TSTP Solution File: SYN336+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN336+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 23:54:48 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN336+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 02:37:31 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(big_f_type, type, (
% 0.21/0.43 big_f: ( $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_Z_1_type, type, (
% 0.21/0.43 tptp_fun_Z_1: ( $i * $i ) > $i)).
% 0.21/0.43 tff(elem_2_type, type, (
% 0.21/0.43 elem_2: $i)).
% 0.21/0.43 tff(tptp_fun_X_0_type, type, (
% 0.21/0.43 tptp_fun_X_0: $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 ((~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))) <=> (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 ((~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(X, Z) => (big_f(Y1, Z) => (big_f(Y2, Z) => (big_f(Y1, X) => big_f(Z, Y2)))))) <=> (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(3,axiom,(~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(X, Z) => (big_f(Y1, Z) => (big_f(Y2, Z) => (big_f(Y1, X) => big_f(Z, Y2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_15_1')).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.43 tff(11,plain,(
% 0.21/0.43 $oeq((~?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X!0, Z)))), ![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1))))))),
% 0.21/0.43 inference(transitivity,[status(sab)],[10])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 ((~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))) <=> (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[13])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0)))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[14, 12])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 ((big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))), X!0))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 ((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 ((~(big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))))) <=> (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[25, 23])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), X!0)) | big_f(tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))) | (~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2))))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))), tptp_fun_Z_1(tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(tptp_fun_Z_1(elem!2, X!0), tptp_fun_Z_1(elem!2, tptp_fun_Z_1(elem!2, elem!2)))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[28, 11, 22])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------