TSTP Solution File: SYN318+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN318+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 23:54:40 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN318+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon Sep 5 02:27:49 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(big_f_type, type, (
% 0.13/0.37 big_f: $i > $o)).
% 0.13/0.37 tff(tptp_fun_X_1_type, type, (
% 0.13/0.37 tptp_fun_X_1: $i > $i)).
% 0.13/0.37 tff(elem_2_type, type, (
% 0.13/0.37 elem_2: $i)).
% 0.13/0.37 tff(big_g_type, type, (
% 0.13/0.37 big_g: $i > $o)).
% 0.13/0.37 tff(k!0_type, type, (
% 0.13/0.37 k!0: $o)).
% 0.13/0.37 tff(p_type, type, (
% 0.13/0.37 p: $o)).
% 0.13/0.37 tff(1,plain,
% 0.13/0.37 (^[Y: $i] : refl((~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> ![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.37 tff(3,plain,
% 0.13/0.37 (^[Y: $i] : rewrite((~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> ![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> ![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.37 tff(6,plain,
% 0.13/0.37 (^[Y: $i] : rewrite(((~k!0) & (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))) & ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))) <=> (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (![Y: $i] : ((~k!0) & (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))) & ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))) <=> ![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 ((~?[Y: $i] : (k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~?[Y: $i] : (k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(9,plain,
% 0.13/0.37 ((~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | k!0 | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~?[Y: $i] : (k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 ((~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | k!0 | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(11,plain,
% 0.13/0.37 ((~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 ((~?[Y: $i] : (![X: $i] : (big_f(X) => (big_f(Y) => big_g(X))) => (p => ![X: $i] : (big_f(X) => big_g(Y))))) <=> (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(13,axiom,(~?[Y: $i] : (![X: $i] : (big_f(X) => (big_f(Y) => big_g(X))) => (p => ![X: $i] : (big_f(X) => big_g(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_2_4')).
% 0.13/0.37 tff(14,plain,
% 0.13/0.37 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.37 tff(15,plain,
% 0.13/0.37 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.13/0.37 tff(16,plain,
% 0.13/0.37 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.37 tff(17,plain,
% 0.13/0.37 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.13/0.37 tff(18,plain,
% 0.13/0.37 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | k!0 | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.13/0.37 tff(19,plain,
% 0.13/0.37 (~?[Y: $i] : (k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[18, 9])).
% 0.13/0.37 tff(20,plain,
% 0.13/0.37 (~?[Y: $i] : (k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[19, 8])).
% 0.13/0.37 tff(21,plain,
% 0.13/0.37 (~?[Y: $i] : (k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[20, 8])).
% 0.13/0.37 tff(22,plain,
% 0.13/0.37 (^[Y: $i] : nnf_neg(refl($oeq((~k!0), (~k!0))), sk($oeq((~![X: $i] : (big_g(Y) | (~big_f(X)))), (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))))), nnf_neg(nnf_pos(proof_bind(^[X: $i] : refl($oeq((big_g(X) | (~big_f(Y)) | (~big_f(X))), (big_g(X) | (~big_f(Y)) | (~big_f(X)))))), $oeq(![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))), ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))), $oeq((~(~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))), ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))), $oeq((~(k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))), ((~k!0) & (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))) & ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(23,plain,(
% 0.13/0.37 ![Y: $i] : ((~k!0) & (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))) & ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))),
% 0.13/0.37 inference(nnf-neg,[status(sab)],[21, 22])).
% 0.13/0.37 tff(24,plain,
% 0.13/0.37 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.13/0.37 tff(25,plain,
% 0.13/0.37 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.13/0.37 tff(26,plain,
% 0.13/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(27,plain,
% 0.13/0.37 ((~(big_g(tptp_fun_X_1(elem!2)) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(X)))))) <=> (~(k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(28,plain,
% 0.13/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(elem!2)) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))))))),
% 0.13/0.37 inference(monotonicity,[status(thm)],[27])).
% 0.13/0.37 tff(29,plain,
% 0.13/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(elem!2)) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))))))),
% 0.13/0.37 inference(transitivity,[status(thm)],[28, 26])).
% 0.13/0.37 tff(30,plain,
% 0.13/0.37 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(elem!2)) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(X))))))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(31,plain,
% 0.13/0.37 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.37 tff(32,plain,
% 0.13/0.37 (~(k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.13/0.37 tff(33,plain,
% 0.13/0.37 ((k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))) | ![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 ((k!0 | big_g(tptp_fun_X_1(elem!2)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))) | big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(elem!2) | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(elem!2) | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 ((~(big_g(elem!2) | k!0 | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))))) <=> (~(k!0 | big_g(elem!2) | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(elem!2) | k!0 | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(elem!2) | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[38])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(elem!2) | k!0 | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(elem!2) | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[39, 37])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(elem!2) | k!0 | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(elem!2) | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (~(k!0 | big_g(elem!2) | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[42, 25])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 ((k!0 | big_g(elem!2) | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))) | big_f(tptp_fun_X_1(elem!2))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (big_f(tptp_fun_X_1(elem!2))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | ((~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) <=> ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 ((big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(tptp_fun_X_1(elem!2)))) <=> ((~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(tptp_fun_X_1(elem!2))))) <=> ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | ((~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(tptp_fun_X_1(elem!2))))) <=> ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[48, 46])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(tptp_fun_X_1(elem!2))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 (big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[51, 45, 36, 34])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 ((k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))) | (~big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 ((~(big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(X)))))) <=> (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))))))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[56])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[57, 55])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(X))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[60, 25, 54])).
% 0.18/0.38 % SZS output end Proof
%------------------------------------------------------------------------------