%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN384+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 05:38:57 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN384+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:33:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(big_p_type, type, (
% 0.20/0.37 big_p: ( $i * $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_U_1_type, type, (
% 0.20/0.37 tptp_fun_U_1: ( $i * $i ) > $i)).
% 0.20/0.37 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.37 tptp_fun_Z_0: $i)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (^[X: $i, Y: $i] : refl((~((~big_p(X, Y, Z!0)) | big_p(tptp_fun_U_1(Y, X), X, X))) <=> (~((~big_p(X, Y, Z!0)) | big_p(tptp_fun_U_1(Y, X), X, X))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~((~big_p(X, Y, Z!0)) | big_p(tptp_fun_U_1(Y, X), X, X))) <=> ![X: $i, Y: $i] : (~((~big_p(X, Y, Z!0)) | big_p(tptp_fun_U_1(Y, X), X, X)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 ((~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : ((~big_p(X, Y, Z)) | big_p(U, X, X))) <=> (~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : ((~big_p(X, Y, Z)) | big_p(U, X, X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 ((~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : (big_p(X, Y, Z) => big_p(U, X, X))) <=> (~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : ((~big_p(X, Y, Z)) | big_p(U, X, X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(5,axiom,(~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : (big_p(X, Y, Z) => big_p(U, X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2136')).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : ((~big_p(X, Y, Z)) | big_p(U, X, X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : ((~big_p(X, Y, Z)) | big_p(U, X, X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : ((~big_p(X, Y, Z)) | big_p(U, X, X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (~![Z: $i] : ?[X: $i, Y: $i] : ![U: $i] : ((~big_p(X, Y, Z)) | big_p(U, X, X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.37 tff(10,plain,(
% 0.20/0.37 $oeq((~?[X: $i, Y: $i] : ![U: $i] : ((~big_p(X, Y, Z!0)) | big_p(U, X, X))), ![X: $i, Y: $i] : (~((~big_p(X, Y, Z!0)) | big_p(tptp_fun_U_1(Y, X), X, X))))),
% 0.20/0.37 inference(transitivity,[status(sab)],[9])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~((~big_p(X, Y, Z!0)) | big_p(tptp_fun_U_1(Y, X), X, X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : (~((~big_p(X, Y, Z!0)) | big_p(tptp_fun_U_1(Y, X), X, X)))) | (~((~big_p(Z!0, Z!0, Z!0)) | big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (~((~big_p(Z!0, Z!0, Z!0)) | big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (((~big_p(Z!0, Z!0, Z!0)) | big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0)) | (~big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (~big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (((~big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0)) | big_p(tptp_fun_U_1(Z!0, tptp_fun_U_1(Z!0, Z!0)), tptp_fun_U_1(Z!0, Z!0), tptp_fun_U_1(Z!0, Z!0))) | big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 ((~big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0)) | big_p(tptp_fun_U_1(Z!0, tptp_fun_U_1(Z!0, Z!0)), tptp_fun_U_1(Z!0, Z!0), tptp_fun_U_1(Z!0, Z!0))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : (~((~big_p(X, Y, Z!0)) | big_p(tptp_fun_U_1(Y, X), X, X)))) | (~((~big_p(tptp_fun_U_1(Z!0, Z!0), Z!0, Z!0)) | big_p(tptp_fun_U_1(Z!0, tptp_fun_U_1(Z!0, Z!0)), tptp_fun_U_1(Z!0, Z!0), tptp_fun_U_1(Z!0, Z!0))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[18, 11, 17])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------