%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN058+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:05 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN058+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:27:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_f_type, type, (
% 0.11/0.36 big_f: $i > $o)).
% 0.11/0.36 tff(tptp_fun_X_2_type, type, (
% 0.11/0.36 tptp_fun_X_2: $i)).
% 0.11/0.36 tff(big_p_type, type, (
% 0.11/0.36 big_p: $i > $o)).
% 0.11/0.36 tff(big_g_type, type, (
% 0.11/0.36 big_g: $i > $o)).
% 0.11/0.36 tff(big_s_type, type, (
% 0.11/0.36 big_s: $i > $o)).
% 0.11/0.36 tff(tptp_fun_X1_1_type, type, (
% 0.11/0.36 tptp_fun_X1_1: $i)).
% 0.11/0.36 tff(big_q_type, type, (
% 0.11/0.36 big_q: $i > $o)).
% 0.11/0.36 tff(big_r_type, type, (
% 0.11/0.36 big_r: $i > $o)).
% 0.11/0.36 tff(tptp_fun_X_0_type, type, (
% 0.11/0.36 tptp_fun_X_0: $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))) <=> (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![X: $i] : ((big_p(X) & big_f(X)) => big_g(X))) <=> (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,axiom,(~![X: $i] : ((big_p(X) & big_f(X)) => big_g(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel28')).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.11/0.36 tff(8,plain,(
% 0.11/0.36 ~(big_g(X!2) | (~(big_p(X!2) & big_f(X!2))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (big_p(X!2) & big_f(X!2)),
% 0.11/0.36 inference(or_elim,[status(thm)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (big_f(X!2)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (~big_g(X!2)),
% 0.11/0.36 inference(or_elim,[status(thm)],[8])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (big_p(X!2)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (^[X: $i] : refl(((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ((~big_p(X)) | ![Z: $i] : big_q(Z)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (^[X: $i] : rewrite(((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ((~big_p(X)) | ![Z: $i] : big_q(Z)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(transitivity,[status(thm)],[16, 14])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (^[X: $i] : rewrite((big_p(X) => ![Z: $i] : big_q(Z)) <=> ((~big_p(X)) | ![Z: $i] : big_q(Z)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (![X: $i] : (big_p(X) => ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.36 tff(21,axiom,(![X: $i] : (big_p(X) => ![Z: $i] : big_q(Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel28_1')).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.11/0.36 tff(24,plain,(
% 0.11/0.36 ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(skolemize,[status(sab)],[23])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (((~![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))) | ((~big_p(X!2)) | ![Z: $i] : big_q(Z))) <=> ((~![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))) | (~big_p(X!2)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 ((~![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))) | ((~big_p(X!2)) | ![Z: $i] : big_q(Z))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 ((~![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))) | (~big_p(X!2)) | ![Z: $i] : big_q(Z)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (![Z: $i] : big_q(Z)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[28, 25, 12])).
% 0.11/0.36 tff(30,assumption,(~big_q(X!0)), introduced(assumption)).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 ((~![Z: $i] : big_q(Z)) | big_q(X!0)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[31, 30, 29])).
% 0.11/0.36 tff(33,plain,(big_q(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 ((big_q(X!0) | big_r(X!0)) | (~big_q(X!0))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (big_q(X!0) | big_r(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (((~(big_q(X!0) | big_r(X!0))) | (big_q(X1!1) & big_s(X1!1))) <=> ((~(big_q(X!0) | big_r(X!0))) | (~((~big_q(X1!1)) | (~big_s(X1!1)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))) <=> ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 ((![X: $i] : (big_q(X) | big_r(X)) => ?[X1: $i] : (big_q(X1) & big_s(X1))) <=> ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(39,axiom,(![X: $i] : (big_q(X) | big_r(X)) => ?[X1: $i] : (big_q(X1) & big_s(X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel28_2')).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.11/0.36 Proof display could not be completed: monotonicity rule is not handled
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------