TSTP Solution File: SYN069+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Thu Sep 29 23:53:31 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 01:41:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % SZS output start Proof
% 0.12/0.35 tff(big_h_type, type, (
% 0.12/0.35 big_h: ( $i * $i ) > $o)).
% 0.12/0.35 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.35 tptp_fun_Y_0: $i > $i)).
% 0.12/0.35 tff(tptp_fun_X_1_type, type, (
% 0.12/0.35 tptp_fun_X_1: $i)).
% 0.12/0.35 tff(big_g_type, type, (
% 0.12/0.35 big_g: $i > $o)).
% 0.12/0.35 tff(big_j_type, type, (
% 0.12/0.35 big_j: ( $i * $i ) > $o)).
% 0.12/0.35 tff(big_k_type, type, (
% 0.12/0.35 big_k: $i > $o)).
% 0.12/0.35 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.35 tptp_fun_Y_2: $i > $i)).
% 0.12/0.35 tff(big_l_type, type, (
% 0.12/0.35 big_l: $i > $o)).
% 0.12/0.35 tff(big_f_type, type, (
% 0.12/0.35 big_f: $i > $o)).
% 0.12/0.35 tff(1,plain,
% 0.12/0.35 (^[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)))))))),
% 0.12/0.35 inference(bind,[status(th)],[])).
% 0.12/0.35 tff(2,plain,
% 0.12/0.35 (![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))))))),
% 0.12/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.35 tff(3,plain,
% 0.12/0.35 (^[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)))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![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))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 ((~?[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)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 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')).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (~?[X: $i] : (big_f(X) & (~?[Y: $i] : (big_g(Y) & big_h(X, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (^[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))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(15,plain,(
% 0.12/0.36 ![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_2(X)) & big_h(X, tptp_fun_Y_2(X))))),
% 0.12/0.36 inference(nnf-neg,[status(sab)],[13, 14])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (![X: $i] : ((~big_f(X)) | (~((~big_g(tptp_fun_Y_2(X))) | (~big_h(X, tptp_fun_Y_2(X))))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 ((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)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 (?[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)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (^[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)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (?[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)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.36 tff(22,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')).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (?[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)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 (?[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)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 (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))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (big_f(X!1)),
% 0.12/0.36 inference(and_elim,[status(thm)],[25])).
% 0.12/0.36 tff(27,plain,
% 0.12/0.36 (((~![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))))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(28,plain,
% 0.12/0.36 ((~![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))))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(29,plain,
% 0.12/0.36 ((~![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)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.36 tff(30,plain,
% 0.12/0.36 (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[29, 26, 17])).
% 0.12/0.36 tff(31,plain,
% 0.12/0.36 (((~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))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(32,plain,
% 0.12/0.36 (big_h(X!1, tptp_fun_Y_2(X!1))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.12/0.36 tff(33,plain,
% 0.12/0.36 (^[Y: $i] : refl((big_l(Y) | (~big_h(X!1, Y))) <=> (big_l(Y) | (~big_h(X!1, Y))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(34,plain,
% 0.12/0.36 (![Y: $i] : (big_l(Y) | (~big_h(X!1, Y))) <=> ![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.36 tff(35,plain,
% 0.12/0.36 (![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))),
% 0.12/0.36 inference(and_elim,[status(thm)],[25])).
% 0.12/0.36 tff(36,plain,
% 0.12/0.36 (![Y: $i] : (big_l(Y) | (~big_h(X!1, Y)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.36 tff(37,plain,
% 0.12/0.36 (((~![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))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(38,plain,
% 0.12/0.36 ((~![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))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(39,plain,
% 0.12/0.36 ((~![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)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.36 tff(40,plain,
% 0.12/0.36 (big_l(tptp_fun_Y_2(X!1))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[39, 36, 32])).
% 0.12/0.36 tff(41,plain,
% 0.12/0.36 (^[Y: $i] : refl(((~big_k(Y)) | (~big_l(Y))) <=> ((~big_k(Y)) | (~big_l(Y))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(42,plain,
% 0.12/0.36 (![Y: $i] : ((~big_k(Y)) | (~big_l(Y))) <=> ![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.36 tff(43,plain,
% 0.12/0.36 (^[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)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(44,plain,
% 0.12/0.36 (![Y: $i] : (~(big_l(Y) & big_k(Y))) <=> ![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.36 tff(45,plain,
% 0.12/0.36 ((~?[Y: $i] : (big_l(Y) & big_k(Y))) <=> (~?[Y: $i] : (big_l(Y) & big_k(Y)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(46,axiom,(~?[Y: $i] : (big_l(Y) & big_k(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel45_2')).
% 0.12/0.36 tff(47,plain,
% 0.12/0.36 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.36 tff(48,plain,
% 0.12/0.36 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[47, 45])).
% 0.12/0.36 tff(49,plain,
% 0.12/0.36 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.12/0.36 tff(50,plain,
% 0.12/0.36 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.12/0.36 tff(51,plain,
% 0.12/0.36 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[50, 45])).
% 0.12/0.36 tff(52,plain,
% 0.12/0.36 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[51, 45])).
% 0.12/0.36 tff(53,plain,
% 0.12/0.36 (~?[Y: $i] : (big_l(Y) & big_k(Y))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.12/0.36 tff(54,plain,
% 0.12/0.36 (^[Y: $i] : refl($oeq((~(big_l(Y) & big_k(Y))), (~(big_l(Y) & big_k(Y)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(55,plain,(
% 0.12/0.36 ![Y: $i] : (~(big_l(Y) & big_k(Y)))),
% 0.12/0.36 inference(nnf-neg,[status(sab)],[53, 54])).
% 0.12/0.36 tff(56,plain,
% 0.12/0.36 (![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[55, 44])).
% 0.12/0.36 tff(57,plain,
% 0.12/0.36 (![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[56, 42])).
% 0.12/0.36 tff(58,plain,
% 0.12/0.36 (((~![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))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(59,plain,
% 0.12/0.36 ((~![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))) | ((~big_k(tptp_fun_Y_2(X!1))) | (~big_l(tptp_fun_Y_2(X!1))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(60,plain,
% 0.12/0.36 ((~![Y: $i] : ((~big_k(Y)) | (~big_l(Y)))) | (~big_k(tptp_fun_Y_2(X!1))) | (~big_l(tptp_fun_Y_2(X!1)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.12/0.36 tff(61,plain,
% 0.12/0.36 (~big_k(tptp_fun_Y_2(X!1))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[60, 57, 40])).
% 0.12/0.36 tff(62,plain,
% 0.12/0.36 (((~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))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(63,plain,
% 0.12/0.36 ((~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)))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.12/0.36 tff(64,assumption,(![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))), introduced(assumption)).
% 0.12/0.36 tff(65,plain,
% 0.12/0.36 (((~![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))))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(66,plain,
% 0.12/0.36 ((~((~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)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(67,plain,
% 0.12/0.36 (((~![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))))))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[66])).
% 0.12/0.36 tff(68,plain,
% 0.12/0.36 (((~![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))))))),
% 0.12/0.36 inference(transitivity,[status(thm)],[67, 65])).
% 0.12/0.36 tff(69,plain,
% 0.12/0.36 ((~![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)))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(70,plain,
% 0.12/0.36 ((~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))) | (~((~big_g(tptp_fun_Y_2(X!1))) | (~big_h(X!1, tptp_fun_Y_2(X!1))) | (~big_k(tptp_fun_Y_2(X!1)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.36 tff(71,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[70, 64, 63])).
% 0.12/0.36 tff(72,plain,(~![Y1: $i] : (~((~big_h(X!1, Y1)) | (~big_g(Y1)) | (~big_k(Y1))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.36 tff(73,plain,
% 0.12/0.36 (^[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)))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(74,plain,
% 0.12/0.36 (![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)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[73])).
% 0.12/0.36 tff(75,plain,
% 0.12/0.36 (^[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)))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(76,plain,
% 0.12/0.36 (![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))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[75])).
% 0.12/0.36 tff(77,plain,
% 0.12/0.36 (^[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)))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(78,plain,
% 0.12/0.36 (![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))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[77])).
% 0.12/0.36 tff(79,plain,
% 0.12/0.36 (![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))))))),
% 0.12/0.36 inference(transitivity,[status(thm)],[78, 76])).
% 0.12/0.36 tff(80,plain,
% 0.12/0.36 (^[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))))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(81,plain,
% 0.12/0.36 (![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))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[80])).
% 0.12/0.36 tff(82,plain,
% 0.12/0.36 (^[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))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(83,plain,
% 0.12/0.36 (![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)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[82])).
% 0.12/0.36 tff(84,plain,
% 0.12/0.36 (![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)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(85,plain,
% 0.12/0.36 (^[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)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(86,plain,
% 0.12/0.36 (![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)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[85])).
% 0.12/0.36 tff(87,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')).
% 0.12/0.36 tff(88,plain,
% 0.12/0.36 (![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)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.12/0.36 tff(89,plain,
% 0.12/0.36 (![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)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.12/0.36 tff(90,plain,(
% 0.12/0.36 ![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)))),
% 0.12/0.36 inference(skolemize,[status(sab)],[89])).
% 0.12/0.36 tff(91,plain,
% 0.12/0.36 (![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)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.12/0.36 tff(92,plain,
% 0.12/0.36 (![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))))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.12/0.36 tff(93,plain,
% 0.12/0.36 (![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))))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[92, 79])).
% 0.12/0.36 tff(94,plain,
% 0.12/0.36 (![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)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[93, 74])).
% 0.12/0.36 tff(95,plain,
% 0.12/0.36 (((~![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_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)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(96,plain,
% 0.12/0.36 ((~![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)))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(97,plain,
% 0.12/0.36 ((~![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))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.12/0.36 tff(98,plain,
% 0.12/0.36 ((~(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))))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[97, 94, 26])).
% 0.12/0.36 tff(99,plain,
% 0.12/0.36 (~(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))))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[98, 72])).
% 0.12/0.36 tff(100,plain,
% 0.12/0.36 ((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)))) | big_h(X!1, tptp_fun_Y_0(X!1))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(101,plain,
% 0.12/0.36 (big_h(X!1, tptp_fun_Y_0(X!1))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.12/0.36 tff(102,plain,
% 0.12/0.36 ((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)))) | big_g(tptp_fun_Y_0(X!1))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(103,plain,
% 0.12/0.36 (big_g(tptp_fun_Y_0(X!1))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.12/0.36 tff(104,plain,
% 0.12/0.36 ((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)))) | (~big_j(X!1, tptp_fun_Y_0(X!1)))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(105,plain,
% 0.12/0.36 (~big_j(X!1, tptp_fun_Y_0(X!1))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[104, 99])).
% 0.12/0.36 tff(106,plain,
% 0.12/0.36 (^[Y1: $i] : refl(((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1))) <=> ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(107,plain,
% 0.12/0.36 (![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1))) <=> ![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[106])).
% 0.12/0.36 tff(108,plain,
% 0.12/0.36 (^[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_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))), (((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1)) <=> ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(109,plain,
% 0.12/0.36 (![Y1: $i] : ((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1)) <=> ![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[108])).
% 0.12/0.36 tff(110,plain,
% 0.12/0.36 (![Y1: $i] : ((~(big_g(Y1) & big_h(X!1, Y1))) | big_j(X!1, Y1))),
% 0.12/0.36 inference(and_elim,[status(thm)],[25])).
% 0.12/0.36 tff(111,plain,
% 0.12/0.36 (![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.12/0.36 tff(112,plain,
% 0.12/0.36 (![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.12/0.36 tff(113,plain,
% 0.12/0.36 (((~![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))) | (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_j(X!1, Y1) | (~big_g(Y1)))) | 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))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(114,plain,
% 0.12/0.36 (((~big_h(X!1, tptp_fun_Y_0(X!1))) | big_j(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))) | (~big_h(X!1, tptp_fun_Y_0(X!1))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(115,plain,
% 0.12/0.36 (((~![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))) | ((~big_h(X!1, tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_g(tptp_fun_Y_0(X!1))))) <=> ((~![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))) | (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)))))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[114])).
% 0.12/0.36 tff(116,plain,
% 0.12/0.36 (((~![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))) | ((~big_h(X!1, tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_g(tptp_fun_Y_0(X!1))))) <=> ((~![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))) | 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))))),
% 0.12/0.36 inference(transitivity,[status(thm)],[115, 113])).
% 0.12/0.36 tff(117,plain,
% 0.12/0.36 ((~![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))) | ((~big_h(X!1, tptp_fun_Y_0(X!1))) | big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_g(tptp_fun_Y_0(X!1))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(118,plain,
% 0.12/0.36 ((~![Y1: $i] : ((~big_h(X!1, Y1)) | big_j(X!1, Y1) | (~big_g(Y1)))) | big_j(X!1, tptp_fun_Y_0(X!1)) | (~big_g(tptp_fun_Y_0(X!1))) | (~big_h(X!1, tptp_fun_Y_0(X!1)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.12/0.36 tff(119,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[118, 112, 105, 103, 101])).
% 0.12/0.36 % SZS output end Proof
%------------------------------------------------------------------------------