%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN070+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:38:08 AM UTC 2025
% Result : Theorem 0.10s 0.35s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SYN070+1 : TPTP v9.0.0. Released v2.0.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Jun 20 12:27:35 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.10/0.35 % SZS status Theorem
% 0.10/0.35 % SZS output start Proof
% 0.10/0.35 tff(big_f_type, type, (
% 0.10/0.35 big_f: $i > $o)).
% 0.10/0.35 tff(tptp_fun_X_1_type, type, (
% 0.10/0.35 tptp_fun_X_1: $i)).
% 0.10/0.35 tff(big_g_type, type, (
% 0.10/0.35 big_g: $i > $o)).
% 0.10/0.35 tff(big_j_type, type, (
% 0.10/0.35 big_j: ( $i * $i ) > $o)).
% 0.10/0.35 tff(tptp_fun_X1_0_type, type, (
% 0.10/0.35 tptp_fun_X1_0: $i)).
% 0.10/0.35 tff(big_h_type, type, (
% 0.10/0.35 big_h: ( $i * $i ) > $o)).
% 0.10/0.35 tff(1,plain,
% 0.10/0.35 ((~![X: $i] : (big_g(X) | (~big_f(X)))) <=> (~![X: $i] : (big_g(X) | (~big_f(X))))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(2,plain,
% 0.10/0.35 ((~![X: $i] : (big_f(X) => big_g(X))) <=> (~![X: $i] : (big_g(X) | (~big_f(X))))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(3,axiom,(~![X: $i] : (big_f(X) => big_g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel46')).
% 0.10/0.35 tff(4,plain,
% 0.10/0.35 (~![X: $i] : (big_g(X) | (~big_f(X)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.10/0.35 tff(5,plain,
% 0.10/0.35 (~![X: $i] : (big_g(X) | (~big_f(X)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.10/0.35 tff(6,plain,
% 0.10/0.35 (~![X: $i] : (big_g(X) | (~big_f(X)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.10/0.35 tff(7,plain,
% 0.10/0.35 (~![X: $i] : (big_g(X) | (~big_f(X)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.10/0.35 tff(8,plain,(
% 0.10/0.35 ~(big_g(X!1) | (~big_f(X!1)))),
% 0.10/0.35 inference(skolemize,[status(sab)],[7])).
% 0.10/0.35 tff(9,plain,
% 0.10/0.35 (big_f(X!1)),
% 0.10/0.35 inference(or_elim,[status(thm)],[8])).
% 0.10/0.35 tff(10,plain,
% 0.10/0.35 (~big_g(X!1)),
% 0.10/0.35 inference(or_elim,[status(thm)],[8])).
% 0.10/0.35 tff(11,assumption,(~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))))), introduced(assumption)).
% 0.10/0.35 tff(12,plain,
% 0.10/0.35 ((big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))) | ![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))),
% 0.10/0.35 inference(tautology,[status(thm)],[])).
% 0.10/0.35 tff(13,plain,
% 0.10/0.35 (![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.10/0.35 tff(14,plain,
% 0.10/0.35 ((big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))) | big_f(X1!0)),
% 0.10/0.35 inference(tautology,[status(thm)],[])).
% 0.10/0.35 tff(15,plain,
% 0.10/0.35 (big_f(X1!0)),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.10/0.35 tff(16,plain,
% 0.10/0.35 ((big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))) | (~big_g(X1!0))),
% 0.10/0.35 inference(tautology,[status(thm)],[])).
% 0.10/0.35 tff(17,plain,
% 0.10/0.35 (~big_g(X1!0)),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.10/0.35 tff(18,plain,
% 0.10/0.35 (((~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))) | (big_g(X1!0) | (~big_f(X1!0)) | big_j(X1!0, X1!0))) <=> ((~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))) | big_g(X1!0) | (~big_f(X1!0)) | big_j(X1!0, X1!0))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(19,plain,
% 0.10/0.35 ((~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))) | (big_g(X1!0) | (~big_f(X1!0)) | big_j(X1!0, X1!0))),
% 0.10/0.35 inference(quant_inst,[status(thm)],[])).
% 0.10/0.35 tff(20,plain,
% 0.10/0.35 ((~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))) | big_g(X1!0) | (~big_f(X1!0)) | big_j(X1!0, X1!0)),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.10/0.35 tff(21,plain,
% 0.10/0.35 (big_j(X1!0, X1!0)),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[20, 17, 15, 13])).
% 0.10/0.35 tff(22,plain,
% 0.10/0.35 (^[X: $i, Y: $i] : refl(((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y))) <=> ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y))))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(23,plain,
% 0.10/0.35 (![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y))) <=> ![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[22])).
% 0.10/0.35 tff(24,plain,
% 0.10/0.35 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_f(X) & big_f(Y) & big_h(X, Y)) <=> (~((~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y))))), ((~(big_f(X) & big_f(Y) & big_h(X, Y))) <=> (~(~((~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y))))))), rewrite((~(~((~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y))))) <=> ((~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))), ((~(big_f(X) & big_f(Y) & big_h(X, Y))) <=> ((~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y))))), (((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y)))) <=> ((~big_j(Y, X)) | ((~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))))), rewrite(((~big_j(Y, X)) | ((~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) <=> ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))), (((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y)))) <=> ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(25,plain,
% 0.10/0.35 (![X: $i, Y: $i] : ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y)))) <=> ![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[24])).
% 0.10/0.35 tff(26,plain,
% 0.10/0.35 (![X: $i, Y: $i] : ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y)))) <=> ![X: $i, Y: $i] : ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y))))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(27,plain,
% 0.10/0.35 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((big_f(X) & big_f(Y)) & big_h(X, Y)) <=> (big_f(X) & big_f(Y) & big_h(X, Y))), ((((big_f(X) & big_f(Y)) & big_h(X, Y)) => (~big_j(Y, X))) <=> ((big_f(X) & big_f(Y) & big_h(X, Y)) => (~big_j(Y, X))))), rewrite(((big_f(X) & big_f(Y) & big_h(X, Y)) => (~big_j(Y, X))) <=> ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y))))), ((((big_f(X) & big_f(Y)) & big_h(X, Y)) => (~big_j(Y, X))) <=> ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y))))))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(28,plain,
% 0.10/0.35 (![X: $i, Y: $i] : (((big_f(X) & big_f(Y)) & big_h(X, Y)) => (~big_j(Y, X))) <=> ![X: $i, Y: $i] : ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y))))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[27])).
% 0.10/0.35 tff(29,axiom,(![X: $i, Y: $i] : (((big_f(X) & big_f(Y)) & big_h(X, Y)) => (~big_j(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel46_3')).
% 0.10/0.35 tff(30,plain,
% 0.10/0.35 (![X: $i, Y: $i] : ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y))))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.10/0.35 tff(31,plain,
% 0.10/0.35 (![X: $i, Y: $i] : ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y))))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.10/0.35 tff(32,plain,(
% 0.10/0.35 ![X: $i, Y: $i] : ((~big_j(Y, X)) | (~(big_f(X) & big_f(Y) & big_h(X, Y))))),
% 0.10/0.35 inference(skolemize,[status(sab)],[31])).
% 0.10/0.35 tff(33,plain,
% 0.10/0.35 (![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.10/0.35 tff(34,plain,
% 0.10/0.35 (![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.10/0.35 tff(35,plain,
% 0.10/0.35 (((~![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) | ((~big_f(X1!0)) | (~big_j(X1!0, X1!0)) | (~big_h(X1!0, X1!0)))) <=> ((~![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) | (~big_f(X1!0)) | (~big_j(X1!0, X1!0)) | (~big_h(X1!0, X1!0)))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(36,plain,
% 0.10/0.35 (((~big_j(X1!0, X1!0)) | (~big_f(X1!0)) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0))) <=> ((~big_f(X1!0)) | (~big_j(X1!0, X1!0)) | (~big_h(X1!0, X1!0)))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(37,plain,
% 0.10/0.35 (((~![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) | ((~big_j(X1!0, X1!0)) | (~big_f(X1!0)) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0)))) <=> ((~![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) | ((~big_f(X1!0)) | (~big_j(X1!0, X1!0)) | (~big_h(X1!0, X1!0))))),
% 0.10/0.35 inference(monotonicity,[status(thm)],[36])).
% 0.10/0.35 tff(38,plain,
% 0.10/0.35 (((~![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) | ((~big_j(X1!0, X1!0)) | (~big_f(X1!0)) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0)))) <=> ((~![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) | (~big_f(X1!0)) | (~big_j(X1!0, X1!0)) | (~big_h(X1!0, X1!0)))),
% 0.10/0.35 inference(transitivity,[status(thm)],[37, 35])).
% 0.10/0.35 tff(39,plain,
% 0.10/0.35 ((~![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) | ((~big_j(X1!0, X1!0)) | (~big_f(X1!0)) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0)))),
% 0.10/0.35 inference(quant_inst,[status(thm)],[])).
% 0.10/0.35 tff(40,plain,
% 0.10/0.35 ((~![X: $i, Y: $i] : ((~big_j(Y, X)) | (~big_f(Y)) | (~big_f(X)) | (~big_h(X, Y)))) | (~big_f(X1!0)) | (~big_j(X1!0, X1!0)) | (~big_h(X1!0, X1!0))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.10/0.35 tff(41,plain,
% 0.10/0.35 (~big_h(X1!0, X1!0)),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[40, 15, 34, 21])).
% 0.10/0.35 tff(42,plain,
% 0.10/0.35 ((big_g(X1!0) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0))) | big_h(X1!0, X1!0)),
% 0.10/0.35 inference(tautology,[status(thm)],[])).
% 0.10/0.35 tff(43,plain,
% 0.10/0.35 (big_g(X1!0) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0))),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.10/0.35 tff(44,plain,
% 0.10/0.35 (^[X: $i, Y: $i] : refl((big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X))))) <=> (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X))))))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(45,plain,
% 0.10/0.35 (![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X))))) <=> ![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[44])).
% 0.10/0.35 tff(46,plain,
% 0.10/0.35 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(Y) & big_h(Y, X)) <=> (~((~big_f(Y)) | (~big_h(Y, X))))), ((~(big_f(Y) & big_h(Y, X))) <=> (~(~((~big_f(Y)) | (~big_h(Y, X))))))), rewrite((~(~((~big_f(Y)) | (~big_h(Y, X))))) <=> ((~big_f(Y)) | (~big_h(Y, X)))), ((~(big_f(Y) & big_h(Y, X))) <=> ((~big_f(Y)) | (~big_h(Y, X))))), ((big_g(Y) | (~(big_f(Y) & big_h(Y, X)))) <=> (big_g(Y) | ((~big_f(Y)) | (~big_h(Y, X)))))), rewrite((big_g(Y) | ((~big_f(Y)) | (~big_h(Y, X)))) <=> (big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))), ((big_g(Y) | (~(big_f(Y) & big_h(Y, X)))) <=> (big_g(Y) | (~big_f(Y)) | (~big_h(Y, X))))), ((big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X))))) <=> (big_f(X) & (big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))), rewrite((big_f(X) & (big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))) <=> (~((~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X))))))), ((big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X))))) <=> (~((~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))))), ((~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))) <=> (~(~((~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X))))))))), rewrite((~(~((~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X))))))) <=> ((~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))), ((~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))) <=> ((~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X))))))), ((big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X))))))) <=> (big_g(X) | ((~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))))), rewrite((big_g(X) | ((~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))) <=> (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))), ((big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X))))))) <=> (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(47,plain,
% 0.10/0.35 (![X: $i, Y: $i] : (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X))))))) <=> ![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[46])).
% 0.10/0.35 tff(48,plain,
% 0.10/0.35 (![X: $i, Y: $i] : (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X))))))) <=> ![X: $i, Y: $i] : (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(49,plain,
% 0.10/0.35 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((big_f(X) & ((big_f(Y) & big_h(Y, X)) => big_g(Y))) <=> (big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))), (((big_f(X) & ((big_f(Y) & big_h(Y, X)) => big_g(Y))) => big_g(X)) <=> ((big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X))))) => big_g(X)))), rewrite(((big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X))))) => big_g(X)) <=> (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))))), (((big_f(X) & ((big_f(Y) & big_h(Y, X)) => big_g(Y))) => big_g(X)) <=> (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(50,plain,
% 0.10/0.36 (![X: $i, Y: $i] : ((big_f(X) & ((big_f(Y) & big_h(Y, X)) => big_g(Y))) => big_g(X)) <=> ![X: $i, Y: $i] : (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[49])).
% 0.10/0.36 tff(51,axiom,(![X: $i, Y: $i] : ((big_f(X) & ((big_f(Y) & big_h(Y, X)) => big_g(Y))) => big_g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel46_1')).
% 0.10/0.36 tff(52,plain,
% 0.10/0.36 (![X: $i, Y: $i] : (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.10/0.36 tff(53,plain,
% 0.10/0.36 (![X: $i, Y: $i] : (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.10/0.36 tff(54,plain,(
% 0.10/0.36 ![X: $i, Y: $i] : (big_g(X) | (~(big_f(X) & (big_g(Y) | (~(big_f(Y) & big_h(Y, X)))))))),
% 0.10/0.36 inference(skolemize,[status(sab)],[53])).
% 0.10/0.36 tff(55,plain,
% 0.10/0.36 (![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.10/0.36 tff(56,plain,
% 0.10/0.36 (![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.10/0.36 tff(57,plain,
% 0.10/0.36 (((~![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))) | (big_g(X1!0) | (~big_f(X1!0)) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0)))))) <=> ((~![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))) | big_g(X1!0) | (~big_f(X1!0)) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0)))))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(58,plain,
% 0.10/0.36 ((~![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))) | (big_g(X1!0) | (~big_f(X1!0)) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0)))))),
% 0.10/0.36 inference(quant_inst,[status(thm)],[])).
% 0.10/0.36 tff(59,plain,
% 0.10/0.36 ((~![X: $i, Y: $i] : (big_g(X) | (~big_f(X)) | (~(big_g(Y) | (~big_f(Y)) | (~big_h(Y, X)))))) | big_g(X1!0) | (~big_f(X1!0)) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~big_h(X1!0, X1!0))))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.10/0.36 tff(60,plain,
% 0.10/0.36 ($false),
% 0.10/0.36 inference(unit_resolution,[status(thm)],[59, 56, 17, 15, 43])).
% 0.10/0.36 tff(61,plain,(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.10/0.36 tff(62,plain,
% 0.10/0.36 ((![X: $i] : (big_g(X) | (~big_f(X))) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))))) <=> (![X: $i] : (big_g(X) | (~big_f(X))) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))))))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(63,plain,
% 0.10/0.36 ((![X: $i] : (big_g(X) | (~big_f(X))) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))))) <=> (![X: $i] : (big_g(X) | (~big_f(X))) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))))))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(64,plain,
% 0.10/0.36 ((big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))) <=> (~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(65,plain,
% 0.10/0.36 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_f(Y) & (~big_g(Y))) <=> (~(big_g(Y) | (~big_f(Y))))), ((~(big_f(Y) & (~big_g(Y)))) <=> (~(~(big_g(Y) | (~big_f(Y))))))), rewrite((~(~(big_g(Y) | (~big_f(Y))))) <=> (big_g(Y) | (~big_f(Y)))), ((~(big_f(Y) & (~big_g(Y)))) <=> (big_g(Y) | (~big_f(Y))))), (((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)) <=> ((big_g(Y) | (~big_f(Y))) | big_j(X1!0, Y)))), rewrite(((big_g(Y) | (~big_f(Y))) | big_j(X1!0, Y)) <=> (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))), (((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)) <=> (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(66,plain,
% 0.10/0.36 (![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)) <=> ![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[65])).
% 0.10/0.36 tff(67,plain,
% 0.10/0.36 ((big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y))) <=> (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))),
% 0.10/0.36 inference(monotonicity,[status(thm)],[66])).
% 0.10/0.36 tff(68,plain,
% 0.10/0.36 ((big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y))) <=> (~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y)))))),
% 0.10/0.36 inference(transitivity,[status(thm)],[67, 64])).
% 0.10/0.36 tff(69,plain,
% 0.10/0.36 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & (~big_g(X))) <=> (~(big_g(X) | (~big_f(X))))), ((~(big_f(X) & (~big_g(X)))) <=> (~(~(big_g(X) | (~big_f(X))))))), rewrite((~(~(big_g(X) | (~big_f(X))))) <=> (big_g(X) | (~big_f(X)))), ((~(big_f(X) & (~big_g(X)))) <=> (big_g(X) | (~big_f(X)))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(70,plain,
% 0.10/0.36 (![X: $i] : (~(big_f(X) & (~big_g(X)))) <=> ![X: $i] : (big_g(X) | (~big_f(X)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[69])).
% 0.10/0.36 tff(71,plain,
% 0.10/0.36 ((![X: $i] : (~(big_f(X) & (~big_g(X)))) | (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)))) <=> (![X: $i] : (big_g(X) | (~big_f(X))) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))))))),
% 0.10/0.36 inference(monotonicity,[status(thm)],[70, 68])).
% 0.10/0.36 tff(72,plain,
% 0.10/0.36 ((![X: $i] : (~(big_f(X) & (~big_g(X)))) | (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)))) <=> (![X: $i] : (big_g(X) | (~big_f(X))) | (~(big_g(X1!0) | (~big_f(X1!0)) | (~![Y: $i] : (big_g(Y) | (~big_f(Y)) | big_j(X1!0, Y))))))),
% 0.10/0.36 inference(transitivity,[status(thm)],[71, 63])).
% 0.10/0.36 tff(73,plain,
% 0.10/0.36 ((![X: $i] : (~(big_f(X) & (~big_g(X)))) | (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)))) <=> (![X: $i] : (~(big_f(X) & (~big_g(X)))) | (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y))))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(74,plain,
% 0.10/0.36 ((big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y))) <=> (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(75,plain,
% 0.10/0.36 ((![X: $i] : (~(big_f(X) & (~big_g(X)))) | (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)))) <=> (![X: $i] : (~(big_f(X) & (~big_g(X)))) | (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y))))),
% 0.10/0.36 inference(monotonicity,[status(thm)],[74])).
% 0.10/0.36 tff(76,plain,
% 0.10/0.36 ((![X: $i] : (~(big_f(X) & (~big_g(X)))) | (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y)))) <=> (![X: $i] : (~(big_f(X) & (~big_g(X)))) | (big_f(X1!0) & (~big_g(X1!0)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1!0, Y))))),
% 0.10/0.36 inference(transitivity,[status(thm)],[75, 73])).
% 0.10/0.36 tff(77,plain,
% 0.10/0.36 (((~?[X: $i] : (big_f(X) & (~big_g(X)))) | ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))) <=> ((~?[X: $i] : (big_f(X) & (~big_g(X)))) | ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y))))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(78,plain,
% 0.10/0.36 ((?[X: $i] : (big_f(X) & (~big_g(X))) => ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))) <=> ((~?[X: $i] : (big_f(X) & (~big_g(X)))) | ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y))))),
% 0.10/0.36 inference(rewrite,[status(thm)],[])).
% 0.10/0.36 tff(79,plain,
% 0.10/0.36 (^[X1: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((big_f(Y) & (~big_g(Y))) => big_j(X1, Y)) <=> ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))), (![Y: $i] : ((big_f(Y) & (~big_g(Y))) => big_j(X1, Y)) <=> ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))), (((big_f(X1) & (~big_g(X1))) & ![Y: $i] : ((big_f(Y) & (~big_g(Y))) => big_j(X1, Y))) <=> ((big_f(X1) & (~big_g(X1))) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y))))), rewrite(((big_f(X1) & (~big_g(X1))) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y))) <=> (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))), (((big_f(X1) & (~big_g(X1))) & ![Y: $i] : ((big_f(Y) & (~big_g(Y))) => big_j(X1, Y))) <=> (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))))),
% 0.10/0.36 inference(bind,[status(th)],[])).
% 0.10/0.36 tff(80,plain,
% 0.10/0.36 (?[X1: $i] : ((big_f(X1) & (~big_g(X1))) & ![Y: $i] : ((big_f(Y) & (~big_g(Y))) => big_j(X1, Y))) <=> ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))),
% 0.10/0.36 inference(quant_intro,[status(thm)],[79])).
% 0.10/0.36 tff(81,plain,
% 0.10/0.36 ((?[X: $i] : (big_f(X) & (~big_g(X))) => ?[X1: $i] : ((big_f(X1) & (~big_g(X1))) & ![Y: $i] : ((big_f(Y) & (~big_g(Y))) => big_j(X1, Y)))) <=> (?[X: $i] : (big_f(X) & (~big_g(X))) => ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y))))),
% 0.10/0.36 inference(monotonicity,[status(thm)],[80])).
% 0.10/0.36 tff(82,plain,
% 0.10/0.36 ((?[X: $i] : (big_f(X) & (~big_g(X))) => ?[X1: $i] : ((big_f(X1) & (~big_g(X1))) & ![Y: $i] : ((big_f(Y) & (~big_g(Y))) => big_j(X1, Y)))) <=> ((~?[X: $i] : (big_f(X) & (~big_g(X)))) | ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y))))),
% 0.10/0.36 inference(transitivity,[status(thm)],[81, 78])).
% 0.10/0.36 tff(83,axiom,(?[X: $i] : (big_f(X) & (~big_g(X))) => ?[X1: $i] : ((big_f(X1) & (~big_g(X1))) & ![Y: $i] : ((big_f(Y) & (~big_g(Y))) => big_j(X1, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel46_2')).
% 0.10/0.36 tff(84,plain,
% 0.10/0.36 ((~?[X: $i] : (big_f(X) & (~big_g(X)))) | ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.10/0.36 tff(85,plain,
% 0.10/0.36 ((~?[X: $i] : (big_f(X) & (~big_g(X)))) | ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.10/0.36 tff(86,plain,
% 0.10/0.36 ((~?[X: $i] : (big_f(X) & (~big_g(X)))) | ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[85, 77])).
% 0.10/0.36 tff(87,plain,
% 0.10/0.36 ((~?[X: $i] : (big_f(X) & (~big_g(X)))) | ?[X1: $i] : (big_f(X1) & (~big_g(X1)) & ![Y: $i] : ((~(big_f(Y) & (~big_g(Y)))) | big_j(X1, Y)))),
% 0.10/0.36 inference(modus_ponens,[status(thm)],[86, 77])).
% 0.10/0.36 Proof display could not be completed: monotonicity rule is not handled
% 0.10/0.36 % E exiting
%------------------------------------------------------------------------------