%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN054+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:38:04 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SYN054+1 : TPTP v9.0.0. Released v2.0.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 12:27:09 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(big_r_type, type, (
% 0.13/0.38 big_r: $i > $o)).
% 0.13/0.38 tff(tptp_fun_X_0_type, type, (
% 0.13/0.38 tptp_fun_X_0: $i)).
% 0.13/0.38 tff(big_p_type, type, (
% 0.13/0.38 big_p: $i > $o)).
% 0.13/0.38 tff(big_q_type, type, (
% 0.13/0.38 big_q: $i > $o)).
% 0.13/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.38 tptp_fun_Y_1: $i)).
% 0.13/0.38 tff(big_s_type, type, (
% 0.13/0.38 big_s: $i > $o)).
% 0.13/0.38 tff(1,assumption,(big_q(Y!1)), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((big_q(Y!1) | big_r(Y!1)) | (~big_q(Y!1))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (big_q(Y!1) | big_r(Y!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (^[X: $i] : refl((big_s(X) | (~(big_q(X) | big_r(X)))) <=> (big_s(X) | (~(big_q(X) | big_r(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X)))) <=> ![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X)))) <=> ![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (^[X: $i] : rewrite(((big_q(X) | big_r(X)) => big_s(X)) <=> (big_s(X) | (~(big_q(X) | big_r(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (![X: $i] : ((big_q(X) | big_r(X)) => big_s(X)) <=> ![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.13/0.38 tff(9,axiom,(![X: $i] : ((big_q(X) | big_r(X)) => big_s(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel24_4')).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.13/0.38 tff(12,plain,(
% 0.13/0.38 ![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))),
% 0.13/0.38 inference(skolemize,[status(sab)],[11])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (((~![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))) | (big_s(Y!1) | (~(big_q(Y!1) | big_r(Y!1))))) <=> ((~![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))) | big_s(Y!1) | (~(big_q(Y!1) | big_r(Y!1))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 ((~![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))) | (big_s(Y!1) | (~(big_q(Y!1) | big_r(Y!1))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 ((~![X: $i] : (big_s(X) | (~(big_q(X) | big_r(X))))) | big_s(Y!1) | (~(big_q(Y!1) | big_r(Y!1)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (big_s(Y!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[16, 13, 3])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (^[X: $i] : refl(((~big_s(X)) | (~big_q(X))) <=> ((~big_s(X)) | (~big_q(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (![X: $i] : ((~big_s(X)) | (~big_q(X))) <=> ![X: $i] : ((~big_s(X)) | (~big_q(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (^[X: $i] : trans(monotonicity(rewrite((big_s(X) & big_q(X)) <=> (~((~big_s(X)) | (~big_q(X))))), ((~(big_s(X) & big_q(X))) <=> (~(~((~big_s(X)) | (~big_q(X))))))), rewrite((~(~((~big_s(X)) | (~big_q(X))))) <=> ((~big_s(X)) | (~big_q(X)))), ((~(big_s(X) & big_q(X))) <=> ((~big_s(X)) | (~big_q(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (![X: $i] : (~(big_s(X) & big_q(X))) <=> ![X: $i] : ((~big_s(X)) | (~big_q(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 ((~?[X: $i] : (big_s(X) & big_q(X))) <=> (~?[X: $i] : (big_s(X) & big_q(X)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(23,axiom,(~?[X: $i] : (big_s(X) & big_q(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel24_1')).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (~?[X: $i] : (big_s(X) & big_q(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (~?[X: $i] : (big_s(X) & big_q(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (~?[X: $i] : (big_s(X) & big_q(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (~?[X: $i] : (big_s(X) & big_q(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (^[X: $i] : refl($oeq((~(big_s(X) & big_q(X))), (~(big_s(X) & big_q(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(29,plain,(
% 0.13/0.38 ![X: $i] : (~(big_s(X) & big_q(X)))),
% 0.13/0.38 inference(nnf-neg,[status(sab)],[27, 28])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (![X: $i] : ((~big_s(X)) | (~big_q(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (![X: $i] : ((~big_s(X)) | (~big_q(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[30, 19])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (((~![X: $i] : ((~big_s(X)) | (~big_q(X)))) | ((~big_s(Y!1)) | (~big_q(Y!1)))) <=> ((~![X: $i] : ((~big_s(X)) | (~big_q(X)))) | (~big_s(Y!1)) | (~big_q(Y!1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 ((~![X: $i] : ((~big_s(X)) | (~big_q(X)))) | ((~big_s(Y!1)) | (~big_q(Y!1)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 ((~![X: $i] : ((~big_s(X)) | (~big_q(X)))) | (~big_s(Y!1)) | (~big_q(Y!1))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[34, 31, 1, 17])).
% 0.13/0.38 tff(36,plain,(~big_q(Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 ((?[X: $i] : big_p(X) | ?[Y: $i] : big_q(Y)) <=> (?[X: $i] : big_p(X) | ?[Y: $i] : big_q(Y))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (((~?[X: $i] : big_p(X)) => ?[Y: $i] : big_q(Y)) <=> (?[X: $i] : big_p(X) | ?[Y: $i] : big_q(Y))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 ((~?[X: $i] : big_p(X)) <=> (~?[X: $i] : big_p(X))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 (((~?[X: $i] : big_p(X)) => ?[Y: $i] : big_q(Y)) <=> ((~?[X: $i] : big_p(X)) => ?[Y: $i] : big_q(Y))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[39])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 (((~?[X: $i] : big_p(X)) => ?[Y: $i] : big_q(Y)) <=> (?[X: $i] : big_p(X) | ?[Y: $i] : big_q(Y))),
% 0.13/0.38 inference(transitivity,[status(thm)],[40, 38])).
% 0.13/0.38 tff(42,axiom,((~?[X: $i] : big_p(X)) => ?[Y: $i] : big_q(Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel24_3')).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 (?[X: $i] : big_p(X) | ?[Y: $i] : big_q(Y)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 (?[X: $i] : big_p(X) | ?[Y: $i] : big_q(Y)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[43, 37])).
% 0.13/0.38 tff(45,plain,
% 0.13/0.38 (?[X: $i] : big_p(X) | ?[Y: $i] : big_q(Y)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 (?[X: $i] : big_p(X) | ?[Y: $i] : big_q(Y)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[45, 37])).
% 0.13/0.38 Proof display could not be completed: monotonicity rule is not handled
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------