TSTP Solution File: LCL109-2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL109-2 : 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 : 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 08:17:27 EDT 2023
% Result : Unsatisfiable 0.19s 0.67s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL109-2 : 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
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 18:46:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.67 Command-line arguments: --ground-connectedness --complete-subsets
% 0.19/0.67
% 0.19/0.67 % SZS status Unsatisfiable
% 0.19/0.67
% 0.19/0.68 % SZS output start Proof
% 0.19/0.68 Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 0.19/0.68 Axiom 2 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.19/0.68 Axiom 3 (wajsberg_4): implies(implies(not(X), not(Y)), implies(Y, X)) = truth.
% 0.19/0.68 Axiom 4 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.19/0.68
% 0.19/0.68 Lemma 5: implies(X, implies(implies(X, Y), Y)) = truth.
% 0.19/0.68 Proof:
% 0.19/0.68 implies(X, implies(implies(X, Y), Y))
% 0.19/0.68 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.68 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 0.19/0.68 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.68 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 0.19/0.68 = { by axiom 4 (wajsberg_2) }
% 0.19/0.68 truth
% 0.19/0.68
% 0.19/0.68 Lemma 6: implies(X, X) = truth.
% 0.19/0.68 Proof:
% 0.19/0.68 implies(X, X)
% 0.19/0.68 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.68 implies(implies(truth, X), X)
% 0.19/0.68 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.68 implies(truth, implies(implies(truth, X), X))
% 0.19/0.68 = { by lemma 5 }
% 0.19/0.68 truth
% 0.19/0.68
% 0.19/0.68 Lemma 7: implies(X, truth) = truth.
% 0.19/0.68 Proof:
% 0.19/0.68 implies(X, truth)
% 0.19/0.68 = { by lemma 6 R->L }
% 0.19/0.68 implies(X, implies(X, X))
% 0.19/0.68 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.68 implies(X, implies(implies(truth, X), X))
% 0.19/0.68 = { by axiom 2 (wajsberg_3) }
% 0.19/0.68 implies(X, implies(implies(X, truth), truth))
% 0.19/0.68 = { by lemma 5 }
% 0.19/0.68 truth
% 0.19/0.68
% 0.19/0.68 Lemma 8: implies(X, implies(Y, X)) = truth.
% 0.19/0.68 Proof:
% 0.19/0.68 implies(X, implies(Y, X))
% 0.19/0.68 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.68 implies(implies(truth, X), implies(Y, X))
% 0.19/0.68 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.68 implies(truth, implies(implies(truth, X), implies(Y, X)))
% 0.19/0.68 = { by lemma 7 R->L }
% 0.19/0.68 implies(implies(Y, truth), implies(implies(truth, X), implies(Y, X)))
% 0.19/0.68 = { by axiom 4 (wajsberg_2) }
% 0.19/0.68 truth
% 0.19/0.68
% 0.19/0.68 Lemma 9: implies(implies(implies(X, Y), Y), X) = implies(Y, X).
% 0.19/0.68 Proof:
% 0.19/0.68 implies(implies(implies(X, Y), Y), X)
% 0.19/0.68 = { by axiom 2 (wajsberg_3) R->L }
% 0.19/0.68 implies(implies(implies(Y, X), X), X)
% 0.19/0.68 = { by axiom 2 (wajsberg_3) }
% 0.19/0.68 implies(implies(X, implies(Y, X)), implies(Y, X))
% 0.19/0.68 = { by lemma 8 }
% 0.19/0.68 implies(truth, implies(Y, X))
% 0.19/0.68 = { by axiom 1 (wajsberg_1) }
% 0.19/0.68 implies(Y, X)
% 0.19/0.68
% 0.19/0.68 Lemma 10: implies(implies(not(X), not(truth)), X) = truth.
% 0.19/0.68 Proof:
% 0.19/0.68 implies(implies(not(X), not(truth)), X)
% 0.19/0.68 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.68 implies(implies(not(X), not(truth)), implies(truth, X))
% 0.19/0.68 = { by axiom 3 (wajsberg_4) }
% 0.19/0.68 truth
% 0.19/0.68
% 0.19/0.68 Lemma 11: implies(not(truth), not(not(truth))) = not(not(truth)).
% 0.19/0.68 Proof:
% 0.19/0.69 implies(not(truth), not(not(truth)))
% 0.19/0.69 = { by lemma 9 R->L }
% 0.19/0.69 implies(implies(implies(not(not(truth)), not(truth)), not(truth)), not(not(truth)))
% 0.19/0.69 = { by lemma 10 }
% 0.19/0.69 implies(truth, not(not(truth)))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 not(not(truth))
% 0.19/0.69
% 0.19/0.69 Lemma 12: implies(not(truth), X) = truth.
% 0.19/0.69 Proof:
% 0.19/0.69 implies(not(truth), X)
% 0.19/0.69 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.69 implies(truth, implies(not(truth), X))
% 0.19/0.69 = { by lemma 7 R->L }
% 0.19/0.69 implies(implies(not(X), truth), implies(not(truth), X))
% 0.19/0.69 = { by axiom 3 (wajsberg_4) R->L }
% 0.19/0.69 implies(implies(not(X), implies(implies(not(not(not(truth))), not(truth)), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.69 implies(implies(not(X), implies(implies(not(not(not(truth))), implies(truth, not(truth))), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by lemma 6 R->L }
% 0.19/0.69 implies(implies(not(X), implies(implies(not(not(not(truth))), implies(implies(not(not(truth)), not(not(truth))), not(truth))), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by lemma 11 R->L }
% 0.19/0.69 implies(implies(not(X), implies(implies(not(not(not(truth))), implies(implies(implies(not(truth), not(not(truth))), not(not(truth))), not(truth))), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by lemma 9 }
% 0.19/0.69 implies(implies(not(X), implies(implies(not(not(not(truth))), implies(not(not(truth)), not(truth))), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.69 implies(implies(not(X), implies(implies(implies(truth, not(not(not(truth)))), implies(not(not(truth)), not(truth))), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by axiom 3 (wajsberg_4) R->L }
% 0.19/0.69 implies(implies(not(X), implies(implies(implies(implies(implies(not(not(not(truth))), not(not(truth))), implies(not(truth), not(not(truth)))), not(not(not(truth)))), implies(not(not(truth)), not(truth))), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by lemma 11 }
% 0.19/0.69 implies(implies(not(X), implies(implies(implies(implies(implies(not(not(not(truth))), not(not(truth))), not(not(truth))), not(not(not(truth)))), implies(not(not(truth)), not(truth))), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by lemma 9 }
% 0.19/0.69 implies(implies(not(X), implies(implies(implies(not(not(truth)), not(not(not(truth)))), implies(not(not(truth)), not(truth))), implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by axiom 3 (wajsberg_4) }
% 0.19/0.69 implies(implies(not(X), implies(truth, implies(truth, not(not(truth))))), implies(not(truth), X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 implies(implies(not(X), implies(truth, not(not(truth)))), implies(not(truth), X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 implies(implies(not(X), not(not(truth))), implies(not(truth), X))
% 0.19/0.69 = { by axiom 3 (wajsberg_4) }
% 0.19/0.69 truth
% 0.19/0.69
% 0.19/0.69 Lemma 13: implies(X, not(truth)) = not(X).
% 0.19/0.69 Proof:
% 0.19/0.69 implies(X, not(truth))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.69 implies(truth, implies(X, not(truth)))
% 0.19/0.69 = { by axiom 4 (wajsberg_2) R->L }
% 0.19/0.69 implies(implies(implies(not(X), implies(not(not(truth)), not(X))), implies(implies(implies(not(not(truth)), not(X)), implies(X, not(truth))), implies(not(X), implies(X, not(truth))))), implies(X, not(truth)))
% 0.19/0.69 = { by lemma 8 }
% 0.19/0.69 implies(implies(truth, implies(implies(implies(not(not(truth)), not(X)), implies(X, not(truth))), implies(not(X), implies(X, not(truth))))), implies(X, not(truth)))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 implies(implies(implies(implies(not(not(truth)), not(X)), implies(X, not(truth))), implies(not(X), implies(X, not(truth)))), implies(X, not(truth)))
% 0.19/0.69 = { by axiom 3 (wajsberg_4) }
% 0.19/0.69 implies(implies(truth, implies(not(X), implies(X, not(truth)))), implies(X, not(truth)))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 implies(implies(not(X), implies(X, not(truth))), implies(X, not(truth)))
% 0.19/0.69 = { by axiom 2 (wajsberg_3) R->L }
% 0.19/0.69 implies(implies(implies(X, not(truth)), not(X)), not(X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.69 implies(implies(implies(X, not(truth)), implies(truth, not(X))), not(X))
% 0.19/0.69 = { by lemma 12 R->L }
% 0.19/0.69 implies(implies(implies(X, not(truth)), implies(implies(not(truth), not(X)), not(X))), not(X))
% 0.19/0.69 = { by axiom 2 (wajsberg_3) R->L }
% 0.19/0.69 implies(implies(implies(X, not(truth)), implies(implies(not(X), not(truth)), not(truth))), not(X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.69 implies(implies(truth, implies(implies(X, not(truth)), implies(implies(not(X), not(truth)), not(truth)))), not(X))
% 0.19/0.69 = { by lemma 10 R->L }
% 0.19/0.69 implies(implies(implies(implies(not(X), not(truth)), X), implies(implies(X, not(truth)), implies(implies(not(X), not(truth)), not(truth)))), not(X))
% 0.19/0.69 = { by axiom 4 (wajsberg_2) }
% 0.19/0.69 implies(truth, not(X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 not(X)
% 0.19/0.69
% 0.19/0.69 Lemma 14: implies(not(X), not(Y)) = implies(Y, X).
% 0.19/0.69 Proof:
% 0.19/0.69 implies(not(X), not(Y))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) R->L }
% 0.19/0.69 implies(truth, implies(not(X), not(Y)))
% 0.19/0.69 = { by axiom 4 (wajsberg_2) R->L }
% 0.19/0.69 implies(implies(implies(Y, X), implies(implies(X, not(truth)), implies(Y, not(truth)))), implies(not(X), not(Y)))
% 0.19/0.69 = { by lemma 13 }
% 0.19/0.69 implies(implies(implies(Y, X), implies(not(X), implies(Y, not(truth)))), implies(not(X), not(Y)))
% 0.19/0.69 = { by lemma 13 }
% 0.19/0.69 implies(implies(implies(Y, X), implies(not(X), not(Y))), implies(not(X), not(Y)))
% 0.19/0.69 = { by axiom 2 (wajsberg_3) }
% 0.19/0.69 implies(implies(implies(not(X), not(Y)), implies(Y, X)), implies(Y, X))
% 0.19/0.69 = { by axiom 3 (wajsberg_4) }
% 0.19/0.69 implies(truth, implies(Y, X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 implies(Y, X)
% 0.19/0.69
% 0.19/0.69 Lemma 15: implies(X, not(Y)) = implies(Y, not(X)).
% 0.19/0.69 Proof:
% 0.19/0.69 implies(X, not(Y))
% 0.19/0.69 = { by lemma 14 R->L }
% 0.19/0.69 implies(not(not(Y)), not(X))
% 0.19/0.69 = { by lemma 13 R->L }
% 0.19/0.69 implies(not(implies(Y, not(truth))), not(X))
% 0.19/0.69 = { by lemma 13 R->L }
% 0.19/0.69 implies(implies(implies(Y, not(truth)), not(truth)), not(X))
% 0.19/0.69 = { by axiom 2 (wajsberg_3) }
% 0.19/0.69 implies(implies(implies(not(truth), Y), Y), not(X))
% 0.19/0.69 = { by lemma 12 }
% 0.19/0.69 implies(implies(truth, Y), not(X))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 implies(Y, not(X))
% 0.19/0.69
% 0.19/0.69 Lemma 16: implies(Y, not(implies(Y, X))) = implies(X, not(implies(X, Y))).
% 0.19/0.69 Proof:
% 0.19/0.69 implies(Y, not(implies(Y, X)))
% 0.19/0.69 = { by lemma 15 R->L }
% 0.19/0.69 implies(implies(Y, X), not(Y))
% 0.19/0.69 = { by lemma 14 R->L }
% 0.19/0.69 implies(implies(not(X), not(Y)), not(Y))
% 0.19/0.69 = { by axiom 2 (wajsberg_3) }
% 0.19/0.69 implies(implies(not(Y), not(X)), not(X))
% 0.19/0.69 = { by lemma 14 }
% 0.19/0.69 implies(implies(X, Y), not(X))
% 0.19/0.69 = { by lemma 15 }
% 0.19/0.69 implies(X, not(implies(X, Y)))
% 0.19/0.69
% 0.19/0.69 Goal 1 (prove_wajsberg_mv_4): implies(implies(implies(a, b), implies(b, a)), implies(b, a)) = truth.
% 0.19/0.69 Proof:
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(b, a))
% 0.19/0.69 = { by lemma 14 R->L }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(not(a), not(b)))
% 0.19/0.69 = { by lemma 13 R->L }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, not(truth)), not(b)))
% 0.19/0.69 = { by lemma 8 R->L }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, not(implies(a, implies(b, a)))), not(b)))
% 0.19/0.69 = { by lemma 16 }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(b, a), a))), not(b)))
% 0.19/0.69 = { by axiom 2 (wajsberg_3) R->L }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(a, b), b))), not(b)))
% 0.19/0.69 = { by lemma 13 R->L }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(a, b), b))), implies(b, not(truth))))
% 0.19/0.69 = { by lemma 8 R->L }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(a, b), b))), implies(b, not(implies(b, implies(implies(a, b), b))))))
% 0.19/0.69 = { by lemma 16 R->L }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(a, b), b))), implies(implies(implies(a, b), b), not(implies(implies(implies(a, b), b), b)))))
% 0.19/0.69 = { by axiom 2 (wajsberg_3) R->L }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(a, b), b))), implies(implies(implies(a, b), b), not(implies(implies(b, implies(a, b)), implies(a, b))))))
% 0.19/0.69 = { by lemma 8 }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(a, b), b))), implies(implies(implies(a, b), b), not(implies(truth, implies(a, b))))))
% 0.19/0.69 = { by axiom 1 (wajsberg_1) }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(a, b), b))), implies(implies(implies(a, b), b), not(implies(a, b)))))
% 0.19/0.69 = { by lemma 15 }
% 0.19/0.69 implies(implies(implies(a, b), implies(b, a)), implies(implies(implies(b, a), not(implies(implies(a, b), b))), implies(implies(a, b), not(implies(implies(a, b), b)))))
% 0.19/0.69 = { by axiom 4 (wajsberg_2) }
% 0.19/0.69 truth
% 0.19/0.69 % SZS output end Proof
% 0.19/0.69
% 0.19/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------