%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN069+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN069+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:26:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(big_j_type, type, (
% 0.20/0.37 big_j: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.37 tptp_fun_Y_0: $i > $i)).
% 0.20/0.37 tff(tptp_fun_X_1_type, type, (
% 0.20/0.37 tptp_fun_X_1: $i)).
% 0.20/0.37 tff(big_g_type, type, (
% 0.20/0.37 big_g: $i > $o)).
% 0.20/0.37 tff(big_h_type, type, (
% 0.20/0.37 big_h: ( $i * $i ) > $o)).
% 0.20/0.37 tff(big_k_type, type, (
% 0.20/0.37 big_k: $i > $o)).
% 0.20/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.37 tptp_fun_Y_2: $i > $i)).
% 0.20/0.37 tff(big_l_type, type, (
% 0.20/0.37 big_l: $i > $o)).
% 0.20/0.37 tff(big_f_type, type, (
% 0.20/0.37 big_f: $i > $o)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (^[X: $i] : refl(((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X)))))) <=> ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X)))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X)))))) <=> ![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (^[X: $i] : rewrite(((~big_f(X)) | (big_g(tptp_fun_Y_2(X)) & big_h(X, tptp_fun_Y_2(X)))) <=> ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X)))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_2(X)) & big_h(X, tptp_fun_Y_2(X)))) <=> ![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 ((~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))) <=> (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(6,axiom,(~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel45')).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (^[X: $i] : nnf_neg(refl($oeq((~big_f(X)), (~big_f(X)))), nnf_neg(sk($oeq(?[Y: $i] : (big_g(Y) & big_h(X, Y)), (big_g(tptp_fun_Y_2(X)) & big_h(X, tptp_fun_Y_2(X))))), $oeq((~(~?[Y: $i] : (big_g(Y) & big_h(X, Y)))), (big_g(tptp_fun_Y_2(X)) & big_h(X, tptp_fun_Y_2(X))))), $oeq((~(big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))), ((~big_f(X)) | (big_g(tptp_fun_Y_2(X)) & big_h(X, tptp_fun_Y_2(X))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(12,plain,(
% 0.20/0.37 ![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_2(X)) & big_h(X, tptp_fun_Y_2(X))))),
% 0.20/0.37 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 ((big_f(X!1) & ![Y: $i] : (big_l(Y) | (~big_h(X!1, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1))) <=> (big_f(X!1) & ![Y: $i] : (big_l(Y) | (~big_h(X!1, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (?[X: $i] : (big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1))) <=> ?[X: $i] : (big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & ![Y: $i] : (big_h(X, Y) => big_l(Y))) <=> (big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y))))), quant_intro(proof_bind(^[Y1: $i] : rewrite(((big_g(Y1) & big_h(X, Y1)) => big_j(X, Y1)) <=> ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1)))), (![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) => big_j(X, Y1)) <=> ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1)))), (((big_f(X) & ![Y: $i] : (big_h(X, Y) => big_l(Y))) & ![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) => big_j(X, Y1))) <=> ((big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y)))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1))))), rewrite(((big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y)))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1))) <=> (big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1)))), (((big_f(X) & ![Y: $i] : (big_h(X, Y) => big_l(Y))) & ![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) => big_j(X, Y1))) <=> (big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (?[X: $i] : ((big_f(X) & ![Y: $i] : (big_h(X, Y) => big_l(Y))) & ![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) => big_j(X, Y1))) <=> ?[X: $i] : (big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.38 tff(19,axiom,(?[X: $i] : ((big_f(X) & ![Y: $i] : (big_h(X, Y) => big_l(Y))) & ![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) => big_j(X, Y1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel45_3')).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (?[X: $i] : (big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (?[X: $i] : (big_f(X) & ![Y: $i] : (big_l(Y) | (~big_h(X, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X, Y1))) | big_j(X, Y1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (big_f(X!1) & ![Y: $i] : (big_l(Y) | (~big_h(X!1, Y))) & ![Y1: $i] : ((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (big_f(X!1)),
% 0.20/0.38 inference(and_elim,[status(thm)],[22])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (((~![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))) | ((~big_f(X!1)) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))))))) <=> ((~![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))) | (~big_f(X!1)) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))) | ((~big_f(X!1)) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))) | (~big_f(X!1)) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[26, 23, 14])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1)))) | big_h(X!1, tptp_fun_Y_2(X!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (big_h(X!1, tptp_fun_Y_2(X!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (^[Y: $i] : refl((big_l(Y) | (~big_h(X!1, Y))) <=> (big_l(Y) | (~big_h(X!1, Y))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![Y: $i] : (big_l(Y) | (~big_h(X!1, Y))) <=> ![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))),
% 0.20/0.38 inference(and_elim,[status(thm)],[22])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (((~![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))) | (big_l(tptp_fun_Y_2(X!1)) | (~big_h(X!1, tptp_fun_Y_2(X!1))))) <=> ((~![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))) | big_l(tptp_fun_Y_2(X!1)) | (~big_h(X!1, tptp_fun_Y_2(X!1))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 ((~![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))) | (big_l(tptp_fun_Y_2(X!1)) | (~big_h(X!1, tptp_fun_Y_2(X!1))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 ((~![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))) | big_l(tptp_fun_Y_2(X!1)) | (~big_h(X!1, tptp_fun_Y_2(X!1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (big_l(tptp_fun_Y_2(X!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[36, 33, 29])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (^[Y: $i] : refl(((~big_k(Y)) | (~big_l(Y))) <=> ((~big_k(Y)) | (~big_l(Y))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![Y: $i] : ((~big_k(Y)) | (~big_l(Y))) <=> ![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (^[Y: $i] : trans(monotonicity(rewrite((big_l(Y) & big_k(Y)) <=> (~((~big_k(Y)) | (~big_l(Y))))), ((~(big_l(Y) & big_k(Y))) <=> (~(~((~big_k(Y)) | (~big_l(Y))))))), rewrite((~(~((~big_k(Y)) | (~big_l(Y))))) <=> ((~big_k(Y)) | (~big_l(Y)))), ((~(big_l(Y) & big_k(Y))) <=> ((~big_k(Y)) | (~big_l(Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![Y: $i] : (~(big_l(Y) & big_k(Y))) <=> ![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 ((~?[Y: $i] : (big_l(Y) & big_k(Y))) <=> (~?[Y: $i] : (big_l(Y) & big_k(Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(43,axiom,(~?[Y: $i] : (big_l(Y) & big_k(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel45_2')).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[44, 42])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (^[Y: $i] : refl($oeq((~(big_l(Y) & big_k(Y))), (~(big_l(Y) & big_k(Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(49,plain,(
% 0.20/0.38 ![Y: $i] : (~(big_l(Y) & big_k(Y)))),
% 0.20/0.38 inference(nnf-neg,[status(sab)],[47, 48])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[49, 41])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[50, 39])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (((~![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))) | ((~big_k(tptp_fun_Y_2(X!1))) | (~big_l(tptp_fun_Y_2(X!1))))) <=> ((~![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))) | (~big_k(tptp_fun_Y_2(X!1))) | (~big_l(tptp_fun_Y_2(X!1))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 ((~![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))) | ((~big_k(tptp_fun_Y_2(X!1))) | (~big_l(tptp_fun_Y_2(X!1))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 ((~![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))) | (~big_k(tptp_fun_Y_2(X!1))) | (~big_l(tptp_fun_Y_2(X!1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (~big_k(tptp_fun_Y_2(X!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[54, 51, 37])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))) | big_k(tptp_fun_Y_2(X!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 ((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.38 tff(58,assumption,(![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))), introduced(assumption)).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))))) <=> ((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 ((~((~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_g(tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1))))) <=> (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_g(tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))))) <=> ((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 (((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_g(tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))))) <=> ((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 ((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_g(tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 ((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[64, 58, 57])).
% 0.20/0.38 tff(66,plain,(~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) <=> (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))), (((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))))), rewrite(((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))), (((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 (![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 (^[X: $i] : refl(((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 (![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 (^[X: $i] : rewrite(((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 (![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 (![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y1: $i] : rewrite((big_g(Y1) & big_h(X, Y1) & big_k(Y1)) <=> (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))), (![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)) <=> ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))), rewrite((~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X)))) <=> (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))), ((![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)) | (~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X))))) <=> (![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))))), rewrite((![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X)))))) <=> ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))))), ((![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)) | (~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X))))) <=> ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(75,plain,
% 0.20/0.38 (![X: $i] : (![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)) | (~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X))))) <=> ![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 (^[X: $i] : rewrite((((~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1))) <=> (![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)) | (~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(77,plain,
% 0.20/0.38 (![X: $i] : (((~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1))) <=> ![X: $i] : (![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)) | (~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.38 tff(78,plain,
% 0.20/0.38 (![X: $i] : ((~(big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y)))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1))) <=> ![X: $i] : ((~(big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y)))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & ![Y: $i] : ((big_g(Y) & big_h(X, Y)) => big_j(X, Y))) <=> (big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y)))), quant_intro(proof_bind(^[Y1: $i] : rewrite(((big_g(Y1) & big_h(X, Y1)) & big_k(Y1)) <=> (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))), (![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) & big_k(Y1)) <=> ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))), (((big_f(X) & ![Y: $i] : ((big_g(Y) & big_h(X, Y)) => big_j(X, Y))) => ![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) & big_k(Y1))) <=> ((big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y))) => ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1))))), rewrite(((big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y))) => ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1))) <=> ((~(big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y)))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))), (((big_f(X) & ![Y: $i] : ((big_g(Y) & big_h(X, Y)) => big_j(X, Y))) => ![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) & big_k(Y1))) <=> ((~(big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y)))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(80,plain,
% 0.20/0.38 (![X: $i] : ((big_f(X) & ![Y: $i] : ((big_g(Y) & big_h(X, Y)) => big_j(X, Y))) => ![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) & big_k(Y1))) <=> ![X: $i] : ((~(big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y)))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.38 tff(81,axiom,(![X: $i] : ((big_f(X) & ![Y: $i] : ((big_g(Y) & big_h(X, Y)) => big_j(X, Y))) => ![Y1: $i] : ((big_g(Y1) & big_h(X, Y1)) & big_k(Y1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel45_1')).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 (![X: $i] : ((~(big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y)))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 (![X: $i] : ((~(big_f(X) & ![Y: $i] : ((~(big_g(Y) & big_h(X, Y))) | big_j(X, Y)))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.38 tff(84,plain,(
% 0.20/0.38 ![X: $i] : (((~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[83])).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 (![X: $i] : (![Y1: $i] : (big_g(Y1) & big_h(X, Y1) & big_k(Y1)) | (~big_f(X)) | (~((~(big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)))) | big_j(X, tptp_fun_Y_0(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.20/0.38 tff(86,plain,
% 0.20/0.38 (![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.20/0.38 tff(87,plain,
% 0.20/0.38 (![X: $i] : ((~big_f(X)) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[86, 73])).
% 0.20/0.38 tff(88,plain,
% 0.20/0.38 (![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[87, 68])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (((~![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) | ((~big_f(X!1)) | (~((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) <=> ((~![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) | (~big_f(X!1)) | (~((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 (((~big_f(X!1)) | (~(big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_g(tptp_fun_Y_0(X!1))) | (~big_h(X!1, tptp_fun_Y_0(X!1))))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) <=> ((~big_f(X!1)) | (~((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (((~![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) | ((~big_f(X!1)) | (~(big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_g(tptp_fun_Y_0(X!1))) | (~big_h(X!1, tptp_fun_Y_0(X!1))))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) <=> ((~![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) | ((~big_f(X!1)) | (~((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (((~![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) | ((~big_f(X!1)) | (~(big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_g(tptp_fun_Y_0(X!1))) | (~big_h(X!1, tptp_fun_Y_0(X!1))))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) <=> ((~![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) | (~big_f(X!1)) | (~((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 ((~![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) | ((~big_f(X!1)) | (~(big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_g(tptp_fun_Y_0(X!1))) | (~big_h(X!1, tptp_fun_Y_0(X!1))))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 ((~![X: $i] : ((~big_f(X)) | (~(big_j(X, tptp_fun_Y_0(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))))) | ![Y1: $i] : (~((~big_h(X, Y1)) | (~big_g(Y1)) | (~big_k(Y1)))))) | (~big_f(X!1)) | (~((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 ((~((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))) | ![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[94, 88, 23])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (~((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[95, 66])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1))) | (~big_j(X!1, tptp_fun_Y_0(X!1)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (~big_j(X!1, tptp_fun_Y_0(X!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 (((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1))) | big_g(tptp_fun_Y_0(X!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (big_g(tptp_fun_Y_0(X!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1))) | big_h(X!1, tptp_fun_Y_0(X!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (big_h(X!1, tptp_fun_Y_0(X!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[101, 96])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 (^[Y1: $i] : refl((big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1))) <=> (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1))) <=> ![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (^[Y1: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_g(Y1) & big_h(X!1, Y1)) <=> (~((~big_g(Y1)) | (~big_h(X!1, Y1))))), ((~(big_g(Y1) & big_h(X!1, Y1))) <=> (~(~((~big_g(Y1)) | (~big_h(X!1, Y1))))))), rewrite((~(~((~big_g(Y1)) | (~big_h(X!1, Y1))))) <=> ((~big_g(Y1)) | (~big_h(X!1, Y1)))), ((~(big_g(Y1) & big_h(X!1, Y1))) <=> ((~big_g(Y1)) | (~big_h(X!1, Y1))))), (((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1)) <=> (((~big_g(Y1)) | (~big_h(X!1, Y1))) | big_j(X!1, Y1)))), rewrite((((~big_g(Y1)) | (~big_h(X!1, Y1))) | big_j(X!1, Y1)) <=> (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))), (((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1)) <=> (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 (![Y1: $i] : ((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1)) <=> ![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (![Y1: $i] : ((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1))),
% 0.20/0.39 inference(and_elim,[status(thm)],[22])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 (![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 (![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 (((~![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))) | ((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))) <=> ((~![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))) | (~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 ((big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1)))) <=> ((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 (((~![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))) | (big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))))) <=> ((~![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))) | ((~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (((~![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))) | (big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))))) <=> ((~![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))) | (~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[112, 110])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 ((~![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))) | (big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 ((~![Y1: $i] : (big_j(X!1, Y1) | (~big_h(X!1, Y1)) | (~big_g(Y1)))) | (~big_h(X!1, tptp_fun_Y_0(X!1))) | (~big_g(tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[115, 109, 102, 100, 98])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------