%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN081+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:38:11 AM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN081+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:27:20 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(big_f_type, type, (
% 0.13/0.37 big_f: $i > $o)).
% 0.13/0.37 tff(f_type, type, (
% 0.13/0.37 f: $i > $i)).
% 0.13/0.37 tff(elem_0_type, type, (
% 0.13/0.37 elem_0: $i)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 (^[X: $i] : refl((~(big_f(f(X)) <=> big_f(X))) <=> (~(big_f(f(X)) <=> big_f(X))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 (![X: $i] : (~(big_f(f(X)) <=> big_f(X))) <=> ![X: $i] : (~(big_f(f(X)) <=> big_f(X)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.37 tff(3,plain,
% 0.13/0.37 (![X: $i] : (~(big_f(f(X)) <=> big_f(X))) <=> ![X: $i] : (~(big_f(f(X)) <=> big_f(X)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 (^[X: $i] : trans(rewrite((big_f(X) <=> (~big_f(f(X)))) <=> (~(big_f(f(X)) <=> big_f(X)))), rewrite((~(big_f(f(X)) <=> big_f(X))) <=> (~(big_f(f(X)) <=> big_f(X)))), ((big_f(X) <=> (~big_f(f(X)))) <=> (~(big_f(f(X)) <=> big_f(X)))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (![X: $i] : (big_f(X) <=> (~big_f(f(X)))) <=> ![X: $i] : (~(big_f(f(X)) <=> big_f(X)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.37 tff(6,axiom,(![X: $i] : (big_f(X) <=> (~big_f(f(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel59_1')).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (![X: $i] : (~(big_f(f(X)) <=> big_f(X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 (![X: $i] : (~(big_f(f(X)) <=> big_f(X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.37 tff(9,plain,(
% 0.13/0.37 ![X: $i] : (~(big_f(f(X)) <=> big_f(X)))),
% 0.13/0.37 inference(skolemize,[status(sab)],[8])).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 (![X: $i] : (~(big_f(f(X)) <=> big_f(X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.37 tff(11,plain,
% 0.13/0.37 ((~![X: $i] : (~(big_f(f(X)) <=> big_f(X)))) | (~(big_f(f(f(elem!0))) <=> big_f(f(elem!0))))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 (~(big_f(f(f(elem!0))) <=> big_f(f(elem!0)))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.37 tff(13,assumption,(~big_f(f(elem!0))), introduced(assumption)).
% 0.13/0.37 tff(14,plain,
% 0.13/0.37 ((~![X: $i] : (~(big_f(f(X)) <=> big_f(X)))) | (~(big_f(f(elem!0)) <=> big_f(elem!0)))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(15,plain,
% 0.13/0.37 (~(big_f(f(elem!0)) <=> big_f(elem!0))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[14, 10])).
% 0.13/0.37 tff(16,plain,
% 0.13/0.37 ((big_f(f(elem!0)) <=> big_f(elem!0)) | big_f(f(elem!0)) | big_f(elem!0)),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(17,plain,
% 0.13/0.37 (big_f(f(elem!0)) | big_f(elem!0)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.13/0.37 tff(18,plain,
% 0.13/0.37 (big_f(elem!0)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[17, 13])).
% 0.13/0.37 tff(19,plain,
% 0.13/0.37 (^[X: $i] : refl((big_f(f(X)) | (~big_f(X))) <=> (big_f(f(X)) | (~big_f(X))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(20,plain,
% 0.13/0.37 (![X: $i] : (big_f(f(X)) | (~big_f(X))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.37 tff(21,plain,
% 0.13/0.37 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & (~big_f(f(X)))) <=> (~(big_f(f(X)) | (~big_f(X))))), ((~(big_f(X) & (~big_f(f(X))))) <=> (~(~(big_f(f(X)) | (~big_f(X))))))), rewrite((~(~(big_f(f(X)) | (~big_f(X))))) <=> (big_f(f(X)) | (~big_f(X)))), ((~(big_f(X) & (~big_f(f(X))))) <=> (big_f(f(X)) | (~big_f(X)))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(22,plain,
% 0.13/0.37 (![X: $i] : (~(big_f(X) & (~big_f(f(X))))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.37 tff(23,plain,
% 0.13/0.37 ((~?[X: $i] : (big_f(X) & (~big_f(f(X))))) <=> (~?[X: $i] : (big_f(X) & (~big_f(f(X)))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(24,axiom,(~?[X: $i] : (big_f(X) & (~big_f(f(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel59')).
% 0.13/0.37 tff(25,plain,
% 0.13/0.37 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.37 tff(26,plain,
% 0.13/0.37 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.13/0.37 tff(27,plain,
% 0.13/0.37 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.13/0.37 tff(28,plain,
% 0.13/0.37 (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.37 tff(29,plain,
% 0.13/0.37 (^[X: $i] : refl($oeq((~(big_f(X) & (~big_f(f(X))))), (~(big_f(X) & (~big_f(f(X)))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(30,plain,(
% 0.13/0.37 ![X: $i] : (~(big_f(X) & (~big_f(f(X)))))),
% 0.13/0.37 inference(nnf-neg,[status(sab)],[28, 29])).
% 0.13/0.37 tff(31,plain,
% 0.13/0.37 (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.13/0.37 tff(32,plain,
% 0.13/0.37 (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[31, 20])).
% 0.13/0.37 tff(33,plain,
% 0.13/0.37 (((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(elem!0)) | (~big_f(elem!0)))) <=> ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(elem!0)) | (~big_f(elem!0)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(34,plain,
% 0.13/0.37 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(elem!0)) | (~big_f(elem!0)))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(35,plain,
% 0.13/0.37 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(elem!0)) | (~big_f(elem!0))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.37 tff(36,plain,
% 0.13/0.37 (big_f(f(elem!0)) | (~big_f(elem!0))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.13/0.37 tff(37,plain,
% 0.13/0.37 ($false),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[36, 18, 13])).
% 0.13/0.37 tff(38,plain,(big_f(f(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.37 tff(39,plain,
% 0.13/0.37 ((big_f(f(f(elem!0))) <=> big_f(f(elem!0))) | (~big_f(f(f(elem!0)))) | (~big_f(f(elem!0)))),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(40,plain,
% 0.13/0.37 ((big_f(f(f(elem!0))) <=> big_f(f(elem!0))) | (~big_f(f(f(elem!0))))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.13/0.37 tff(41,plain,
% 0.13/0.37 (~big_f(f(f(elem!0)))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[40, 12])).
% 0.13/0.37 tff(42,plain,
% 0.13/0.37 (((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(f(elem!0))) | (~big_f(f(elem!0))))) <=> ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(f(elem!0))) | (~big_f(f(elem!0))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(43,plain,
% 0.13/0.37 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(f(elem!0))) | (~big_f(f(elem!0))))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(44,plain,
% 0.13/0.37 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(f(elem!0))) | (~big_f(f(elem!0)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.13/0.37 tff(45,plain,
% 0.13/0.37 ($false),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[44, 32, 38, 41])).
% 0.13/0.37 % SZS output end Proof
% 0.13/0.37 % E exiting
%------------------------------------------------------------------------------