TSTP Solution File: SYN332+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN332+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 23:54:46 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN332+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 02:35:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(big_f_type, type, (
% 0.20/0.40 big_f: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.40 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(elem_1_type, type, (
% 0.20/0.40 elem_1: $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl((~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X))))) <=> (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X))))) <=> ![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : rewrite((~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, tptp_fun_Z_0(Y, X))) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)))) <=> (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, tptp_fun_Z_0(Y, X))) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)))) <=> ![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 ((~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))) <=> (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 ((~?[X: $i, Y: $i] : ![Z: $i] : ((~((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z))) => ((big_f(X, Z) <=> big_f(Z, X)) => ((big_f(X, Z) <=> big_f(Y, Z)) => (((big_f(Y, X) => big_f(X, Y)) <=> big_f(Z, Z)) => ((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y))))))) <=> (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,axiom,(~?[X: $i, Y: $i] : ![Z: $i] : ((~((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z))) => ((big_f(X, Z) <=> big_f(Z, X)) => ((big_f(X, Z) <=> big_f(Y, Z)) => (((big_f(Y, X) => big_f(X, Y)) <=> big_f(Z, Z)) => ((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_14_4')).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : sk($oeq((~![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(Z, Z)) | ((~big_f(X, Z)) <=> big_f(Y, Z)) | ((~big_f(X, Z)) <=> big_f(Z, X)))), (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, tptp_fun_Z_0(Y, X))) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, tptp_fun_Z_0(Y, X))) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X))))),
% 0.20/0.40 inference(nnf-neg,[status(sab)],[14, 15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 2])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 ((~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))) <=> (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[21, 19])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (~((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[30, 25])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[32, 31, 29])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), elem!1)) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), elem!1)) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[34, 18])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 ((((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), elem!1)) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (~((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (~(((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[38, 18])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 ((((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 ((((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (~((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~(((big_f(elem!1, elem!1) <=> big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | ((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | ((~((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(((big_f(elem!1, elem!1) <=> big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | ((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | ((~((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(((big_f(elem!1, elem!1) <=> big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | ((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | ((~((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(((big_f(elem!1, elem!1) <=> big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | ((~((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | ((~((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((~((~big_f(Y, X)) | big_f(X, Y))) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(Y, tptp_fun_Z_0(Y, X))) | ((~big_f(X, tptp_fun_Z_0(Y, X))) <=> big_f(tptp_fun_Z_0(Y, X), X)) | ((~((~big_f(Y, X)) | (~big_f(X, Y)))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[49, 18])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 ((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[53, 50])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[55, 54, 52])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[60, 43])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[62, 61, 41])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ((((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))) | ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (~((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[64, 39])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 ((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[66, 54, 56])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[69, 65])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) | (~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[71, 70, 63])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[74, 37])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.46 ((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 ((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[77, 33, 27])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------