TSTP Solution File: SYN333+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n002.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 0.12s 0.38s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n002.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Sep  5 02:50:33 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.12/0.38  % SZS status Theorem
% 0.12/0.38  % SZS output start Proof
% 0.12/0.38  tff(big_g_type, type, (
% 0.12/0.38     big_g: ( $i * $i ) > $o)).
% 0.12/0.38  tff(tptp_fun_Z_0_type, type, (
% 0.12/0.38     tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.12/0.38  tff(elem_1_type, type, (
% 0.12/0.38     elem_1: $i)).
% 0.12/0.38  tff(big_f_type, type, (
% 0.12/0.38     big_f: ( $i * $i ) > $o)).
% 0.12/0.38  tff(1,assumption,((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))))), introduced(assumption)).
% 0.12/0.38  tff(2,plain,
% 0.12/0.38      (^[X: $i, Y: $i] : refl((~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))))))) <=> (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))))))))),
% 0.12/0.38      inference(bind,[status(th)],[])).
% 0.12/0.38  tff(3,plain,
% 0.12/0.38      (![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))))))) <=> ![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))),
% 0.12/0.38      inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38  tff(4,plain,
% 0.12/0.38      (^[X: $i, Y: $i] : rewrite((~((~big_f(X, Y)) | (big_f(Y, tptp_fun_Z_0(Y, X)) & big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, tptp_fun_Z_0(Y, X)) & big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))) <=> (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))))))))),
% 0.12/0.38      inference(bind,[status(th)],[])).
% 0.12/0.38  tff(5,plain,
% 0.12/0.38      (![X: $i, Y: $i] : (~((~big_f(X, Y)) | (big_f(Y, tptp_fun_Z_0(Y, X)) & big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, tptp_fun_Z_0(Y, X)) & big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))) <=> ![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))),
% 0.12/0.38      inference(quant_intro,[status(thm)],[4])).
% 0.12/0.38  tff(6,plain,
% 0.12/0.38      ((~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))) <=> (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z))))))),
% 0.12/0.38      inference(rewrite,[status(thm)],[])).
% 0.12/0.38  tff(7,plain,
% 0.12/0.38      ((~?[X: $i, Y: $i] : ![Z: $i] : (big_f(X, Y) => ((big_f(Y, Z) & big_f(Z, Z)) & ((big_f(X, Y) & big_g(X, Y)) => (big_g(X, Z) & big_g(Z, Z)))))) <=> (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z))))))),
% 0.12/0.38      inference(rewrite,[status(thm)],[])).
% 0.12/0.38  tff(8,axiom,(~?[X: $i, Y: $i] : ![Z: $i] : (big_f(X, Y) => ((big_f(Y, Z) & big_f(Z, Z)) & ((big_f(X, Y) & big_g(X, Y)) => (big_g(X, Z) & big_g(Z, Z)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_14_5')).
% 0.12/0.38  tff(9,plain,
% 0.12/0.38      (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.38  tff(10,plain,
% 0.12/0.38      (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[9, 6])).
% 0.12/0.38  tff(11,plain,
% 0.12/0.38      (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[10, 6])).
% 0.12/0.38  tff(12,plain,
% 0.12/0.38      (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[11, 6])).
% 0.12/0.38  tff(13,plain,
% 0.12/0.38      (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[12, 6])).
% 0.12/0.38  tff(14,plain,
% 0.12/0.38      (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.38  tff(15,plain,
% 0.12/0.38      (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[14, 6])).
% 0.12/0.38  tff(16,plain,
% 0.12/0.38      (^[X: $i, Y: $i] : sk($oeq((~![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))), (~((~big_f(X, Y)) | (big_f(Y, tptp_fun_Z_0(Y, X)) & big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, tptp_fun_Z_0(Y, X)) & big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))),
% 0.12/0.38      inference(bind,[status(th)],[])).
% 0.12/0.38  tff(17,plain,(
% 0.12/0.38      ![X: $i, Y: $i] : (~((~big_f(X, Y)) | (big_f(Y, tptp_fun_Z_0(Y, X)) & big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, tptp_fun_Z_0(Y, X)) & big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))),
% 0.12/0.38      inference(nnf-neg,[status(sab)],[15, 16])).
% 0.12/0.38  tff(18,plain,
% 0.12/0.38      (![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[17, 5])).
% 0.12/0.38  tff(19,plain,
% 0.12/0.38      (![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))),
% 0.12/0.38      inference(modus_ponens,[status(thm)],[18, 3])).
% 0.12/0.38  tff(20,plain,
% 0.12/0.38      ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))))))),
% 0.12/0.39      inference(quant_inst,[status(thm)],[])).
% 0.12/0.39  tff(21,plain,
% 0.12/0.39      ($false),
% 0.12/0.39      inference(unit_resolution,[status(thm)],[20, 19, 1])).
% 0.12/0.39  tff(22,plain,(~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39  tff(23,plain,
% 0.12/0.39      (((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))))) | big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.12/0.39      inference(tautology,[status(thm)],[])).
% 0.12/0.39  tff(24,plain,
% 0.12/0.39      (big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.12/0.39      inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.39  tff(25,assumption,((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))), introduced(assumption)).
% 0.12/0.39  tff(26,plain,
% 0.12/0.39      ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))))),
% 0.12/0.39      inference(quant_inst,[status(thm)],[])).
% 0.12/0.39  tff(27,plain,
% 0.12/0.39      ($false),
% 0.12/0.39      inference(unit_resolution,[status(thm)],[26, 19, 25])).
% 0.12/0.39  tff(28,plain,(~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40  tff(29,plain,
% 0.12/0.40      (((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))) | big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.12/0.40      inference(tautology,[status(thm)],[])).
% 0.12/0.40  tff(30,plain,
% 0.12/0.40      (big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.12/0.40      inference(unit_resolution,[status(thm)],[29, 28])).
% 0.12/0.40  tff(31,assumption,((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))))))))))), introduced(assumption)).
% 0.12/0.40  tff(32,plain,
% 0.12/0.40      ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))))))))))))),
% 0.12/0.40      inference(quant_inst,[status(thm)],[])).
% 0.12/0.40  tff(33,plain,
% 0.12/0.40      ($false),
% 0.12/0.40      inference(unit_resolution,[status(thm)],[32, 19, 31])).
% 0.12/0.40  tff(34,plain,(~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40  tff(35,plain,
% 0.12/0.40      (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))))))))))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.12/0.40      inference(tautology,[status(thm)],[])).
% 0.12/0.40  tff(36,plain,
% 0.12/0.40      (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.12/0.40      inference(unit_resolution,[status(thm)],[35, 34])).
% 0.12/0.40  tff(37,assumption,((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))), introduced(assumption)).
% 0.12/0.40  tff(38,plain,
% 0.12/0.40      ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))))),
% 0.12/0.40      inference(quant_inst,[status(thm)],[])).
% 0.12/0.40  tff(39,plain,
% 0.12/0.40      ($false),
% 0.12/0.40      inference(unit_resolution,[status(thm)],[38, 19, 37])).
% 0.12/0.40  tff(40,plain,(~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40  tff(41,plain,
% 0.12/0.40      (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.19/0.41      inference(tautology,[status(thm)],[])).
% 0.19/0.41  tff(42,plain,
% 0.19/0.41      ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.41  tff(43,plain,
% 0.19/0.41      ((~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.19/0.41      inference(tautology,[status(thm)],[])).
% 0.19/0.41  tff(44,plain,
% 0.19/0.41      ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.41  tff(45,plain,
% 0.19/0.41      (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[44, 36, 30])).
% 0.19/0.41  tff(46,plain,
% 0.19/0.41      (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))) | big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.41      inference(tautology,[status(thm)],[])).
% 0.19/0.41  tff(47,plain,
% 0.19/0.41      (big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.41  tff(48,plain,
% 0.19/0.41      (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, 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, elem!1))),
% 0.19/0.41      inference(tautology,[status(thm)],[])).
% 0.19/0.41  tff(49,plain,
% 0.19/0.41      (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[48, 40])).
% 0.19/0.41  tff(50,assumption,((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))), introduced(assumption)).
% 0.19/0.41  tff(51,plain,
% 0.19/0.41      ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))))),
% 0.19/0.41      inference(quant_inst,[status(thm)],[])).
% 0.19/0.41  tff(52,plain,
% 0.19/0.41      ($false),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[51, 19, 50])).
% 0.19/0.41  tff(53,plain,(~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41  tff(54,plain,
% 0.19/0.41      (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))) | big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.41      inference(tautology,[status(thm)],[])).
% 0.19/0.41  tff(55,plain,
% 0.19/0.41      (big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.41  tff(56,plain,
% 0.19/0.41      ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~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), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))),
% 0.19/0.41      inference(quant_inst,[status(thm)],[])).
% 0.19/0.41  tff(57,plain,
% 0.19/0.41      (~((~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), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[56, 19])).
% 0.19/0.41  tff(58,plain,
% 0.19/0.41      (((~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), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(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), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.19/0.41      inference(tautology,[status(thm)],[])).
% 0.19/0.41  tff(59,plain,
% 0.19/0.41      ((~big_f(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, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.41  tff(60,plain,
% 0.19/0.41      ((~((~big_f(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, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(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), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.41      inference(tautology,[status(thm)],[])).
% 0.19/0.41  tff(61,plain,
% 0.19/0.41      ((~big_f(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, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.42  tff(62,plain,
% 0.19/0.42      (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[61, 55, 49])).
% 0.19/0.42  tff(63,plain,
% 0.19/0.42      (((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))),
% 0.19/0.42      inference(tautology,[status(thm)],[])).
% 0.19/0.42  tff(64,plain,
% 0.19/0.42      ((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.42  tff(65,plain,
% 0.19/0.42      ((~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.42      inference(tautology,[status(thm)],[])).
% 0.19/0.42  tff(66,plain,
% 0.19/0.42      ((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.42  tff(67,plain,
% 0.19/0.42      (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[66, 47])).
% 0.19/0.42  tff(68,plain,
% 0.19/0.42      (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))) | big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.42      inference(tautology,[status(thm)],[])).
% 0.19/0.42  tff(69,plain,
% 0.19/0.42      ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.42  tff(70,plain,
% 0.19/0.42      (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))),
% 0.19/0.42      inference(tautology,[status(thm)],[])).
% 0.19/0.42  tff(71,plain,
% 0.19/0.42      ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[70, 53])).
% 0.19/0.42  tff(72,plain,
% 0.19/0.42      ((~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))),
% 0.19/0.42      inference(tautology,[status(thm)],[])).
% 0.19/0.42  tff(73,plain,
% 0.19/0.42      ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.42  tff(74,plain,
% 0.19/0.42      (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[73, 69, 24])).
% 0.19/0.42  tff(75,plain,
% 0.19/0.42      (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.19/0.42      inference(tautology,[status(thm)],[])).
% 0.19/0.42  tff(76,plain,
% 0.19/0.42      ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.42  tff(77,plain,
% 0.19/0.42      ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))))),
% 0.19/0.42      inference(quant_inst,[status(thm)],[])).
% 0.19/0.42  tff(78,plain,
% 0.19/0.42      ($false),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[77, 19, 76])).
% 0.19/0.42  % SZS output end Proof
%------------------------------------------------------------------------------