TSTP Solution File: LCL140-1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : LCL140-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n018.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 08:17:37 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL140-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 00:38:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 0.20/0.40 Axiom 2 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.20/0.40 Axiom 3 (wajsberg_4): implies(implies(not(X), not(Y)), implies(Y, X)) = truth.
% 0.20/0.41 Axiom 4 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.20/0.41
% 0.20/0.41 Lemma 5: implies(X, implies(implies(X, Y), Y)) = truth.
% 0.20/0.41 Proof:
% 0.20/0.41 implies(X, implies(implies(X, Y), Y))
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 0.20/0.41 = { by axiom 4 (wajsberg_2) }
% 0.20/0.41 truth
% 0.20/0.41
% 0.20/0.41 Lemma 6: implies(X, implies(Y, X)) = truth.
% 0.20/0.41 Proof:
% 0.20/0.41 implies(X, implies(Y, X))
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(truth, implies(X, implies(Y, X)))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 implies(implies(Y, implies(implies(Y, truth), truth)), implies(X, implies(Y, X)))
% 0.20/0.41 = { by axiom 2 (wajsberg_3) R->L }
% 0.20/0.41 implies(implies(Y, implies(implies(truth, Y), Y)), implies(X, implies(Y, X)))
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(implies(Y, implies(truth, implies(implies(truth, Y), Y))), implies(X, implies(Y, X)))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 implies(implies(Y, truth), implies(X, implies(Y, X)))
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(implies(Y, truth), implies(implies(truth, X), implies(Y, X)))
% 0.20/0.41 = { by axiom 4 (wajsberg_2) }
% 0.20/0.41 truth
% 0.20/0.41
% 0.20/0.41 Lemma 7: implies(implies(not(X), not(truth)), X) = truth.
% 0.20/0.41 Proof:
% 0.20/0.41 implies(implies(not(X), not(truth)), X)
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(implies(not(X), not(truth)), implies(truth, X))
% 0.20/0.41 = { by axiom 3 (wajsberg_4) }
% 0.20/0.41 truth
% 0.20/0.41
% 0.20/0.41 Lemma 8: implies(not(not(X)), X) = truth.
% 0.20/0.41 Proof:
% 0.20/0.41 implies(not(not(X)), X)
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(implies(truth, not(not(X))), X)
% 0.20/0.41 = { by axiom 4 (wajsberg_2) R->L }
% 0.20/0.41 implies(implies(implies(implies(not(truth), implies(not(not(not(truth))), not(truth))), implies(implies(implies(not(not(not(truth))), not(truth)), not(not(truth))), implies(not(truth), not(not(truth))))), not(not(X))), X)
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 implies(implies(implies(truth, implies(implies(implies(not(not(not(truth))), not(truth)), not(not(truth))), implies(not(truth), not(not(truth))))), not(not(X))), X)
% 0.20/0.41 = { by axiom 1 (wajsberg_1) }
% 0.20/0.41 implies(implies(implies(implies(implies(not(not(not(truth))), not(truth)), not(not(truth))), implies(not(truth), not(not(truth)))), not(not(X))), X)
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 implies(implies(implies(truth, implies(not(truth), not(not(truth)))), not(not(X))), X)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 implies(implies(implies(implies(not(not(truth)), implies(not(truth), not(not(truth)))), implies(not(truth), not(not(truth)))), not(not(X))), X)
% 0.20/0.41 = { by axiom 2 (wajsberg_3) }
% 0.20/0.41 implies(implies(implies(implies(implies(not(truth), not(not(truth))), not(not(truth))), not(not(truth))), not(not(X))), X)
% 0.20/0.41 = { by axiom 2 (wajsberg_3) }
% 0.20/0.41 implies(implies(implies(implies(implies(not(not(truth)), not(truth)), not(truth)), not(not(truth))), not(not(X))), X)
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 implies(implies(implies(truth, not(not(truth))), not(not(X))), X)
% 0.20/0.41 = { by axiom 1 (wajsberg_1) }
% 0.20/0.41 implies(implies(not(not(truth)), not(not(X))), X)
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(truth, implies(implies(not(not(truth)), not(not(X))), X))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 implies(implies(implies(not(X), not(truth)), X), implies(implies(not(not(truth)), not(not(X))), X))
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(truth, implies(implies(implies(not(X), not(truth)), X), implies(implies(not(not(truth)), not(not(X))), X)))
% 0.20/0.41 = { by axiom 3 (wajsberg_4) R->L }
% 0.20/0.41 implies(implies(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))), implies(implies(implies(not(X), not(truth)), X), implies(implies(not(not(truth)), not(not(X))), X)))
% 0.20/0.41 = { by axiom 4 (wajsberg_2) }
% 0.20/0.41 truth
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_wajsberg_lemma): not(not(x)) = x.
% 0.20/0.41 Proof:
% 0.20/0.41 not(not(x))
% 0.20/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.41 implies(truth, not(not(x)))
% 0.20/0.41 = { by axiom 3 (wajsberg_4) R->L }
% 0.20/0.41 implies(implies(implies(not(not(not(x))), not(x)), implies(x, not(not(x)))), not(not(x)))
% 0.20/0.41 = { by lemma 8 }
% 0.20/0.41 implies(implies(truth, implies(x, not(not(x)))), not(not(x)))
% 0.20/0.41 = { by axiom 1 (wajsberg_1) }
% 0.20/0.41 implies(implies(x, not(not(x))), not(not(x)))
% 0.20/0.41 = { by axiom 2 (wajsberg_3) }
% 0.20/0.41 implies(implies(not(not(x)), x), x)
% 0.20/0.41 = { by lemma 8 }
% 0.20/0.41 implies(truth, x)
% 0.20/0.41 = { by axiom 1 (wajsberg_1) }
% 0.20/0.41 x
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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