%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN361+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 05:38:53 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN361+1 : TPTP v9.0.0. Released v2.0.0.
% 0.04/0.12 % 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 12:32:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(big_p_type, type, (
% 0.12/0.37 big_p: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_V_0_type, type, (
% 0.12/0.37 tptp_fun_V_0: $i)).
% 0.12/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.37 tptp_fun_Y_1: $i > $i)).
% 0.12/0.37 tff(big_q_type, type, (
% 0.12/0.37 big_q: ( $i * $i ) > $o)).
% 0.12/0.37 tff(big_s_type, type, (
% 0.12/0.37 big_s: $i > $o)).
% 0.12/0.37 tff(1,assumption,(~big_s(V!0)), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[U: $i] : refl(big_s(U) <=> big_s(U))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![U: $i] : big_s(U) <=> ![U: $i] : big_s(U)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~?[U: $i] : (~big_s(U))) <=> (~?[U: $i] : (~big_s(U)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((~(((?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : (big_s(X) => ?[Y: $i] : big_q(Y, X))) & ![X: $i, Y: $i] : (big_p(X, Y) => (~big_q(X, Y)))) => ?[U: $i] : (~big_s(U)))) <=> (~((~(?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X)) & ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y))))) | ?[U: $i] : (~big_s(U))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,axiom,(~(((?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : (big_s(X) => ?[Y: $i] : big_q(Y, X))) & ![X: $i, Y: $i] : (big_p(X, Y) => (~big_q(X, Y)))) => ?[U: $i] : (~big_s(U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2112')).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~((~(?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X)) & ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y))))) | ?[U: $i] : (~big_s(U)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~?[U: $i] : (~big_s(U))),
% 0.12/0.37 inference(or_elim,[status(thm)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~?[U: $i] : (~big_s(U))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~?[U: $i] : (~big_s(U))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (~?[U: $i] : (~big_s(U))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (^[U: $i] : refl($oeq(big_s(U), big_s(U)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(13,plain,(
% 0.12/0.37 ![U: $i] : big_s(U)),
% 0.12/0.37 inference(nnf-neg,[status(sab)],[11, 12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![U: $i] : big_s(U)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((~![U: $i] : big_s(U)) | big_s(V!0)),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.12/0.37 tff(17,plain,(big_s(V!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (^[X: $i] : refl(((~big_s(X)) | big_q(tptp_fun_Y_1(X), X)) <=> ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X)) <=> ![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X)) <=> ![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X)) & ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[7])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X))),
% 0.12/0.37 inference(and_elim,[status(thm)],[21])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.12/0.37 tff(24,plain,(
% 0.12/0.37 ![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[23])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (((~![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))) | ((~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0))) <=> ((~![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))) | (~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 ((~![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))) | ((~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((~![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))) | (~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 ((~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (big_q(tptp_fun_Y_1(V!0), V!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[29, 17])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (^[X: $i, Y: $i] : refl(((~big_p(X, Y)) | (~big_q(X, Y))) <=> ((~big_p(X, Y)) | (~big_q(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y))) <=> ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y))) <=> ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.19/0.37 inference(and_elim,[status(thm)],[21])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.37 tff(36,plain,(
% 0.19/0.37 ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[35])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))) | ((~big_p(tptp_fun_Y_1(V!0), V!0)) | (~big_q(tptp_fun_Y_1(V!0), V!0)))) <=> ((~![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))) | (~big_p(tptp_fun_Y_1(V!0), V!0)) | (~big_q(tptp_fun_Y_1(V!0), V!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))) | ((~big_p(tptp_fun_Y_1(V!0), V!0)) | (~big_q(tptp_fun_Y_1(V!0), V!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))) | (~big_p(tptp_fun_Y_1(V!0), V!0)) | (~big_q(tptp_fun_Y_1(V!0), V!0))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (~big_p(tptp_fun_Y_1(V!0), V!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[40, 37, 30])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (^[X: $i] : refl(big_p(X, V!0) <=> big_p(X, V!0))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (![X: $i] : big_p(X, V!0) <=> ![X: $i] : big_p(X, V!0)),
% 0.19/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (?[V: $i] : ![X: $i] : big_p(X, V) <=> ?[V: $i] : ![X: $i] : big_p(X, V)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (?[V: $i] : ![X: $i] : big_p(X, V)),
% 0.19/0.37 inference(and_elim,[status(thm)],[21])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (?[V: $i] : ![X: $i] : big_p(X, V)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.37 tff(47,plain,(
% 0.19/0.37 $oeq(![X: $i] : big_p(X, V!0), ![X: $i] : big_p(X, V!0))),
% 0.19/0.37 inference(transitivity,[status(sab)],[46])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (![X: $i] : big_p(X, V!0)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 ((~![X: $i] : big_p(X, V!0)) | big_p(tptp_fun_Y_1(V!0), V!0)),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[49, 48, 41])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------