TSTP Solution File: SET014-4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET014-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Tue Sep 20 05:04:46 EDT 2022
% Result : Unsatisfiable 0.11s 0.35s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET014-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 01:20:08 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.11/0.35 % SZS status Unsatisfiable
% 0.11/0.35 % SZS output start Proof
% 0.11/0.35 tff(member_type, type, (
% 0.11/0.35 member: ( $i * $i ) > $o)).
% 0.11/0.35 tff(as_type, type, (
% 0.11/0.35 as: $i)).
% 0.11/0.35 tff(f17_type, type, (
% 0.11/0.35 f17: ( $i * $i ) > $i)).
% 0.11/0.35 tff(cs_type, type, (
% 0.11/0.35 cs: $i)).
% 0.11/0.35 tff(union_type, type, (
% 0.11/0.35 union: ( $i * $i ) > $i)).
% 0.11/0.35 tff(bs_type, type, (
% 0.11/0.35 bs: $i)).
% 0.11/0.35 tff(complement_type, type, (
% 0.11/0.35 complement: $i > $i)).
% 0.11/0.35 tff(subset_type, type, (
% 0.11/0.35 subset: ( $i * $i ) > $o)).
% 0.11/0.35 tff(little_set_type, type, (
% 0.11/0.35 little_set: $i > $o)).
% 0.11/0.35 tff(intersection_type, type, (
% 0.11/0.35 intersection: ( $i * $i ) > $i)).
% 0.11/0.35 tff(1,assumption,(member(f17(union(as, bs), cs), bs)), introduced(assumption)).
% 0.11/0.35 tff(2,plain,
% 0.11/0.35 ((~subset(union(as, bs), cs)) <=> (~subset(union(as, bs), cs))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(3,axiom,(~subset(union(as, bs), cs)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_a_union_b_subset_of_c')).
% 0.11/0.35 tff(4,plain,
% 0.11/0.35 (~subset(union(as, bs), cs)),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.35 tff(5,plain,
% 0.11/0.35 (^[Y: $i, X: $i] : refl((subset(X, Y) | (~member(f17(X, Y), Y))) <=> (subset(X, Y) | (~member(f17(X, Y), Y))))),
% 0.11/0.35 inference(bind,[status(th)],[])).
% 0.11/0.35 tff(6,plain,
% 0.11/0.35 (![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y))) <=> ![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 0.11/0.35 inference(quant_intro,[status(thm)],[5])).
% 0.11/0.35 tff(7,plain,
% 0.11/0.35 (![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y))) <=> ![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(8,axiom,(![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset3')).
% 0.11/0.35 tff(9,plain,
% 0.11/0.35 (![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.11/0.35 tff(10,plain,(
% 0.11/0.35 ![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 0.11/0.35 inference(skolemize,[status(sab)],[9])).
% 0.11/0.35 tff(11,plain,
% 0.11/0.35 (![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.11/0.35 tff(12,plain,
% 0.11/0.35 (((~![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))) | (subset(union(as, bs), cs) | (~member(f17(union(as, bs), cs), cs)))) <=> ((~![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))) | subset(union(as, bs), cs) | (~member(f17(union(as, bs), cs), cs)))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(13,plain,
% 0.11/0.35 ((~![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))) | (subset(union(as, bs), cs) | (~member(f17(union(as, bs), cs), cs)))),
% 0.11/0.35 inference(quant_inst,[status(thm)],[])).
% 0.11/0.35 tff(14,plain,
% 0.11/0.35 ((~![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))) | subset(union(as, bs), cs) | (~member(f17(union(as, bs), cs), cs))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.35 tff(15,plain,
% 0.11/0.35 (~member(f17(union(as, bs), cs), cs)),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 0.11/0.35 tff(16,plain,
% 0.11/0.35 (subset(bs, cs) <=> subset(bs, cs)),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(17,axiom,(subset(bs, cs)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_subset_of_c')).
% 0.11/0.35 tff(18,plain,
% 0.11/0.35 (subset(bs, cs)),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.11/0.35 tff(19,plain,
% 0.11/0.35 (^[Y: $i, U: $i, X: $i] : refl(((~member(U, X)) | member(U, Y) | (~subset(X, Y))) <=> ((~member(U, X)) | member(U, Y) | (~subset(X, Y))))),
% 0.11/0.35 inference(bind,[status(th)],[])).
% 0.11/0.35 tff(20,plain,
% 0.11/0.35 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y))) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 0.11/0.35 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.35 tff(21,plain,
% 0.11/0.35 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y))) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(22,plain,
% 0.11/0.35 (^[Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~subset(X, Y)) | (~member(U, X))) <=> ((~member(U, X)) | (~subset(X, Y)))), ((((~subset(X, Y)) | (~member(U, X))) | member(U, Y)) <=> (((~member(U, X)) | (~subset(X, Y))) | member(U, Y)))), rewrite((((~member(U, X)) | (~subset(X, Y))) | member(U, Y)) <=> ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))), ((((~subset(X, Y)) | (~member(U, X))) | member(U, Y)) <=> ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![Y: $i, U: $i, X: $i] : (((~subset(X, Y)) | (~member(U, X))) | member(U, Y)) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.36 tff(24,axiom,(![Y: $i, U: $i, X: $i] : (((~subset(X, Y)) | (~member(U, X))) | member(U, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset1')).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.11/0.36 tff(27,plain,(
% 0.11/0.36 ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[26])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)) | (~subset(bs, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)) | (~subset(bs, cs)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (((~member(f17(union(as, bs), cs), bs)) | member(f17(union(as, bs), cs), cs) | (~subset(bs, cs))) <=> (member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)) | (~subset(bs, cs)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), bs)) | member(f17(union(as, bs), cs), cs) | (~subset(bs, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)) | (~subset(bs, cs))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[30])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), bs)) | member(f17(union(as, bs), cs), cs) | (~subset(bs, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)) | (~subset(bs, cs)))),
% 0.11/0.36 inference(transitivity,[status(thm)],[31, 29])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), bs)) | member(f17(union(as, bs), cs), cs) | (~subset(bs, cs)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)) | (~subset(bs, cs))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[34, 28, 18, 15, 1])).
% 0.11/0.36 tff(36,plain,(~member(f17(union(as, bs), cs), bs)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(37,assumption,(~member(f17(union(as, bs), cs), complement(bs))), introduced(assumption)).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((union(X, Y) = complement(intersection(complement(X), complement(Y)))) <=> (union(X, Y) = complement(intersection(complement(X), complement(Y)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y)))) <=> ![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y)))) <=> ![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(41,axiom,(![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union')).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.36 tff(43,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[42])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))) | (union(as, bs) = complement(intersection(complement(as), complement(bs))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 (union(as, bs) = complement(intersection(complement(as), complement(bs)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 (complement(intersection(complement(as), complement(bs))) = union(as, bs)),
% 0.11/0.36 inference(symmetry,[status(thm)],[46])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 (member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))) <=> member(f17(union(as, bs), cs), union(as, bs))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[47])).
% 0.11/0.36 tff(49,plain,
% 0.11/0.36 (member(f17(union(as, bs), cs), union(as, bs)) <=> member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))),
% 0.11/0.36 inference(symmetry,[status(thm)],[48])).
% 0.11/0.36 tff(50,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((subset(X, Y) | member(f17(X, Y), X)) <=> (subset(X, Y) | member(f17(X, Y), X)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(51,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X)) <=> ![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[50])).
% 0.11/0.36 tff(52,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X)) <=> ![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(53,axiom,(![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset2')).
% 0.11/0.36 tff(54,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.11/0.36 tff(55,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 0.11/0.36 inference(skolemize,[status(sab)],[54])).
% 0.11/0.36 tff(56,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.11/0.36 tff(57,plain,
% 0.11/0.36 (((~![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))) | (subset(union(as, bs), cs) | member(f17(union(as, bs), cs), union(as, bs)))) <=> ((~![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))) | subset(union(as, bs), cs) | member(f17(union(as, bs), cs), union(as, bs)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(58,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))) | (subset(union(as, bs), cs) | member(f17(union(as, bs), cs), union(as, bs)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(59,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))) | subset(union(as, bs), cs) | member(f17(union(as, bs), cs), union(as, bs))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.11/0.36 tff(60,plain,
% 0.11/0.36 (member(f17(union(as, bs), cs), union(as, bs))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[59, 56, 4])).
% 0.11/0.36 tff(61,plain,
% 0.11/0.36 (member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[60, 49])).
% 0.11/0.36 tff(62,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((little_set(X) | (~member(X, Y))) <=> (little_set(X) | (~member(X, Y))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(63,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[62])).
% 0.11/0.36 tff(64,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(65,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : rewrite(((~member(X, Y)) | little_set(X)) <=> (little_set(X) | (~member(X, Y))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(66,plain,
% 0.11/0.36 (![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X)) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[65])).
% 0.11/0.36 tff(67,axiom,(![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a2')).
% 0.11/0.36 tff(68,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.36 tff(69,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.11/0.36 tff(70,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[69])).
% 0.11/0.36 tff(71,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.11/0.36 tff(72,plain,
% 0.11/0.36 (((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))) <=> ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(73,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(74,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.11/0.36 tff(75,plain,
% 0.11/0.36 (little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.11/0.36 tff(76,plain,
% 0.11/0.36 (little_set(f17(union(as, bs), cs))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[75, 61])).
% 0.11/0.36 tff(77,plain,
% 0.11/0.36 (^[Z: $i, X: $i] : refl((member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(78,plain,
% 0.11/0.36 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[77])).
% 0.11/0.36 tff(79,plain,
% 0.11/0.36 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(80,plain,
% 0.11/0.36 (^[Z: $i, X: $i] : trans(monotonicity(rewrite((member(Z, complement(X)) | (~little_set(Z))) <=> (member(Z, complement(X)) | (~little_set(Z)))), (((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)))), rewrite(((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))), (((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(81,plain,
% 0.11/0.36 (![Z: $i, X: $i] : ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[80])).
% 0.11/0.36 tff(82,axiom,(![Z: $i, X: $i] : ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','complement2')).
% 0.11/0.36 tff(83,plain,
% 0.11/0.36 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.11/0.36 tff(84,plain,
% 0.11/0.36 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.11/0.36 tff(85,plain,(
% 0.11/0.36 ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[84])).
% 0.11/0.36 tff(86,plain,
% 0.11/0.36 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.11/0.36 tff(87,plain,
% 0.11/0.36 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(bs)) | member(f17(union(as, bs), cs), bs))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(bs)) | member(f17(union(as, bs), cs), bs))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(88,plain,
% 0.11/0.36 ((member(f17(union(as, bs), cs), bs) | member(f17(union(as, bs), cs), complement(bs)) | (~little_set(f17(union(as, bs), cs)))) <=> ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(bs)) | member(f17(union(as, bs), cs), bs))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(89,plain,
% 0.11/0.36 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f17(union(as, bs), cs), bs) | member(f17(union(as, bs), cs), complement(bs)) | (~little_set(f17(union(as, bs), cs))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(bs)) | member(f17(union(as, bs), cs), bs)))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[88])).
% 0.11/0.36 tff(90,plain,
% 0.11/0.36 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f17(union(as, bs), cs), bs) | member(f17(union(as, bs), cs), complement(bs)) | (~little_set(f17(union(as, bs), cs))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(bs)) | member(f17(union(as, bs), cs), bs))),
% 0.11/0.36 inference(transitivity,[status(thm)],[89, 87])).
% 0.11/0.36 tff(91,plain,
% 0.11/0.36 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f17(union(as, bs), cs), bs) | member(f17(union(as, bs), cs), complement(bs)) | (~little_set(f17(union(as, bs), cs))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(92,plain,
% 0.11/0.36 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(bs)) | member(f17(union(as, bs), cs), bs)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.11/0.36 tff(93,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[92, 86, 76, 37, 36])).
% 0.11/0.36 tff(94,plain,(member(f17(union(as, bs), cs), complement(bs))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(95,plain,
% 0.11/0.36 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(96,plain,
% 0.11/0.36 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[95])).
% 0.11/0.36 tff(97,plain,
% 0.11/0.36 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(98,plain,
% 0.11/0.36 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(99,plain,
% 0.11/0.36 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[98])).
% 0.11/0.36 tff(100,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','complement1')).
% 0.11/0.36 tff(101,plain,
% 0.11/0.36 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.11/0.36 tff(102,plain,
% 0.11/0.36 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.11/0.36 tff(103,plain,(
% 0.11/0.36 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[102])).
% 0.11/0.36 tff(104,plain,
% 0.11/0.36 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.11/0.36 tff(105,plain,
% 0.11/0.36 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(106,plain,
% 0.11/0.36 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(107,plain,
% 0.11/0.36 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.11/0.36 tff(108,plain,
% 0.11/0.36 ((~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.11/0.36 tff(109,plain,
% 0.11/0.36 (~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[108, 61])).
% 0.11/0.36 tff(110,plain,
% 0.11/0.36 (^[Z: $i, Y: $i, X: $i] : refl((member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(111,plain,
% 0.11/0.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[110])).
% 0.11/0.36 tff(112,plain,
% 0.11/0.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(113,plain,
% 0.11/0.36 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((member(Z, intersection(X, Y)) | (~member(Z, X))) <=> (member(Z, intersection(X, Y)) | (~member(Z, X)))), (((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> ((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))))), rewrite(((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))), (((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(114,plain,
% 0.11/0.36 (![Z: $i, Y: $i, X: $i] : ((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[113])).
% 0.11/0.36 tff(115,axiom,(![Z: $i, Y: $i, X: $i] : ((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection3')).
% 0.11/0.36 tff(116,plain,
% 0.11/0.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.11/0.36 tff(117,plain,
% 0.11/0.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.11/0.36 tff(118,plain,(
% 0.11/0.36 ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[117])).
% 0.11/0.36 tff(119,plain,
% 0.11/0.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.11/0.36 tff(120,plain,
% 0.11/0.36 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(121,plain,
% 0.11/0.36 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(122,plain,
% 0.11/0.36 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.11/0.36 tff(123,plain,
% 0.11/0.36 ((~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[122, 119, 109])).
% 0.11/0.36 tff(124,plain,
% 0.11/0.36 (~member(f17(union(as, bs), cs), complement(as))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[123, 94])).
% 0.11/0.36 tff(125,plain,
% 0.11/0.36 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(as)) | member(f17(union(as, bs), cs), as))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(as)) | member(f17(union(as, bs), cs), as))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(126,plain,
% 0.11/0.36 ((member(f17(union(as, bs), cs), as) | member(f17(union(as, bs), cs), complement(as)) | (~little_set(f17(union(as, bs), cs)))) <=> ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(as)) | member(f17(union(as, bs), cs), as))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(127,plain,
% 0.11/0.36 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f17(union(as, bs), cs), as) | member(f17(union(as, bs), cs), complement(as)) | (~little_set(f17(union(as, bs), cs))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(as)) | member(f17(union(as, bs), cs), as)))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[126])).
% 0.11/0.36 tff(128,plain,
% 0.11/0.36 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f17(union(as, bs), cs), as) | member(f17(union(as, bs), cs), complement(as)) | (~little_set(f17(union(as, bs), cs))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(as)) | member(f17(union(as, bs), cs), as))),
% 0.11/0.36 inference(transitivity,[status(thm)],[127, 125])).
% 0.11/0.36 tff(129,plain,
% 0.11/0.36 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f17(union(as, bs), cs), as) | member(f17(union(as, bs), cs), complement(as)) | (~little_set(f17(union(as, bs), cs))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(130,plain,
% 0.11/0.36 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), complement(as)) | member(f17(union(as, bs), cs), as)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.11/0.36 tff(131,plain,
% 0.11/0.36 (member(f17(union(as, bs), cs), as)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[130, 86, 76, 124])).
% 0.11/0.36 tff(132,plain,
% 0.11/0.36 (subset(as, cs) <=> subset(as, cs)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(133,axiom,(subset(as, cs)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_subset_of_c')).
% 0.11/0.36 tff(134,plain,
% 0.11/0.36 (subset(as, cs)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.11/0.36 tff(135,plain,
% 0.11/0.36 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)) | (~subset(as, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)) | (~subset(as, cs)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(136,plain,
% 0.11/0.36 (((~member(f17(union(as, bs), cs), as)) | member(f17(union(as, bs), cs), cs) | (~subset(as, cs))) <=> (member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)) | (~subset(as, cs)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(137,plain,
% 0.11/0.36 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), as)) | member(f17(union(as, bs), cs), cs) | (~subset(as, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)) | (~subset(as, cs))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[136])).
% 0.11/0.36 tff(138,plain,
% 0.11/0.36 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), as)) | member(f17(union(as, bs), cs), cs) | (~subset(as, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)) | (~subset(as, cs)))),
% 0.11/0.36 inference(transitivity,[status(thm)],[137, 135])).
% 0.11/0.36 tff(139,plain,
% 0.11/0.36 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), as)) | member(f17(union(as, bs), cs), cs) | (~subset(as, cs)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(140,plain,
% 0.11/0.36 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)) | (~subset(as, cs))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.11/0.36 tff(141,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[140, 28, 134, 15, 131])).
% 0.11/0.36 % SZS output end Proof
%------------------------------------------------------------------------------