%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 1.95s 0.73s
% Output : Proof 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 15:25:38 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.95/0.73 Command-line arguments: --no-flatten-goal
% 1.95/0.73
% 1.95/0.73 % SZS status Unsatisfiable
% 1.95/0.73
% 1.95/0.74 % SZS output start Proof
% 1.95/0.74 Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 1.95/0.74 Axiom 2 (big_hat_definition): big_hat(X, Y) = not(big_V(not(X), not(Y))).
% 1.95/0.74 Axiom 3 (big_V_definition): big_V(X, Y) = implies(implies(X, Y), Y).
% 1.95/0.74 Axiom 4 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 1.95/0.74 Axiom 5 (wajsberg_4): implies(implies(not(X), not(Y)), implies(Y, X)) = truth.
% 1.95/0.74 Axiom 6 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 1.95/0.74
% 1.95/0.74 Lemma 7: implies(X, big_V(X, Y)) = truth.
% 1.95/0.74 Proof:
% 1.95/0.74 implies(X, big_V(X, Y))
% 1.95/0.74 = { by axiom 3 (big_V_definition) }
% 1.95/0.74 implies(X, implies(implies(X, Y), Y))
% 1.95/0.74 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.74 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 1.95/0.74 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.74 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 1.95/0.74 = { by axiom 6 (wajsberg_2) }
% 1.95/0.74 truth
% 1.95/0.74
% 1.95/0.74 Lemma 8: implies(implies(X, Y), implies(X, big_V(Y, Z))) = truth.
% 1.95/0.74 Proof:
% 1.95/0.74 implies(implies(X, Y), implies(X, big_V(Y, Z)))
% 1.95/0.74 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.74 implies(implies(X, Y), implies(truth, implies(X, big_V(Y, Z))))
% 1.95/0.74 = { by lemma 7 R->L }
% 1.95/0.74 implies(implies(X, Y), implies(implies(Y, big_V(Y, Z)), implies(X, big_V(Y, Z))))
% 1.95/0.74 = { by axiom 6 (wajsberg_2) }
% 1.95/0.74 truth
% 1.95/0.74
% 1.95/0.74 Lemma 9: big_V(Y, X) = big_V(X, Y).
% 1.95/0.74 Proof:
% 1.95/0.74 big_V(Y, X)
% 1.95/0.74 = { by axiom 3 (big_V_definition) }
% 1.95/0.74 implies(implies(Y, X), X)
% 1.95/0.74 = { by axiom 4 (wajsberg_3) R->L }
% 1.95/0.74 implies(implies(X, Y), Y)
% 1.95/0.74 = { by axiom 3 (big_V_definition) R->L }
% 1.95/0.74 big_V(X, Y)
% 1.95/0.74
% 1.95/0.74 Lemma 10: implies(not(not(X)), X) = truth.
% 1.95/0.74 Proof:
% 1.95/0.74 implies(not(not(X)), X)
% 1.95/0.74 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.74 implies(not(not(X)), implies(truth, X))
% 1.95/0.74 = { by axiom 5 (wajsberg_4) R->L }
% 1.95/0.74 implies(not(not(X)), implies(implies(implies(not(X), not(truth)), implies(truth, X)), X))
% 1.95/0.74 = { by axiom 1 (wajsberg_1) }
% 1.95/0.74 implies(not(not(X)), implies(implies(implies(not(X), not(truth)), X), X))
% 1.95/0.74 = { by axiom 3 (big_V_definition) R->L }
% 1.95/0.74 implies(not(not(X)), big_V(implies(not(X), not(truth)), X))
% 1.95/0.74 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.74 implies(truth, implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.95/0.74 = { by lemma 8 R->L }
% 1.95/0.74 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)))
% 1.95/0.74 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.75 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)))
% 1.95/0.75 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.75 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)))
% 1.95/0.75 = { by lemma 7 R->L }
% 1.95/0.75 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)))
% 1.95/0.75 = { by lemma 9 }
% 1.95/0.75 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)))
% 1.95/0.75 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.75 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)))
% 1.95/0.75 = { by lemma 7 }
% 1.95/0.75 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)))
% 1.95/0.75 = { by axiom 6 (wajsberg_2) }
% 1.95/0.75 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)))
% 1.95/0.75 = { by axiom 1 (wajsberg_1) }
% 1.95/0.75 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)))
% 1.95/0.75 = { by axiom 3 (big_V_definition) }
% 1.95/0.75 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)))
% 1.95/0.75 = { by axiom 5 (wajsberg_4) }
% 1.95/0.75 implies(implies(not(not(X)), implies(truth, implies(not(X), not(truth)))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.95/0.75 = { by axiom 1 (wajsberg_1) }
% 1.95/0.75 implies(implies(not(not(X)), implies(not(X), not(truth))), implies(not(not(X)), big_V(implies(not(X), not(truth)), X)))
% 1.95/0.75 = { by lemma 8 }
% 1.95/0.75 truth
% 1.95/0.75
% 1.95/0.75 Lemma 11: not(not(X)) = X.
% 1.95/0.75 Proof:
% 1.95/0.75 not(not(X))
% 1.95/0.75 = { by axiom 1 (wajsberg_1) R->L }
% 1.95/0.75 implies(truth, not(not(X)))
% 1.95/0.75 = { by axiom 5 (wajsberg_4) R->L }
% 1.95/0.75 implies(implies(implies(not(not(not(X))), not(X)), implies(X, not(not(X)))), not(not(X)))
% 1.95/0.75 = { by lemma 10 }
% 1.95/0.75 implies(implies(truth, implies(X, not(not(X)))), not(not(X)))
% 1.95/0.75 = { by axiom 1 (wajsberg_1) }
% 1.95/0.75 implies(implies(X, not(not(X))), not(not(X)))
% 1.95/0.75 = { by axiom 3 (big_V_definition) R->L }
% 1.95/0.75 big_V(X, not(not(X)))
% 1.95/0.75 = { by lemma 9 }
% 1.95/0.75 big_V(not(not(X)), X)
% 1.95/0.75 = { by axiom 3 (big_V_definition) }
% 1.95/0.75 implies(implies(not(not(X)), X), X)
% 1.95/0.75 = { by lemma 10 }
% 1.95/0.75 implies(truth, X)
% 1.95/0.75 = { by axiom 1 (wajsberg_1) }
% 1.95/0.75 X
% 1.95/0.75
% 1.95/0.75 Goal 1 (prove_wajsberg_theorem): not(big_V(x, y)) = big_hat(not(x), not(y)).
% 1.95/0.75 Proof:
% 1.95/0.75 not(big_V(x, y))
% 1.95/0.75 = { by lemma 11 R->L }
% 1.95/0.75 not(big_V(x, not(not(y))))
% 1.95/0.75 = { by lemma 11 R->L }
% 1.95/0.75 not(big_V(not(not(x)), not(not(y))))
% 1.95/0.75 = { by axiom 2 (big_hat_definition) R->L }
% 1.95/0.75 big_hat(not(x), not(y))
% 1.95/0.75 % SZS output end Proof
% 1.95/0.75
% 1.95/0.75 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------