%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL109-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 11:49:03 AM UTC 2026
% Result : Unsatisfiable 3.72s 1.01s
% Output : Proof 4.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:22:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/1.01 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.72/1.01
% 3.72/1.01 % SZS status Unsatisfiable
% 3.72/1.01
% 4.50/1.01 % SZS output start Proof
% 4.50/1.01 Axiom 1 (lemma_9): not(not(X)) = X.
% 4.50/1.01 Axiom 2 (lemma_1): implies(X, X) = truth.
% 4.50/1.01 Axiom 3 (lemma_8): implies(X, not(truth)) = not(X).
% 4.50/1.01 Axiom 4 (wajsberg_1): implies(truth, X) = X.
% 4.50/1.01 Axiom 5 (lemma_10): implies(not(X), not(Y)) = implies(Y, X).
% 4.50/1.01 Axiom 6 (lemma_4): implies(X, implies(Y, X)) = truth.
% 4.50/1.01 Axiom 7 (lemma_7): implies(X, implies(Y, Z)) = implies(Y, implies(X, Z)).
% 4.50/1.01 Axiom 8 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 4.50/1.01
% 4.50/1.01 Lemma 9: implies(not(X), Y) = implies(not(Y), X).
% 4.50/1.01 Proof:
% 4.50/1.01 implies(not(X), Y)
% 4.50/1.01 = { by axiom 5 (lemma_10) R->L }
% 4.50/1.01 implies(not(Y), not(not(X)))
% 4.50/1.01 = { by axiom 1 (lemma_9) }
% 4.50/1.01 implies(not(Y), X)
% 4.50/1.01
% 4.50/1.01 Lemma 10: implies(not(implies(X, Y)), Z) = implies(X, implies(not(Y), Z)).
% 4.50/1.01 Proof:
% 4.50/1.01 implies(not(implies(X, Y)), Z)
% 4.50/1.01 = { by lemma 9 R->L }
% 4.50/1.01 implies(not(Z), implies(X, Y))
% 4.50/1.01 = { by axiom 7 (lemma_7) R->L }
% 4.50/1.01 implies(X, implies(not(Z), Y))
% 4.50/1.01 = { by lemma 9 }
% 4.50/1.01 implies(X, implies(not(Y), Z))
% 4.50/1.01
% 4.50/1.01 Lemma 11: implies(not(Y), not(implies(X, Y))) = implies(not(X), not(implies(Y, X))).
% 4.50/1.01 Proof:
% 4.50/1.01 implies(not(Y), not(implies(X, Y)))
% 4.50/1.01 = { by axiom 5 (lemma_10) }
% 4.50/1.01 implies(implies(X, Y), Y)
% 4.50/1.01 = { by axiom 8 (wajsberg_3) R->L }
% 4.50/1.01 implies(implies(Y, X), X)
% 4.50/1.01 = { by axiom 5 (lemma_10) R->L }
% 4.50/1.01 implies(not(X), not(implies(Y, X)))
% 4.50/1.01
% 4.50/1.01 Goal 1 (prove_wajsberg_mv_4): implies(implies(implies(a, b), implies(b, a)), implies(b, a)) = truth.
% 4.50/1.01 Proof:
% 4.50/1.01 implies(implies(implies(a, b), implies(b, a)), implies(b, a))
% 4.50/1.01 = { by axiom 4 (wajsberg_1) R->L }
% 4.50/1.01 implies(implies(implies(a, b), implies(b, a)), implies(truth, implies(b, a)))
% 4.50/1.01 = { by axiom 6 (lemma_4) R->L }
% 4.50/1.01 implies(implies(implies(a, b), implies(b, a)), implies(implies(b, implies(a, b)), implies(b, a)))
% 4.50/1.01 = { by axiom 7 (lemma_7) }
% 4.50/1.01 implies(implies(implies(a, b), implies(b, a)), implies(b, implies(implies(b, implies(a, b)), a)))
% 4.50/1.01 = { by axiom 1 (lemma_9) R->L }
% 4.50/1.01 implies(implies(implies(a, b), implies(b, a)), implies(b, implies(not(not(implies(b, implies(a, b)))), a)))
% 4.50/1.02 = { by lemma 10 R->L }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(not(implies(b, not(implies(b, implies(a, b))))), a))
% 4.50/1.02 = { by axiom 5 (lemma_10) R->L }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(not(implies(b, not(implies(not(implies(a, b)), not(b))))), a))
% 4.50/1.02 = { by axiom 1 (lemma_9) R->L }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(not(implies(not(not(b)), not(implies(not(implies(a, b)), not(b))))), a))
% 4.50/1.02 = { by lemma 11 }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(not(implies(not(not(implies(a, b))), not(implies(not(b), not(implies(a, b)))))), a))
% 4.50/1.02 = { by lemma 9 }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(not(implies(not(not(implies(a, b))), not(implies(not(not(implies(a, b))), b)))), a))
% 4.50/1.02 = { by axiom 1 (lemma_9) }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(not(implies(not(not(implies(a, b))), not(implies(implies(a, b), b)))), a))
% 4.50/1.02 = { by axiom 1 (lemma_9) }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(not(implies(implies(a, b), not(implies(implies(a, b), b)))), a))
% 4.50/1.02 = { by lemma 10 }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(not(not(implies(implies(a, b), b))), a)))
% 4.50/1.02 = { by axiom 1 (lemma_9) }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(implies(implies(a, b), b), a)))
% 4.50/1.02 = { by axiom 5 (lemma_10) R->L }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(not(a), not(implies(implies(a, b), b)))))
% 4.50/1.02 = { by axiom 5 (lemma_10) R->L }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(not(a), not(implies(not(b), not(implies(a, b)))))))
% 4.50/1.02 = { by lemma 11 R->L }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(not(a), not(implies(not(a), not(implies(b, a)))))))
% 4.50/1.02 = { by axiom 5 (lemma_10) }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(not(a), not(implies(implies(b, a), a)))))
% 4.50/1.02 = { by lemma 11 }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(not(implies(b, a)), not(implies(a, implies(b, a))))))
% 4.50/1.02 = { by axiom 6 (lemma_4) }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(not(implies(b, a)), not(truth))))
% 4.50/1.02 = { by axiom 3 (lemma_8) }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), not(not(implies(b, a)))))
% 4.50/1.02 = { by axiom 1 (lemma_9) }
% 4.50/1.02 implies(implies(implies(a, b), implies(b, a)), implies(implies(a, b), implies(b, a)))
% 4.50/1.02 = { by axiom 2 (lemma_1) }
% 4.50/1.02 truth
% 4.50/1.02 % SZS output end Proof
% 4.50/1.02
% 4.50/1.02 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------