%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET013-2 : 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 05:24:46 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET013-2 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:02:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(member_type, type, (
% 0.20/0.42 member: ( $i * $i ) > $o)).
% 0.20/0.42 tff(intersection_type, type, (
% 0.20/0.42 intersection: ( $i * $i ) > $i)).
% 0.20/0.42 tff(as_type, type, (
% 0.20/0.42 as: $i)).
% 0.20/0.42 tff(bs_type, type, (
% 0.20/0.42 bs: $i)).
% 0.20/0.42 tff(member_of_1_not_of_2_type, type, (
% 0.20/0.42 member_of_1_not_of_2: ( $i * $i ) > $i)).
% 0.20/0.42 tff(cs_type, type, (
% 0.20/0.42 cs: $i)).
% 0.20/0.42 tff(ds_type, type, (
% 0.20/0.42 ds: $i)).
% 0.20/0.42 tff(subset_type, type, (
% 0.20/0.42 subset: ( $i * $i ) > $o)).
% 0.20/0.42 tff(equal_sets_type, type, (
% 0.20/0.42 equal_sets: ( $i * $i ) > $o)).
% 0.20/0.42 tff(1,assumption,(~subset(intersection(bs, as), cs)), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 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')).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.42 tff(7,plain,(
% 0.20/0.42 ![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.20/0.42 inference(skolemize,[status(sab)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | (subset(intersection(bs, as), cs) | member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as)))) <=> ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | subset(intersection(bs, as), cs) | member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | (subset(intersection(bs, as), cs) | member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 ((~![Subset: $i, Superset: $i] : (subset(Subset, Superset) | member(member_of_1_not_of_2(Subset, Superset), Subset))) | subset(intersection(bs, as), cs) | member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (^[Xs: $i, X: $i, Ys: $i] : refl(((~member(X, intersection(Xs, Ys))) | member(X, Xs)) <=> ((~member(X, intersection(Xs, Ys))) | member(X, Xs)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(16,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')).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.42 tff(18,plain,(
% 0.20/0.42 ![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))),
% 0.20/0.42 inference(skolemize,[status(sab)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))) | member(member_of_1_not_of_2(intersection(bs, as), cs), bs))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))) | member(member_of_1_not_of_2(intersection(bs, as), cs), bs))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))) | member(member_of_1_not_of_2(intersection(bs, as), cs), bs))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Xs))) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))) | member(member_of_1_not_of_2(intersection(bs, as), cs), bs)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (member(member_of_1_not_of_2(intersection(bs, as), cs), bs)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[22, 19, 12])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (^[Xs: $i, X: $i, Ys: $i] : refl(((~member(X, intersection(Xs, Ys))) | member(X, Ys)) <=> ((~member(X, intersection(Xs, Ys))) | member(X, Ys)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(27,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')).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.42 tff(29,plain,(
% 0.20/0.42 ![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))),
% 0.20/0.42 inference(skolemize,[status(sab)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))) | member(member_of_1_not_of_2(intersection(bs, as), cs), as))) <=> ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))) | member(member_of_1_not_of_2(intersection(bs, as), cs), as))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))) | member(member_of_1_not_of_2(intersection(bs, as), cs), as))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, intersection(Xs, Ys))) | member(X, Ys))) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(bs, as))) | member(member_of_1_not_of_2(intersection(bs, as), cs), as)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (member(member_of_1_not_of_2(intersection(bs, as), cs), as)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 30, 12])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(38,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')).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.42 tff(40,plain,(
% 0.20/0.42 ![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.20/0.42 inference(skolemize,[status(sab)],[39])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), cs)) | subset(intersection(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(intersection(bs, as), cs), cs)) | subset(intersection(bs, as), cs))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), cs)) | subset(intersection(bs, as), cs))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~![Subset: $i, Superset: $i] : ((~member(member_of_1_not_of_2(Subset, Superset), Superset)) | subset(Subset, Superset))) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), cs)) | subset(intersection(bs, as), cs)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (~member(member_of_1_not_of_2(intersection(bs, as), cs), cs)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 41, 1])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (equal_sets(intersection(as, bs), cs) <=> equal_sets(intersection(as, bs), cs)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(47,axiom,(equal_sets(intersection(as, bs), cs)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_of_a_and_b_is_c')).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (equal_sets(intersection(as, bs), cs)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (^[Subset: $i, Superset: $i] : refl(((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(52,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')).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.42 tff(54,plain,(
% 0.20/0.42 ![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.20/0.42 inference(skolemize,[status(sab)],[53])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(as, bs), cs)) | subset(intersection(as, bs), cs))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(intersection(as, bs), cs)) | subset(intersection(as, bs), cs)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (subset(intersection(as, bs), cs)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 55, 48])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.42 tff(65,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')).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.43 tff(68,plain,(
% 0.20/0.43 ![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[67])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), cs))) <=> ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), cs))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((member(member_of_1_not_of_2(intersection(bs, as), cs), cs) | (~subset(intersection(as, bs), cs)) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs)))) <=> ((~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), cs))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(intersection(bs, as), cs), cs) | (~subset(intersection(as, bs), cs)) | (~member(member_of_1_not_of_2(intersection(bs, as), 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(intersection(bs, as), cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), cs)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(intersection(bs, as), cs), cs) | (~subset(intersection(as, bs), cs)) | (~member(member_of_1_not_of_2(intersection(bs, as), 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(intersection(bs, as), cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), cs))),
% 0.20/0.43 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (member(member_of_1_not_of_2(intersection(bs, as), cs), cs) | (~subset(intersection(as, bs), cs)) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs))) | (~subset(intersection(as, bs), cs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), cs)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (~member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[75, 69, 59, 45])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.43 tff(82,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')).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.43 tff(85,plain,(
% 0.20/0.43 ![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[84])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), as)) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), bs)) | member(member_of_1_not_of_2(intersection(bs, as), 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(intersection(bs, as), cs), as)) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), bs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | ((~member(member_of_1_not_of_2(intersection(bs, as), cs), as)) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), bs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), as)) | (~member(member_of_1_not_of_2(intersection(bs, as), cs), bs)) | member(member_of_1_not_of_2(intersection(bs, as), cs), intersection(as, bs))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[89, 86, 76, 34, 23])).
% 0.20/0.43 tff(91,plain,(subset(intersection(bs, as), cs)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(92,assumption,(~subset(cs, ds)), introduced(assumption)).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 ((~![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)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (member(member_of_1_not_of_2(cs, ds), cs)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[95, 8, 92])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (^[Subset: $i, Superset: $i] : refl(((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset)) <=> ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(100,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')).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.43 tff(102,plain,(
% 0.20/0.43 ![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.20/0.43 inference(skolemize,[status(sab)],[101])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(as, bs), cs)) | subset(cs, intersection(as, bs)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(intersection(as, bs), cs)) | subset(cs, intersection(as, bs))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (subset(cs, intersection(as, bs))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[106, 103, 48])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (member(member_of_1_not_of_2(cs, ds), intersection(as, bs)) | (~member(member_of_1_not_of_2(cs, ds), cs))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[110, 69, 107])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (member(member_of_1_not_of_2(cs, ds), intersection(as, bs))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[111, 96])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((~![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)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (member(member_of_1_not_of_2(cs, ds), as)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[115, 19, 112])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 ((~![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)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (member(member_of_1_not_of_2(cs, ds), bs)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[119, 30, 112])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 ((~![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)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (~member(member_of_1_not_of_2(cs, ds), ds)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[123, 41, 92])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (equal_sets(intersection(bs, as), ds) <=> equal_sets(intersection(bs, as), ds)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(126,axiom,(equal_sets(intersection(bs, as), ds)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_of_b_and_a_is_d')).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (equal_sets(intersection(bs, as), ds)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(bs, as), ds)) | subset(intersection(bs, as), ds))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Subset, Superset)) | subset(Subset, Superset))) | (~equal_sets(intersection(bs, as), ds)) | subset(intersection(bs, as), ds)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (subset(intersection(bs, as), ds)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[130, 55, 127])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (~member(member_of_1_not_of_2(cs, ds), intersection(bs, as))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[134, 69, 131, 124])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (((~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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[138, 136])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 ((~![Xs: $i, X: $i, Ys: $i] : ((~member(X, Xs)) | (~member(X, Ys)) | member(X, intersection(Xs, Ys)))) | member(member_of_1_not_of_2(cs, ds), intersection(bs, as)) | (~member(member_of_1_not_of_2(cs, ds), bs)) | (~member(member_of_1_not_of_2(cs, ds), as))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[141, 86, 135, 120, 116])).
% 0.20/0.44 tff(143,plain,(subset(cs, ds)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 ((~equal_sets(cs, ds)) <=> (~equal_sets(cs, ds))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(145,axiom,(~equal_sets(cs, ds)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_c_equals_d')).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (~equal_sets(cs, ds)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.44 tff(152,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')).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.20/0.44 tff(155,plain,(
% 0.20/0.44 ![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[154])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 ((~![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))) | (equal_sets(cs, ds) | (~subset(cs, ds)) | (~subset(ds, cs)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 ((~![Set1: $i, Set2: $i] : (equal_sets(Set2, Set1) | (~subset(Set2, Set1)) | (~subset(Set1, Set2)))) | equal_sets(cs, ds) | (~subset(cs, ds)) | (~subset(ds, cs))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 ((~subset(cs, ds)) | (~subset(ds, cs))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[159, 156, 146])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (~subset(ds, cs)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[160, 143])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 ((~![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))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 ((~![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)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (~member(member_of_1_not_of_2(ds, cs), cs)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[164, 41, 161])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (((~![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(bs, as), cs)) | (~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), cs) | (~subset(intersection(bs, as), cs)) | (~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 ((~![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(bs, as), cs)) | (~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 ((~![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(bs, as), cs)) | (~member(member_of_1_not_of_2(ds, cs), intersection(bs, as)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 (~member(member_of_1_not_of_2(ds, cs), intersection(bs, as))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[168, 69, 165, 91])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 ((~![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))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 ((~![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)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 (member(member_of_1_not_of_2(ds, cs), ds)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[172, 8, 161])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | ((~equal_sets(intersection(bs, as), ds)) | subset(ds, intersection(bs, as)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 ((~![Subset: $i, Superset: $i] : ((~equal_sets(Superset, Subset)) | subset(Subset, Superset))) | (~equal_sets(intersection(bs, as), ds)) | subset(ds, intersection(bs, as))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 (subset(ds, intersection(bs, as))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[176, 103, 127])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 (((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | ((~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | 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)))) | (~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 ((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(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 (((~![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)))) | ((~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 (((~![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)))) | (~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 ((~![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)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 ((~![Subset: $i, Element: $i, Superset: $i] : (member(Element, Superset) | (~subset(Subset, Superset)) | (~member(Element, Subset)))) | (~subset(ds, intersection(bs, as))) | (~member(member_of_1_not_of_2(ds, cs), ds)) | member(member_of_1_not_of_2(ds, cs), intersection(bs, as))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.45 tff(184,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[183, 69, 177, 173, 169])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------