TSTP Solution File: LCL153-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL153-1 : 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 : n019.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 08:17:40 EDT 2023
% Result : Unsatisfiable 0.19s 0.46s
% 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 : LCL153-1 : 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
% 0.12/0.34 % Computer : n019.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 02:09:29 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Command-line arguments: --no-flatten-goal
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% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 Axiom 1 (false_definition): not(truth) = falsehood.
% 0.19/0.47 Axiom 2 (and_star_commutativity): and_star(X, Y) = and_star(Y, X).
% 0.19/0.47 Axiom 3 (or_commutativity): or(X, Y) = or(Y, X).
% 0.19/0.47 Axiom 4 (wajsberg_1): implies(truth, X) = X.
% 0.19/0.47 Axiom 5 (or_definition): or(X, Y) = implies(not(X), Y).
% 0.19/0.47 Axiom 6 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.19/0.47 Axiom 7 (and_star_definition): and_star(X, Y) = not(or(not(X), not(Y))).
% 0.19/0.47 Axiom 8 (and_definition): and(X, Y) = not(or(not(X), not(Y))).
% 0.19/0.47 Axiom 9 (xor_definition): xor(X, Y) = or(and(X, not(Y)), and(not(X), Y)).
% 0.19/0.47 Axiom 10 (wajsberg_4): implies(implies(not(X), not(Y)), implies(Y, X)) = truth.
% 0.19/0.47 Axiom 11 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.19/0.47
% 0.19/0.47 Lemma 12: implies(or(X, falsehood), X) = truth.
% 0.19/0.47 Proof:
% 0.19/0.47 implies(or(X, falsehood), X)
% 0.19/0.48 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.48 implies(or(X, falsehood), implies(truth, X))
% 0.19/0.48 = { by axiom 1 (false_definition) R->L }
% 0.19/0.48 implies(or(X, not(truth)), implies(truth, X))
% 0.19/0.48 = { by axiom 5 (or_definition) }
% 0.19/0.48 implies(implies(not(X), not(truth)), implies(truth, X))
% 0.19/0.48 = { by axiom 10 (wajsberg_4) }
% 0.19/0.48 truth
% 0.19/0.48
% 0.19/0.48 Lemma 13: implies(or(falsehood, X), X) = truth.
% 0.19/0.48 Proof:
% 0.19/0.48 implies(or(falsehood, X), X)
% 0.19/0.48 = { by axiom 3 (or_commutativity) R->L }
% 0.19/0.48 implies(or(X, falsehood), X)
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 truth
% 0.19/0.48
% 0.19/0.48 Lemma 14: implies(implies(X, truth), truth) = implies(X, X).
% 0.19/0.48 Proof:
% 0.19/0.48 implies(implies(X, truth), truth)
% 0.19/0.48 = { by axiom 6 (wajsberg_3) R->L }
% 0.19/0.48 implies(implies(truth, X), X)
% 0.19/0.48 = { by axiom 4 (wajsberg_1) }
% 0.19/0.48 implies(X, X)
% 0.19/0.48
% 0.19/0.48 Lemma 15: not(falsehood) = truth.
% 0.19/0.48 Proof:
% 0.19/0.48 not(falsehood)
% 0.19/0.48 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.48 implies(truth, not(falsehood))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 implies(implies(or(falsehood, truth), truth), not(falsehood))
% 0.19/0.48 = { by axiom 5 (or_definition) }
% 0.19/0.48 implies(implies(implies(not(falsehood), truth), truth), not(falsehood))
% 0.19/0.48 = { by lemma 14 }
% 0.19/0.48 implies(implies(not(falsehood), not(falsehood)), not(falsehood))
% 0.19/0.48 = { by axiom 5 (or_definition) R->L }
% 0.19/0.48 implies(or(falsehood, not(falsehood)), not(falsehood))
% 0.19/0.48 = { by lemma 13 }
% 0.19/0.48 truth
% 0.19/0.48
% 0.19/0.48 Lemma 16: or(X, falsehood) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 or(X, falsehood)
% 0.19/0.48 = { by axiom 3 (or_commutativity) R->L }
% 0.19/0.48 or(falsehood, X)
% 0.19/0.48 = { by axiom 5 (or_definition) }
% 0.19/0.48 implies(not(falsehood), X)
% 0.19/0.48 = { by lemma 15 }
% 0.19/0.48 implies(truth, X)
% 0.19/0.48 = { by axiom 4 (wajsberg_1) }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 17: or(X, truth) = truth.
% 0.19/0.48 Proof:
% 0.19/0.48 or(X, truth)
% 0.19/0.48 = { by axiom 5 (or_definition) }
% 0.19/0.48 implies(not(X), truth)
% 0.19/0.48 = { by lemma 12 R->L }
% 0.19/0.48 implies(not(X), implies(or(not(X), falsehood), not(X)))
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 implies(not(X), implies(not(X), not(X)))
% 0.19/0.48 = { by lemma 14 R->L }
% 0.19/0.48 implies(not(X), implies(implies(not(X), truth), truth))
% 0.19/0.48 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.48 implies(not(X), implies(implies(not(X), truth), implies(truth, truth)))
% 0.19/0.48 = { by axiom 4 (wajsberg_1) R->L }
% 0.19/0.48 implies(implies(truth, not(X)), implies(implies(not(X), truth), implies(truth, truth)))
% 0.19/0.48 = { by axiom 11 (wajsberg_2) }
% 0.19/0.48 truth
% 0.19/0.48
% 0.19/0.48 Lemma 18: or(falsehood, X) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 or(falsehood, X)
% 0.19/0.48 = { by axiom 3 (or_commutativity) R->L }
% 0.19/0.48 or(X, falsehood)
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 19: and(X, Y) = and_star(X, Y).
% 0.19/0.48 Proof:
% 0.19/0.48 and(X, Y)
% 0.19/0.48 = { by axiom 8 (and_definition) }
% 0.19/0.48 not(or(not(X), not(Y)))
% 0.19/0.48 = { by axiom 7 (and_star_definition) R->L }
% 0.19/0.48 and_star(X, Y)
% 0.19/0.48
% 0.19/0.48 Goal 1 (prove_alternative_wajsberg_axiom): not(x) = xor(x, truth).
% 0.19/0.48 Proof:
% 0.19/0.48 not(x)
% 0.19/0.48 = { by lemma 16 R->L }
% 0.19/0.48 or(not(x), falsehood)
% 0.19/0.48 = { by axiom 5 (or_definition) }
% 0.19/0.48 implies(not(not(x)), falsehood)
% 0.19/0.48 = { by lemma 16 R->L }
% 0.19/0.48 implies(or(not(not(x)), falsehood), falsehood)
% 0.19/0.48 = { by axiom 5 (or_definition) }
% 0.19/0.48 implies(implies(not(not(not(x))), falsehood), falsehood)
% 0.19/0.48 = { by axiom 6 (wajsberg_3) R->L }
% 0.19/0.48 implies(implies(falsehood, not(not(not(x)))), not(not(not(x))))
% 0.19/0.48 = { by axiom 1 (false_definition) R->L }
% 0.19/0.48 implies(implies(not(truth), not(not(not(x)))), not(not(not(x))))
% 0.19/0.48 = { by axiom 5 (or_definition) R->L }
% 0.19/0.48 implies(or(truth, not(not(not(x)))), not(not(not(x))))
% 0.19/0.48 = { by axiom 3 (or_commutativity) }
% 0.19/0.48 implies(or(not(not(not(x))), truth), not(not(not(x))))
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 implies(truth, not(not(not(x))))
% 0.19/0.48 = { by axiom 4 (wajsberg_1) }
% 0.19/0.48 not(not(not(x)))
% 0.19/0.48 = { by lemma 18 R->L }
% 0.19/0.48 not(or(falsehood, not(not(x))))
% 0.19/0.48 = { by axiom 1 (false_definition) R->L }
% 0.19/0.48 not(or(not(truth), not(not(x))))
% 0.19/0.48 = { by axiom 7 (and_star_definition) R->L }
% 0.19/0.48 and_star(truth, not(x))
% 0.19/0.48 = { by axiom 2 (and_star_commutativity) }
% 0.19/0.48 and_star(not(x), truth)
% 0.19/0.48 = { by lemma 18 R->L }
% 0.19/0.48 or(falsehood, and_star(not(x), truth))
% 0.19/0.48 = { by axiom 1 (false_definition) R->L }
% 0.19/0.48 or(not(truth), and_star(not(x), truth))
% 0.19/0.48 = { by lemma 17 R->L }
% 0.19/0.48 or(not(or(not(x), truth)), and_star(not(x), truth))
% 0.19/0.48 = { by axiom 3 (or_commutativity) }
% 0.19/0.48 or(not(or(truth, not(x))), and_star(not(x), truth))
% 0.19/0.48 = { by lemma 15 R->L }
% 0.19/0.48 or(not(or(not(falsehood), not(x))), and_star(not(x), truth))
% 0.19/0.48 = { by axiom 7 (and_star_definition) R->L }
% 0.19/0.48 or(and_star(falsehood, x), and_star(not(x), truth))
% 0.19/0.48 = { by axiom 2 (and_star_commutativity) }
% 0.19/0.48 or(and_star(x, falsehood), and_star(not(x), truth))
% 0.19/0.48 = { by axiom 1 (false_definition) R->L }
% 0.19/0.48 or(and_star(x, not(truth)), and_star(not(x), truth))
% 0.19/0.48 = { by lemma 19 R->L }
% 0.19/0.48 or(and_star(x, not(truth)), and(not(x), truth))
% 0.19/0.48 = { by lemma 19 R->L }
% 0.19/0.48 or(and(x, not(truth)), and(not(x), truth))
% 0.19/0.48 = { by axiom 9 (xor_definition) R->L }
% 0.19/0.48 xor(x, truth)
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48
% 0.19/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
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