%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.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 : Fri Sep 30 01:55:46 EDT 2022

% Result   : Unsatisfiable 0.18s 0.45s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15  % Problem  : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.16  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.36  % Computer : n009.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Mon Aug 29 09:08:06 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.13/0.37  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.37  Usage: tptp [options] [-file:]file
% 0.13/0.37    -h, -?       prints this message.
% 0.13/0.37    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.37    -m, -model   generate model.
% 0.13/0.37    -p, -proof   generate proof.
% 0.13/0.37    -c, -core    generate unsat core of named formulas.
% 0.13/0.37    -st, -statistics display statistics.
% 0.13/0.37    -t:timeout   set timeout (in second).
% 0.13/0.37    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.37    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.37    -<param>:<value> configuration parameter and value.
% 0.13/0.37    -o:<output-file> file to place output in.
% 0.18/0.45  % SZS status Unsatisfiable
% 0.18/0.45  % SZS output start Proof
% 0.18/0.45  tff(element_of_set_type, type, (
% 0.18/0.45     element_of_set: ( $i * $i ) > $o)).
% 0.18/0.45  tff(union_of_members_type, type, (
% 0.18/0.45     union_of_members: $i > $i)).
% 0.18/0.45  tff(f_type, type, (
% 0.18/0.45     f: $i)).
% 0.18/0.45  tff(in_1st_set_type, type, (
% 0.18/0.45     in_1st_set: ( $i * $i ) > $i)).
% 0.18/0.45  tff(cx_type, type, (
% 0.18/0.45     cx: $i)).
% 0.18/0.45  tff(f1_type, type, (
% 0.18/0.45     f1: ( $i * $i ) > $i)).
% 0.18/0.45  tff(top_of_basis_type, type, (
% 0.18/0.45     top_of_basis: $i > $i)).
% 0.18/0.45  tff(subset_sets_type, type, (
% 0.18/0.45     subset_sets: ( $i * $i ) > $o)).
% 0.18/0.45  tff(element_of_collection_type, type, (
% 0.18/0.45     element_of_collection: ( $i * $i ) > $o)).
% 0.18/0.45  tff(equal_sets_type, type, (
% 0.18/0.45     equal_sets: ( $i * $i ) > $o)).
% 0.18/0.45  tff(basis_type, type, (
% 0.18/0.45     basis: ( $i * $i ) > $o)).
% 0.18/0.45  tff(f10_type, type, (
% 0.18/0.45     f10: ( $i * $i * $i ) > $i)).
% 0.18/0.45  tff(1,assumption,(element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f))), introduced(assumption)).
% 0.18/0.45  tff(2,plain,
% 0.18/0.45      ((~subset_sets(union_of_members(top_of_basis(f)), cx)) <=> (~subset_sets(union_of_members(top_of_basis(f)), cx))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(3,axiom,(~subset_sets(union_of_members(top_of_basis(f)), cx)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_1a_2')).
% 0.18/0.45  tff(4,plain,
% 0.18/0.45      (~subset_sets(union_of_members(top_of_basis(f)), cx)),
% 0.18/0.45      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.45  tff(5,plain,
% 0.18/0.45      (^[Y: $i, X: $i] : refl((subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X)) <=> (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X)))),
% 0.18/0.45      inference(bind,[status(th)],[])).
% 0.18/0.45  tff(6,plain,
% 0.18/0.45      (![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X)) <=> ![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))),
% 0.18/0.45      inference(quant_intro,[status(thm)],[5])).
% 0.18/0.45  tff(7,plain,
% 0.18/0.45      (![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X)) <=> ![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(8,axiom,(![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','set_theory_4')).
% 0.18/0.45  tff(9,plain,
% 0.18/0.45      (![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))),
% 0.18/0.45      inference(modus_ponens,[status(thm)],[8, 7])).
% 0.18/0.45  tff(10,plain,(
% 0.18/0.45      ![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))),
% 0.18/0.45      inference(skolemize,[status(sab)],[9])).
% 0.18/0.45  tff(11,plain,
% 0.18/0.45      (![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))),
% 0.18/0.45      inference(modus_ponens,[status(thm)],[10, 6])).
% 0.18/0.45  tff(12,plain,
% 0.18/0.45      (((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | (subset_sets(union_of_members(top_of_basis(f)), cx) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f))))) <=> ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | subset_sets(union_of_members(top_of_basis(f)), cx) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f))))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(13,plain,
% 0.18/0.45      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | (subset_sets(union_of_members(top_of_basis(f)), cx) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f))))),
% 0.18/0.45      inference(quant_inst,[status(thm)],[])).
% 0.18/0.45  tff(14,plain,
% 0.18/0.45      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | subset_sets(union_of_members(top_of_basis(f)), cx) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))),
% 0.18/0.45      inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.45  tff(15,plain,
% 0.18/0.45      (element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))),
% 0.18/0.45      inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 0.18/0.45  tff(16,plain,
% 0.18/0.45      (^[Vf: $i, U: $i] : refl(((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U))) <=> ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U))))),
% 0.18/0.45      inference(bind,[status(th)],[])).
% 0.18/0.45  tff(17,plain,
% 0.18/0.45      (![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U))) <=> ![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))),
% 0.18/0.45      inference(quant_intro,[status(thm)],[16])).
% 0.18/0.45  tff(18,plain,
% 0.18/0.45      (![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U))) <=> ![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(19,axiom,(![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_of_members_1')).
% 0.18/0.45  tff(20,plain,
% 0.18/0.45      (![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))),
% 0.18/0.45      inference(modus_ponens,[status(thm)],[19, 18])).
% 0.18/0.45  tff(21,plain,(
% 0.18/0.45      ![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))),
% 0.18/0.45      inference(skolemize,[status(sab)],[20])).
% 0.18/0.45  tff(22,plain,
% 0.18/0.45      (![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))),
% 0.18/0.45      inference(modus_ponens,[status(thm)],[21, 17])).
% 0.18/0.45  tff(23,plain,
% 0.18/0.45      (((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | ((~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx))))) <=> ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx))))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(24,plain,
% 0.18/0.45      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | ((~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx))))),
% 0.18/0.45      inference(quant_inst,[status(thm)],[])).
% 0.18/0.45  tff(25,plain,
% 0.18/0.45      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))),
% 0.18/0.45      inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.45  tff(26,plain,
% 0.18/0.45      (element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))),
% 0.18/0.45      inference(unit_resolution,[status(thm)],[25, 22, 15])).
% 0.18/0.45  tff(27,plain,
% 0.18/0.45      (^[Y: $i, X: $i] : refl((subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y))) <=> (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y))))),
% 0.18/0.45      inference(bind,[status(th)],[])).
% 0.18/0.45  tff(28,plain,
% 0.18/0.45      (![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y))) <=> ![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))),
% 0.18/0.45      inference(quant_intro,[status(thm)],[27])).
% 0.18/0.45  tff(29,plain,
% 0.18/0.45      (![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y))) <=> ![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(30,axiom,(![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','set_theory_5')).
% 0.18/0.45  tff(31,plain,
% 0.18/0.45      (![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))),
% 0.18/0.45      inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.46  tff(32,plain,(
% 0.18/0.46      ![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))),
% 0.18/0.46      inference(skolemize,[status(sab)],[31])).
% 0.18/0.46  tff(33,plain,
% 0.18/0.46      (![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[32, 28])).
% 0.18/0.46  tff(34,plain,
% 0.18/0.46      (((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | (subset_sets(union_of_members(top_of_basis(f)), cx) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx)))) <=> ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | subset_sets(union_of_members(top_of_basis(f)), cx) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx)))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(35,plain,
% 0.18/0.46      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | (subset_sets(union_of_members(top_of_basis(f)), cx) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx)))),
% 0.18/0.46      inference(quant_inst,[status(thm)],[])).
% 0.18/0.46  tff(36,plain,
% 0.18/0.46      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | subset_sets(union_of_members(top_of_basis(f)), cx) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.46  tff(37,plain,
% 0.18/0.46      (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx)),
% 0.18/0.46      inference(unit_resolution,[status(thm)],[36, 33, 4])).
% 0.18/0.46  tff(38,plain,
% 0.18/0.46      (^[Y: $i, U: $i, X: $i] : refl((element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y))) <=> (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y))))),
% 0.18/0.46      inference(bind,[status(th)],[])).
% 0.18/0.46  tff(39,plain,
% 0.18/0.46      (![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y))) <=> ![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))),
% 0.18/0.46      inference(quant_intro,[status(thm)],[38])).
% 0.18/0.46  tff(40,plain,
% 0.18/0.46      (![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y))) <=> ![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(41,plain,
% 0.18/0.46      (^[Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~subset_sets(X, Y)) | (~element_of_set(U, X))) <=> ((~element_of_set(U, X)) | (~subset_sets(X, Y)))), ((((~subset_sets(X, Y)) | (~element_of_set(U, X))) | element_of_set(U, Y)) <=> (((~element_of_set(U, X)) | (~subset_sets(X, Y))) | element_of_set(U, Y)))), rewrite((((~element_of_set(U, X)) | (~subset_sets(X, Y))) | element_of_set(U, Y)) <=> (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))), ((((~subset_sets(X, Y)) | (~element_of_set(U, X))) | element_of_set(U, Y)) <=> (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))))),
% 0.18/0.46      inference(bind,[status(th)],[])).
% 0.18/0.46  tff(42,plain,
% 0.18/0.46      (![Y: $i, U: $i, X: $i] : (((~subset_sets(X, Y)) | (~element_of_set(U, X))) | element_of_set(U, Y)) <=> ![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))),
% 0.18/0.46      inference(quant_intro,[status(thm)],[41])).
% 0.18/0.46  tff(43,axiom,(![Y: $i, U: $i, X: $i] : (((~subset_sets(X, Y)) | (~element_of_set(U, X))) | element_of_set(U, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','set_theory_2')).
% 0.18/0.46  tff(44,plain,
% 0.18/0.46      (![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.46  tff(45,plain,
% 0.18/0.46      (![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[44, 40])).
% 0.18/0.46  tff(46,plain,(
% 0.18/0.46      ![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))),
% 0.18/0.46      inference(skolemize,[status(sab)],[45])).
% 0.18/0.46  tff(47,plain,
% 0.18/0.46      (![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[46, 39])).
% 0.18/0.46  tff(48,plain,
% 0.18/0.46      (((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | (element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))) | (~subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) <=> ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))) | (~subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(49,plain,
% 0.18/0.46      ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | (element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))) | (~subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))),
% 0.18/0.46      inference(quant_inst,[status(thm)],[])).
% 0.18/0.46  tff(50,plain,
% 0.18/0.46      ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), cx) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))) | (~subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.46  tff(51,plain,
% 0.18/0.46      (~subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)),
% 0.18/0.46      inference(unit_resolution,[status(thm)],[50, 47, 37, 26])).
% 0.18/0.46  tff(52,plain,
% 0.18/0.46      (((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | (subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx))))) <=> ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx))))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(53,plain,
% 0.18/0.46      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | (subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx))))),
% 0.18/0.46      inference(quant_inst,[status(thm)],[])).
% 0.18/0.46  tff(54,plain,
% 0.18/0.46      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.46  tff(55,plain,
% 0.18/0.46      (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))),
% 0.18/0.46      inference(unit_resolution,[status(thm)],[54, 11, 51])).
% 0.18/0.46  tff(56,plain,
% 0.18/0.46      (^[Vf: $i, U: $i] : refl(((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf)) <=> ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf)))),
% 0.18/0.46      inference(bind,[status(th)],[])).
% 0.18/0.46  tff(57,plain,
% 0.18/0.46      (![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf)) <=> ![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))),
% 0.18/0.46      inference(quant_intro,[status(thm)],[56])).
% 0.18/0.46  tff(58,plain,
% 0.18/0.46      (![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf)) <=> ![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(59,axiom,(![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_of_members_2')).
% 0.18/0.46  tff(60,plain,
% 0.18/0.46      (![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.46  tff(61,plain,(
% 0.18/0.46      ![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))),
% 0.18/0.46      inference(skolemize,[status(sab)],[60])).
% 0.18/0.46  tff(62,plain,
% 0.18/0.46      (![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[61, 57])).
% 0.18/0.46  tff(63,plain,
% 0.18/0.46      (((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | ((~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f)))) <=> ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f)))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(64,plain,
% 0.18/0.46      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | ((~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f)))),
% 0.18/0.46      inference(quant_inst,[status(thm)],[])).
% 0.18/0.46  tff(65,plain,
% 0.18/0.46      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | (~element_of_set(in_1st_set(union_of_members(top_of_basis(f)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.46  tff(66,plain,
% 0.18/0.46      (element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f))),
% 0.18/0.46      inference(unit_resolution,[status(thm)],[65, 62, 15])).
% 0.18/0.46  tff(67,plain,
% 0.18/0.46      (^[Vf: $i, Uu1: $i, U: $i] : refl(((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf))) <=> ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf))))),
% 0.18/0.46      inference(bind,[status(th)],[])).
% 0.18/0.46  tff(68,plain,
% 0.18/0.46      (![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf))) <=> ![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))),
% 0.18/0.46      inference(quant_intro,[status(thm)],[67])).
% 0.18/0.46  tff(69,plain,
% 0.18/0.46      (![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf))) <=> ![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(70,plain,
% 0.18/0.46      (^[Vf: $i, Uu1: $i, U: $i] : trans(monotonicity(rewrite((element_of_set(U, union_of_members(Vf)) | (~element_of_set(U, Uu1))) <=> ((~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))), (((element_of_set(U, union_of_members(Vf)) | (~element_of_set(U, Uu1))) | (~element_of_collection(Uu1, Vf))) <=> (((~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf))) | (~element_of_collection(Uu1, Vf))))), rewrite((((~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf))) | (~element_of_collection(Uu1, Vf))) <=> ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))), (((element_of_set(U, union_of_members(Vf)) | (~element_of_set(U, Uu1))) | (~element_of_collection(Uu1, Vf))) <=> ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))))),
% 0.18/0.46      inference(bind,[status(th)],[])).
% 0.18/0.46  tff(71,plain,
% 0.18/0.46      (![Vf: $i, Uu1: $i, U: $i] : ((element_of_set(U, union_of_members(Vf)) | (~element_of_set(U, Uu1))) | (~element_of_collection(Uu1, Vf))) <=> ![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))),
% 0.18/0.46      inference(quant_intro,[status(thm)],[70])).
% 0.18/0.46  tff(72,axiom,(![Vf: $i, Uu1: $i, U: $i] : ((element_of_set(U, union_of_members(Vf)) | (~element_of_set(U, Uu1))) | (~element_of_collection(Uu1, Vf)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_of_members_3')).
% 0.18/0.46  tff(73,plain,
% 0.18/0.46      (![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.46  tff(74,plain,
% 0.18/0.46      (![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[73, 69])).
% 0.18/0.46  tff(75,plain,(
% 0.18/0.46      ![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))),
% 0.18/0.46      inference(skolemize,[status(sab)],[74])).
% 0.18/0.46  tff(76,plain,
% 0.18/0.46      (![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))),
% 0.18/0.46      inference(modus_ponens,[status(thm)],[75, 68])).
% 0.18/0.46  tff(77,plain,
% 0.18/0.46      (((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | ((~element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f))))) <=> ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f))))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(78,plain,
% 0.18/0.46      ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | ((~element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f))))),
% 0.18/0.46      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(79,plain,
% 0.18/0.47      ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), top_of_basis(f))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.47  tff(80,plain,
% 0.18/0.47      (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[79, 76, 66, 55])).
% 0.18/0.47  tff(81,plain,
% 0.18/0.47      (((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx))))) <=> ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx))))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(82,plain,
% 0.18/0.47      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx))))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(83,plain,
% 0.18/0.47      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.47  tff(84,plain,
% 0.18/0.47      (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[83, 22, 80])).
% 0.18/0.47  tff(85,plain,
% 0.18/0.47      (((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | (subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx)))) <=> ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx)))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(86,plain,
% 0.18/0.47      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | (subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx)))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(87,plain,
% 0.18/0.47      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | subset_sets(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.47  tff(88,plain,
% 0.18/0.47      (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx)),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[87, 33, 51])).
% 0.18/0.47  tff(89,plain,
% 0.18/0.47      (((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) | (~subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) <=> ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) | (~subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(90,plain,
% 0.18/0.47      ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) | (~subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(91,plain,
% 0.18/0.47      ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) | (~subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[90, 89])).
% 0.18/0.47  tff(92,plain,
% 0.18/0.47      (~subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[91, 47, 88, 84])).
% 0.18/0.47  tff(93,plain,
% 0.18/0.47      (((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | (subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx)))) <=> ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx)))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(94,plain,
% 0.18/0.47      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | (subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx)))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(95,plain,
% 0.18/0.47      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | (~element_of_set(in_1st_set(X, Y), Y)))) | subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.47  tff(96,plain,
% 0.18/0.47      (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx)),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[95, 33, 92])).
% 0.18/0.47  tff(97,plain,
% 0.18/0.47      (basis(cx, f) <=> basis(cx, f)),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(98,axiom,(basis(cx, f)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_1a_1')).
% 0.18/0.47  tff(99,plain,
% 0.18/0.47      (basis(cx, f)),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.47  tff(100,plain,
% 0.18/0.47      (^[Vf: $i, X: $i] : refl(((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X)) <=> ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X)))),
% 0.18/0.47      inference(bind,[status(th)],[])).
% 0.18/0.47  tff(101,plain,
% 0.18/0.47      (![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X)) <=> ![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))),
% 0.18/0.47      inference(quant_intro,[status(thm)],[100])).
% 0.18/0.47  tff(102,plain,
% 0.18/0.47      (![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X)) <=> ![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(103,axiom,(![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','basis_for_topology_28')).
% 0.18/0.47  tff(104,plain,
% 0.18/0.47      (![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.47  tff(105,plain,(
% 0.18/0.47      ![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))),
% 0.18/0.47      inference(skolemize,[status(sab)],[104])).
% 0.18/0.47  tff(106,plain,
% 0.18/0.47      (![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[105, 101])).
% 0.18/0.47  tff(107,plain,
% 0.18/0.47      (((~![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))) | ((~basis(cx, f)) | equal_sets(union_of_members(f), cx))) <=> ((~![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))) | (~basis(cx, f)) | equal_sets(union_of_members(f), cx))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(108,plain,
% 0.18/0.47      ((~![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))) | ((~basis(cx, f)) | equal_sets(union_of_members(f), cx))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(109,plain,
% 0.18/0.47      ((~![Vf: $i, X: $i] : ((~basis(X, Vf)) | equal_sets(union_of_members(Vf), X))) | (~basis(cx, f)) | equal_sets(union_of_members(f), cx)),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[108, 107])).
% 0.18/0.47  tff(110,plain,
% 0.18/0.47      (equal_sets(union_of_members(f), cx)),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[109, 106, 99])).
% 0.18/0.47  tff(111,plain,
% 0.18/0.47      (^[Y: $i, X: $i] : refl(((~equal_sets(X, Y)) | subset_sets(X, Y)) <=> ((~equal_sets(X, Y)) | subset_sets(X, Y)))),
% 0.18/0.47      inference(bind,[status(th)],[])).
% 0.18/0.47  tff(112,plain,
% 0.18/0.47      (![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y)) <=> ![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))),
% 0.18/0.47      inference(quant_intro,[status(thm)],[111])).
% 0.18/0.47  tff(113,plain,
% 0.18/0.47      (![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y)) <=> ![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(114,axiom,(![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','set_theory_3')).
% 0.18/0.47  tff(115,plain,
% 0.18/0.47      (![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.47  tff(116,plain,(
% 0.18/0.47      ![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))),
% 0.18/0.47      inference(skolemize,[status(sab)],[115])).
% 0.18/0.47  tff(117,plain,
% 0.18/0.47      (![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[116, 112])).
% 0.18/0.47  tff(118,plain,
% 0.18/0.47      (((~![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))) | ((~equal_sets(union_of_members(f), cx)) | subset_sets(union_of_members(f), cx))) <=> ((~![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))) | (~equal_sets(union_of_members(f), cx)) | subset_sets(union_of_members(f), cx))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(119,plain,
% 0.18/0.47      ((~![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))) | ((~equal_sets(union_of_members(f), cx)) | subset_sets(union_of_members(f), cx))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(120,plain,
% 0.18/0.47      ((~![Y: $i, X: $i] : ((~equal_sets(X, Y)) | subset_sets(X, Y))) | (~equal_sets(union_of_members(f), cx)) | subset_sets(union_of_members(f), cx)),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[119, 118])).
% 0.18/0.47  tff(121,plain,
% 0.18/0.47      (subset_sets(union_of_members(f), cx)),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[120, 117, 110])).
% 0.18/0.47  tff(122,plain,
% 0.18/0.47      (((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f))) | (~subset_sets(union_of_members(f), cx)))) <=> ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f))) | (~subset_sets(union_of_members(f), cx)))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(123,plain,
% 0.18/0.47      ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f))) | (~subset_sets(union_of_members(f), cx)))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(124,plain,
% 0.18/0.47      ((~![Y: $i, U: $i, X: $i] : (element_of_set(U, Y) | (~element_of_set(U, X)) | (~subset_sets(X, Y)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), cx) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f))) | (~subset_sets(union_of_members(f), cx))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[123, 122])).
% 0.18/0.47  tff(125,plain,
% 0.18/0.47      ($false),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[124, 47, 121, 96, 1])).
% 0.18/0.47  tff(126,plain,(~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47  tff(127,plain,
% 0.18/0.47      (((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | (subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx))))) <=> ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx))))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(128,plain,
% 0.18/0.47      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | (subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx))))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(129,plain,
% 0.18/0.47      ((~![Y: $i, X: $i] : (subset_sets(X, Y) | element_of_set(in_1st_set(X, Y), X))) | subset_sets(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[128, 127])).
% 0.18/0.47  tff(130,plain,
% 0.18/0.47      (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[129, 11, 92])).
% 0.18/0.47  tff(131,plain,
% 0.18/0.47      (((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f)))) <=> ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f)))),
% 0.18/0.47      inference(rewrite,[status(thm)],[])).
% 0.18/0.47  tff(132,plain,
% 0.18/0.47      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f)))),
% 0.18/0.47      inference(quant_inst,[status(thm)],[])).
% 0.18/0.47  tff(133,plain,
% 0.18/0.47      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f))),
% 0.18/0.47      inference(modus_ponens,[status(thm)],[132, 131])).
% 0.18/0.47  tff(134,plain,
% 0.18/0.47      (element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f))),
% 0.18/0.47      inference(unit_resolution,[status(thm)],[133, 62, 80])).
% 0.18/0.48  tff(135,plain,
% 0.18/0.48      (((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | ((~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f))))) <=> ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f))))),
% 0.18/0.48      inference(rewrite,[status(thm)],[])).
% 0.18/0.48  tff(136,plain,
% 0.18/0.48      ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | ((~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f))))),
% 0.18/0.48      inference(quant_inst,[status(thm)],[])).
% 0.18/0.48  tff(137,plain,
% 0.18/0.48      ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), top_of_basis(f))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.48  tff(138,plain,
% 0.18/0.48      (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))),
% 0.18/0.48      inference(unit_resolution,[status(thm)],[137, 76, 134, 130])).
% 0.18/0.48  tff(139,plain,
% 0.18/0.48      (((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f)))) <=> ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f)))),
% 0.18/0.48      inference(rewrite,[status(thm)],[])).
% 0.18/0.48  tff(140,plain,
% 0.18/0.48      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f)))),
% 0.18/0.48      inference(quant_inst,[status(thm)],[])).
% 0.18/0.48  tff(141,plain,
% 0.18/0.48      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_collection(f1(Vf, U), Vf))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[140, 139])).
% 0.18/0.48  tff(142,plain,
% 0.18/0.48      (element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))),
% 0.18/0.48      inference(unit_resolution,[status(thm)],[141, 62, 138])).
% 0.18/0.48  tff(143,plain,
% 0.18/0.48      (((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))))) <=> ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))))),
% 0.18/0.48      inference(rewrite,[status(thm)],[])).
% 0.18/0.48  tff(144,plain,
% 0.18/0.48      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))))),
% 0.18/0.48      inference(quant_inst,[status(thm)],[])).
% 0.18/0.48  tff(145,plain,
% 0.18/0.48      ((~![Vf: $i, U: $i] : ((~element_of_set(U, union_of_members(Vf))) | element_of_set(U, f1(Vf, U)))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(top_of_basis(f)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[144, 143])).
% 0.18/0.48  tff(146,plain,
% 0.18/0.48      (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))),
% 0.18/0.48      inference(unit_resolution,[status(thm)],[145, 22, 138])).
% 0.18/0.48  tff(147,plain,
% 0.18/0.48      (^[Vf: $i, U: $i, X: $i] : refl(((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf)) <=> ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf)))),
% 0.18/0.48      inference(bind,[status(th)],[])).
% 0.18/0.48  tff(148,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf)) <=> ![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))),
% 0.18/0.48      inference(quant_intro,[status(thm)],[147])).
% 0.18/0.48  tff(149,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf)) <=> ![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))),
% 0.18/0.48      inference(rewrite,[status(thm)],[])).
% 0.18/0.48  tff(150,plain,
% 0.18/0.48      (^[Vf: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) <=> ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))))), ((((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) | element_of_collection(f10(Vf, U, X), Vf)) <=> (((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf)))) | element_of_collection(f10(Vf, U, X), Vf)))), rewrite((((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf)))) | element_of_collection(f10(Vf, U, X), Vf)) <=> ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))), ((((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) | element_of_collection(f10(Vf, U, X), Vf)) <=> ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))))),
% 0.18/0.48      inference(bind,[status(th)],[])).
% 0.18/0.48  tff(151,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : (((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) | element_of_collection(f10(Vf, U, X), Vf)) <=> ![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))),
% 0.18/0.48      inference(quant_intro,[status(thm)],[150])).
% 0.18/0.48  tff(152,axiom,(![Vf: $i, U: $i, X: $i] : (((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) | element_of_collection(f10(Vf, U, X), Vf))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','topology_generated_38')).
% 0.18/0.48  tff(153,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[152, 151])).
% 0.18/0.48  tff(154,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[153, 149])).
% 0.18/0.48  tff(155,plain,(
% 0.18/0.48      ![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))),
% 0.18/0.48      inference(skolemize,[status(sab)],[154])).
% 0.18/0.48  tff(156,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[155, 148])).
% 0.18/0.48  tff(157,plain,
% 0.18/0.48      (((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f))) <=> ((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f))),
% 0.18/0.48      inference(rewrite,[status(thm)],[])).
% 0.18/0.48  tff(158,plain,
% 0.18/0.48      ((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f))),
% 0.18/0.48      inference(quant_inst,[status(thm)],[])).
% 0.18/0.48  tff(159,plain,
% 0.18/0.48      ((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))) | element_of_collection(f10(Vf, U, X), Vf))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f)),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[158, 157])).
% 0.18/0.48  tff(160,plain,
% 0.18/0.48      (element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f)),
% 0.18/0.48      inference(unit_resolution,[status(thm)],[159, 156, 146, 142])).
% 0.18/0.48  tff(161,plain,
% 0.18/0.48      (^[Vf: $i, U: $i, X: $i] : refl(((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf)))) <=> ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf)))))),
% 0.18/0.48      inference(bind,[status(th)],[])).
% 0.18/0.48  tff(162,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf)))) <=> ![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))),
% 0.18/0.48      inference(quant_intro,[status(thm)],[161])).
% 0.18/0.48  tff(163,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf)))) <=> ![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))),
% 0.18/0.48      inference(rewrite,[status(thm)],[])).
% 0.18/0.48  tff(164,plain,
% 0.18/0.48      (^[Vf: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) <=> ((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf))))), ((((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) | element_of_set(X, f10(Vf, U, X))) <=> (((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf)))) | element_of_set(X, f10(Vf, U, X))))), rewrite((((~element_of_set(X, U)) | (~element_of_collection(U, top_of_basis(Vf)))) | element_of_set(X, f10(Vf, U, X))) <=> ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))), ((((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) | element_of_set(X, f10(Vf, U, X))) <=> ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))))),
% 0.18/0.48      inference(bind,[status(th)],[])).
% 0.18/0.48  tff(165,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : (((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) | element_of_set(X, f10(Vf, U, X))) <=> ![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))),
% 0.18/0.48      inference(quant_intro,[status(thm)],[164])).
% 0.18/0.48  tff(166,axiom,(![Vf: $i, U: $i, X: $i] : (((~element_of_collection(U, top_of_basis(Vf))) | (~element_of_set(X, U))) | element_of_set(X, f10(Vf, U, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','topology_generated_37')).
% 0.18/0.48  tff(167,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[166, 165])).
% 0.18/0.48  tff(168,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[167, 163])).
% 0.18/0.48  tff(169,plain,(
% 0.18/0.48      ![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))),
% 0.18/0.48      inference(skolemize,[status(sab)],[168])).
% 0.18/0.48  tff(170,plain,
% 0.18/0.48      (![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))),
% 0.18/0.48      inference(modus_ponens,[status(thm)],[169, 162])).
% 0.18/0.48  tff(171,plain,
% 0.18/0.48      (((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))))) <=> ((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))))),
% 0.18/0.49      inference(rewrite,[status(thm)],[])).
% 0.18/0.49  tff(172,plain,
% 0.18/0.49      (((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f)))) <=> ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))))),
% 0.18/0.49      inference(rewrite,[status(thm)],[])).
% 0.18/0.49  tff(173,plain,
% 0.18/0.49      (((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))))) <=> ((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))))),
% 0.18/0.49      inference(monotonicity,[status(thm)],[172])).
% 0.18/0.49  tff(174,plain,
% 0.18/0.49      (((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))))) <=> ((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))))),
% 0.18/0.49      inference(transitivity,[status(thm)],[173, 171])).
% 0.18/0.49  tff(175,plain,
% 0.18/0.49      ((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))) | ((~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))))),
% 0.18/0.49      inference(quant_inst,[status(thm)],[])).
% 0.18/0.49  tff(176,plain,
% 0.18/0.49      ((~![Vf: $i, U: $i, X: $i] : ((~element_of_set(X, U)) | element_of_set(X, f10(Vf, U, X)) | (~element_of_collection(U, top_of_basis(Vf))))) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | (~element_of_collection(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), top_of_basis(f))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))),
% 0.18/0.49      inference(modus_ponens,[status(thm)],[175, 174])).
% 0.18/0.49  tff(177,plain,
% 0.18/0.49      (element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))),
% 0.18/0.49      inference(unit_resolution,[status(thm)],[176, 170, 146, 142])).
% 0.18/0.49  tff(178,plain,
% 0.18/0.49      (((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | ((~element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f)) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f)))) <=> ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | (~element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f)) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f)))),
% 0.18/0.49      inference(rewrite,[status(thm)],[])).
% 0.18/0.49  tff(179,plain,
% 0.18/0.49      ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | ((~element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f)) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f)))),
% 0.18/0.49      inference(quant_inst,[status(thm)],[])).
% 0.18/0.49  tff(180,plain,
% 0.18/0.49      ((~![Vf: $i, Uu1: $i, U: $i] : ((~element_of_collection(Uu1, Vf)) | (~element_of_set(U, Uu1)) | element_of_set(U, union_of_members(Vf)))) | (~element_of_collection(f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), f)) | (~element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), f10(f, f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)), in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx)))) | element_of_set(in_1st_set(f1(top_of_basis(f), in_1st_set(f1(top_of_basis(f), in_1st_set(union_of_members(top_of_basis(f)), cx)), cx)), cx), union_of_members(f))),
% 0.18/0.49      inference(modus_ponens,[status(thm)],[179, 178])).
% 0.18/0.49  tff(181,plain,
% 0.18/0.49      ($false),
% 0.18/0.49      inference(unit_resolution,[status(thm)],[180, 76, 177, 160, 126])).
% 0.18/0.49  % SZS output end Proof
%------------------------------------------------------------------------------