TSTP Solution File: LCL115-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL115-2 : 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 : n014.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 08:17:31 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% 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 : LCL115-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 23:02:18 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 0.21/0.41 Axiom 2 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.21/0.41 Axiom 3 (wajsberg_4): implies(implies(not(X), not(Y)), implies(Y, X)) = truth.
% 0.21/0.41 Axiom 4 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.21/0.41
% 0.21/0.41 Lemma 5: implies(implies(X, implies(not(Y), not(Z))), implies(X, implies(Z, Y))) = truth.
% 0.21/0.41 Proof:
% 0.21/0.41 implies(implies(X, implies(not(Y), not(Z))), implies(X, implies(Z, Y)))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(implies(X, implies(not(Y), not(Z))), implies(truth, implies(X, implies(Z, Y))))
% 0.21/0.41 = { by axiom 3 (wajsberg_4) R->L }
% 0.21/0.41 implies(implies(X, implies(not(Y), not(Z))), implies(implies(implies(not(Y), not(Z)), implies(Z, Y)), implies(X, implies(Z, Y))))
% 0.21/0.41 = { by axiom 4 (wajsberg_2) }
% 0.21/0.41 truth
% 0.21/0.41
% 0.21/0.41 Lemma 6: implies(X, implies(implies(X, Y), Y)) = truth.
% 0.21/0.41 Proof:
% 0.21/0.41 implies(X, implies(implies(X, Y), Y))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 0.21/0.41 = { by axiom 4 (wajsberg_2) }
% 0.21/0.41 truth
% 0.21/0.41
% 0.21/0.41 Lemma 7: implies(X, implies(Y, X)) = truth.
% 0.21/0.41 Proof:
% 0.21/0.41 implies(X, implies(Y, X))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(implies(truth, X), implies(Y, X))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(truth, implies(implies(truth, X), implies(Y, X)))
% 0.21/0.41 = { by lemma 6 R->L }
% 0.21/0.41 implies(implies(Y, implies(implies(Y, truth), truth)), implies(implies(truth, X), implies(Y, X)))
% 0.21/0.41 = { by axiom 2 (wajsberg_3) }
% 0.21/0.41 implies(implies(Y, implies(implies(truth, Y), Y)), implies(implies(truth, X), implies(Y, X)))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(implies(Y, implies(truth, implies(implies(truth, Y), Y))), implies(implies(truth, X), implies(Y, X)))
% 0.21/0.41 = { by lemma 6 }
% 0.21/0.41 implies(implies(Y, truth), implies(implies(truth, X), implies(Y, X)))
% 0.21/0.41 = { by axiom 4 (wajsberg_2) }
% 0.21/0.41 truth
% 0.21/0.41
% 0.21/0.41 Lemma 8: implies(not(not(X)), X) = truth.
% 0.21/0.41 Proof:
% 0.21/0.41 implies(not(not(X)), X)
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(not(not(X)), implies(truth, X))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(truth, implies(not(not(X)), implies(truth, X)))
% 0.21/0.41 = { by lemma 5 R->L }
% 0.21/0.41 implies(implies(implies(not(not(X)), implies(not(not(truth)), not(not(X)))), implies(not(not(X)), implies(not(X), not(truth)))), implies(not(not(X)), implies(truth, X)))
% 0.21/0.41 = { by lemma 7 }
% 0.21/0.41 implies(implies(truth, implies(not(not(X)), implies(not(X), not(truth)))), implies(not(not(X)), implies(truth, X)))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) }
% 0.21/0.41 implies(implies(not(not(X)), implies(not(X), not(truth))), implies(not(not(X)), implies(truth, X)))
% 0.21/0.41 = { by lemma 5 }
% 0.21/0.41 truth
% 0.21/0.41
% 0.21/0.41 Lemma 9: not(not(X)) = X.
% 0.21/0.41 Proof:
% 0.21/0.41 not(not(X))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(truth, not(not(X)))
% 0.21/0.41 = { by axiom 3 (wajsberg_4) R->L }
% 0.21/0.41 implies(implies(implies(not(not(not(X))), not(X)), implies(X, not(not(X)))), not(not(X)))
% 0.21/0.41 = { by lemma 8 }
% 0.21/0.41 implies(implies(truth, implies(X, not(not(X)))), not(not(X)))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) }
% 0.21/0.41 implies(implies(X, not(not(X))), not(not(X)))
% 0.21/0.41 = { by axiom 2 (wajsberg_3) }
% 0.21/0.41 implies(implies(not(not(X)), X), X)
% 0.21/0.41 = { by lemma 8 }
% 0.21/0.41 implies(truth, X)
% 0.21/0.41 = { by axiom 1 (wajsberg_1) }
% 0.21/0.41 X
% 0.21/0.41
% 0.21/0.41 Lemma 10: implies(implies(X, not(Y)), implies(Y, not(X))) = truth.
% 0.21/0.41 Proof:
% 0.21/0.41 implies(implies(X, not(Y)), implies(Y, not(X)))
% 0.21/0.41 = { by lemma 9 R->L }
% 0.21/0.41 implies(implies(not(not(X)), not(Y)), implies(Y, not(X)))
% 0.21/0.41 = { by axiom 3 (wajsberg_4) }
% 0.21/0.41 truth
% 0.21/0.41
% 0.21/0.41 Goal 1 (prove_mv_39): implies(not(implies(a, b)), not(b)) = truth.
% 0.21/0.41 Proof:
% 0.21/0.41 implies(not(implies(a, b)), not(b))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) R->L }
% 0.21/0.41 implies(truth, implies(not(implies(a, b)), not(b)))
% 0.21/0.41 = { by lemma 10 R->L }
% 0.21/0.41 implies(implies(implies(b, not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(not(implies(a, b)), not(b)))
% 0.21/0.41 = { by axiom 2 (wajsberg_3) R->L }
% 0.21/0.41 implies(implies(implies(not(implies(a, b)), not(b)), implies(b, not(not(implies(a, b))))), implies(b, not(not(implies(a, b)))))
% 0.21/0.41 = { by lemma 10 }
% 0.21/0.41 implies(truth, implies(b, not(not(implies(a, b)))))
% 0.21/0.41 = { by axiom 1 (wajsberg_1) }
% 0.21/0.41 implies(b, not(not(implies(a, b))))
% 0.21/0.41 = { by lemma 9 }
% 0.21/0.41 implies(b, implies(a, b))
% 0.21/0.41 = { by lemma 7 }
% 0.21/0.41 truth
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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