TSTP Solution File: LCL138-1 by Twee---2.5.0
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- Process Solution
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% File : Twee---2.5.0
% Problem : LCL138-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 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 : Mon Jun 24 11:20:32 EDT 2024
% Result : Unsatisfiable 2.02s 0.63s
% Output : Proof 2.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL138-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 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 : Sat Jun 22 13:31:39 EDT 2024
% 0.13/0.34 % CPUTime :
% 2.02/0.63 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 2.02/0.63
% 2.02/0.63 % SZS status Unsatisfiable
% 2.02/0.63
% 2.02/0.63 % SZS output start Proof
% 2.02/0.63 Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 2.02/0.63 Axiom 2 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 2.02/0.63 Axiom 3 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 2.02/0.63
% 2.02/0.63 Lemma 4: implies(X, implies(implies(X, Y), Y)) = truth.
% 2.02/0.63 Proof:
% 2.02/0.63 implies(X, implies(implies(X, Y), Y))
% 2.02/0.63 = { by axiom 1 (wajsberg_1) R->L }
% 2.02/0.63 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 2.02/0.63 = { by axiom 1 (wajsberg_1) R->L }
% 2.02/0.63 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 2.02/0.63 = { by axiom 3 (wajsberg_2) }
% 2.21/0.63 truth
% 2.21/0.63
% 2.21/0.63 Lemma 5: implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))) = truth.
% 2.21/0.63 Proof:
% 2.21/0.63 implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))
% 2.21/0.63 = { by axiom 1 (wajsberg_1) R->L }
% 2.21/0.63 implies(truth, implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.21/0.63 = { by axiom 3 (wajsberg_2) R->L }
% 2.21/0.63 implies(implies(implies(Y, implies(implies(Z, Y), Y)), implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z)))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.21/0.63 = { by axiom 1 (wajsberg_1) R->L }
% 2.21/0.63 implies(implies(implies(implies(truth, Y), implies(implies(Z, Y), Y)), implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z)))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.21/0.63 = { by axiom 1 (wajsberg_1) R->L }
% 2.21/0.63 implies(implies(implies(truth, implies(implies(truth, Y), implies(implies(Z, Y), Y))), implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z)))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.21/0.63 = { by lemma 4 R->L }
% 2.22/0.63 implies(implies(implies(implies(implies(Z, Y), implies(implies(implies(Z, Y), truth), truth)), implies(implies(truth, Y), implies(implies(Z, Y), Y))), implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z)))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.22/0.63 = { by axiom 2 (wajsberg_3) R->L }
% 2.22/0.63 implies(implies(implies(implies(implies(Z, Y), implies(implies(truth, implies(Z, Y)), implies(Z, Y))), implies(implies(truth, Y), implies(implies(Z, Y), Y))), implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z)))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.22/0.63 = { by axiom 1 (wajsberg_1) R->L }
% 2.22/0.63 implies(implies(implies(implies(implies(Z, Y), implies(truth, implies(implies(truth, implies(Z, Y)), implies(Z, Y)))), implies(implies(truth, Y), implies(implies(Z, Y), Y))), implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z)))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.22/0.63 = { by lemma 4 }
% 2.22/0.63 implies(implies(implies(implies(implies(Z, Y), truth), implies(implies(truth, Y), implies(implies(Z, Y), Y))), implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z)))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.22/0.63 = { by axiom 3 (wajsberg_2) }
% 2.22/0.63 implies(implies(truth, implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z)))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.22/0.63 = { by axiom 1 (wajsberg_1) }
% 2.22/0.63 implies(implies(implies(implies(implies(Z, Y), Y), implies(X, Z)), implies(Y, implies(X, Z))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.22/0.63 = { by axiom 2 (wajsberg_3) }
% 2.22/0.63 implies(implies(implies(implies(implies(Y, Z), Z), implies(X, Z)), implies(Y, implies(X, Z))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 2.22/0.63 = { by axiom 1 (wajsberg_1) R->L }
% 2.22/0.63 implies(truth, implies(implies(implies(implies(implies(Y, Z), Z), implies(X, Z)), implies(Y, implies(X, Z))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))))
% 2.22/0.63 = { by axiom 3 (wajsberg_2) R->L }
% 2.22/0.63 implies(implies(implies(X, implies(Y, Z)), implies(implies(implies(Y, Z), Z), implies(X, Z))), implies(implies(implies(implies(implies(Y, Z), Z), implies(X, Z)), implies(Y, implies(X, Z))), implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))))
% 2.22/0.63 = { by axiom 3 (wajsberg_2) }
% 2.22/0.63 truth
% 2.22/0.63
% 2.22/0.63 Goal 1 (prove_wajsberg_lemma): implies(x, implies(y, z)) = implies(y, implies(x, z)).
% 2.22/0.63 Proof:
% 2.22/0.63 implies(x, implies(y, z))
% 2.22/0.63 = { by axiom 1 (wajsberg_1) R->L }
% 2.22/0.63 implies(truth, implies(x, implies(y, z)))
% 2.22/0.63 = { by lemma 5 R->L }
% 2.22/0.63 implies(implies(implies(y, implies(x, z)), implies(x, implies(y, z))), implies(x, implies(y, z)))
% 2.22/0.63 = { by axiom 2 (wajsberg_3) }
% 2.22/0.63 implies(implies(implies(x, implies(y, z)), implies(y, implies(x, z))), implies(y, implies(x, z)))
% 2.22/0.63 = { by lemma 5 }
% 2.22/0.63 implies(truth, implies(y, implies(x, z)))
% 2.22/0.63 = { by axiom 1 (wajsberg_1) }
% 2.22/0.64 implies(y, implies(x, z))
% 2.22/0.64 % SZS output end Proof
% 2.22/0.64
% 2.22/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
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