%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:09 AM UTC 2026
% Result : Unsatisfiable 1.67s 0.74s
% Output : Proof 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n001.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 15:29:15 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.67/0.74 Command-line arguments: --no-flatten-goal
% 1.67/0.74
% 1.67/0.74 % SZS status Unsatisfiable
% 1.67/0.74
% 1.67/0.76 % SZS output start Proof
% 1.67/0.76 Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 1.67/0.76 Axiom 2 (big_hat_definition): big_hat(X, Y) = not(big_V(not(X), not(Y))).
% 1.67/0.76 Axiom 3 (big_V_definition): big_V(X, Y) = implies(implies(X, Y), Y).
% 1.67/0.76 Axiom 4 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 1.67/0.76 Axiom 5 (wajsberg_4): implies(implies(not(X), not(Y)), implies(Y, X)) = truth.
% 1.67/0.76 Axiom 6 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 1.67/0.76
% 1.67/0.76 Lemma 7: big_V(Y, X) = big_V(X, Y).
% 1.67/0.76 Proof:
% 1.67/0.76 big_V(Y, X)
% 1.67/0.76 = { by axiom 3 (big_V_definition) }
% 1.67/0.76 implies(implies(Y, X), X)
% 1.67/0.76 = { by axiom 4 (wajsberg_3) R->L }
% 1.67/0.76 implies(implies(X, Y), Y)
% 1.67/0.76 = { by axiom 3 (big_V_definition) R->L }
% 1.67/0.76 big_V(X, Y)
% 1.67/0.76
% 1.67/0.76 Lemma 8: implies(X, big_V(X, Y)) = truth.
% 1.67/0.76 Proof:
% 1.67/0.76 implies(X, big_V(X, Y))
% 1.67/0.76 = { by axiom 3 (big_V_definition) }
% 1.67/0.76 implies(X, implies(implies(X, Y), Y))
% 1.67/0.76 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.76 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 1.67/0.76 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.76 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 1.67/0.76 = { by axiom 6 (wajsberg_2) }
% 1.67/0.76 truth
% 1.67/0.76
% 1.67/0.76 Lemma 9: implies(implies(X, Y), implies(X, big_V(Y, Z))) = truth.
% 1.67/0.76 Proof:
% 1.67/0.76 implies(implies(X, Y), implies(X, big_V(Y, Z)))
% 1.67/0.76 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.76 implies(implies(X, Y), implies(truth, implies(X, big_V(Y, Z))))
% 1.67/0.76 = { by lemma 8 R->L }
% 1.67/0.76 implies(implies(X, Y), implies(implies(Y, big_V(Y, Z)), implies(X, big_V(Y, Z))))
% 1.67/0.76 = { by axiom 6 (wajsberg_2) }
% 1.67/0.76 truth
% 1.67/0.76
% 1.67/0.76 Lemma 10: implies(not(not(X)), X) = truth.
% 1.67/0.76 Proof:
% 1.67/0.76 implies(not(not(X)), X)
% 1.67/0.76 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.76 implies(not(not(X)), implies(truth, X))
% 1.67/0.76 = { by axiom 5 (wajsberg_4) R->L }
% 1.67/0.76 implies(not(not(X)), implies(implies(implies(not(X), not(truth)), implies(truth, X)), X))
% 1.67/0.76 = { by axiom 1 (wajsberg_1) }
% 1.67/0.76 implies(not(not(X)), implies(implies(implies(not(X), not(truth)), X), X))
% 1.67/0.76 = { by axiom 3 (big_V_definition) R->L }
% 1.67/0.76 implies(not(not(X)), big_V(implies(not(X), not(truth)), X))
% 1.67/0.76 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.76 implies(truth, implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.76 = { by lemma 9 R->L }
% 1.67/0.76 implies(implies(implies(not(not(X)), implies(not(not(truth)), not(not(X)))), implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.76 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.76 implies(implies(implies(implies(truth, not(not(X))), implies(not(not(truth)), not(not(X)))), implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.76 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.76 implies(implies(implies(truth, implies(implies(truth, not(not(X))), implies(not(not(truth)), not(not(X))))), implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.76 = { by lemma 8 R->L }
% 1.67/0.76 implies(implies(implies(implies(not(not(truth)), big_V(not(not(truth)), truth)), implies(implies(truth, not(not(X))), implies(not(not(truth)), not(not(X))))), implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.76 = { by lemma 7 }
% 1.67/0.77 implies(implies(implies(implies(not(not(truth)), big_V(truth, not(not(truth)))), implies(implies(truth, not(not(X))), implies(not(not(truth)), not(not(X))))), implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.77 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.77 implies(implies(implies(implies(not(not(truth)), implies(truth, big_V(truth, not(not(truth))))), implies(implies(truth, not(not(X))), implies(not(not(truth)), not(not(X))))), implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.77 = { by lemma 8 }
% 1.67/0.77 implies(implies(implies(implies(not(not(truth)), truth), implies(implies(truth, not(not(X))), implies(not(not(truth)), not(not(X))))), implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.77 = { by axiom 6 (wajsberg_2) }
% 1.67/0.77 implies(implies(truth, implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.77 = { by axiom 1 (wajsberg_1) }
% 1.67/0.77 implies(implies(not(not(X)), big_V(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth)))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.77 = { by axiom 3 (big_V_definition) }
% 1.67/0.77 implies(implies(not(not(X)), implies(implies(implies(not(not(truth)), not(not(X))), implies(not(X), not(truth))), implies(not(X), not(truth)))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.77 = { by axiom 5 (wajsberg_4) }
% 1.67/0.77 implies(implies(not(not(X)), implies(truth, implies(not(X), not(truth)))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.77 = { by axiom 1 (wajsberg_1) }
% 1.67/0.77 implies(implies(not(not(X)), implies(not(X), not(truth))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.67/0.77 = { by lemma 9 }
% 1.67/0.77 truth
% 1.67/0.77
% 1.67/0.77 Goal 1 (prove_wajsberg_theorem): not(big_hat(x, y)) = big_V(not(x), not(y)).
% 1.67/0.77 Proof:
% 1.67/0.77 not(big_hat(x, y))
% 1.67/0.77 = { by axiom 2 (big_hat_definition) }
% 1.67/0.77 not(not(big_V(not(x), not(y))))
% 1.67/0.77 = { by lemma 7 }
% 1.67/0.77 not(not(big_V(not(y), not(x))))
% 1.67/0.77 = { by axiom 1 (wajsberg_1) R->L }
% 1.67/0.77 implies(truth, not(not(big_V(not(y), not(x)))))
% 1.67/0.77 = { by axiom 5 (wajsberg_4) R->L }
% 1.67/0.77 implies(implies(implies(not(not(not(big_V(not(y), not(x))))), not(big_V(not(y), not(x)))), implies(big_V(not(y), not(x)), not(not(big_V(not(y), not(x)))))), not(not(big_V(not(y), not(x)))))
% 1.67/0.77 = { by lemma 10 }
% 1.67/0.77 implies(implies(truth, implies(big_V(not(y), not(x)), not(not(big_V(not(y), not(x)))))), not(not(big_V(not(y), not(x)))))
% 1.67/0.77 = { by axiom 1 (wajsberg_1) }
% 1.67/0.77 implies(implies(big_V(not(y), not(x)), not(not(big_V(not(y), not(x))))), not(not(big_V(not(y), not(x)))))
% 1.67/0.77 = { by axiom 3 (big_V_definition) R->L }
% 1.67/0.77 big_V(big_V(not(y), not(x)), not(not(big_V(not(y), not(x)))))
% 1.67/0.77 = { by lemma 7 }
% 1.67/0.77 big_V(not(not(big_V(not(y), not(x)))), big_V(not(y), not(x)))
% 1.67/0.77 = { by axiom 3 (big_V_definition) }
% 1.67/0.77 implies(implies(not(not(big_V(not(y), not(x)))), big_V(not(y), not(x))), big_V(not(y), not(x)))
% 1.67/0.77 = { by lemma 10 }
% 1.67/0.77 implies(truth, big_V(not(y), not(x)))
% 1.67/0.77 = { by axiom 1 (wajsberg_1) }
% 1.67/0.77 big_V(not(y), not(x))
% 1.67/0.77 = { by lemma 7 R->L }
% 1.67/0.77 big_V(not(x), not(y))
% 1.67/0.77 % SZS output end Proof
% 1.67/0.77
% 1.67/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------