%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN057+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN057+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:27:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(big_h_type, type, (
% 0.13/0.38 big_h: $i > $o)).
% 0.13/0.38 tff(tptp_fun_X_1_type, type, (
% 0.13/0.38 tptp_fun_X_1: $i)).
% 0.13/0.38 tff(big_f_type, type, (
% 0.13/0.38 big_f: $i > $o)).
% 0.13/0.38 tff(big_j_type, type, (
% 0.13/0.38 big_j: $i > $o)).
% 0.13/0.38 tff(big_i_type, type, (
% 0.13/0.38 big_i: $i > $o)).
% 0.13/0.38 tff(big_g_type, type, (
% 0.13/0.38 big_g: $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(1,plain,
% 0.13/0.38 ((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) <=> (~![X: $i] : ((~big_i(X)) | (~big_j(X))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((~![X: $i] : (big_j(X) => (~big_i(X)))) <=> (~![X: $i] : ((~big_i(X)) | (~big_j(X))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,axiom,(~![X: $i] : (big_j(X) => (~big_i(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel27')).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (~![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (~![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.38 tff(8,plain,(
% 0.13/0.38 ~((~big_i(X!1)) | (~big_j(X!1)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[7])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (big_j(X!1)),
% 0.13/0.38 inference(or_elim,[status(thm)],[8])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (big_i(X!1)),
% 0.13/0.38 inference(or_elim,[status(thm)],[8])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (^[X: $i] : refl((big_f(X) | (~big_i(X)) | (~big_j(X))) <=> (big_f(X) | (~big_i(X)) | (~big_j(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X))) <=> ![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_j(X) & big_i(X)) <=> (~((~big_i(X)) | (~big_j(X))))), ((~(big_j(X) & big_i(X))) <=> (~(~((~big_i(X)) | (~big_j(X))))))), rewrite((~(~((~big_i(X)) | (~big_j(X))))) <=> ((~big_i(X)) | (~big_j(X)))), ((~(big_j(X) & big_i(X))) <=> ((~big_i(X)) | (~big_j(X))))), ((big_f(X) | (~(big_j(X) & big_i(X)))) <=> (big_f(X) | ((~big_i(X)) | (~big_j(X)))))), rewrite((big_f(X) | ((~big_i(X)) | (~big_j(X)))) <=> (big_f(X) | (~big_i(X)) | (~big_j(X)))), ((big_f(X) | (~(big_j(X) & big_i(X)))) <=> (big_f(X) | (~big_i(X)) | (~big_j(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![X: $i] : (big_f(X) | (~(big_j(X) & big_i(X)))) <=> ![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (![X: $i] : (big_f(X) | (~(big_j(X) & big_i(X)))) <=> ![X: $i] : (big_f(X) | (~(big_j(X) & big_i(X))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (^[X: $i] : rewrite(((big_j(X) & big_i(X)) => big_f(X)) <=> (big_f(X) | (~(big_j(X) & big_i(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (![X: $i] : ((big_j(X) & big_i(X)) => big_f(X)) <=> ![X: $i] : (big_f(X) | (~(big_j(X) & big_i(X))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.38 tff(18,axiom,(![X: $i] : ((big_j(X) & big_i(X)) => big_f(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel27_3')).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (![X: $i] : (big_f(X) | (~(big_j(X) & big_i(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (![X: $i] : (big_f(X) | (~(big_j(X) & big_i(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.13/0.38 tff(21,plain,(
% 0.13/0.38 ![X: $i] : (big_f(X) | (~(big_j(X) & big_i(X))))),
% 0.13/0.38 inference(skolemize,[status(sab)],[20])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (((~![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X)))) | (big_f(X!1) | (~big_i(X!1)) | (~big_j(X!1)))) <=> ((~![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X)))) | big_f(X!1) | (~big_i(X!1)) | (~big_j(X!1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X)))) | (big_f(X!1) | (~big_i(X!1)) | (~big_j(X!1)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(X) | (~big_i(X)) | (~big_j(X)))) | big_f(X!1) | (~big_i(X!1)) | (~big_j(X!1))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (big_f(X!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[26, 23, 10, 9])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (^[X: $i] : refl((big_h(X) | (~big_f(X))) <=> (big_h(X) | (~big_f(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (![X: $i] : (big_h(X) | (~big_f(X))) <=> ![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (![X: $i] : (big_h(X) | (~big_f(X))) <=> ![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (^[X: $i] : rewrite((big_f(X) => big_h(X)) <=> (big_h(X) | (~big_f(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (![X: $i] : (big_f(X) => big_h(X)) <=> ![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.38 tff(33,axiom,(![X: $i] : (big_f(X) => big_h(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel27_2')).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.13/0.38 tff(36,plain,(
% 0.13/0.38 ![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[35])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 (![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(X!1) | (~big_f(X!1)))) <=> ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(X!1) | (~big_f(X!1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(X!1) | (~big_f(X!1)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(X!1) | (~big_f(X!1))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 (big_h(X!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 (?[X: $i] : (big_f(X) & (~big_g(X))) <=> ?[X: $i] : (big_f(X) & (~big_g(X)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(43,axiom,(?[X: $i] : (big_f(X) & (~big_g(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel27_1')).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 (?[X: $i] : (big_f(X) & (~big_g(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.13/0.38 tff(45,plain,(
% 0.13/0.38 big_f(X!0) & (~big_g(X!0))),
% 0.13/0.38 inference(skolemize,[status(sab)],[44])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 (big_f(X!0)),
% 0.13/0.38 inference(and_elim,[status(thm)],[45])).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(X!0) | (~big_f(X!0)))) <=> ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(X!0) | (~big_f(X!0)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(48,plain,
% 0.13/0.38 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(X!0) | (~big_f(X!0)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(49,plain,
% 0.13/0.38 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(X!0) | (~big_f(X!0))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.38 tff(50,plain,
% 0.13/0.38 (big_h(X!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[49, 46, 37])).
% 0.13/0.38 tff(51,assumption,(![X: $i] : (big_g(X) | (~big_h(X)))), introduced(assumption)).
% 0.13/0.38 tff(52,plain,
% 0.13/0.38 (~big_g(X!0)),
% 0.13/0.38 inference(and_elim,[status(thm)],[45])).
% 0.13/0.38 tff(53,plain,
% 0.13/0.38 (((~![X: $i] : (big_g(X) | (~big_h(X)))) | (big_g(X!0) | (~big_h(X!0)))) <=> ((~![X: $i] : (big_g(X) | (~big_h(X)))) | big_g(X!0) | (~big_h(X!0)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(54,plain,
% 0.13/0.38 ((~![X: $i] : (big_g(X) | (~big_h(X)))) | (big_g(X!0) | (~big_h(X!0)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(55,plain,
% 0.13/0.38 ((~![X: $i] : (big_g(X) | (~big_h(X)))) | big_g(X!0) | (~big_h(X!0))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.38 tff(56,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[55, 52, 51, 50])).
% 0.13/0.38 tff(57,plain,(~![X: $i] : (big_g(X) | (~big_h(X)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(58,plain,
% 0.13/0.38 ((![X: $i] : (big_g(X) | (~big_h(X))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))) <=> (![X: $i] : (big_g(X) | (~big_h(X))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(59,plain,
% 0.13/0.38 ((![X: $i] : (~(big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))) <=> (![X: $i] : (big_g(X) | (~big_h(X))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(60,plain,
% 0.13/0.38 ((![X: $i] : (~(big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))) <=> (![X: $i] : (~(big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(61,plain,
% 0.13/0.38 (((~?[X: $i] : (big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))) <=> ((~?[X: $i] : (big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(62,plain,
% 0.13/0.38 ((?[X: $i] : (big_h(X) & (~big_g(X))) => ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))) <=> ((~?[X: $i] : (big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(63,plain,
% 0.13/0.38 (^[X1: $i] : rewrite((big_i(X1) => (~big_h(X1))) <=> ((~big_h(X1)) | (~big_i(X1))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(64,plain,
% 0.13/0.38 (![X1: $i] : (big_i(X1) => (~big_h(X1))) <=> ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.13/0.38 tff(65,plain,
% 0.13/0.38 ((?[X: $i] : (big_h(X) & (~big_g(X))) => ![X1: $i] : (big_i(X1) => (~big_h(X1)))) <=> (?[X: $i] : (big_h(X) & (~big_g(X))) => ![X1: $i] : ((~big_h(X1)) | (~big_i(X1))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[64])).
% 0.13/0.38 tff(66,plain,
% 0.13/0.38 ((?[X: $i] : (big_h(X) & (~big_g(X))) => ![X1: $i] : (big_i(X1) => (~big_h(X1)))) <=> ((~?[X: $i] : (big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[65, 62])).
% 0.13/0.38 tff(67,axiom,(?[X: $i] : (big_h(X) & (~big_g(X))) => ![X1: $i] : (big_i(X1) => (~big_h(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel27_4')).
% 0.13/0.38 tff(68,plain,
% 0.13/0.38 ((~?[X: $i] : (big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.38 tff(69,plain,
% 0.13/0.38 ((~?[X: $i] : (big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.13/0.38 tff(70,plain,
% 0.13/0.38 ((~?[X: $i] : (big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[69, 61])).
% 0.13/0.38 tff(71,plain,
% 0.13/0.38 ((~?[X: $i] : (big_h(X) & (~big_g(X)))) | ![X1: $i] : ((~big_h(X1)) | (~big_i(X1)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[70, 61])).
% 0.13/0.38 Proof display could not be completed: monotonicity rule is not handled
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------