%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN362+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:54 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN362+1 : TPTP v9.0.0. Released v2.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:33:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(big_p_type, type, (
% 0.12/0.36 big_p: $i > $o)).
% 0.12/0.36 tff(tptp_fun_W_0_type, type, (
% 0.12/0.36 tptp_fun_W_0: $i > $i)).
% 0.12/0.36 tff(tptp_fun_Z_1_type, type, (
% 0.12/0.36 tptp_fun_Z_1: $i)).
% 0.12/0.36 tff(big_r_type, type, (
% 0.12/0.36 big_r: ( $i * $i ) > $o)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (![Y: $i] : ?[W: $i] : big_r(Y, W) <=> ![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 ((~((![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : (big_p(X) => (~big_r(Z, X)))) => ?[X: $i] : (~big_p(X)))) <=> (~((~(![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))))) | ?[X: $i] : (~big_p(X))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(3,axiom,(~((![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : (big_p(X) => (~big_r(Z, X)))) => ?[X: $i] : (~big_p(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2113')).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (~((~(![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))))) | ?[X: $i] : (~big_p(X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.12/0.36 inference(or_elim,[status(thm)],[4])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.12/0.36 inference(and_elim,[status(thm)],[5])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.36 tff(8,plain,(
% 0.12/0.36 ![Y: $i] : big_r(Y, tptp_fun_W_0(Y))),
% 0.12/0.36 inference(skolemize,[status(sab)],[7])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 ((~![Y: $i] : big_r(Y, tptp_fun_W_0(Y))) | big_r(Z!1, tptp_fun_W_0(Z!1))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (big_r(Z!1, tptp_fun_W_0(Z!1))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (^[X: $i] : refl(((~big_p(X)) | (~big_r(Z!1, X))) <=> ((~big_p(X)) | (~big_r(Z!1, X))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))) <=> ![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))) <=> ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.12/0.36 inference(and_elim,[status(thm)],[5])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.36 tff(16,plain,(
% 0.12/0.36 $oeq(![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))), ![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))))),
% 0.12/0.36 inference(transitivity,[status(sab)],[15])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | ((~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))) <=> ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | (~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | ((~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | (~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (~big_p(tptp_fun_W_0(Z!1))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[20, 17, 10])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 (^[X: $i] : refl(big_p(X) <=> big_p(X))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (![X: $i] : big_p(X) <=> ![X: $i] : big_p(X)),
% 0.12/0.36 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 ((~?[X: $i] : (~big_p(X))) <=> (~?[X: $i] : (~big_p(X)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 (~?[X: $i] : (~big_p(X))),
% 0.12/0.36 inference(or_elim,[status(thm)],[4])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (~?[X: $i] : (~big_p(X))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.36 tff(27,plain,
% 0.12/0.37 (~?[X: $i] : (~big_p(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 24])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (~?[X: $i] : (~big_p(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (^[X: $i] : refl($oeq(big_p(X), big_p(X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(30,plain,(
% 0.12/0.37 ![X: $i] : big_p(X)),
% 0.12/0.37 inference(nnf-neg,[status(sab)],[28, 29])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![X: $i] : big_p(X)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ((~![X: $i] : big_p(X)) | big_p(tptp_fun_W_0(Z!1))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[32, 31, 21])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------