TSTP Solution File: LCL157-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL157-1 : 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 : n003.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 08:17:41 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% 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 : LCL157-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Fri Aug 25 07:26:23 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
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% 0.19/0.40 % SZS status Unsatisfiable
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% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Axiom 1 (false_definition): not(truth) = falsehood.
% 0.19/0.41 Axiom 2 (and_star_commutativity): and_star(X, Y) = and_star(Y, X).
% 0.19/0.41 Axiom 3 (or_commutativity): or(X, Y) = or(Y, X).
% 0.19/0.41 Axiom 4 (wajsberg_1): implies(truth, X) = X.
% 0.19/0.41 Axiom 5 (or_definition): or(X, Y) = implies(not(X), Y).
% 0.19/0.41 Axiom 6 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.19/0.41 Axiom 7 (and_star_definition): and_star(X, Y) = not(or(not(X), not(Y))).
% 0.19/0.41 Axiom 8 (wajsberg_4): implies(implies(not(X), not(Y)), implies(Y, X)) = truth.
% 0.19/0.41 Axiom 9 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.19/0.41
% 0.19/0.41 Lemma 10: implies(X, implies(implies(X, Y), Y)) = truth.
% 0.19/0.41 Proof:
% 0.19/0.41 implies(X, implies(implies(X, Y), Y))
% 0.19/0.41 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.41 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 0.19/0.41 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.41 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 0.19/0.41 = { by axiom 9 (wajsberg_2) }
% 0.19/0.41 truth
% 0.19/0.41
% 0.19/0.41 Lemma 11: implies(X, X) = truth.
% 0.19/0.41 Proof:
% 0.19/0.41 implies(X, X)
% 0.19/0.41 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.41 implies(implies(truth, X), X)
% 0.19/0.41 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.41 implies(truth, implies(implies(truth, X), X))
% 0.19/0.41 = { by lemma 10 }
% 0.19/0.41 truth
% 0.19/0.41
% 0.19/0.41 Goal 1 (prove_alternative_wajsberg_axiom): and_star(x, falsehood) = falsehood.
% 0.19/0.41 Proof:
% 0.19/0.41 and_star(x, falsehood)
% 0.19/0.41 = { by axiom 2 (and_star_commutativity) R->L }
% 0.19/0.41 and_star(falsehood, x)
% 0.19/0.41 = { by axiom 7 (and_star_definition) }
% 0.19/0.41 not(or(not(falsehood), not(x)))
% 0.19/0.41 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.41 not(or(implies(truth, not(falsehood)), not(x)))
% 0.19/0.41 = { by lemma 11 R->L }
% 0.19/0.41 not(or(implies(implies(not(falsehood), not(falsehood)), not(falsehood)), not(x)))
% 0.19/0.41 = { by axiom 5 (or_definition) R->L }
% 0.19/0.41 not(or(implies(or(falsehood, not(falsehood)), not(falsehood)), not(x)))
% 0.19/0.41 = { by axiom 3 (or_commutativity) R->L }
% 0.19/0.41 not(or(implies(or(not(falsehood), falsehood), not(falsehood)), not(x)))
% 0.19/0.41 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.41 not(or(implies(or(not(falsehood), falsehood), implies(truth, not(falsehood))), not(x)))
% 0.19/0.41 = { by axiom 1 (false_definition) R->L }
% 0.19/0.41 not(or(implies(or(not(falsehood), not(truth)), implies(truth, not(falsehood))), not(x)))
% 0.19/0.41 = { by axiom 5 (or_definition) }
% 0.19/0.41 not(or(implies(implies(not(not(falsehood)), not(truth)), implies(truth, not(falsehood))), not(x)))
% 0.19/0.41 = { by axiom 8 (wajsberg_4) }
% 0.19/0.41 not(or(truth, not(x)))
% 0.19/0.41 = { by axiom 3 (or_commutativity) R->L }
% 0.19/0.41 not(or(not(x), truth))
% 0.19/0.41 = { by axiom 5 (or_definition) }
% 0.19/0.41 not(implies(not(not(x)), truth))
% 0.19/0.41 = { by lemma 11 R->L }
% 0.19/0.41 not(implies(not(not(x)), implies(not(not(x)), not(not(x)))))
% 0.19/0.41 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.41 not(implies(not(not(x)), implies(implies(truth, not(not(x))), not(not(x)))))
% 0.19/0.41 = { by axiom 6 (wajsberg_3) }
% 0.19/0.41 not(implies(not(not(x)), implies(implies(not(not(x)), truth), truth)))
% 0.19/0.41 = { by lemma 10 }
% 0.19/0.41 not(truth)
% 0.19/0.41 = { by axiom 1 (false_definition) }
% 0.19/0.41 falsehood
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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