TSTP Solution File: SET013-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET013-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 05:04:44 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET013-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 01:07:14 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(member_type, type, (
% 0.21/0.47 member: ( $i * $i ) > $o)).
% 0.21/0.47 tff(as_type, type, (
% 0.21/0.47 as: $i)).
% 0.21/0.47 tff(member_of_1_not_of_2_type, type, (
% 0.21/0.47 member_of_1_not_of_2: ( $i * $i ) > $i)).
% 0.21/0.47 tff(cs_type, type, (
% 0.21/0.47 cs: $i)).
% 0.21/0.47 tff(ds_type, type, (
% 0.21/0.47 ds: $i)).
% 0.21/0.47 tff(intersection_type, type, (
% 0.21/0.47 intersection: ( $i * $i ) > $i)).
% 0.21/0.47 tff(bs_type, type, (
% 0.21/0.47 bs: $i)).
% 0.21/0.47 tff(subset_type, type, (
% 0.21/0.47 subset: ( $i * $i ) > $o)).
% 0.21/0.47 tff(equal_sets_type, type, (
% 0.21/0.47 equal_sets: ( $i * $i ) > $o)).
% 0.21/0.47 tff(1,assumption,(~subset(cs, ds)), introduced(assumption)).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 (^[Subset: $i, Superset: $i] : refl((subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset)) <=> (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset)) <=> ![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset)) <=> ![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(5,axiom,(![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','subsets_axiom1')).
% 0.21/0.47 tff(6,plain,
% 0.21/0.47 (![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.47 tff(7,plain,(
% 0.21/0.47 ![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.21/0.47 inference(skolemize,[status(sab)],[6])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 (![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | (subset(cs, ds) | member(member_of_1_not_of_2(cs, ds), cs))) <=> ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | subset(cs, ds) | member(member_of_1_not_of_2(cs, ds), cs))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | (subset(cs, ds) | member(member_of_1_not_of_2(cs, ds), cs))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | subset(cs, ds) | member(member_of_1_not_of_2(cs, ds), cs)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 (member(member_of_1_not_of_2(cs, ds), cs)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (equal_sets(intersection(as, bs), cs) <=> equal_sets(intersection(as, bs), cs)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(14,axiom,(equal_sets(intersection(as, bs), cs)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_of_a_and_b_is_c')).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (equal_sets(intersection(as, bs), cs)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (^[Subset: $i, Superset: $i] : refl(((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(19,axiom,(![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','set_equal_sets_are_subsets2')).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.47 tff(21,plain,(
% 0.21/0.47 ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.21/0.47 inference(skolemize,[status(sab)],[20])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(as, bs), cs)) | subset(cs, intersection(as, bs)))) <=> ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(intersection(as, bs), cs)) | subset(cs, intersection(as, bs)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(as, bs), cs)) | subset(cs, intersection(as, bs)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(intersection(as, bs), cs)) | subset(cs, intersection(as, bs))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (subset(cs, intersection(as, bs))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[25, 22, 15])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 (^[Subset: $i, Element: $i, Superset: $i] : refl((member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset))) <=> (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset))) <=> ![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset))) <=> ![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (^[Subset: $i, Element: $i, Superset: $i] : rewrite((((~member(Element, Subset)) | (~subset(Subset, Superset))) | member(Element, Superset)) <=> (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (![Subset: $i, Element: $i, Superset: $i] : (((~member(Element, Subset)) | (~subset(Subset, Superset))) | member(Element, Superset)) <=> ![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.47 tff(32,axiom,(![Subset: $i, Element: $i, Superset: $i] : (((~member(Element, Subset)) | (~subset(Subset, Superset))) | member(Element, Superset))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','membership_in_subsets')).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.47 tff(35,plain,(
% 0.21/0.47 ![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[34])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(cs, ds), intersection(as, bs)) | (~subset(cs, intersection(as, bs))) | (~member(member_of_1_not_of_2(cs, ds), cs)))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | member(member_of_1_not_of_2(cs, ds), intersection(as, bs)) | (~subset(cs, intersection(as, bs))) | (~member(member_of_1_not_of_2(cs, ds), cs)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(cs, ds), intersection(as, bs)) | (~subset(cs, intersection(as, bs))) | (~member(member_of_1_not_of_2(cs, ds), cs)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(39,plain,
% 0.21/0.47 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | member(member_of_1_not_of_2(cs, ds), intersection(as, bs)) | (~subset(cs, intersection(as, bs))) | (~member(member_of_1_not_of_2(cs, ds), cs))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (member(member_of_1_not_of_2(cs, ds), intersection(as, bs)) | (~member(member_of_1_not_of_2(cs, ds), cs))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (member(member_of_1_not_of_2(cs, ds), intersection(as, bs))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[40, 12])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (^[Xs: $i, X: $i, Ys: $i] : refl(((~member(X, intersection(Xs, Ys))) | member(X, Ys)) <=> ((~member(X, intersection(Xs, Ys))) | member(X, Ys)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys)) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys)) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(45,axiom,(![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','member_of_intersection_is_member_of_set2')).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.47 tff(47,plain,(
% 0.21/0.47 ![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))),
% 0.21/0.47 inference(skolemize,[status(sab)],[46])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | ((~member(member_of_1_not_of_2(cs, ds), intersection(as, bs))) | member(member_of_1_not_of_2(cs, ds), bs))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | (~member(member_of_1_not_of_2(cs, ds), intersection(as, bs))) | member(member_of_1_not_of_2(cs, ds), bs))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | ((~member(member_of_1_not_of_2(cs, ds), intersection(as, bs))) | member(member_of_1_not_of_2(cs, ds), bs))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(51,plain,
% 0.21/0.48 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | (~member(member_of_1_not_of_2(cs, ds), intersection(as, bs))) | member(member_of_1_not_of_2(cs, ds), bs)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.48 tff(52,plain,
% 0.21/0.48 (member(member_of_1_not_of_2(cs, ds), bs)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[51, 48, 41])).
% 0.21/0.48 tff(53,plain,
% 0.21/0.48 (^[Subset: $i, Superset: $i] : refl(((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset)) <=> ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(54,plain,
% 0.21/0.48 (![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.48 tff(55,plain,
% 0.21/0.48 (![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(56,axiom,(![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','subsets_axiom2')).
% 0.21/0.48 tff(57,plain,
% 0.21/0.48 (![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.48 tff(58,plain,(
% 0.21/0.48 ![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(skolemize,[status(sab)],[57])).
% 0.21/0.48 tff(59,plain,
% 0.21/0.48 (![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.21/0.48 tff(60,plain,
% 0.21/0.48 (((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | ((~member(member_of_1_not_of_2(cs, ds), ds)) | subset(cs, ds))) <=> ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | (~member(member_of_1_not_of_2(cs, ds), ds)) | subset(cs, ds))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | ((~member(member_of_1_not_of_2(cs, ds), ds)) | subset(cs, ds))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(62,plain,
% 0.21/0.48 ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | (~member(member_of_1_not_of_2(cs, ds), ds)) | subset(cs, ds)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (~member(member_of_1_not_of_2(cs, ds), ds)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[62, 59, 1])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (equal_sets(intersection(bs, as), ds) <=> equal_sets(intersection(bs, as), ds)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(65,axiom,(equal_sets(intersection(bs, as), ds)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_of_b_and_a_is_d')).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 (equal_sets(intersection(bs, as), ds)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 (^[Subset: $i, Superset: $i] : refl(((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(70,axiom,(![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','set_equal_sets_are_subsets1')).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.48 tff(72,plain,(
% 0.21/0.48 ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(skolemize,[status(sab)],[71])).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(bs, as), ds)) | subset(intersection(bs, as), ds))) <=> ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(intersection(bs, as), ds)) | subset(intersection(bs, as), ds))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(bs, as), ds)) | subset(intersection(bs, as), ds))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(intersection(bs, as), ds)) | subset(intersection(bs, as), ds)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 (subset(intersection(bs, as), ds)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[76, 73, 66])).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(cs, ds), ds) | (~subset(intersection(bs, as), ds)) | (~member(member_of_1_not_of_2(cs, ds), intersection(bs, as))))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | member(member_of_1_not_of_2(cs, ds), ds) | (~subset(intersection(bs, as), ds)) | (~member(member_of_1_not_of_2(cs, ds), intersection(bs, as))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(cs, ds), ds) | (~subset(intersection(bs, as), ds)) | (~member(member_of_1_not_of_2(cs, ds), intersection(bs, as))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | member(member_of_1_not_of_2(cs, ds), ds) | (~subset(intersection(bs, as), ds)) | (~member(member_of_1_not_of_2(cs, ds), intersection(bs, as)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 (~member(member_of_1_not_of_2(cs, ds), intersection(bs, as))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[80, 36, 77, 63])).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 (^[Xs: $i, X: $i, Ys: $i] : refl(((~member(X, intersection(Xs, Ys))) | member(X, Xs)) <=> ((~member(X, intersection(Xs, Ys))) | member(X, Xs)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs)) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs)) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(85,axiom,(![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','member_of_intersection_is_member_of_set1')).
% 0.21/0.48 tff(86,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.48 tff(87,plain,(
% 0.21/0.48 ![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))),
% 0.21/0.48 inference(skolemize,[status(sab)],[86])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | ((~member(member_of_1_not_of_2(cs, ds), intersection(as, bs))) | member(member_of_1_not_of_2(cs, ds), as))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | (~member(member_of_1_not_of_2(cs, ds), intersection(as, bs))) | member(member_of_1_not_of_2(cs, ds), as))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | ((~member(member_of_1_not_of_2(cs, ds), intersection(as, bs))) | member(member_of_1_not_of_2(cs, ds), as))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | (~member(member_of_1_not_of_2(cs, ds), intersection(as, bs))) | member(member_of_1_not_of_2(cs, ds), as)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 (member(member_of_1_not_of_2(cs, ds), as)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[91, 88, 41])).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 (^[Xs: $i, X: $i, Ys: $i] : refl(((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys))) <=> ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys))) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys))) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 (^[Xs: $i, X: $i, Ys: $i] : trans(monotonicity(rewrite(((~member(X, Xs)) | (~member(X, Ys))) <=> ((~member(X, Xs)) | (~member(X, Ys)))), ((((~member(X, Xs)) | (~member(X, Ys))) | member(X, intersection(Xs, Ys))) <=> (((~member(X, Xs)) | (~member(X, Ys))) | member(X, intersection(Xs, Ys))))), rewrite((((~member(X, Xs)) | (~member(X, Ys))) | member(X, intersection(Xs, Ys))) <=> ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))), ((((~member(X, Xs)) | (~member(X, Ys))) | member(X, intersection(Xs, Ys))) <=> ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : (((~member(X, Xs)) | (~member(X, Ys))) | member(X, intersection(Xs, Ys))) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.48 tff(98,axiom,(![Xs: $i, X: $i, Ys: $i] : (((~member(X, Xs)) | (~member(X, Ys))) | member(X, intersection(Xs, Ys)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','member_of_both_is_member_of_intersection')).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.48 tff(101,plain,(
% 0.21/0.48 ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[100])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | (member(member_of_1_not_of_2(cs, ds), intersection(bs, as)) | (~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as)))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | member(member_of_1_not_of_2(cs, ds), intersection(bs, as)) | (~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 (((~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as)) | member(member_of_1_not_of_2(cs, ds), intersection(bs, as))) <=> (member(member_of_1_not_of_2(cs, ds), intersection(bs, as)) | (~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | ((~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as)) | member(member_of_1_not_of_2(cs, ds), intersection(bs, as)))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | (member(member_of_1_not_of_2(cs, ds), intersection(bs, as)) | (~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | ((~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as)) | member(member_of_1_not_of_2(cs, ds), intersection(bs, as)))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | member(member_of_1_not_of_2(cs, ds), intersection(bs, as)) | (~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | ((~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as)) | member(member_of_1_not_of_2(cs, ds), intersection(bs, as)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | member(member_of_1_not_of_2(cs, ds), intersection(bs, as)) | (~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[108, 102, 92, 81, 52])).
% 0.21/0.48 tff(110,plain,(subset(cs, ds)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 ((~equal_sets(cs, ds)) <=> (~equal_sets(cs, ds))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(112,axiom,(~equal_sets(cs, ds)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_c_equals_d')).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (~equal_sets(cs, ds)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (^[Set1: $i, Set2: $i] : refl((equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2))) <=> (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2))) <=> ![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2))) <=> ![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 (^[Set1: $i, Set2: $i] : trans(monotonicity(rewrite(((~subset(Set1, Set2)) | (~subset(Set2, Set1))) <=> ((~subset(Set2, Set1)) | (~subset(Set1, Set2)))), ((((~subset(Set1, Set2)) | (~subset(Set2, Set1))) | equal_sets(Set2, Set1)) <=> (((~subset(Set2, Set1)) | (~subset(Set1, Set2))) | equal_sets(Set2, Set1)))), rewrite((((~subset(Set2, Set1)) | (~subset(Set1, Set2))) | equal_sets(Set2, Set1)) <=> (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))), ((((~subset(Set1, Set2)) | (~subset(Set2, Set1))) | equal_sets(Set2, Set1)) <=> (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 (![Set1: $i, Set2: $i] : (((~subset(Set1, Set2)) | (~subset(Set2, Set1))) | equal_sets(Set2, Set1)) <=> ![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.48 tff(119,axiom,(![Set1: $i, Set2: $i] : (((~subset(Set1, Set2)) | (~subset(Set2, Set1))) | equal_sets(Set2, Set1))), file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax','subsets_are_set_equal_sets')).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.21/0.48 tff(122,plain,(
% 0.21/0.48 ![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[121])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (((~![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))) | (equal_sets(cs, ds) | (~subset(cs, ds)) | (~subset(ds, cs)))) <=> ((~![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))) | equal_sets(cs, ds) | (~subset(cs, ds)) | (~subset(ds, cs)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 ((~![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))) | (equal_sets(cs, ds) | (~subset(cs, ds)) | (~subset(ds, cs)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 ((~![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))) | equal_sets(cs, ds) | (~subset(cs, ds)) | (~subset(ds, cs))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 ((~subset(cs, ds)) | (~subset(ds, cs))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[126, 123, 113])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (~subset(ds, cs)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[127, 110])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | (subset(ds, cs) | member(member_of_1_not_of_2(ds, cs), ds))) <=> ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | subset(ds, cs) | member(member_of_1_not_of_2(ds, cs), ds))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | (subset(ds, cs) | member(member_of_1_not_of_2(ds, cs), ds))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | subset(ds, cs) | member(member_of_1_not_of_2(ds, cs), ds)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (member(member_of_1_not_of_2(ds, cs), ds)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[131, 8, 128])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(bs, as), ds)) | subset(ds, intersection(bs, as)))) <=> ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(intersection(bs, as), ds)) | subset(ds, intersection(bs, as)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(bs, as), ds)) | subset(ds, intersection(bs, as)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(intersection(bs, as), ds)) | subset(ds, intersection(bs, as))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 (subset(ds, intersection(bs, as))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[135, 22, 66])).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | ((~member(member_of_1_not_of_2(ds, cs), ds)) | (~subset(ds, intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as)))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | (~subset(ds, intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 ((member(member_of_1_not_of_2(ds, cs), intersection(bs, as)) | (~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds))) <=> ((~member(member_of_1_not_of_2(ds, cs), ds)) | (~subset(ds, intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), intersection(bs, as)) | (~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | ((~member(member_of_1_not_of_2(ds, cs), ds)) | (~subset(ds, intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), intersection(bs, as)) | (~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | (~subset(ds, intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[139, 137])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), intersection(bs, as)) | (~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | (~subset(ds, intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.49 tff(143,plain,
% 0.21/0.49 (member(member_of_1_not_of_2(ds, cs), intersection(bs, as))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[142, 36, 136, 132])).
% 0.21/0.49 tff(144,plain,
% 0.21/0.49 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | ((~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), as))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | (~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), as))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(145,plain,
% 0.21/0.49 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | ((~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), as))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(146,plain,
% 0.21/0.49 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | (~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), as)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.49 tff(147,plain,
% 0.21/0.49 (member(member_of_1_not_of_2(ds, cs), as)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[146, 48, 143])).
% 0.21/0.49 tff(148,plain,
% 0.21/0.49 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | ((~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), bs))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | (~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), bs))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(149,plain,
% 0.21/0.49 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | ((~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), bs))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(150,plain,
% 0.21/0.49 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | (~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))) | member(member_of_1_not_of_2(ds, cs), bs)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 (member(member_of_1_not_of_2(ds, cs), bs)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[150, 88, 143])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 (((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | ((~member(member_of_1_not_of_2(ds, cs), cs)) | subset(ds, cs))) <=> ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | (~member(member_of_1_not_of_2(ds, cs), cs)) | subset(ds, cs))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(153,plain,
% 0.21/0.49 ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | ((~member(member_of_1_not_of_2(ds, cs), cs)) | subset(ds, cs))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | (~member(member_of_1_not_of_2(ds, cs), cs)) | subset(ds, cs)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.49 tff(155,plain,
% 0.21/0.49 (~member(member_of_1_not_of_2(ds, cs), cs)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[154, 59, 128])).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 (((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(as, bs), cs)) | subset(intersection(as, bs), cs))) <=> ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(intersection(as, bs), cs)) | subset(intersection(as, bs), cs))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(157,plain,
% 0.21/0.49 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(as, bs), cs)) | subset(intersection(as, bs), cs))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(158,plain,
% 0.21/0.49 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(intersection(as, bs), cs)) | subset(intersection(as, bs), cs)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.49 tff(159,plain,
% 0.21/0.49 (subset(intersection(as, bs), cs)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[158, 73, 15])).
% 0.21/0.49 tff(160,plain,
% 0.21/0.49 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | ((~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(ds, cs), cs))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(ds, cs), cs))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(161,plain,
% 0.21/0.49 ((member(member_of_1_not_of_2(ds, cs), cs) | (~subset(intersection(as, bs), cs)) | (~member(member_of_1_not_of_2(ds, cs), intersection(as, bs)))) <=> ((~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(ds, cs), cs))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(162,plain,
% 0.21/0.49 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), cs) | (~subset(intersection(as, bs), cs)) | (~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | ((~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(ds, cs), cs)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[161])).
% 0.21/0.49 tff(163,plain,
% 0.21/0.49 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), cs) | (~subset(intersection(as, bs), cs)) | (~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(ds, cs), cs))),
% 0.21/0.49 inference(transitivity,[status(thm)],[162, 160])).
% 0.21/0.49 tff(164,plain,
% 0.21/0.49 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), cs) | (~subset(intersection(as, bs), cs)) | (~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(ds, cs), cs)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 (~member(member_of_1_not_of_2(ds, cs), intersection(as, bs))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[165, 36, 159, 155])).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | ((~member(member_of_1_not_of_2(ds, cs), as)) | (~member(member_of_1_not_of_2(ds, cs), bs)) | member(member_of_1_not_of_2(ds, cs), intersection(as, bs)))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | (~member(member_of_1_not_of_2(ds, cs), as)) | (~member(member_of_1_not_of_2(ds, cs), bs)) | member(member_of_1_not_of_2(ds, cs), intersection(as, bs)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | ((~member(member_of_1_not_of_2(ds, cs), as)) | (~member(member_of_1_not_of_2(ds, cs), bs)) | member(member_of_1_not_of_2(ds, cs), intersection(as, bs)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(169,plain,
% 0.21/0.49 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | (~member(member_of_1_not_of_2(ds, cs), as)) | (~member(member_of_1_not_of_2(ds, cs), bs)) | member(member_of_1_not_of_2(ds, cs), intersection(as, bs))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.49 tff(170,plain,
% 0.21/0.49 ((~member(member_of_1_not_of_2(ds, cs), as)) | (~member(member_of_1_not_of_2(ds, cs), bs))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[169, 102, 166])).
% 0.21/0.49 tff(171,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[170, 151, 147])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------