() = implies(not(implies(implies(not(X12), X13), X13)), X12).
% 1.32/1.70 Proof: A critical pair between equations 126 and 2.
% 1.32/1.70
% 1.32/1.70 147: truth() = implies(not(implies(truth(), implies(X15, X14))), not(X14)).
% 1.32/1.70 Proof: A critical pair between equations 133 and 108.
% 1.32/1.70
% 1.32/1.70 164: truth() = implies(not(implies(X15, X14)), not(X14)).
% 1.32/1.70 Proof: Rewrite equation 147,
% 1.32/1.70 lhs with equations []
% 1.32/1.70 rhs with equations [0].
% 1.32/1.70
% 1.32/1.70 165: implies(not(implies(a(), b())), not(b())) = truth().
% 1.32/1.70 Proof: Rewrite lhs with equations [164]
% 1.32/1.70 rhs with equations [].
% 1.32/1.70
% 1.32/1.70 % SZS output end Proof
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