TSTP Solution File: SYN068+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN068+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN068+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 01:33:39 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(big_g_type, type, (
% 0.14/0.39 big_g: $i > $o)).
% 0.14/0.39 tff(tptp_fun_Y1_1_type, type, (
% 0.14/0.39 tptp_fun_Y1_1: $i > $i)).
% 0.14/0.39 tff(tptp_fun_X_2_type, type, (
% 0.14/0.39 tptp_fun_X_2: $i)).
% 0.14/0.39 tff(big_h_type, type, (
% 0.14/0.39 big_h: ( $i * $i ) > $o)).
% 0.14/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.39 tptp_fun_Y_0: $i > $i)).
% 0.14/0.39 tff(big_f_type, type, (
% 0.14/0.39 big_f: $i > $o)).
% 0.14/0.39 tff(big_j_type, type, (
% 0.14/0.39 big_j: $i > $o)).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 (^[X: $i] : refl((big_f(X) | (~big_j(X))) <=> (big_f(X) | (~big_j(X))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (![X: $i] : (big_f(X) | (~big_j(X))) <=> ![X: $i] : (big_f(X) | (~big_j(X)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (^[X: $i] : trans(monotonicity(rewrite((big_j(X) & (~big_f(X))) <=> (~(big_f(X) | (~big_j(X))))), ((~(big_j(X) & (~big_f(X)))) <=> (~(~(big_f(X) | (~big_j(X))))))), rewrite((~(~(big_f(X) | (~big_j(X))))) <=> (big_f(X) | (~big_j(X)))), ((~(big_j(X) & (~big_f(X)))) <=> (big_f(X) | (~big_j(X)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 (![X: $i] : (~(big_j(X) & (~big_f(X)))) <=> ![X: $i] : (big_f(X) | (~big_j(X)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 ((~?[X: $i] : (big_j(X) & (~big_f(X)))) <=> (~?[X: $i] : (big_j(X) & (~big_f(X))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(6,axiom,(~?[X: $i] : (big_j(X) & (~big_f(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel44')).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 (^[X: $i] : refl($oeq((~(big_j(X) & (~big_f(X)))), (~(big_j(X) & (~big_f(X))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(15,plain,(
% 0.14/0.39 ![X: $i] : (~(big_j(X) & (~big_f(X))))),
% 0.14/0.39 inference(nnf-neg,[status(sab)],[13, 14])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (![X: $i] : (big_f(X) | (~big_j(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 (![X: $i] : (big_f(X) | (~big_j(X)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 ((big_j(X!2) & ![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) <=> (big_j(X!2) & ![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y))) <=> ?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(20,plain,
% 0.14/0.39 (^[X: $i] : rewrite((big_j(X) & ![Y: $i] : (big_g(Y) => big_h(X, Y))) <=> (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(21,plain,
% 0.14/0.39 (?[X: $i] : (big_j(X) & ![Y: $i] : (big_g(Y) => big_h(X, Y))) <=> ?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.39 tff(22,axiom,(?[X: $i] : (big_j(X) & ![Y: $i] : (big_g(Y) => big_h(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel44_2')).
% 0.14/0.39 tff(23,plain,
% 0.14/0.39 (?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 (big_j(X!2) & ![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (big_j(X!2)),
% 0.14/0.39 inference(and_elim,[status(thm)],[25])).
% 0.14/0.39 tff(27,plain,
% 0.14/0.39 (((~![X: $i] : (big_f(X) | (~big_j(X)))) | (big_f(X!2) | (~big_j(X!2)))) <=> ((~![X: $i] : (big_f(X) | (~big_j(X)))) | big_f(X!2) | (~big_j(X!2)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(28,plain,
% 0.14/0.39 ((~![X: $i] : (big_f(X) | (~big_j(X)))) | (big_f(X!2) | (~big_j(X!2)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 ((~![X: $i] : (big_f(X) | (~big_j(X)))) | big_f(X!2) | (~big_j(X!2))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 (big_f(X!2)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[29, 26, 17])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (^[X: $i] : refl(((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X)))))) <=> ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X)))))) <=> ![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (^[X: $i] : rewrite(((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X))))) <=> ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X))))) <=> ![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (^[X: $i] : rewrite(((~big_f(X)) | ((big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X))) & (big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X)))))) <=> ((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | ((big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X))) & (big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X)))))) <=> ![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X)))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> ![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 (^[X: $i] : trans(monotonicity(rewrite((?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))) <=> (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))), ((big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> (big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))))), rewrite((big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))), ((big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (![X: $i] : (big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> ![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.39 tff(40,axiom,(![X: $i] : (big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel44_1')).
% 0.14/0.39 tff(41,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.14/0.39 tff(42,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.14/0.39 tff(43,plain,(
% 0.14/0.39 ![X: $i] : ((~big_f(X)) | ((big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X))) & (big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X))))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[42])).
% 0.14/0.39 tff(44,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.14/0.39 tff(45,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.14/0.39 tff(46,plain,
% 0.14/0.39 (![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[45, 32])).
% 0.14/0.39 tff(47,plain,
% 0.14/0.39 (((~![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))) | ((~big_f(X!2)) | (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2))))))) <=> ((~![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))) | (~big_f(X!2)) | (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(48,plain,
% 0.14/0.39 ((~![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))) | ((~big_f(X!2)) | (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(49,plain,
% 0.14/0.39 ((~![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))) | (~big_f(X!2)) | (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.14/0.39 tff(50,plain,
% 0.14/0.39 (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[49, 46, 30])).
% 0.14/0.39 tff(51,plain,
% 0.14/0.39 ((big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2)))) | big_g(tptp_fun_Y1_1(X!2))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(52,plain,
% 0.14/0.39 (big_g(tptp_fun_Y1_1(X!2))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.14/0.39 tff(53,plain,
% 0.14/0.39 ((big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2)))) | (~big_h(X!2, tptp_fun_Y1_1(X!2)))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(54,plain,
% 0.14/0.39 (~big_h(X!2, tptp_fun_Y1_1(X!2))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[53, 50])).
% 0.14/0.39 tff(55,plain,
% 0.14/0.39 (^[Y: $i] : refl(((~big_g(Y)) | big_h(X!2, Y)) <=> ((~big_g(Y)) | big_h(X!2, Y)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(56,plain,
% 0.14/0.39 (![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y)) <=> ![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.14/0.39 tff(57,plain,
% 0.14/0.39 (![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))),
% 0.14/0.39 inference(and_elim,[status(thm)],[25])).
% 0.14/0.39 tff(58,plain,
% 0.14/0.39 (![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.14/0.39 tff(59,plain,
% 0.14/0.39 (((~![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) | ((~big_g(tptp_fun_Y1_1(X!2))) | big_h(X!2, tptp_fun_Y1_1(X!2)))) <=> ((~![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) | (~big_g(tptp_fun_Y1_1(X!2))) | big_h(X!2, tptp_fun_Y1_1(X!2)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(60,plain,
% 0.14/0.39 ((~![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) | ((~big_g(tptp_fun_Y1_1(X!2))) | big_h(X!2, tptp_fun_Y1_1(X!2)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(61,plain,
% 0.14/0.39 ((~![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) | (~big_g(tptp_fun_Y1_1(X!2))) | big_h(X!2, tptp_fun_Y1_1(X!2))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.14/0.39 tff(62,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[61, 58, 54, 52])).
% 0.14/0.39 % SZS output end Proof
%------------------------------------------------------------------------------