%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN359+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 05:38:53 AM UTC 2025
% Result : Theorem 0.20s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SYN359+1 : TPTP v9.0.0. Released v2.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 12:31:52 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.36 % SZS status Theorem
% 0.20/0.36 % SZS output start Proof
% 0.20/0.36 tff(big_q_type, type, (
% 0.20/0.36 big_q: ( $i * $i ) > $o)).
% 0.20/0.36 tff(tptp_fun_X_0_type, type, (
% 0.20/0.36 tptp_fun_X_0: $i)).
% 0.20/0.36 tff(tptp_fun_Z_1_type, type, (
% 0.20/0.36 tptp_fun_Z_1: $i > $i)).
% 0.20/0.36 tff(big_r_type, type, (
% 0.20/0.36 big_r: $i > $o)).
% 0.20/0.36 tff(1,plain,
% 0.20/0.36 (^[Y: $i] : refl(((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y))) <=> ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y))))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(2,plain,
% 0.20/0.36 (![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y))) <=> ![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))),
% 0.20/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.36 tff(3,plain,
% 0.20/0.36 (![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z)) <=> ![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(4,plain,
% 0.20/0.36 ((~(((?[X: $i] : big_r(X) & ![Y: $i] : (big_r(Y) => ?[Z: $i] : big_q(Y, Z))) & ![X: $i, Y: $i] : (big_q(X, Y) => big_q(X, X))) => ?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y)))) <=> (~((~(?[X: $i] : big_r(X) & ![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z)) & ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X)))) | ?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(5,axiom,(~(((?[X: $i] : big_r(X) & ![Y: $i] : (big_r(Y) => ?[Z: $i] : big_q(Y, Z))) & ![X: $i, Y: $i] : (big_q(X, Y) => big_q(X, X))) => ?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2110')).
% 0.20/0.36 tff(6,plain,
% 0.20/0.36 (~((~(?[X: $i] : big_r(X) & ![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z)) & ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X)))) | ?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.36 tff(7,plain,
% 0.20/0.36 (?[X: $i] : big_r(X) & ![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z)) & ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.20/0.36 inference(or_elim,[status(thm)],[6])).
% 0.20/0.36 tff(8,plain,
% 0.20/0.36 (![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z))),
% 0.20/0.36 inference(and_elim,[status(thm)],[7])).
% 0.20/0.36 tff(9,plain,
% 0.20/0.36 (![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.36 tff(10,plain,(
% 0.20/0.36 ![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))),
% 0.20/0.36 inference(skolemize,[status(sab)],[9])).
% 0.20/0.36 tff(11,plain,
% 0.20/0.36 (![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.36 tff(12,plain,
% 0.20/0.36 (?[X: $i] : big_r(X) <=> ?[X: $i] : big_r(X)),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(13,plain,
% 0.20/0.36 (?[X: $i] : big_r(X)),
% 0.20/0.36 inference(and_elim,[status(thm)],[7])).
% 0.20/0.36 tff(14,plain,
% 0.20/0.36 (?[X: $i] : big_r(X)),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.36 tff(15,plain,(
% 0.20/0.36 big_r(X!0)),
% 0.20/0.36 inference(skolemize,[status(sab)],[14])).
% 0.20/0.36 tff(16,plain,
% 0.20/0.36 (((~![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))) | ((~big_r(X!0)) | big_q(X!0, tptp_fun_Z_1(X!0)))) <=> ((~![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))) | (~big_r(X!0)) | big_q(X!0, tptp_fun_Z_1(X!0)))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(17,plain,
% 0.20/0.36 ((~![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))) | ((~big_r(X!0)) | big_q(X!0, tptp_fun_Z_1(X!0)))),
% 0.20/0.36 inference(quant_inst,[status(thm)],[])).
% 0.20/0.36 tff(18,plain,
% 0.20/0.36 ((~![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))) | (~big_r(X!0)) | big_q(X!0, tptp_fun_Z_1(X!0))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.36 tff(19,plain,
% 0.20/0.36 (big_q(X!0, tptp_fun_Z_1(X!0))),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[18, 15, 11])).
% 0.20/0.36 tff(20,plain,
% 0.20/0.36 (^[X: $i, Y: $i] : refl(((~big_q(X, Y)) | big_q(X, X)) <=> ((~big_q(X, Y)) | big_q(X, X)))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(21,plain,
% 0.20/0.36 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X)) <=> ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.20/0.36 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.36 tff(22,plain,
% 0.20/0.36 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X)) <=> ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(23,plain,
% 0.20/0.36 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.20/0.36 inference(and_elim,[status(thm)],[7])).
% 0.20/0.36 tff(24,plain,
% 0.20/0.36 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.37 tff(25,plain,(
% 0.20/0.37 ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.20/0.37 inference(skolemize,[status(sab)],[24])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (((~![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))) | ((~big_q(X!0, tptp_fun_Z_1(X!0))) | big_q(X!0, X!0))) <=> ((~![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))) | (~big_q(X!0, tptp_fun_Z_1(X!0))) | big_q(X!0, X!0))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))) | ((~big_q(X!0, tptp_fun_Z_1(X!0))) | big_q(X!0, X!0))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))) | (~big_q(X!0, tptp_fun_Z_1(X!0))) | big_q(X!0, X!0)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (big_q(X!0, X!0)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[29, 26, 19])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (^[X: $i, Y: $i] : refl(((~big_r(Y)) | (~big_q(X, Y))) <=> ((~big_r(Y)) | (~big_q(X, Y))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y))) <=> ![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((big_q(X, Y) & big_r(Y)) <=> (~((~big_r(Y)) | (~big_q(X, Y))))), ((~(big_q(X, Y) & big_r(Y))) <=> (~(~((~big_r(Y)) | (~big_q(X, Y))))))), rewrite((~(~((~big_r(Y)) | (~big_q(X, Y))))) <=> ((~big_r(Y)) | (~big_q(X, Y)))), ((~(big_q(X, Y) & big_r(Y))) <=> ((~big_r(Y)) | (~big_q(X, Y)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~(big_q(X, Y) & big_r(Y))) <=> ![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 ((~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))) <=> (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.20/0.37 inference(or_elim,[status(thm)],[6])).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 (^[X: $i, Y: $i] : refl($oeq((~(big_q(X, Y) & big_r(Y))), (~(big_q(X, Y) & big_r(Y)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(41,plain,(
% 0.20/0.37 ![X: $i, Y: $i] : (~(big_q(X, Y) & big_r(Y)))),
% 0.20/0.37 inference(nnf-neg,[status(sab)],[39, 40])).
% 0.20/0.37 tff(42,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 (((~![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))) | ((~big_r(X!0)) | (~big_q(X!0, X!0)))) <=> ((~![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))) | (~big_r(X!0)) | (~big_q(X!0, X!0)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(45,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))) | ((~big_r(X!0)) | (~big_q(X!0, X!0)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(46,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))) | (~big_r(X!0)) | (~big_q(X!0, X!0))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.37 tff(47,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[46, 15, 43, 30])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------