TSTP Solution File: LCL158-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL158-1 : 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 08:17:41 EDT 2023
% Result : Unsatisfiable 0.15s 0.40s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL158-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.31 % Computer : n019.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Thu Aug 24 18:17:43 EDT 2023
% 0.13/0.32 % CPUTime :
% 0.15/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.15/0.40
% 0.15/0.40 % SZS status Unsatisfiable
% 0.15/0.40
% 0.15/0.42 % SZS output start Proof
% 0.15/0.42 Axiom 1 (false_definition): not(truth) = falsehood.
% 0.15/0.42 Axiom 2 (wajsberg_1): implies(truth, X) = X.
% 0.15/0.42 Axiom 3 (or_commutativity): or(X, Y) = or(Y, X).
% 0.15/0.42 Axiom 4 (and_commutativity): and(X, Y) = and(Y, X).
% 0.15/0.42 Axiom 5 (xor_commutativity): xor(X, Y) = xor(Y, X).
% 0.15/0.42 Axiom 6 (or_definition): or(X, Y) = implies(not(X), Y).
% 0.15/0.42 Axiom 7 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.15/0.42 Axiom 8 (or_associativity): or(or(X, Y), Z) = or(X, or(Y, Z)).
% 0.15/0.42 Axiom 9 (and_definition): and(X, Y) = not(or(not(X), not(Y))).
% 0.15/0.42 Axiom 10 (and_star_definition): and_star(X, Y) = not(or(not(X), not(Y))).
% 0.15/0.42 Axiom 11 (wajsberg_4): implies(implies(not(X), not(Y)), implies(Y, X)) = truth.
% 0.15/0.42 Axiom 12 (xor_definition): xor(X, Y) = or(and(X, not(Y)), and(not(X), Y)).
% 0.15/0.42 Axiom 13 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.15/0.42
% 0.15/0.42 Lemma 14: implies(X, implies(implies(X, Y), Y)) = truth.
% 0.15/0.42 Proof:
% 0.15/0.42 implies(X, implies(implies(X, Y), Y))
% 0.15/0.42 = { by axiom 2 (wajsberg_1) R->L }
% 0.15/0.42 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 0.15/0.42 = { by axiom 2 (wajsberg_1) R->L }
% 0.15/0.42 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 0.15/0.42 = { by axiom 13 (wajsberg_2) }
% 0.15/0.42 truth
% 0.15/0.42
% 0.15/0.42 Lemma 15: implies(X, X) = truth.
% 0.15/0.42 Proof:
% 0.15/0.42 implies(X, X)
% 0.15/0.42 = { by axiom 2 (wajsberg_1) R->L }
% 0.15/0.42 implies(implies(truth, X), X)
% 0.15/0.42 = { by axiom 2 (wajsberg_1) R->L }
% 0.15/0.42 implies(truth, implies(implies(truth, X), X))
% 0.15/0.42 = { by lemma 14 }
% 0.15/0.42 truth
% 0.15/0.42
% 0.15/0.42 Lemma 16: implies(X, truth) = truth.
% 0.15/0.42 Proof:
% 0.15/0.42 implies(X, truth)
% 0.15/0.42 = { by lemma 15 R->L }
% 0.15/0.42 implies(X, implies(X, X))
% 0.15/0.42 = { by axiom 2 (wajsberg_1) R->L }
% 0.15/0.42 implies(X, implies(implies(truth, X), X))
% 0.15/0.42 = { by axiom 7 (wajsberg_3) }
% 0.15/0.42 implies(X, implies(implies(X, truth), truth))
% 0.15/0.42 = { by lemma 14 }
% 0.15/0.42 truth
% 0.15/0.42
% 0.15/0.42 Lemma 17: implies(or(X, not(Y)), implies(Y, X)) = truth.
% 0.15/0.42 Proof:
% 0.15/0.42 implies(or(X, not(Y)), implies(Y, X))
% 0.15/0.42 = { by axiom 6 (or_definition) }
% 0.15/0.42 implies(implies(not(X), not(Y)), implies(Y, X))
% 0.15/0.42 = { by axiom 11 (wajsberg_4) }
% 0.15/0.42 truth
% 0.15/0.42
% 0.15/0.42 Lemma 18: implies(or(X, falsehood), X) = truth.
% 0.15/0.42 Proof:
% 0.15/0.42 implies(or(X, falsehood), X)
% 0.15/0.42 = { by axiom 2 (wajsberg_1) R->L }
% 0.15/0.42 implies(or(X, falsehood), implies(truth, X))
% 0.15/0.42 = { by axiom 1 (false_definition) R->L }
% 0.15/0.42 implies(or(X, not(truth)), implies(truth, X))
% 0.15/0.42 = { by lemma 17 }
% 0.15/0.42 truth
% 0.15/0.42
% 0.15/0.42 Lemma 19: or(X, falsehood) = X.
% 0.15/0.42 Proof:
% 0.15/0.42 or(X, falsehood)
% 0.15/0.42 = { by axiom 2 (wajsberg_1) R->L }
% 0.15/0.42 implies(truth, or(X, falsehood))
% 0.15/0.42 = { by axiom 13 (wajsberg_2) R->L }
% 0.15/0.42 implies(implies(implies(not(falsehood), truth), implies(implies(truth, X), implies(not(falsehood), X))), or(X, falsehood))
% 0.15/0.42 = { by axiom 2 (wajsberg_1) }
% 0.15/0.42 implies(implies(implies(not(falsehood), truth), implies(X, implies(not(falsehood), X))), or(X, falsehood))
% 0.15/0.42 = { by lemma 16 }
% 0.15/0.42 implies(implies(truth, implies(X, implies(not(falsehood), X))), or(X, falsehood))
% 0.15/0.42 = { by axiom 2 (wajsberg_1) }
% 0.15/0.42 implies(implies(X, implies(not(falsehood), X)), or(X, falsehood))
% 0.15/0.42 = { by axiom 6 (or_definition) R->L }
% 0.15/0.42 implies(implies(X, or(falsehood, X)), or(X, falsehood))
% 0.15/0.42 = { by axiom 3 (or_commutativity) }
% 0.15/0.42 implies(implies(X, or(X, falsehood)), or(X, falsehood))
% 0.15/0.42 = { by axiom 7 (wajsberg_3) R->L }
% 0.15/0.42 implies(implies(or(X, falsehood), X), X)
% 0.15/0.42 = { by lemma 18 }
% 0.15/0.42 implies(truth, X)
% 0.15/0.42 = { by axiom 2 (wajsberg_1) }
% 0.15/0.42 X
% 0.15/0.42
% 0.15/0.42 Lemma 20: or(X, truth) = truth.
% 0.15/0.42 Proof:
% 0.15/0.42 or(X, truth)
% 0.15/0.42 = { by axiom 6 (or_definition) }
% 0.15/0.42 implies(not(X), truth)
% 0.15/0.42 = { by lemma 16 }
% 0.15/0.42 truth
% 0.15/0.42
% 0.15/0.42 Lemma 21: implies(implies(X, falsehood), falsehood) = X.
% 0.15/0.42 Proof:
% 0.15/0.42 implies(implies(X, falsehood), falsehood)
% 0.15/0.42 = { by axiom 1 (false_definition) R->L }
% 0.15/0.42 implies(implies(X, falsehood), not(truth))
% 0.15/0.42 = { by axiom 1 (false_definition) R->L }
% 0.15/0.42 implies(implies(X, not(truth)), not(truth))
% 0.15/0.42 = { by axiom 7 (wajsberg_3) R->L }
% 0.15/0.42 implies(implies(not(truth), X), X)
% 0.15/0.42 = { by axiom 6 (or_definition) R->L }
% 0.15/0.42 implies(or(truth, X), X)
% 0.15/0.42 = { by axiom 3 (or_commutativity) }
% 0.15/0.42 implies(or(X, truth), X)
% 0.15/0.42 = { by lemma 20 }
% 0.15/0.42 implies(truth, X)
% 0.15/0.42 = { by axiom 2 (wajsberg_1) }
% 0.15/0.42 X
% 0.15/0.42
% 0.15/0.42 Lemma 22: implies(X, falsehood) = not(X).
% 0.15/0.42 Proof:
% 0.15/0.42 implies(X, falsehood)
% 0.15/0.42 = { by lemma 19 R->L }
% 0.15/0.42 implies(or(X, falsehood), falsehood)
% 0.15/0.42 = { by axiom 6 (or_definition) }
% 0.15/0.42 implies(implies(not(X), falsehood), falsehood)
% 0.15/0.42 = { by lemma 21 }
% 0.15/0.42 not(X)
% 0.15/0.42
% 0.15/0.42 Lemma 23: or(falsehood, X) = X.
% 0.15/0.42 Proof:
% 0.15/0.42 or(falsehood, X)
% 0.15/0.42 = { by axiom 3 (or_commutativity) R->L }
% 0.15/0.42 or(X, falsehood)
% 0.15/0.42 = { by lemma 19 }
% 0.15/0.42 X
% 0.15/0.42
% 0.15/0.42 Lemma 24: not(or(falsehood, not(X))) = and(X, truth).
% 0.15/0.42 Proof:
% 0.15/0.42 not(or(falsehood, not(X)))
% 0.15/0.42 = { by axiom 1 (false_definition) R->L }
% 0.15/0.42 not(or(not(truth), not(X)))
% 0.15/0.42 = { by axiom 9 (and_definition) R->L }
% 0.15/0.42 and(truth, X)
% 0.15/0.42 = { by axiom 4 (and_commutativity) }
% 0.15/0.42 and(X, truth)
% 0.15/0.42
% 0.15/0.42 Lemma 25: and(X, truth) = X.
% 0.15/0.42 Proof:
% 0.15/0.42 and(X, truth)
% 0.15/0.42 = { by lemma 24 R->L }
% 0.15/0.42 not(or(falsehood, not(X)))
% 0.15/0.42 = { by lemma 23 }
% 0.15/0.42 not(not(X))
% 0.15/0.42 = { by lemma 22 R->L }
% 0.15/0.42 implies(not(X), falsehood)
% 0.15/0.42 = { by axiom 6 (or_definition) R->L }
% 0.15/0.42 or(X, falsehood)
% 0.15/0.42 = { by lemma 19 }
% 0.15/0.42 X
% 0.15/0.42
% 0.15/0.42 Lemma 26: or(X, not(Y)) = implies(Y, X).
% 0.15/0.42 Proof:
% 0.15/0.42 or(X, not(Y))
% 0.15/0.42 = { by axiom 3 (or_commutativity) R->L }
% 0.15/0.42 or(not(Y), X)
% 0.15/0.42 = { by lemma 23 R->L }
% 0.15/0.42 or(falsehood, or(not(Y), X))
% 0.15/0.42 = { by axiom 8 (or_associativity) R->L }
% 0.15/0.42 or(or(falsehood, not(Y)), X)
% 0.15/0.42 = { by axiom 6 (or_definition) }
% 0.15/0.42 implies(not(or(falsehood, not(Y))), X)
% 0.15/0.42 = { by lemma 24 }
% 0.15/0.42 implies(and(Y, truth), X)
% 0.15/0.42 = { by lemma 25 }
% 0.15/0.42 implies(Y, X)
% 0.15/0.42
% 0.15/0.42 Lemma 27: or(not(X), Y) = implies(X, Y).
% 0.15/0.42 Proof:
% 0.15/0.42 or(not(X), Y)
% 0.15/0.42 = { by axiom 3 (or_commutativity) R->L }
% 0.15/0.42 or(Y, not(X))
% 0.15/0.42 = { by lemma 26 }
% 0.15/0.42 implies(X, Y)
% 0.15/0.42
% 0.15/0.42 Goal 1 (prove_alternative_wajsberg_axiom): and_star(xor(truth, x), x) = falsehood.
% 0.15/0.42 Proof:
% 0.15/0.42 and_star(xor(truth, x), x)
% 0.15/0.42 = { by lemma 23 R->L }
% 0.15/0.42 or(falsehood, and_star(xor(truth, x), x))
% 0.15/0.42 = { by lemma 21 R->L }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), falsehood), falsehood)
% 0.15/0.42 = { by axiom 2 (wajsberg_1) R->L }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(truth, falsehood)), falsehood)
% 0.15/0.42 = { by lemma 15 R->L }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, x), falsehood)), falsehood)
% 0.15/0.42 = { by lemma 25 R->L }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, and(x, truth)), falsehood)), falsehood)
% 0.15/0.42 = { by lemma 24 R->L }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, not(x)))), falsehood)), falsehood)
% 0.15/0.42 = { by lemma 22 R->L }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, falsehood)))), falsehood)), falsehood)
% 0.15/0.42 = { by axiom 1 (false_definition) R->L }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(truth))))), falsehood)), falsehood)
% 0.15/0.42 = { by lemma 18 R->L }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(or(implies(falsehood, not(x)), falsehood), implies(falsehood, not(x)))))))), falsehood)), falsehood)
% 0.15/0.42 = { by axiom 3 (or_commutativity) }
% 0.15/0.42 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(or(falsehood, implies(falsehood, not(x))), implies(falsehood, not(x)))))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 1 (false_definition) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(or(falsehood, implies(not(truth), not(x))), implies(falsehood, not(x)))))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 6 (or_definition) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(or(falsehood, or(truth, not(x))), implies(falsehood, not(x)))))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 8 (or_associativity) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(or(or(falsehood, truth), not(x)), implies(falsehood, not(x)))))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 3 (or_commutativity) }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(or(not(x), or(falsehood, truth)), implies(falsehood, not(x)))))))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 20 }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(or(not(x), truth), implies(falsehood, not(x)))))))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 20 }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(truth, implies(falsehood, not(x)))))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 2 (wajsberg_1) }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(implies(falsehood, not(x))))))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 26 R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, not(or(not(x), not(falsehood))))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 9 (and_definition) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, and(x, falsehood))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 4 (and_commutativity) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(x, and(falsehood, x))))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 27 R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, or(not(x), and(falsehood, x))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 6 (or_definition) }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, implies(not(not(x)), and(falsehood, x))))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 26 R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, or(and(falsehood, x), not(not(not(x))))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 4 (and_commutativity) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, or(and(x, falsehood), not(not(not(x))))))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 19 R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, or(and(x, falsehood), not(or(not(not(x)), falsehood)))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 3 (or_commutativity) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, or(and(x, falsehood), not(or(falsehood, not(not(x)))))))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 24 }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, or(and(x, falsehood), and(not(x), truth))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 1 (false_definition) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, or(and(x, not(truth)), and(not(x), truth))))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 12 (xor_definition) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, xor(x, truth)))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 5 (xor_commutativity) }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(or(falsehood, xor(truth, x)))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 23 }
% 0.15/0.43 implies(implies(or(falsehood, and_star(xor(truth, x), x)), implies(implies(x, not(xor(truth, x))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 10 (and_star_definition) }
% 0.15/0.43 implies(implies(or(falsehood, not(or(not(xor(truth, x)), not(x)))), implies(implies(x, not(xor(truth, x))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 9 (and_definition) R->L }
% 0.15/0.43 implies(implies(or(falsehood, and(xor(truth, x), x)), implies(implies(x, not(xor(truth, x))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 4 (and_commutativity) }
% 0.15/0.43 implies(implies(or(falsehood, and(x, xor(truth, x))), implies(implies(x, not(xor(truth, x))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 27 R->L }
% 0.15/0.43 implies(implies(or(falsehood, and(x, xor(truth, x))), implies(or(not(x), not(xor(truth, x))), falsehood)), falsehood)
% 0.15/0.43 = { by axiom 9 (and_definition) }
% 0.15/0.43 implies(implies(or(falsehood, not(or(not(x), not(xor(truth, x))))), implies(or(not(x), not(xor(truth, x))), falsehood)), falsehood)
% 0.15/0.43 = { by lemma 17 }
% 0.15/0.43 implies(truth, falsehood)
% 0.15/0.43 = { by axiom 2 (wajsberg_1) }
% 0.15/0.43 falsehood
% 0.15/0.43 % SZS output end Proof
% 0.15/0.43
% 0.15/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------