TSTP Solution File: SYN334-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN334-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 23:54:47 EDT 2022
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN334-1 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:41:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 tff(g_type, type, (
% 0.21/0.46 g: ( $i * $i ) > $o)).
% 0.21/0.46 tff(z_type, type, (
% 0.21/0.46 z: ( $i * $i ) > $i)).
% 0.21/0.46 tff(elem_0_type, type, (
% 0.21/0.46 elem_0: $i)).
% 0.21/0.46 tff(f_type, type, (
% 0.21/0.46 f: ( $i * $i ) > $o)).
% 0.21/0.46 tff(1,assumption,(f(elem!0, elem!0)), introduced(assumption)).
% 0.21/0.46 tff(2,assumption,(~f(elem!0, z(elem!0, elem!0))), introduced(assumption)).
% 0.21/0.46 tff(3,plain,
% 0.21/0.46 (^[Y: $i, X: $i] : refl(((~g(z(X, Y), z(X, Y))) | f(X, Y)) <=> ((~g(z(X, Y), z(X, Y))) | f(X, Y)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(4,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y)) <=> ![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y)) <=> ![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(6,axiom,(![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 0.21/0.46 tff(7,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.46 tff(8,plain,(
% 0.21/0.46 ![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.21/0.46 inference(skolemize,[status(sab)],[7])).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | ((~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | f(elem!0, z(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | (~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | f(elem!0, z(elem!0, elem!0)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(11,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | ((~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | f(elem!0, z(elem!0, elem!0)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(12,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | (~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | f(elem!0, z(elem!0, elem!0))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.46 tff(13,plain,
% 0.21/0.46 ((~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | f(elem!0, z(elem!0, elem!0))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.21/0.46 tff(14,plain,
% 0.21/0.46 (~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[13, 2])).
% 0.21/0.46 tff(15,plain,
% 0.21/0.46 (^[Y: $i, X: $i] : refl(((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y))) <=> ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(16,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y))) <=> ![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.46 tff(17,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y))) <=> ![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(18,plain,
% 0.21/0.46 (^[Y: $i, X: $i] : rewrite((((~f(X, Y)) | f(X, z(X, Y))) | (~g(Y, z(X, Y)))) <=> ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (((~f(X, Y)) | f(X, z(X, Y))) | (~g(Y, z(X, Y)))) <=> ![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.46 tff(20,axiom,(![Y: $i, X: $i] : (((~f(X, Y)) | f(X, z(X, Y))) | (~g(Y, z(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.46 tff(23,plain,(
% 0.21/0.46 ![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[22])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~f(elem!0, elem!0)) | f(elem!0, z(elem!0, elem!0)) | (~g(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | (~f(elem!0, elem!0)) | f(elem!0, z(elem!0, elem!0)) | (~g(elem!0, z(elem!0, elem!0))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (((~g(elem!0, z(elem!0, elem!0))) | f(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0))) <=> ((~f(elem!0, elem!0)) | f(elem!0, z(elem!0, elem!0)) | (~g(elem!0, z(elem!0, elem!0))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~g(elem!0, z(elem!0, elem!0))) | f(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~f(elem!0, elem!0)) | f(elem!0, z(elem!0, elem!0)) | (~g(elem!0, z(elem!0, elem!0)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~g(elem!0, z(elem!0, elem!0))) | f(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | (~f(elem!0, elem!0)) | f(elem!0, z(elem!0, elem!0)) | (~g(elem!0, z(elem!0, elem!0))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[27, 25])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~g(elem!0, z(elem!0, elem!0))) | f(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | (~f(elem!0, elem!0)) | f(elem!0, z(elem!0, elem!0)) | (~g(elem!0, z(elem!0, elem!0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (f(elem!0, z(elem!0, elem!0)) | (~g(elem!0, z(elem!0, elem!0)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[30, 24, 1])).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 (~g(elem!0, z(elem!0, elem!0))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[31, 2])).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 (^[Y: $i, X: $i] : refl((g(X, Y) | g(z(X, Y), z(X, Y))) <=> (g(X, Y) | g(z(X, Y), z(X, Y))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y))) <=> ![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y))) <=> ![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(36,axiom,(![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.46 tff(38,plain,(
% 0.21/0.46 ![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[37])).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | (g(elem!0, z(elem!0, elem!0)) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | g(elem!0, z(elem!0, elem!0)) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | (g(elem!0, z(elem!0, elem!0)) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | g(elem!0, z(elem!0, elem!0)) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.46 tff(43,plain,
% 0.21/0.46 (g(elem!0, z(elem!0, elem!0)) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[43, 32, 14])).
% 0.21/0.47 tff(45,plain,(f(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (f(elem!0, z(elem!0, elem!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[45, 1])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : refl((g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y)))) <=> (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y)))) <=> ![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y)))) <=> ![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : rewrite((((~f(X, Y)) | (~f(X, z(X, Y)))) | g(Y, z(X, Y))) <=> (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (((~f(X, Y)) | (~f(X, z(X, Y)))) | g(Y, z(X, Y))) <=> ![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.47 tff(52,axiom,(![Y: $i, X: $i] : (((~f(X, Y)) | (~f(X, z(X, Y)))) | g(Y, z(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.21/0.47 tff(55,plain,(
% 0.21/0.47 ![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[54])).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | ((~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))) | g(elem!0, z(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))) | g(elem!0, z(elem!0, elem!0)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 ((g(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0)))) <=> ((~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))) | g(elem!0, z(elem!0, elem!0)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (g(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | ((~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))) | g(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (g(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))) | g(elem!0, z(elem!0, elem!0)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.47 tff(61,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (g(elem!0, z(elem!0, elem!0)) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(62,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))) | g(elem!0, z(elem!0, elem!0))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.47 tff(63,plain,
% 0.21/0.47 ((~f(elem!0, z(elem!0, elem!0))) | g(elem!0, z(elem!0, elem!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[62, 56, 1])).
% 0.21/0.47 tff(64,plain,
% 0.21/0.47 (g(elem!0, z(elem!0, elem!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[63, 46])).
% 0.21/0.47 tff(65,assumption,(~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))), introduced(assumption)).
% 0.21/0.47 tff(66,assumption,(~g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))), introduced(assumption)).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | (g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(68,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | (g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(69,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[69, 39, 65, 66])).
% 0.21/0.47 tff(71,plain,(g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 (g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | ((~g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))) | f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | (~g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))) | f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | ((~g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))) | f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | (~g(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))) | f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 (f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[75, 9, 72])).
% 0.21/0.47 tff(77,assumption,(f(elem!0, z(elem!0, elem!0))), introduced(assumption)).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : refl(((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y)))) <=> ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(79,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : rewrite((((~f(z(X, Y), z(X, Y))) | g(z(X, Y), z(X, Y))) | (~f(X, Y))) <=> ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (((~f(z(X, Y), z(X, Y))) | g(z(X, Y), z(X, Y))) | (~f(X, Y))) <=> ![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.47 tff(83,axiom,(![Y: $i, X: $i] : (((~f(z(X, Y), z(X, Y))) | g(z(X, Y), z(X, Y))) | (~f(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.21/0.47 tff(86,plain,(
% 0.21/0.47 ![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[85])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | ((~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | (~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (((~f(elem!0, z(elem!0, elem!0))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))) <=> ((~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(90,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | ((~f(elem!0, z(elem!0, elem!0))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | ((~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.47 tff(91,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | ((~f(elem!0, z(elem!0, elem!0))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | (~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[90, 88])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | ((~f(elem!0, z(elem!0, elem!0))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(93,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | (~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.47 tff(94,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[93, 87, 77, 76, 65])).
% 0.21/0.47 tff(95,plain,(g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))) | (~f(elem!0, z(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(96,plain,
% 0.21/0.47 (g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[95, 46])).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : refl(((~g(X, Y)) | (~g(z(X, Y), z(X, Y)))) <=> ((~g(X, Y)) | (~g(z(X, Y), z(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(100,axiom,(![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 0.21/0.47 tff(101,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.47 tff(102,plain,(
% 0.21/0.47 ![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[101])).
% 0.21/0.47 tff(103,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))) | ((~g(elem!0, z(elem!0, elem!0))) | (~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))) | (~g(elem!0, z(elem!0, elem!0))) | (~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))) | ((~g(elem!0, z(elem!0, elem!0))) | (~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))) | (~g(elem!0, z(elem!0, elem!0))) | (~g(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[106, 103, 96, 64])).
% 0.21/0.47 tff(108,plain,(~f(elem!0, elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : refl((f(X, Y) | f(z(X, Y), z(X, Y))) <=> (f(X, Y) | f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y))) <=> ![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y))) <=> ![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : rewrite((f(z(X, Y), z(X, Y)) | f(X, Y)) <=> (f(X, Y) | f(z(X, Y), z(X, Y))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(X, Y)) <=> ![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[112])).
% 0.21/0.47 tff(114,axiom,(![Y: $i, X: $i] : (f(z(X, Y), z(X, Y)) | f(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.21/0.47 tff(117,plain,(
% 0.21/0.47 ![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[116])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))) | (f(elem!0, elem!0) | f(z(elem!0, elem!0), z(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))) | f(elem!0, elem!0) | f(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))) | (f(elem!0, elem!0) | f(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (f(X, Y) | f(z(X, Y), z(X, Y)))) | f(elem!0, elem!0) | f(z(elem!0, elem!0), z(elem!0, elem!0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 (f(elem!0, elem!0) | f(z(elem!0, elem!0), z(elem!0, elem!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (f(z(elem!0, elem!0), z(elem!0, elem!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[122, 108])).
% 0.21/0.48 tff(124,assumption,(~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), introduced(assumption)).
% 0.21/0.48 tff(125,assumption,(f(z(elem!0, elem!0), z(elem!0, elem!0))), introduced(assumption)).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 ((g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))) <=> ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (g(Y, z(X, Y)) | (~f(X, Y)) | (~f(X, z(X, Y))))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[131, 56, 125, 124])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | ((~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | ((~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[135, 9, 132])).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | (g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | (g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[139, 39, 124, 136])).
% 0.21/0.48 tff(141,plain,(g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[141, 123])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))) | ((~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))) | ((~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~g(X, Y)) | (~g(z(X, Y), z(X, Y))))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 ((~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[145, 103])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (~g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[146, 142])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 (((~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0)))) <=> ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[149])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[150, 148])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | ((~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~g(Y, z(X, Y))) | f(X, z(X, Y)) | (~f(X, Y)))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[153, 24])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[154, 142, 123])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | ((~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | ((~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~f(X, Y)) | g(z(X, Y), z(X, Y)) | (~f(z(X, Y), z(X, Y))))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (~f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[158, 87, 155, 147])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | ((~g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) | f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | (~g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) | f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | ((~g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) | f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : ((~g(z(X, Y), z(X, Y))) | f(X, Y))) | (~g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) | f(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 (~g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[162, 9, 159])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | (g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | (g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : (g(X, Y) | g(z(X, Y), z(X, Y)))) | g(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | g(z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), z(z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))), z(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[166, 39, 147, 163])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------