%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET015-2 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 : Sat Jun 21 05:24:48 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET015-2 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 04:02:56 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(member_type, type, (
% 0.18/0.38 member: ( $i * $i ) > $o)).
% 0.18/0.38 tff(union_type, type, (
% 0.18/0.38 union: ( $i * $i ) > $i)).
% 0.18/0.38 tff(as_type, type, (
% 0.18/0.38 as: $i)).
% 0.18/0.38 tff(bs_type, type, (
% 0.18/0.38 bs: $i)).
% 0.18/0.38 tff(member_of_1_not_of_2_type, type, (
% 0.18/0.38 member_of_1_not_of_2: ( $i * $i ) > $i)).
% 0.18/0.38 tff(cs_type, type, (
% 0.18/0.38 cs: $i)).
% 0.18/0.38 tff(ds_type, type, (
% 0.18/0.38 ds: $i)).
% 0.18/0.38 tff(subset_type, type, (
% 0.18/0.38 subset: ( $i * $i ) > $o)).
% 0.18/0.38 tff(equal_sets_type, type, (
% 0.18/0.38 equal_sets: ( $i * $i ) > $o)).
% 0.18/0.38 tff(1,assumption,(~subset(cs, ds)), introduced(assumption)).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (^[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)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![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))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (![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))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(5,axiom,(![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','subsets_axiom2')).
% 0.18/0.38 tff(6,plain,
% 0.18/0.38 (![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.38 tff(7,plain,(
% 0.18/0.38 ![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.18/0.38 inference(skolemize,[status(sab)],[6])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 (![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (((~![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))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 ((~![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))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 ((~![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)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (~member(member_of_1_not_of_2(cs, ds), ds)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (equal_sets(union(bs, as), ds) <=> equal_sets(union(bs, as), ds)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(14,axiom,(equal_sets(union(bs, as), ds)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_union_a_is_d')).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (equal_sets(union(bs, as), ds)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (^[Subset: $i, Superset: $i] : refl(((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(19,axiom,(![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','set_equal_sets_are_subsets1')).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.18/0.38 tff(21,plain,(
% 0.18/0.38 ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.18/0.38 inference(skolemize,[status(sab)],[20])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(union(bs, as), ds)) | subset(union(bs, as), ds))) <=> ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(union(bs, as), ds)) | subset(union(bs, as), ds))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(union(bs, as), ds)) | subset(union(bs, as), ds))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(union(bs, as), ds)) | subset(union(bs, as), ds)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (subset(union(bs, as), ds)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[25, 22, 15])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.38 tff(32,axiom,(![Subset: $i, Element: $i, Superset: $i] : (((~member(Element, Subset)) | (~subset(Subset, Superset))) | member(Element, Superset))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','membership_in_subsets')).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.18/0.39 tff(35,plain,(
% 0.18/0.39 ![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[34])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (((~![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(union(bs, as), ds)) | (~member(member_of_1_not_of_2(cs, ds), union(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(union(bs, as), ds)) | (~member(member_of_1_not_of_2(cs, ds), union(bs, as))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 ((~![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(union(bs, as), ds)) | (~member(member_of_1_not_of_2(cs, ds), union(bs, as))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 ((~![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(union(bs, as), ds)) | (~member(member_of_1_not_of_2(cs, ds), union(bs, as)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (~member(member_of_1_not_of_2(cs, ds), union(bs, as))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[39, 36, 26, 12])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (^[Xs: $i, X: $i, Ys: $i] : refl(((~member(X, Xs)) | member(X, union(Xs, Ys))) <=> ((~member(X, Xs)) | member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys))) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys))) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(44,axiom,(![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','member_of_set1_is_member_of_union')).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.39 tff(46,plain,(
% 0.18/0.39 ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[45])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))) | ((~member(member_of_1_not_of_2(cs, ds), bs)) | member(member_of_1_not_of_2(cs, ds), union(bs, as)))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))) | (~member(member_of_1_not_of_2(cs, ds), bs)) | member(member_of_1_not_of_2(cs, ds), union(bs, as)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))) | ((~member(member_of_1_not_of_2(cs, ds), bs)) | member(member_of_1_not_of_2(cs, ds), union(bs, as)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))) | (~member(member_of_1_not_of_2(cs, ds), bs)) | member(member_of_1_not_of_2(cs, ds), union(bs, as))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (~member(member_of_1_not_of_2(cs, ds), bs)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[50, 47, 40])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (^[Xs: $i, X: $i, Ys: $i] : refl(((~member(X, Ys)) | member(X, union(Xs, Ys))) <=> ((~member(X, Ys)) | member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys))) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys))) <=> ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(55,axiom,(![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','member_of_set2_is_member_of_union')).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.39 tff(57,plain,(
% 0.18/0.39 ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[56])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))) | ((~member(member_of_1_not_of_2(cs, ds), as)) | member(member_of_1_not_of_2(cs, ds), union(bs, as)))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))) | (~member(member_of_1_not_of_2(cs, ds), as)) | member(member_of_1_not_of_2(cs, ds), union(bs, as)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))) | ((~member(member_of_1_not_of_2(cs, ds), as)) | member(member_of_1_not_of_2(cs, ds), union(bs, as)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))) | (~member(member_of_1_not_of_2(cs, ds), as)) | member(member_of_1_not_of_2(cs, ds), union(bs, as))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (~member(member_of_1_not_of_2(cs, ds), as)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[61, 58, 40])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (^[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)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(66,axiom,(![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','subsets_axiom1')).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.39 tff(68,plain,(
% 0.18/0.39 ![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.18/0.39 inference(skolemize,[status(sab)],[67])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (((~![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))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 ((~![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))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 ((~![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)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 (member(member_of_1_not_of_2(cs, ds), cs)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[72, 69, 1])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (equal_sets(union(as, bs), cs) <=> equal_sets(union(as, bs), cs)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(75,axiom,(equal_sets(union(as, bs), cs)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_union_b_is_c')).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (equal_sets(union(as, bs), cs)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (^[Subset: $i, Superset: $i] : refl(((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[77])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(80,axiom,(![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','set_equal_sets_are_subsets2')).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.39 tff(82,plain,(
% 0.18/0.39 ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.18/0.39 inference(skolemize,[status(sab)],[81])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(union(as, bs), cs)) | subset(cs, union(as, bs)))) <=> ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(union(as, bs), cs)) | subset(cs, union(as, bs)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(union(as, bs), cs)) | subset(cs, union(as, bs)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(union(as, bs), cs)) | subset(cs, union(as, bs))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 (subset(cs, union(as, bs))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[86, 83, 76])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(cs, ds), union(as, bs)) | (~subset(cs, union(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), union(as, bs)) | (~subset(cs, union(as, bs))) | (~member(member_of_1_not_of_2(cs, ds), cs)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(cs, ds), union(as, bs)) | (~subset(cs, union(as, bs))) | (~member(member_of_1_not_of_2(cs, ds), cs)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | member(member_of_1_not_of_2(cs, ds), union(as, bs)) | (~subset(cs, union(as, bs))) | (~member(member_of_1_not_of_2(cs, ds), cs))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 (member(member_of_1_not_of_2(cs, ds), union(as, bs)) | (~member(member_of_1_not_of_2(cs, ds), cs))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[90, 36, 87])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (member(member_of_1_not_of_2(cs, ds), union(as, bs))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[91, 73])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (^[Xs: $i, X: $i, Ys: $i] : refl((member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys)))) <=> (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys)))) <=> ![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[93])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys)))) <=> ![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 (^[Xs: $i, X: $i, Ys: $i] : rewrite((((~member(X, union(Xs, Ys))) | member(X, Xs)) | member(X, Ys)) <=> (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : (((~member(X, union(Xs, Ys))) | member(X, Xs)) | member(X, Ys)) <=> ![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[96])).
% 0.18/0.39 tff(98,axiom,(![Xs: $i, X: $i, Ys: $i] : (((~member(X, union(Xs, Ys))) | member(X, Xs)) | member(X, Ys))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','member_of_union_is_member_of_one_set')).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.18/0.39 tff(101,plain,(
% 0.18/0.39 ![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[100])).
% 0.18/0.39 tff(102,plain,
% 0.18/0.39 (![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.18/0.39 tff(103,plain,
% 0.18/0.39 (((~![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(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), union(as, bs))))) <=> ((~![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(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), union(as, bs))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(104,plain,
% 0.18/0.39 ((~![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(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), union(as, bs))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(105,plain,
% 0.18/0.39 ((~![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))) | member(member_of_1_not_of_2(cs, ds), bs) | member(member_of_1_not_of_2(cs, ds), as) | (~member(member_of_1_not_of_2(cs, ds), union(as, bs)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (member(member_of_1_not_of_2(cs, ds), bs) | member(member_of_1_not_of_2(cs, ds), as)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[105, 102, 92])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[106, 62, 51])).
% 0.18/0.40 tff(108,plain,(subset(cs, ds)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 ((~equal_sets(cs, ds)) <=> (~equal_sets(cs, ds))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(110,axiom,(~equal_sets(cs, ds)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_c_equals_d')).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 (~equal_sets(cs, ds)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[112])).
% 0.18/0.40 tff(114,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(115,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(116,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[115])).
% 0.18/0.40 tff(117,axiom,(![Set1: $i, Set2: $i] : (((~subset(Set1, Set2)) | (~subset(Set2, Set1))) | equal_sets(Set2, Set1))), file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax','subsets_are_set_equal_sets')).
% 0.18/0.40 tff(118,plain,
% 0.18/0.40 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.18/0.40 tff(119,plain,
% 0.18/0.40 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.18/0.40 tff(120,plain,(
% 0.18/0.40 ![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[119])).
% 0.18/0.40 tff(121,plain,
% 0.18/0.40 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.18/0.40 tff(122,plain,
% 0.18/0.40 (((~![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(123,plain,
% 0.18/0.40 ((~![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))) | (equal_sets(cs, ds) | (~subset(cs, ds)) | (~subset(ds, cs)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(124,plain,
% 0.18/0.40 ((~![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))) | equal_sets(cs, ds) | (~subset(cs, ds)) | (~subset(ds, cs))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.18/0.40 tff(125,plain,
% 0.18/0.40 ((~subset(cs, ds)) | (~subset(ds, cs))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[124, 121, 111])).
% 0.18/0.40 tff(126,plain,
% 0.18/0.40 (~subset(ds, cs)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[125, 108])).
% 0.18/0.40 tff(127,plain,
% 0.18/0.40 (((~![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))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(128,plain,
% 0.18/0.40 ((~![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))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(129,plain,
% 0.18/0.40 ((~![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)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.18/0.40 tff(130,plain,
% 0.18/0.40 (~member(member_of_1_not_of_2(ds, cs), cs)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[129, 8, 126])).
% 0.18/0.40 tff(131,assumption,(~subset(union(bs, as), cs)), introduced(assumption)).
% 0.18/0.40 tff(132,plain,
% 0.18/0.40 (((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | ((~member(member_of_1_not_of_2(union(bs, as), cs), cs)) | subset(union(bs, as), 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(union(bs, as), cs), cs)) | subset(union(bs, as), cs))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(133,plain,
% 0.18/0.40 ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | ((~member(member_of_1_not_of_2(union(bs, as), cs), cs)) | subset(union(bs, as), cs))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(134,plain,
% 0.18/0.40 ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | (~member(member_of_1_not_of_2(union(bs, as), cs), cs)) | subset(union(bs, as), cs)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.18/0.40 tff(135,plain,
% 0.18/0.40 (~member(member_of_1_not_of_2(union(bs, as), cs), cs)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[134, 8, 131])).
% 0.18/0.40 tff(136,plain,
% 0.18/0.40 (((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(union(as, bs), cs)) | subset(union(as, bs), cs))) <=> ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(union(as, bs), cs)) | subset(union(as, bs), cs))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(137,plain,
% 0.18/0.40 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(union(as, bs), cs)) | subset(union(as, bs), cs))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(138,plain,
% 0.18/0.40 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(union(as, bs), cs)) | subset(union(as, bs), cs)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.18/0.40 tff(139,plain,
% 0.18/0.40 (subset(union(as, bs), cs)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[138, 22, 76])).
% 0.18/0.40 tff(140,plain,
% 0.18/0.40 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))) | (~subset(union(as, bs), cs)))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))) | (~subset(union(as, bs), cs)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(141,plain,
% 0.18/0.40 ((member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~subset(union(as, bs), cs)) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs)))) <=> (member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))) | (~subset(union(as, bs), cs)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(142,plain,
% 0.18/0.40 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~subset(union(as, bs), cs)) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))) | (~subset(union(as, bs), cs))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[141])).
% 0.18/0.40 tff(143,plain,
% 0.18/0.40 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~subset(union(as, bs), cs)) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))) | (~subset(union(as, bs), cs)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[142, 140])).
% 0.18/0.40 tff(144,plain,
% 0.18/0.40 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~subset(union(as, bs), cs)) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(145,plain,
% 0.18/0.40 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | member(member_of_1_not_of_2(union(bs, as), cs), cs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))) | (~subset(union(as, bs), cs))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.18/0.40 tff(146,plain,
% 0.18/0.40 (~member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[145, 36, 139, 135])).
% 0.18/0.40 tff(147,plain,
% 0.18/0.40 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))) | ((~member(member_of_1_not_of_2(union(bs, as), cs), as)) | member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs)))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))) | (~member(member_of_1_not_of_2(union(bs, as), cs), as)) | member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(148,plain,
% 0.18/0.40 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))) | ((~member(member_of_1_not_of_2(union(bs, as), cs), as)) | member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(149,plain,
% 0.18/0.40 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | member(X, union(Xs, Ys)))) | (~member(member_of_1_not_of_2(union(bs, as), cs), as)) | member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.18/0.40 tff(150,plain,
% 0.18/0.40 (~member(member_of_1_not_of_2(union(bs, as), cs), as)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[149, 47, 146])).
% 0.18/0.40 tff(151,plain,
% 0.18/0.40 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))) | ((~member(member_of_1_not_of_2(union(bs, as), cs), bs)) | member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs)))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))) | (~member(member_of_1_not_of_2(union(bs, as), cs), bs)) | member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(152,plain,
% 0.18/0.41 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))) | ((~member(member_of_1_not_of_2(union(bs, as), cs), bs)) | member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(153,plain,
% 0.18/0.41 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Ys)) | member(X, union(Xs, Ys)))) | (~member(member_of_1_not_of_2(union(bs, as), cs), bs)) | member(member_of_1_not_of_2(union(bs, as), cs), union(as, bs))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.18/0.41 tff(154,plain,
% 0.18/0.41 (~member(member_of_1_not_of_2(union(bs, as), cs), bs)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[153, 58, 146])).
% 0.18/0.41 tff(155,plain,
% 0.18/0.41 (((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | (subset(union(bs, as), cs) | member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as)))) <=> ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | subset(union(bs, as), cs) | member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(156,plain,
% 0.18/0.41 ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | (subset(union(bs, as), cs) | member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(157,plain,
% 0.18/0.41 ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | subset(union(bs, as), cs) | member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.18/0.41 tff(158,plain,
% 0.18/0.41 (member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[157, 69, 131])).
% 0.18/0.41 tff(159,plain,
% 0.18/0.41 (((~![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))) | (member(member_of_1_not_of_2(union(bs, as), cs), as) | member(member_of_1_not_of_2(union(bs, as), cs), bs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as))))) <=> ((~![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))) | member(member_of_1_not_of_2(union(bs, as), cs), as) | member(member_of_1_not_of_2(union(bs, as), cs), bs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(160,plain,
% 0.18/0.41 ((~![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))) | (member(member_of_1_not_of_2(union(bs, as), cs), as) | member(member_of_1_not_of_2(union(bs, as), cs), bs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(161,plain,
% 0.18/0.41 ((~![Xs: $i, X: $i, Ys: $i] : (member(X, Ys) | member(X, Xs) | (~member(X, union(Xs, Ys))))) | member(member_of_1_not_of_2(union(bs, as), cs), as) | member(member_of_1_not_of_2(union(bs, as), cs), bs) | (~member(member_of_1_not_of_2(union(bs, as), cs), union(bs, as)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.41 tff(162,plain,
% 0.18/0.41 (member(member_of_1_not_of_2(union(bs, as), cs), as) | member(member_of_1_not_of_2(union(bs, as), cs), bs)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[161, 102, 158])).
% 0.18/0.41 tff(163,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[162, 154, 150])).
% 0.18/0.41 tff(164,plain,(subset(union(bs, as), cs)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(165,plain,
% 0.18/0.41 (((~![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) | (~member(member_of_1_not_of_2(ds, cs), union(bs, as))) | (~subset(union(bs, as), 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), cs) | (~member(member_of_1_not_of_2(ds, cs), union(bs, as))) | (~subset(union(bs, as), cs)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(166,plain,
% 0.18/0.41 ((member(member_of_1_not_of_2(ds, cs), cs) | (~subset(union(bs, as), cs)) | (~member(member_of_1_not_of_2(ds, cs), union(bs, as)))) <=> (member(member_of_1_not_of_2(ds, cs), cs) | (~member(member_of_1_not_of_2(ds, cs), union(bs, as))) | (~subset(union(bs, as), cs)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(167,plain,
% 0.18/0.41 (((~![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(union(bs, as), cs)) | (~member(member_of_1_not_of_2(ds, cs), union(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), cs) | (~member(member_of_1_not_of_2(ds, cs), union(bs, as))) | (~subset(union(bs, as), cs))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[166])).
% 0.18/0.41 tff(168,plain,
% 0.18/0.41 (((~![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(union(bs, as), cs)) | (~member(member_of_1_not_of_2(ds, cs), union(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), cs) | (~member(member_of_1_not_of_2(ds, cs), union(bs, as))) | (~subset(union(bs, as), cs)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[167, 165])).
% 0.18/0.41 tff(169,plain,
% 0.18/0.41 ((~![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(union(bs, as), cs)) | (~member(member_of_1_not_of_2(ds, cs), union(bs, as))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(170,plain,
% 0.18/0.41 ((~![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) | (~member(member_of_1_not_of_2(ds, cs), union(bs, as))) | (~subset(union(bs, as), cs))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.18/0.41 tff(171,plain,
% 0.18/0.41 (~member(member_of_1_not_of_2(ds, cs), union(bs, as))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[170, 36, 164, 130])).
% 0.18/0.41 tff(172,plain,
% 0.18/0.41 (((~![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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(173,plain,
% 0.18/0.41 ((~![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))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(174,plain,
% 0.18/0.41 ((~![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)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.18/0.41 tff(175,plain,
% 0.18/0.41 (member(member_of_1_not_of_2(ds, cs), ds)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[174, 69, 126])).
% 0.18/0.41 tff(176,plain,
% 0.18/0.41 (((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(union(bs, as), ds)) | subset(ds, union(bs, as)))) <=> ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(union(bs, as), ds)) | subset(ds, union(bs, as)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(177,plain,
% 0.18/0.41 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(union(bs, as), ds)) | subset(ds, union(bs, as)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(178,plain,
% 0.18/0.41 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(union(bs, as), ds)) | subset(ds, union(bs, as))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.18/0.41 tff(179,plain,
% 0.18/0.41 (subset(ds, union(bs, as))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[178, 83, 15])).
% 0.18/0.41 tff(180,plain,
% 0.18/0.41 (((~![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, union(bs, as))) | member(member_of_1_not_of_2(ds, cs), union(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, union(bs, as))) | member(member_of_1_not_of_2(ds, cs), union(bs, as)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(181,plain,
% 0.18/0.41 ((member(member_of_1_not_of_2(ds, cs), union(bs, as)) | (~subset(ds, union(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds))) <=> ((~member(member_of_1_not_of_2(ds, cs), ds)) | (~subset(ds, union(bs, as))) | member(member_of_1_not_of_2(ds, cs), union(bs, as)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(182,plain,
% 0.18/0.41 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), union(bs, as)) | (~subset(ds, union(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, union(bs, as))) | member(member_of_1_not_of_2(ds, cs), union(bs, as))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[181])).
% 0.18/0.41 tff(183,plain,
% 0.18/0.41 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), union(bs, as)) | (~subset(ds, union(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, union(bs, as))) | member(member_of_1_not_of_2(ds, cs), union(bs, as)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[182, 180])).
% 0.18/0.41 tff(184,plain,
% 0.18/0.41 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(ds, cs), union(bs, as)) | (~subset(ds, union(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(185,plain,
% 0.18/0.41 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | (~subset(ds, union(bs, as))) | member(member_of_1_not_of_2(ds, cs), union(bs, as))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.18/0.41 tff(186,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[185, 36, 179, 175, 171])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------