%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN925+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:41:00 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN925+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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 : Fri Jun 20 13:02:46 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(p_type, type, (
% 0.20/0.38 p: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (((~![Y: $i] : (~((~p(Y)) | p(X!0)))) | $false) <=> (~![Y: $i] : (~((~p(Y)) | p(X!0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((~$true) <=> $false),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (((~p(X!0)) | p(X!0)) <=> $true),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 ((~((~p(X!0)) | p(X!0))) <=> (~$true)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~((~p(X!0)) | p(X!0))) <=> $false),
% 0.20/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (((~![Y: $i] : (~((~p(Y)) | p(X!0)))) | (~((~p(X!0)) | p(X!0)))) <=> ((~![Y: $i] : (~((~p(Y)) | p(X!0)))) | $false)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[5])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (((~![Y: $i] : (~((~p(Y)) | p(X!0)))) | (~((~p(X!0)) | p(X!0)))) <=> (~![Y: $i] : (~((~p(Y)) | p(X!0))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[6, 1])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~![Y: $i] : (~((~p(Y)) | p(X!0)))) | (~((~p(X!0)) | p(X!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (~![Y: $i] : (~((~p(Y)) | p(X!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (^[Y: $i] : refl((~((~p(Y)) | p(X!0))) <=> (~((~p(Y)) | p(X!0))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![Y: $i] : (~((~p(Y)) | p(X!0))) <=> ![Y: $i] : (~((~p(Y)) | p(X!0)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[Y: $i] : rewrite((p(Y) & (~p(X!0))) <=> (~((~p(Y)) | p(X!0))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![Y: $i] : (p(Y) & (~p(X!0))) <=> ![Y: $i] : (~((~p(Y)) | p(X!0)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((~?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X))) <=> (~?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~?[Y: $i] : (p(Y) => ![X: $i] : p(X))) <=> (~?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(16,axiom,(~?[Y: $i] : (p(Y) => ![X: $i] : p(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (~?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (~?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (~?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (~?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (^[Y: $i] : nnf_neg(refl($oeq(p(Y), p(Y))), sk($oeq((~![X: $i] : p(X)), (~p(X!0)))), $oeq((~((~p(Y)) | ![X: $i] : p(X))), (p(Y) & (~p(X!0)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(22,plain,(
% 0.20/0.38 ![Y: $i] : (p(Y) & (~p(X!0)))),
% 0.20/0.38 inference(nnf-neg,[status(sab)],[20, 21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![Y: $i] : (~((~p(Y)) | p(X!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![Y: $i] : (~((~p(Y)) | p(X!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 11])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------