%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN064+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:38:07 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN064+1 : TPTP v9.0.0. Released v2.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:26:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(big_p_type, type, (
% 0.11/0.37 big_p: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_W_0_type, type, (
% 0.11/0.37 tptp_fun_W_0: $i)).
% 0.11/0.37 tff(tptp_fun_Z_1_type, type, (
% 0.11/0.37 tptp_fun_Z_1: $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | $false) <=> (~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 ((~$true) <=> $false),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (((~big_p(Z!1, W!0)) | big_p(Z!1, W!0)) <=> $true),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0))) <=> (~$true)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 ((~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0))) <=> $false),
% 0.11/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | (~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0)))) <=> ((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | $false)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | (~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0)))) <=> (~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[6, 1])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))) | (~((~big_p(Z!1, W!0)) | big_p(Z!1, W!0)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (~![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl((~((~big_p(X, Y)) | big_p(Z!1, W!0))) <=> (~((~big_p(X, Y)) | big_p(Z!1, W!0))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0))) <=> ![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : rewrite((big_p(X, Y) & (~big_p(Z!1, W!0))) <=> (~((~big_p(X, Y)) | big_p(Z!1, W!0))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (big_p(X, Y) & (~big_p(Z!1, W!0))) <=> ![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 ((~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))) <=> (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 ((~?[X: $i, Y: $i] : (big_p(X, Y) => ![Z: $i, W: $i] : big_p(Z, W))) <=> (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,axiom,(~?[X: $i, Y: $i] : (big_p(X, Y) => ![Z: $i, W: $i] : big_p(Z, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel35')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : nnf_neg(refl($oeq(big_p(X, Y), big_p(X, Y))), sk($oeq((~![Z: $i, W: $i] : big_p(Z, W)), (~big_p(Z!1, W!0)))), $oeq((~((~big_p(X, Y)) | ![Z: $i, W: $i] : big_p(Z, W))), (big_p(X, Y) & (~big_p(Z!1, W!0)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(22,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : (big_p(X, Y) & (~big_p(Z!1, W!0)))),
% 0.11/0.37 inference(nnf-neg,[status(sab)],[20, 21])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~big_p(X, Y)) | big_p(Z!1, W!0)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 11])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------