TSTP Solution File: SYN012-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN012-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 23:53:10 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN012-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.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 01:00:00 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.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(big_g_type, type, (
% 0.20/0.44 big_g: ( $i * $i ) > $o)).
% 0.20/0.44 tff(g_type, type, (
% 0.20/0.44 g: ( $i * $i ) > $i)).
% 0.20/0.44 tff(elem_0_type, type, (
% 0.20/0.44 elem_0: $i)).
% 0.20/0.44 tff(big_f_type, type, (
% 0.20/0.44 big_f: ( $i * $i ) > $o)).
% 0.20/0.44 tff(1,assumption,(big_f(elem!0, elem!0)), introduced(assumption)).
% 0.20/0.44 tff(2,assumption,(~big_f(elem!0, g(elem!0, elem!0))), introduced(assumption)).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : refl((big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y)))) <=> (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y)))) <=> ![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y)))) <=> ![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : rewrite((((~big_f(X, Y)) | big_f(X, g(X, Y))) | (~big_g(Y, g(X, Y)))) <=> (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (((~big_f(X, Y)) | big_f(X, g(X, Y))) | (~big_g(Y, g(X, Y)))) <=> ![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.44 tff(8,axiom,(![Y: $i, X: $i] : (((~big_f(X, Y)) | big_f(X, g(X, Y))) | (~big_g(Y, g(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.44 tff(11,plain,(
% 0.20/0.44 ![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[10])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | ((~big_f(elem!0, elem!0)) | big_f(elem!0, g(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (~big_f(elem!0, elem!0)) | big_f(elem!0, g(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 ((big_f(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0)))) <=> ((~big_f(elem!0, elem!0)) | big_f(elem!0, g(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (big_f(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | ((~big_f(elem!0, elem!0)) | big_f(elem!0, g(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[14])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (big_f(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (~big_f(elem!0, elem!0)) | big_f(elem!0, g(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (big_f(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (~big_f(elem!0, elem!0)) | big_f(elem!0, g(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (big_f(elem!0, g(elem!0, elem!0)) | (~big_g(elem!0, g(elem!0, elem!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[18, 12, 1])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (~big_g(elem!0, g(elem!0, elem!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[19, 2])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : refl(((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y)) <=> ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 (![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y)) <=> ![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y)) <=> ![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : rewrite((big_f(X, Y) | (~big_g(g(X, Y), g(X, Y)))) <=> ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_f(X, Y) | (~big_g(g(X, Y), g(X, Y)))) <=> ![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.44 tff(26,axiom,(![Y: $i, X: $i] : (big_f(X, Y) | (~big_g(g(X, Y), g(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5')).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.44 tff(29,plain,(
% 0.20/0.44 ![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))),
% 0.20/0.44 inference(skolemize,[status(sab)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | ((~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | big_f(elem!0, g(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | (~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | big_f(elem!0, g(elem!0, elem!0)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | ((~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | big_f(elem!0, g(elem!0, elem!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | (~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | big_f(elem!0, g(elem!0, elem!0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 ((~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | big_f(elem!0, g(elem!0, elem!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[34, 2])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : refl((big_g(X, Y) | big_g(g(X, Y), g(X, Y))) <=> (big_g(X, Y) | big_g(g(X, Y), g(X, Y))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y))) <=> ![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y))) <=> ![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(39,axiom,(![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.44 tff(41,plain,(
% 0.20/0.44 ![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[40])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | (big_g(elem!0, g(elem!0, elem!0)) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | big_g(elem!0, g(elem!0, elem!0)) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | (big_g(elem!0, g(elem!0, elem!0)) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | big_g(elem!0, g(elem!0, elem!0)) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[45, 42, 35, 20])).
% 0.20/0.44 tff(47,plain,(big_f(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (big_f(elem!0, g(elem!0, elem!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[47, 1])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : refl((big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y))) <=> (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y))) <=> ![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y))) <=> ![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : rewrite((((~big_f(X, Y)) | (~big_f(X, g(X, Y)))) | big_g(Y, g(X, Y))) <=> (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (((~big_f(X, Y)) | (~big_f(X, g(X, Y)))) | big_g(Y, g(X, Y))) <=> ![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.44 tff(54,axiom,(![Y: $i, X: $i] : (((~big_f(X, Y)) | (~big_f(X, g(X, Y)))) | big_g(Y, g(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.44 tff(57,plain,(
% 0.20/0.44 ![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[56])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | ((~big_f(elem!0, elem!0)) | big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (~big_f(elem!0, elem!0)) | big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 ((big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0))) | (~big_f(elem!0, elem!0))) <=> ((~big_f(elem!0, elem!0)) | big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0))) | (~big_f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | ((~big_f(elem!0, elem!0)) | big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0))) | (~big_f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (~big_f(elem!0, elem!0)) | big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0))) | (~big_f(elem!0, elem!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (~big_f(elem!0, elem!0)) | big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (big_g(elem!0, g(elem!0, elem!0)) | (~big_f(elem!0, g(elem!0, elem!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[64, 58, 1])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (big_g(elem!0, g(elem!0, elem!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[65, 48])).
% 0.20/0.45 tff(67,assumption,(~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))), introduced(assumption)).
% 0.20/0.45 tff(68,assumption,(~big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))), introduced(assumption)).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | (big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | (big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[71, 42, 67, 68])).
% 0.20/0.45 tff(73,plain,(big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[73, 67])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | ((~big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))) | big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | (~big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))) | big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | ((~big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))) | big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | (~big_g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))), g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))) | big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[77, 30, 74])).
% 0.20/0.45 tff(79,assumption,(big_f(elem!0, g(elem!0, elem!0))), introduced(assumption)).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : refl(((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y)))) <=> ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y)))) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y)))) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : rewrite((((~big_f(X, Y)) | (~big_f(g(X, Y), g(X, Y)))) | big_g(g(X, Y), g(X, Y))) <=> ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (((~big_f(X, Y)) | (~big_f(g(X, Y), g(X, Y)))) | big_g(g(X, Y), g(X, Y))) <=> ![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.45 tff(85,axiom,(![Y: $i, X: $i] : (((~big_f(X, Y)) | (~big_f(g(X, Y), g(X, Y)))) | big_g(g(X, Y), g(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.45 tff(88,plain,(
% 0.20/0.45 ![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[87])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | (big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | (~big_f(elem!0, g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | (~big_f(elem!0, g(elem!0, elem!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (((~big_f(elem!0, g(elem!0, elem!0))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))) <=> (big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | (~big_f(elem!0, g(elem!0, elem!0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | ((~big_f(elem!0, g(elem!0, elem!0))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | (big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | (~big_f(elem!0, g(elem!0, elem!0)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | ((~big_f(elem!0, g(elem!0, elem!0))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | (~big_f(elem!0, g(elem!0, elem!0))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | ((~big_f(elem!0, g(elem!0, elem!0))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))) | (~big_f(elem!0, g(elem!0, elem!0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 89, 79, 78, 67])).
% 0.20/0.46 tff(97,plain,(big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))) | (~big_f(elem!0, g(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[97, 48])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : refl(((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y)))) <=> ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y)))) <=> ![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y)))) <=> ![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(102,axiom,(![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7')).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.46 tff(104,plain,(
% 0.20/0.46 ![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[103])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))) | ((~big_g(elem!0, g(elem!0, elem!0))) | (~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))) | (~big_g(elem!0, g(elem!0, elem!0))) | (~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))) | ((~big_g(elem!0, g(elem!0, elem!0))) | (~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))) | (~big_g(elem!0, g(elem!0, elem!0))) | (~big_g(g(elem!0, g(elem!0, elem!0)), g(elem!0, g(elem!0, elem!0))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[108, 105, 98, 66])).
% 0.20/0.47 tff(110,plain,(~big_f(elem!0, elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (^[Y: $i, X: $i] : refl((big_f(X, Y) | big_f(g(X, Y), g(X, Y))) <=> (big_f(X, Y) | big_f(g(X, Y), g(X, Y))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y))) <=> ![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y))) <=> ![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(114,axiom,(![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.47 tff(116,plain,(
% 0.20/0.47 ![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[115])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))) | (big_f(elem!0, elem!0) | big_f(g(elem!0, elem!0), g(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))) | big_f(elem!0, elem!0) | big_f(g(elem!0, elem!0), g(elem!0, elem!0)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))) | (big_f(elem!0, elem!0) | big_f(g(elem!0, elem!0), g(elem!0, elem!0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (big_f(X, Y) | big_f(g(X, Y), g(X, Y)))) | big_f(elem!0, elem!0) | big_f(g(elem!0, elem!0), g(elem!0, elem!0))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (big_f(elem!0, elem!0) | big_f(g(elem!0, elem!0), g(elem!0, elem!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (big_f(g(elem!0, elem!0), g(elem!0, elem!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[121, 110])).
% 0.20/0.47 tff(123,assumption,(~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), introduced(assumption)).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | ((~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | ((~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[126, 30, 123])).
% 0.20/0.47 tff(128,assumption,(big_f(g(elem!0, elem!0), g(elem!0, elem!0))), introduced(assumption)).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | ((~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 ((big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))) <=> ((~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | ((~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (big_f(X, g(X, Y)) | (~big_f(X, Y)) | (~big_g(Y, g(X, Y))))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 ((~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[134, 12])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[135, 123, 128])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | (big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | (big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[139, 42, 136, 127])).
% 0.20/0.47 tff(141,plain,(big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[141, 122])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | ((~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 ((big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0)))) <=> ((~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | ((~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[145, 143])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (big_g(Y, g(X, Y)) | (~big_f(X, g(X, Y))) | (~big_f(X, Y)))) | (~big_f(g(elem!0, elem!0), g(elem!0, elem!0))) | big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 (big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[148, 58, 122, 142])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))) | ((~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))) | ((~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~big_g(X, Y)) | (~big_g(g(X, Y), g(X, Y))))) | (~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 ((~big_g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[152, 105])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (~big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[153, 149])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | ((~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | ((~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~big_f(X, Y)) | big_g(g(X, Y), g(X, Y)) | (~big_f(g(X, Y), g(X, Y))))) | (~big_f(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | (~big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (~big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[157, 89, 142, 154])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | ((~big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) | big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | (~big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) | big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | ((~big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) | big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~big_g(g(X, Y), g(X, Y))) | big_f(X, Y))) | (~big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))) | big_f(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 (~big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[161, 30, 158])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | (big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | (big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (big_g(X, Y) | big_g(g(X, Y), g(X, Y)))) | big_g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))) | big_g(g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))), g(g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0))), g(g(elem!0, elem!0), g(g(elem!0, elem!0), g(elem!0, elem!0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[165, 42, 154, 162])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------