TSTP Solution File: SYN328+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN328+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 23:54:44 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN328+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n021.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 02:32:01 EDT 2022
% 0.14/0.35 % 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.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(big_g_type, type, (
% 0.14/0.40 big_g: $i > $o)).
% 0.14/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.14/0.40 tptp_fun_Z_0: $i > $i)).
% 0.14/0.40 tff(elem_2_type, type, (
% 0.14/0.40 elem_2: $i)).
% 0.14/0.40 tff(big_f_type, type, (
% 0.14/0.40 big_f: $i > $o)).
% 0.14/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.40 tptp_fun_Y_1: $i > $i)).
% 0.14/0.40 tff(big_h_type, type, (
% 0.14/0.40 big_h: $i > $o)).
% 0.14/0.40 tff(1,assumption,(((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))), introduced(assumption)).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (^[X: $i] : refl((~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X))))))) <=> (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X))))))) <=> ![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (^[X: $i] : rewrite((~((big_f(tptp_fun_Z_0(X)) & big_g(tptp_fun_Z_0(X)) & big_h(tptp_fun_Z_0(X))) | ((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)))) <=> (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (![X: $i] : (~((big_f(tptp_fun_Z_0(X)) & big_g(tptp_fun_Z_0(X)) & big_h(tptp_fun_Z_0(X))) | ((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)))) <=> ![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 ((~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 ((~?[X: $i] : ![Y: $i, Z: $i] : (((big_f(Y) => big_g(Y)) <=> big_f(X)) => (((big_f(Y) => big_h(Y)) <=> big_g(X)) => ((((big_f(Y) => big_g(Y)) => big_h(Y)) <=> big_h(X)) => ((big_f(Z) & big_g(Z)) & big_h(Z)))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(8,axiom,(~?[X: $i] : ![Y: $i, Z: $i] : (((big_f(Y) => big_g(Y)) <=> big_f(X)) => (((big_f(Y) => big_h(Y)) <=> big_g(X)) => ((((big_f(Y) => big_g(Y)) => big_h(Y)) <=> big_h(X)) => ((big_f(Z) & big_g(Z)) & big_h(Z)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_12_3')).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (^[X: $i] : sk($oeq((~![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | ((~(big_h(Y) | (~(big_g(Y) | (~big_f(Y)))))) <=> big_h(X)) | ((~(big_h(Y) | (~big_f(Y)))) <=> big_g(X)) | ((~(big_g(Y) | (~big_f(Y)))) <=> big_f(X)))), (~((big_f(tptp_fun_Z_0(X)) & big_g(tptp_fun_Z_0(X)) & big_h(tptp_fun_Z_0(X))) | ((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(17,plain,(
% 0.14/0.40 ![X: $i] : (~((big_f(tptp_fun_Z_0(X)) & big_g(tptp_fun_Z_0(X)) & big_h(tptp_fun_Z_0(X))) | ((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X))))),
% 0.21/0.40 inference(nnf-neg,[status(sab)],[15, 16])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[17, 5])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[18, 3])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 ((~![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~(((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[20, 19, 1])).
% 0.21/0.40 tff(22,plain,(~(((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 ((~![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~(((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (~(((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 ((~![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~(((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (~(((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[29, 19])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((~![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~(((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (~(((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[33, 19])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.41 tff(37,assumption,(~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))), introduced(assumption)).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[41, 36])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) | big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[46, 32])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) | big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[51, 28])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) | (~((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (~((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[53, 26])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[55, 30])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (~((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[57, 34])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 ((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[59, 37])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[62, 58])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[64, 42])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[66, 65, 63])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[69, 56])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[71, 49, 70])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[74, 54])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) | (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[76, 75, 52])).
% 0.21/0.41 tff(78,plain,(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (~((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[79, 34])).
% 0.21/0.42 tff(81,assumption,(~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))), introduced(assumption)).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 ((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (~big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[85, 80])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[45, 88])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 32])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (~((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[91, 30])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 81])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 86])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[97, 96, 58])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 98, 94])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[101, 100, 36])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 ((~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[103, 102, 88])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (((~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[106, 92])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[108, 107, 90])).
% 0.21/0.42 tff(110,plain,(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 ((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[112, 78])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[116, 22])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Z_0(elem!2))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))) | big_h(tptp_fun_Z_0(elem!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[118, 110])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (big_h(tptp_fun_Z_0(elem!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[119, 117])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 ((((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_h(tptp_fun_Z_0(elem!2))) | ((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2))) | ((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))) | (~((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (~((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[121, 22])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (big_f(tptp_fun_Z_0(elem!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[123, 78, 122])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 ((~![X: $i] : (~(((~(big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))))) <=> big_h(X)) | ((~(big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_g(X)) | ((~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X))))) <=> big_f(X)) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~(((~(big_h(tptp_fun_Y_1(elem!2)) | (~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))))) <=> big_h(elem!2)) | ((~(big_h(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))) <=> big_g(elem!2)) | ((~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))) <=> big_f(elem!2)) | (~((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (~(((~(big_h(tptp_fun_Y_1(elem!2)) | (~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))))) <=> big_h(elem!2)) | ((~(big_h(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))) <=> big_g(elem!2)) | ((~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))) <=> big_f(elem!2)) | (~((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[125, 19])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 ((((~(big_h(tptp_fun_Y_1(elem!2)) | (~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))))) <=> big_h(elem!2)) | ((~(big_h(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))) <=> big_g(elem!2)) | ((~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2))))) <=> big_f(elem!2)) | (~((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))))) | ((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 ((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 ((~((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 ((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (~big_g(tptp_fun_Z_0(elem!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[130, 124, 120])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_g(tptp_fun_Z_0(elem!2))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | big_g(tptp_fun_Z_0(elem!2))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[132, 131, 115, 24])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------