%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET013-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 100.24s 100.53s
% Output : Proof 100.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET013-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:00:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 100.24/100.53 % SZS status Unsatisfiable
% 100.24/100.53 % SZS output start Proof
% 100.24/100.53 tff(member_type, type, (
% 100.24/100.53 member: ( $i * $i ) > $o)).
% 100.24/100.53 tff(intersection_type, type, (
% 100.24/100.53 intersection: ( $i * $i ) > $i)).
% 100.24/100.53 tff(as_type, type, (
% 100.24/100.53 as: $i)).
% 100.24/100.53 tff(bs_type, type, (
% 100.24/100.53 bs: $i)).
% 100.24/100.53 tff(f1_type, type, (
% 100.24/100.53 f1: ( $i * $i ) > $i)).
% 100.24/100.53 tff(ds_type, type, (
% 100.24/100.53 ds: $i)).
% 100.24/100.53 tff(universal_set_type, type, (
% 100.24/100.53 universal_set: $i)).
% 100.24/100.53 tff(cs_type, type, (
% 100.24/100.53 cs: $i)).
% 100.24/100.53 tff(little_set_type, type, (
% 100.24/100.53 little_set: $i > $o)).
% 100.24/100.53 tff(1,plain,
% 100.24/100.53 ((intersection(bs, as) = ds) <=> (intersection(bs, as) = ds)),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(2,axiom,(intersection(bs, as) = ds), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_of_b_and_a_is_d')).
% 100.24/100.53 tff(3,plain,
% 100.24/100.53 (intersection(bs, as) = ds),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[2, 1])).
% 100.24/100.53 tff(4,plain,
% 100.24/100.53 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)),
% 100.24/100.53 inference(monotonicity,[status(thm)],[3])).
% 100.24/100.53 tff(5,plain,
% 100.24/100.53 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))),
% 100.24/100.53 inference(symmetry,[status(thm)],[4])).
% 100.24/100.53 tff(6,plain,
% 100.24/100.53 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)) <=> (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)))),
% 100.24/100.53 inference(monotonicity,[status(thm)],[5])).
% 100.24/100.53 tff(7,assumption,(~(universal_set = intersection(universal_set, universal_set))), introduced(assumption)).
% 100.24/100.53 tff(8,assumption,(~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))), introduced(assumption)).
% 100.24/100.53 tff(9,plain,
% 100.24/100.53 (^[Z: $i, Y: $i, X: $i] : refl((member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))))),
% 100.24/100.53 inference(bind,[status(th)],[])).
% 100.24/100.53 tff(10,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 100.24/100.53 inference(quant_intro,[status(thm)],[9])).
% 100.24/100.53 tff(11,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(12,plain,
% 100.24/100.53 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((member(Z, intersection(X, Y)) | (~member(Z, X))) <=> (member(Z, intersection(X, Y)) | (~member(Z, X)))), (((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> ((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))))), rewrite(((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))), (((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))))),
% 100.24/100.53 inference(bind,[status(th)],[])).
% 100.24/100.53 tff(13,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : ((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 100.24/100.53 inference(quant_intro,[status(thm)],[12])).
% 100.24/100.53 tff(14,axiom,(![Z: $i, Y: $i, X: $i] : ((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection3')).
% 100.24/100.53 tff(15,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[14, 13])).
% 100.24/100.53 tff(16,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[15, 11])).
% 100.24/100.53 tff(17,plain,(
% 100.24/100.53 ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 100.24/100.53 inference(skolemize,[status(sab)],[16])).
% 100.24/100.53 tff(18,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[17, 10])).
% 100.24/100.53 tff(19,plain,
% 100.24/100.53 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(20,plain,
% 100.24/100.53 ((member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))) <=> (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(21,plain,
% 100.24/100.53 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))))),
% 100.24/100.53 inference(monotonicity,[status(thm)],[20])).
% 100.24/100.53 tff(22,plain,
% 100.24/100.53 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))),
% 100.24/100.53 inference(transitivity,[status(thm)],[21, 19])).
% 100.24/100.53 tff(23,plain,
% 100.24/100.53 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))),
% 100.24/100.53 inference(quant_inst,[status(thm)],[])).
% 100.24/100.53 tff(24,plain,
% 100.24/100.53 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[23, 22])).
% 100.24/100.53 tff(25,plain,
% 100.24/100.53 (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)),
% 100.24/100.53 inference(unit_resolution,[status(thm)],[24, 18, 8])).
% 100.24/100.53 tff(26,plain,
% 100.24/100.53 (^[Y: $i, X: $i] : refl(((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)))),
% 100.24/100.53 inference(bind,[status(th)],[])).
% 100.24/100.53 tff(27,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 100.24/100.53 inference(quant_intro,[status(thm)],[26])).
% 100.24/100.53 tff(28,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(29,plain,
% 100.24/100.53 (^[Y: $i, X: $i] : rewrite(((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y)) <=> ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)))),
% 100.24/100.53 inference(bind,[status(th)],[])).
% 100.24/100.53 tff(30,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 100.24/100.53 inference(quant_intro,[status(thm)],[29])).
% 100.24/100.53 tff(31,axiom,(![Y: $i, X: $i] : ((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','extensionality2')).
% 100.24/100.53 tff(32,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[31, 30])).
% 100.24/100.53 tff(33,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[32, 28])).
% 100.24/100.53 tff(34,plain,(
% 100.24/100.53 ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 100.24/100.53 inference(skolemize,[status(sab)],[33])).
% 100.24/100.53 tff(35,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[34, 27])).
% 100.24/100.53 tff(36,plain,
% 100.24/100.53 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(37,plain,
% 100.24/100.53 (((universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)) <=> (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(38,plain,
% 100.24/100.53 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))),
% 100.24/100.53 inference(monotonicity,[status(thm)],[37])).
% 100.24/100.53 tff(39,plain,
% 100.24/100.53 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(transitivity,[status(thm)],[38, 36])).
% 100.24/100.53 tff(40,plain,
% 100.24/100.53 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(quant_inst,[status(thm)],[])).
% 100.24/100.53 tff(41,plain,
% 100.24/100.53 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (universal_set = intersection(universal_set, universal_set)) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[40, 39])).
% 100.24/100.53 tff(42,plain,
% 100.24/100.53 ($false),
% 100.24/100.53 inference(unit_resolution,[status(thm)],[41, 35, 7, 8, 25])).
% 100.24/100.53 tff(43,plain,(member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set)) | (universal_set = intersection(universal_set, universal_set))), inference(lemma,lemma(discharge,[]))).
% 100.24/100.53 tff(44,plain,
% 100.24/100.53 (member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))),
% 100.24/100.53 inference(unit_resolution,[status(thm)],[43, 7])).
% 100.24/100.53 tff(45,plain,
% 100.24/100.53 (^[Y: $i, X: $i] : refl(((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))))),
% 100.24/100.53 inference(bind,[status(th)],[])).
% 100.24/100.53 tff(46,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 100.24/100.53 inference(quant_intro,[status(thm)],[45])).
% 100.24/100.53 tff(47,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(48,plain,
% 100.24/100.53 (^[Y: $i, X: $i] : rewrite((((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y)) <=> ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))))),
% 100.24/100.53 inference(bind,[status(th)],[])).
% 100.24/100.53 tff(49,plain,
% 100.24/100.53 (![Y: $i, X: $i] : (((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 100.24/100.53 inference(quant_intro,[status(thm)],[48])).
% 100.24/100.53 tff(50,axiom,(![Y: $i, X: $i] : (((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','extensionality3')).
% 100.24/100.53 tff(51,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[50, 49])).
% 100.24/100.53 tff(52,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[51, 47])).
% 100.24/100.53 tff(53,plain,(
% 100.24/100.53 ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 100.24/100.53 inference(skolemize,[status(sab)],[52])).
% 100.24/100.53 tff(54,plain,
% 100.24/100.53 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[53, 46])).
% 100.24/100.53 tff(55,plain,
% 100.24/100.53 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((universal_set = intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (universal_set = intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(56,plain,
% 100.24/100.53 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((universal_set = intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)))),
% 100.24/100.53 inference(quant_inst,[status(thm)],[])).
% 100.24/100.53 tff(57,plain,
% 100.24/100.53 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (universal_set = intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[56, 55])).
% 100.24/100.53 tff(58,plain,
% 100.24/100.53 ((universal_set = intersection(universal_set, universal_set)) | (~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(unit_resolution,[status(thm)],[57, 54])).
% 100.24/100.53 tff(59,plain,
% 100.24/100.53 (~member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)),
% 100.24/100.53 inference(unit_resolution,[status(thm)],[58, 44, 7])).
% 100.24/100.53 tff(60,plain,
% 100.24/100.53 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ((~member(Z, intersection(X, Y))) | member(Z, X)))),
% 100.24/100.53 inference(bind,[status(th)],[])).
% 100.24/100.53 tff(61,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 100.24/100.53 inference(quant_intro,[status(thm)],[60])).
% 100.24/100.53 tff(62,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(63,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection1')).
% 100.24/100.53 tff(64,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[63, 62])).
% 100.24/100.53 tff(65,plain,(
% 100.24/100.53 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 100.24/100.53 inference(skolemize,[status(sab)],[64])).
% 100.24/100.53 tff(66,plain,
% 100.24/100.53 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[65, 61])).
% 100.24/100.53 tff(67,plain,
% 100.24/100.53 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(68,plain,
% 100.24/100.53 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set))),
% 100.24/100.53 inference(quant_inst,[status(thm)],[])).
% 100.24/100.53 tff(69,plain,
% 100.24/100.53 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(universal_set, intersection(universal_set, universal_set)), intersection(universal_set, universal_set))) | member(f1(universal_set, intersection(universal_set, universal_set)), universal_set)),
% 100.24/100.53 inference(modus_ponens,[status(thm)],[68, 67])).
% 100.24/100.53 tff(70,plain,
% 100.24/100.53 ($false),
% 100.24/100.53 inference(unit_resolution,[status(thm)],[69, 66, 44, 59])).
% 100.24/100.53 tff(71,plain,(universal_set = intersection(universal_set, universal_set)), inference(lemma,lemma(discharge,[]))).
% 100.24/100.53 tff(72,plain,
% 100.24/100.53 (intersection(universal_set, universal_set) = universal_set),
% 100.24/100.53 inference(symmetry,[status(thm)],[71])).
% 100.24/100.53 tff(73,plain,
% 100.24/100.53 (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.24/100.53 inference(monotonicity,[status(thm)],[72])).
% 100.24/100.53 tff(74,plain,
% 100.24/100.53 (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set))) <=> member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.24/100.53 inference(monotonicity,[status(thm)],[73])).
% 100.24/100.53 tff(75,plain,
% 100.24/100.53 (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))),
% 100.24/100.53 inference(symmetry,[status(thm)],[74])).
% 100.24/100.53 tff(76,plain,
% 100.24/100.53 ((~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set))))),
% 100.24/100.53 inference(monotonicity,[status(thm)],[75])).
% 100.24/100.53 tff(77,assumption,(~(intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))), introduced(assumption)).
% 100.24/100.53 tff(78,assumption,(~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))), introduced(assumption)).
% 100.24/100.53 tff(79,plain,
% 100.24/100.53 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(80,plain,
% 100.24/100.53 (((intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) <=> (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.24/100.53 inference(rewrite,[status(thm)],[])).
% 100.24/100.53 tff(81,plain,
% 100.24/100.53 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.24/100.53 inference(monotonicity,[status(thm)],[80])).
% 100.24/100.53 tff(82,plain,
% 100.24/100.53 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.24/100.53 inference(transitivity,[status(thm)],[81, 79])).
% 100.24/100.53 tff(83,plain,
% 100.24/100.53 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))),
% 100.24/100.53 inference(quant_inst,[status(thm)],[])).
% 100.24/100.53 tff(84,plain,
% 100.24/100.53 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[83, 82])).
% 100.24/100.54 tff(85,plain,
% 100.24/100.54 (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[84, 35])).
% 100.24/100.54 tff(86,plain,
% 100.24/100.54 (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[85, 78, 77])).
% 100.24/100.54 tff(87,plain,
% 100.24/100.54 (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[86, 75])).
% 100.24/100.54 tff(88,plain,
% 100.24/100.54 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))),
% 100.24/100.54 inference(rewrite,[status(thm)],[])).
% 100.24/100.54 tff(89,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))),
% 100.24/100.54 inference(quant_inst,[status(thm)],[])).
% 100.24/100.54 tff(90,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[89, 88])).
% 100.24/100.54 tff(91,plain,
% 100.24/100.54 (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[90, 66, 78])).
% 100.24/100.54 tff(92,plain,
% 100.24/100.54 ($false),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[91, 87])).
% 100.24/100.54 tff(93,plain,(member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))), inference(lemma,lemma(discharge,[]))).
% 100.24/100.54 tff(94,plain,
% 100.24/100.54 (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[93, 77])).
% 100.24/100.54 tff(95,plain,
% 100.24/100.54 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))))),
% 100.24/100.54 inference(rewrite,[status(thm)],[])).
% 100.24/100.54 tff(96,plain,
% 100.24/100.54 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))))),
% 100.24/100.54 inference(quant_inst,[status(thm)],[])).
% 100.24/100.54 tff(97,plain,
% 100.24/100.54 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[96, 95])).
% 100.24/100.54 tff(98,plain,
% 100.24/100.54 (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[97, 54, 94, 77])).
% 100.24/100.54 tff(99,plain,
% 100.24/100.54 (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[98, 76])).
% 100.24/100.54 tff(100,plain,
% 100.24/100.54 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set)))),
% 100.24/100.54 inference(rewrite,[status(thm)],[])).
% 100.24/100.54 tff(101,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set)))),
% 100.24/100.54 inference(quant_inst,[status(thm)],[])).
% 100.24/100.54 tff(102,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[101, 100])).
% 100.24/100.54 tff(103,plain,
% 100.24/100.54 (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[102, 66, 94])).
% 100.24/100.54 tff(104,plain,
% 100.24/100.54 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))))),
% 100.24/100.54 inference(rewrite,[status(thm)],[])).
% 100.24/100.54 tff(105,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))))),
% 100.24/100.54 inference(quant_inst,[status(thm)],[])).
% 100.24/100.54 tff(106,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[105, 104])).
% 100.24/100.54 tff(107,plain,
% 100.24/100.54 (member(f1(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), intersection(universal_set, universal_set)))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[106, 18, 94, 103])).
% 100.24/100.54 tff(108,plain,
% 100.24/100.54 ($false),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[107, 99])).
% 100.24/100.54 tff(109,plain,(intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), inference(lemma,lemma(discharge,[]))).
% 100.24/100.54 tff(110,plain,
% 100.24/100.54 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set)) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), universal_set)),
% 100.24/100.54 inference(monotonicity,[status(thm)],[72])).
% 100.24/100.54 tff(111,plain,
% 100.24/100.54 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), universal_set) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))),
% 100.24/100.54 inference(symmetry,[status(thm)],[110])).
% 100.24/100.54 tff(112,assumption,(~(intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs))), introduced(assumption)).
% 100.24/100.54 tff(113,assumption,(~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))), introduced(assumption)).
% 100.24/100.54 tff(114,plain,
% 100.24/100.54 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)))),
% 100.24/100.54 inference(rewrite,[status(thm)],[])).
% 100.24/100.54 tff(115,plain,
% 100.24/100.54 (((intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) <=> (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)))),
% 100.24/100.54 inference(rewrite,[status(thm)],[])).
% 100.24/100.54 tff(116,plain,
% 100.24/100.54 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs))))),
% 100.24/100.54 inference(monotonicity,[status(thm)],[115])).
% 100.24/100.54 tff(117,plain,
% 100.24/100.54 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)))),
% 100.24/100.54 inference(transitivity,[status(thm)],[116, 114])).
% 100.24/100.54 tff(118,plain,
% 100.24/100.54 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)))),
% 100.24/100.54 inference(quant_inst,[status(thm)],[])).
% 100.24/100.54 tff(119,plain,
% 100.24/100.54 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[118, 117])).
% 100.24/100.54 tff(120,plain,
% 100.24/100.54 (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[119, 35, 113, 112])).
% 100.24/100.54 tff(121,plain,
% 100.24/100.54 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)))),
% 100.24/100.54 inference(rewrite,[status(thm)],[])).
% 100.24/100.54 tff(122,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)))),
% 100.24/100.54 inference(quant_inst,[status(thm)],[])).
% 100.24/100.54 tff(123,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))),
% 100.24/100.54 inference(modus_ponens,[status(thm)],[122, 121])).
% 100.24/100.54 tff(124,plain,
% 100.24/100.54 ($false),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[123, 66, 113, 120])).
% 100.24/100.54 tff(125,plain,(member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs))), inference(lemma,lemma(discharge,[]))).
% 100.24/100.54 tff(126,plain,
% 100.24/100.54 (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))),
% 100.24/100.54 inference(unit_resolution,[status(thm)],[125, 112])).
% 100.24/100.54 tff(127,plain,
% 100.24/100.54 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs))),
% 100.24/100.54 inference(rewrite,[status(thm)],[])).
% 100.24/100.54 tff(128,plain,
% 100.24/100.54 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs))),
% 100.24/100.55 inference(quant_inst,[status(thm)],[])).
% 100.24/100.55 tff(129,plain,
% 100.24/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[128, 127])).
% 100.24/100.55 tff(130,plain,
% 100.24/100.55 (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)),
% 100.24/100.55 inference(unit_resolution,[status(thm)],[129, 66, 126])).
% 100.24/100.55 tff(131,plain,
% 100.24/100.55 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))))),
% 100.24/100.55 inference(rewrite,[status(thm)],[])).
% 100.24/100.55 tff(132,plain,
% 100.24/100.55 (((intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)))) <=> ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))))),
% 100.24/100.55 inference(rewrite,[status(thm)],[])).
% 100.24/100.55 tff(133,plain,
% 100.24/100.55 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)))))),
% 100.24/100.55 inference(monotonicity,[status(thm)],[132])).
% 100.24/100.55 tff(134,plain,
% 100.24/100.55 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))))),
% 100.24/100.55 inference(transitivity,[status(thm)],[133, 131])).
% 100.24/100.55 tff(135,plain,
% 100.24/100.55 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))))),
% 100.24/100.55 inference(quant_inst,[status(thm)],[])).
% 100.24/100.55 tff(136,plain,
% 100.24/100.55 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)))),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[135, 134])).
% 100.24/100.55 tff(137,plain,
% 100.24/100.55 ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | (intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)))),
% 100.24/100.55 inference(unit_resolution,[status(thm)],[136, 54])).
% 100.24/100.55 tff(138,plain,
% 100.24/100.55 (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs))),
% 100.24/100.55 inference(unit_resolution,[status(thm)],[137, 126, 112])).
% 100.24/100.55 tff(139,plain,
% 100.24/100.55 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)))),
% 100.24/100.55 inference(rewrite,[status(thm)],[])).
% 100.24/100.55 tff(140,plain,
% 100.24/100.55 ((member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set)))) <=> ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)))),
% 100.24/100.55 inference(rewrite,[status(thm)],[])).
% 100.24/100.55 tff(141,plain,
% 100.24/100.55 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs))))),
% 100.24/100.55 inference(monotonicity,[status(thm)],[140])).
% 100.24/100.55 tff(142,plain,
% 100.24/100.55 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)))),
% 100.24/100.55 inference(transitivity,[status(thm)],[141, 139])).
% 100.24/100.55 tff(143,plain,
% 100.24/100.55 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))))),
% 100.24/100.55 inference(quant_inst,[status(thm)],[])).
% 100.24/100.55 tff(144,plain,
% 100.24/100.55 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(bs, universal_set))) | member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), intersection(intersection(bs, universal_set), bs)) | (~member(f1(intersection(bs, universal_set), intersection(intersection(bs, universal_set), bs)), bs))),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[143, 142])).
% 100.24/100.55 tff(145,plain,
% 100.24/100.55 ($false),
% 100.24/100.55 inference(unit_resolution,[status(thm)],[144, 18, 126, 138, 130])).
% 100.24/100.55 tff(146,plain,(intersection(bs, universal_set) = intersection(intersection(bs, universal_set), bs)), inference(lemma,lemma(discharge,[]))).
% 100.24/100.55 tff(147,plain,
% 100.24/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)) <=> member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))),
% 100.24/100.55 inference(monotonicity,[status(thm)],[146])).
% 100.24/100.55 tff(148,plain,
% 100.24/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs)) <=> member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))),
% 100.24/100.55 inference(symmetry,[status(thm)],[147])).
% 100.24/100.55 tff(149,plain,
% 100.24/100.55 ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))) <=> (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)))),
% 100.24/100.55 inference(monotonicity,[status(thm)],[148])).
% 100.24/100.55 tff(150,plain,
% 100.24/100.55 ((intersection(as, bs) = cs) <=> (intersection(as, bs) = cs)),
% 100.24/100.55 inference(rewrite,[status(thm)],[])).
% 100.24/100.55 tff(151,axiom,(intersection(as, bs) = cs), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_of_a_and_b_is_c')).
% 100.24/100.55 tff(152,plain,
% 100.24/100.55 (intersection(as, bs) = cs),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[151, 150])).
% 100.24/100.55 tff(153,plain,
% 100.24/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs)) <=> member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)),
% 100.24/100.55 inference(monotonicity,[status(thm)],[152])).
% 100.24/100.55 tff(154,plain,
% 100.24/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs) <=> member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))),
% 100.24/100.55 inference(symmetry,[status(thm)],[153])).
% 100.24/100.55 tff(155,assumption,(~(intersection(intersection(intersection(bs, universal_set), bs), as) = cs)), introduced(assumption)).
% 100.24/100.55 tff(156,plain,
% 100.24/100.55 ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)) <=> (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs)))),
% 100.24/100.55 inference(monotonicity,[status(thm)],[154])).
% 100.24/100.55 tff(157,assumption,(~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)), introduced(assumption)).
% 100.24/100.55 tff(158,plain,
% 100.24/100.55 (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[157, 156])).
% 100.24/100.55 tff(159,plain,
% 100.24/100.55 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.24/100.55 inference(rewrite,[status(thm)],[])).
% 100.24/100.55 tff(160,plain,
% 100.24/100.55 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.24/100.55 inference(quant_inst,[status(thm)],[])).
% 100.24/100.55 tff(161,plain,
% 100.24/100.55 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[160, 159])).
% 100.24/100.55 tff(162,plain,
% 100.24/100.55 ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.24/100.55 inference(unit_resolution,[status(thm)],[161, 35])).
% 100.24/100.55 tff(163,plain,
% 100.24/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.24/100.55 inference(unit_resolution,[status(thm)],[162, 157, 155])).
% 100.24/100.55 tff(164,plain,
% 100.24/100.55 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs)))),
% 100.24/100.55 inference(rewrite,[status(thm)],[])).
% 100.24/100.55 tff(165,plain,
% 100.24/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs)))),
% 100.24/100.55 inference(quant_inst,[status(thm)],[])).
% 100.24/100.55 tff(166,plain,
% 100.24/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[165, 164])).
% 100.24/100.55 tff(167,plain,
% 100.24/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))),
% 100.24/100.55 inference(unit_resolution,[status(thm)],[166, 66, 163])).
% 100.24/100.55 tff(168,plain,
% 100.24/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[167, 148])).
% 100.24/100.55 tff(169,plain,
% 100.24/100.55 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs))),
% 100.24/100.55 inference(rewrite,[status(thm)],[])).
% 100.24/100.55 tff(170,plain,
% 100.24/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs))),
% 100.24/100.55 inference(quant_inst,[status(thm)],[])).
% 100.24/100.55 tff(171,plain,
% 100.24/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)),
% 100.24/100.55 inference(modus_ponens,[status(thm)],[170, 169])).
% 100.24/100.55 tff(172,plain,
% 100.24/100.55 ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)),
% 100.24/100.55 inference(unit_resolution,[status(thm)],[171, 66])).
% 100.24/100.55 tff(173,plain,
% 100.24/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)),
% 100.34/100.55 inference(unit_resolution,[status(thm)],[172, 168])).
% 100.34/100.55 tff(174,plain,
% 100.34/100.55 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ((~member(Z, intersection(X, Y))) | member(Z, Y)))),
% 100.34/100.55 inference(bind,[status(th)],[])).
% 100.34/100.55 tff(175,plain,
% 100.34/100.55 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 100.34/100.55 inference(quant_intro,[status(thm)],[174])).
% 100.34/100.55 tff(176,plain,
% 100.34/100.55 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 100.34/100.55 inference(rewrite,[status(thm)],[])).
% 100.34/100.55 tff(177,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection2')).
% 100.34/100.55 tff(178,plain,
% 100.34/100.55 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 100.34/100.55 inference(modus_ponens,[status(thm)],[177, 176])).
% 100.34/100.55 tff(179,plain,(
% 100.34/100.55 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 100.34/100.55 inference(skolemize,[status(sab)],[178])).
% 100.34/100.55 tff(180,plain,
% 100.34/100.55 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 100.34/100.55 inference(modus_ponens,[status(thm)],[179, 175])).
% 100.34/100.55 tff(181,plain,
% 100.34/100.55 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))),
% 100.34/100.55 inference(rewrite,[status(thm)],[])).
% 100.34/100.55 tff(182,plain,
% 100.34/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))),
% 100.34/100.55 inference(quant_inst,[status(thm)],[])).
% 100.34/100.55 tff(183,plain,
% 100.34/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)),
% 100.34/100.55 inference(modus_ponens,[status(thm)],[182, 181])).
% 100.34/100.55 tff(184,plain,
% 100.34/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)),
% 100.34/100.55 inference(unit_resolution,[status(thm)],[183, 180, 163])).
% 100.34/100.55 tff(185,plain,
% 100.34/100.55 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)))),
% 100.34/100.55 inference(rewrite,[status(thm)],[])).
% 100.34/100.55 tff(186,plain,
% 100.34/100.55 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)))),
% 100.34/100.55 inference(quant_inst,[status(thm)],[])).
% 100.34/100.55 tff(187,plain,
% 100.34/100.55 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))),
% 100.34/100.55 inference(modus_ponens,[status(thm)],[186, 185])).
% 100.34/100.55 tff(188,plain,
% 100.34/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs))),
% 100.34/100.55 inference(unit_resolution,[status(thm)],[187, 18, 184])).
% 100.34/100.55 tff(189,plain,
% 100.34/100.55 ($false),
% 100.34/100.55 inference(unit_resolution,[status(thm)],[188, 173, 158])).
% 100.34/100.55 tff(190,plain,(member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs) | (intersection(intersection(intersection(bs, universal_set), bs), as) = cs)), inference(lemma,lemma(discharge,[]))).
% 100.34/100.55 tff(191,plain,
% 100.34/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)),
% 100.34/100.55 inference(unit_resolution,[status(thm)],[190, 155])).
% 100.34/100.55 tff(192,plain,
% 100.34/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))),
% 100.34/100.55 inference(modus_ponens,[status(thm)],[191, 154])).
% 100.34/100.55 tff(193,plain,
% 100.34/100.55 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))),
% 100.34/100.55 inference(rewrite,[status(thm)],[])).
% 100.34/100.55 tff(194,plain,
% 100.34/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))),
% 100.34/100.55 inference(quant_inst,[status(thm)],[])).
% 100.34/100.55 tff(195,plain,
% 100.34/100.55 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)),
% 100.34/100.55 inference(modus_ponens,[status(thm)],[194, 193])).
% 100.34/100.55 tff(196,plain,
% 100.34/100.55 ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)),
% 100.34/100.55 inference(unit_resolution,[status(thm)],[195, 66])).
% 100.34/100.55 tff(197,plain,
% 100.34/100.55 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)),
% 100.34/100.55 inference(unit_resolution,[status(thm)],[196, 192])).
% 100.34/100.55 tff(198,plain,
% 100.34/100.55 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(199,plain,
% 100.34/100.56 (((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)))) <=> ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(200,plain,
% 100.34/100.56 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs))))),
% 100.34/100.56 inference(monotonicity,[status(thm)],[199])).
% 100.34/100.56 tff(201,plain,
% 100.34/100.56 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)))),
% 100.34/100.56 inference(transitivity,[status(thm)],[200, 198])).
% 100.34/100.56 tff(202,plain,
% 100.34/100.56 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.34/100.56 inference(quant_inst,[status(thm)],[])).
% 100.34/100.56 tff(203,plain,
% 100.34/100.56 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(bs, universal_set), bs), as) = cs) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[202, 201])).
% 100.34/100.56 tff(204,plain,
% 100.34/100.56 (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[203, 54, 155, 191])).
% 100.34/100.56 tff(205,plain,
% 100.34/100.56 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(206,plain,
% 100.34/100.56 ((member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs)))) <=> (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(207,plain,
% 100.34/100.56 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))))),
% 100.34/100.56 inference(monotonicity,[status(thm)],[206])).
% 100.34/100.56 tff(208,plain,
% 100.34/100.56 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)))),
% 100.34/100.56 inference(transitivity,[status(thm)],[207, 205])).
% 100.34/100.56 tff(209,plain,
% 100.34/100.56 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))))),
% 100.34/100.56 inference(quant_inst,[status(thm)],[])).
% 100.34/100.56 tff(210,plain,
% 100.34/100.56 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(intersection(bs, universal_set), bs), as)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[209, 208])).
% 100.34/100.56 tff(211,plain,
% 100.34/100.56 ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), as))),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[210, 18, 204])).
% 100.34/100.56 tff(212,plain,
% 100.34/100.56 (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(intersection(bs, universal_set), bs))),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[211, 197])).
% 100.34/100.56 tff(213,plain,
% 100.34/100.56 (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[212, 149])).
% 100.34/100.56 tff(214,plain,
% 100.34/100.56 (^[Y: $i, X: $i] : refl((little_set(X) | (~member(X, Y))) <=> (little_set(X) | (~member(X, Y))))),
% 100.34/100.56 inference(bind,[status(th)],[])).
% 100.34/100.56 tff(215,plain,
% 100.34/100.56 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 100.34/100.56 inference(quant_intro,[status(thm)],[214])).
% 100.34/100.56 tff(216,plain,
% 100.34/100.56 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(217,plain,
% 100.34/100.56 (^[Y: $i, X: $i] : rewrite(((~member(X, Y)) | little_set(X)) <=> (little_set(X) | (~member(X, Y))))),
% 100.34/100.56 inference(bind,[status(th)],[])).
% 100.34/100.56 tff(218,plain,
% 100.34/100.56 (![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X)) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 100.34/100.56 inference(quant_intro,[status(thm)],[217])).
% 100.34/100.56 tff(219,axiom,(![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a2')).
% 100.34/100.56 tff(220,plain,
% 100.34/100.56 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[219, 218])).
% 100.34/100.56 tff(221,plain,
% 100.34/100.56 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[220, 216])).
% 100.34/100.56 tff(222,plain,(
% 100.34/100.56 ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 100.34/100.56 inference(skolemize,[status(sab)],[221])).
% 100.34/100.56 tff(223,plain,
% 100.34/100.56 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[222, 215])).
% 100.34/100.56 tff(224,plain,
% 100.34/100.56 (((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)))) <=> ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(225,plain,
% 100.34/100.56 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs)))),
% 100.34/100.56 inference(quant_inst,[status(thm)],[])).
% 100.34/100.56 tff(226,plain,
% 100.34/100.56 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), cs))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[225, 224])).
% 100.34/100.56 tff(227,plain,
% 100.34/100.56 (little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs))),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[226, 223, 191])).
% 100.34/100.56 tff(228,plain,
% 100.34/100.56 (^[Z: $i] : refl(((~little_set(Z)) | member(Z, universal_set)) <=> ((~little_set(Z)) | member(Z, universal_set)))),
% 100.34/100.56 inference(bind,[status(th)],[])).
% 100.34/100.56 tff(229,plain,
% 100.34/100.56 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set)) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 100.34/100.56 inference(quant_intro,[status(thm)],[228])).
% 100.34/100.56 tff(230,plain,
% 100.34/100.56 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set)) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(231,plain,
% 100.34/100.56 (^[Z: $i] : rewrite((member(Z, universal_set) | (~little_set(Z))) <=> ((~little_set(Z)) | member(Z, universal_set)))),
% 100.34/100.56 inference(bind,[status(th)],[])).
% 100.34/100.56 tff(232,plain,
% 100.34/100.56 (![Z: $i] : (member(Z, universal_set) | (~little_set(Z))) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 100.34/100.56 inference(quant_intro,[status(thm)],[231])).
% 100.34/100.56 tff(233,axiom,(![Z: $i] : (member(Z, universal_set) | (~little_set(Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','universal_set')).
% 100.34/100.56 tff(234,plain,
% 100.34/100.56 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[233, 232])).
% 100.34/100.56 tff(235,plain,
% 100.34/100.56 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[234, 230])).
% 100.34/100.56 tff(236,plain,(
% 100.34/100.56 ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 100.34/100.56 inference(skolemize,[status(sab)],[235])).
% 100.34/100.56 tff(237,plain,
% 100.34/100.56 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[236, 229])).
% 100.34/100.56 tff(238,plain,
% 100.34/100.56 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(239,plain,
% 100.34/100.56 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set))),
% 100.34/100.56 inference(quant_inst,[status(thm)],[])).
% 100.34/100.56 tff(240,plain,
% 100.34/100.56 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[239, 238])).
% 100.34/100.56 tff(241,plain,
% 100.34/100.56 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[240, 237, 227])).
% 100.34/100.56 tff(242,plain,
% 100.34/100.56 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(243,plain,
% 100.34/100.56 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs))),
% 100.34/100.56 inference(quant_inst,[status(thm)],[])).
% 100.34/100.56 tff(244,plain,
% 100.34/100.56 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[243, 242])).
% 100.34/100.56 tff(245,plain,
% 100.34/100.56 ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(as, bs))) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[244, 180])).
% 100.34/100.56 tff(246,plain,
% 100.34/100.56 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[245, 192])).
% 100.34/100.56 tff(247,plain,
% 100.34/100.56 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(248,plain,
% 100.34/100.56 ((member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs))) <=> ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(249,plain,
% 100.34/100.56 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))))),
% 100.34/100.56 inference(monotonicity,[status(thm)],[248])).
% 100.34/100.56 tff(250,plain,
% 100.34/100.56 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)))),
% 100.34/100.56 inference(transitivity,[status(thm)],[249, 247])).
% 100.34/100.56 tff(251,plain,
% 100.34/100.56 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)))),
% 100.34/100.56 inference(quant_inst,[status(thm)],[])).
% 100.34/100.56 tff(252,plain,
% 100.34/100.56 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), universal_set)) | (~member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), bs)) | member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))),
% 100.34/100.56 inference(modus_ponens,[status(thm)],[251, 250])).
% 100.34/100.56 tff(253,plain,
% 100.34/100.56 (member(f1(intersection(intersection(intersection(bs, universal_set), bs), as), cs), intersection(bs, universal_set))),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[252, 18, 246, 241])).
% 100.34/100.56 tff(254,plain,
% 100.34/100.56 ($false),
% 100.34/100.56 inference(unit_resolution,[status(thm)],[253, 213])).
% 100.34/100.56 tff(255,plain,(intersection(intersection(intersection(bs, universal_set), bs), as) = cs), inference(lemma,lemma(discharge,[]))).
% 100.34/100.56 tff(256,plain,
% 100.34/100.56 (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.34/100.56 inference(monotonicity,[status(thm)],[255])).
% 100.34/100.56 tff(257,plain,
% 100.34/100.56 (intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.34/100.56 inference(symmetry,[status(thm)],[256])).
% 100.34/100.56 tff(258,plain,
% 100.34/100.56 (cs = intersection(intersection(intersection(bs, universal_set), bs), as)),
% 100.34/100.56 inference(symmetry,[status(thm)],[255])).
% 100.34/100.56 tff(259,plain,
% 100.34/100.56 (intersection(cs, cs) = intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.34/100.56 inference(monotonicity,[status(thm)],[258])).
% 100.34/100.56 tff(260,plain,
% 100.34/100.56 (intersection(cs, cs) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.34/100.56 inference(transitivity,[status(thm)],[259, 257])).
% 100.34/100.56 tff(261,plain,
% 100.34/100.56 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.34/100.56 inference(monotonicity,[status(thm)],[260])).
% 100.34/100.56 tff(262,plain,
% 100.34/100.56 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))),
% 100.34/100.56 inference(symmetry,[status(thm)],[261])).
% 100.34/100.56 tff(263,assumption,(~(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as)))), introduced(assumption)).
% 100.34/100.56 tff(264,assumption,(~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))), introduced(assumption)).
% 100.34/100.56 tff(265,plain,
% 100.34/100.56 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.34/100.56 inference(rewrite,[status(thm)],[])).
% 100.34/100.56 tff(266,plain,
% 100.34/100.56 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.34/100.57 inference(quant_inst,[status(thm)],[])).
% 100.34/100.57 tff(267,plain,
% 100.34/100.57 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.34/100.57 inference(modus_ponens,[status(thm)],[266, 265])).
% 100.34/100.57 tff(268,plain,
% 100.34/100.57 ((intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[267, 35])).
% 100.34/100.57 tff(269,plain,
% 100.34/100.57 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[268, 264, 263])).
% 100.34/100.57 tff(270,assumption,(~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))), introduced(assumption)).
% 100.34/100.57 tff(271,assumption,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))), introduced(assumption)).
% 100.34/100.57 tff(272,plain,
% 100.34/100.57 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as)))),
% 100.34/100.57 inference(rewrite,[status(thm)],[])).
% 100.34/100.57 tff(273,plain,
% 100.34/100.57 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as)))),
% 100.34/100.57 inference(quant_inst,[status(thm)],[])).
% 100.34/100.57 tff(274,plain,
% 100.34/100.57 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))),
% 100.34/100.57 inference(modus_ponens,[status(thm)],[273, 272])).
% 100.34/100.57 tff(275,plain,
% 100.34/100.57 ($false),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[274, 180, 271, 270])).
% 100.34/100.57 tff(276,plain,((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))), inference(lemma,lemma(discharge,[]))).
% 100.34/100.57 tff(277,plain,
% 100.34/100.57 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[276, 269])).
% 100.34/100.57 tff(278,assumption,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))), introduced(assumption)).
% 100.34/100.57 tff(279,assumption,(~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)), introduced(assumption)).
% 100.34/100.57 tff(280,plain,
% 100.34/100.57 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs))),
% 100.34/100.57 inference(rewrite,[status(thm)],[])).
% 100.34/100.57 tff(281,plain,
% 100.34/100.57 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs))),
% 100.34/100.57 inference(quant_inst,[status(thm)],[])).
% 100.34/100.57 tff(282,plain,
% 100.34/100.57 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)),
% 100.34/100.57 inference(modus_ponens,[status(thm)],[281, 280])).
% 100.34/100.57 tff(283,plain,
% 100.34/100.57 ($false),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[282, 66, 279, 278])).
% 100.34/100.57 tff(284,plain,((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)), inference(lemma,lemma(discharge,[]))).
% 100.34/100.57 tff(285,plain,
% 100.34/100.57 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[284, 277])).
% 100.34/100.57 tff(286,plain,
% 100.34/100.57 ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))) <=> (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)))),
% 100.34/100.57 inference(monotonicity,[status(thm)],[262])).
% 100.34/100.57 tff(287,plain,
% 100.34/100.57 (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))),
% 100.34/100.57 inference(modus_ponens,[status(thm)],[264, 286])).
% 100.34/100.57 tff(288,assumption,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))), introduced(assumption)).
% 100.34/100.57 tff(289,plain,
% 100.34/100.57 ($false),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[288, 287])).
% 100.34/100.57 tff(290,plain,((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))), inference(lemma,lemma(discharge,[]))).
% 100.34/100.57 tff(291,plain,
% 100.34/100.57 (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[290, 264])).
% 100.34/100.57 tff(292,plain,
% 100.34/100.57 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)))),
% 100.34/100.57 inference(rewrite,[status(thm)],[])).
% 100.34/100.57 tff(293,plain,
% 100.34/100.57 ((member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs))) <=> ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)))),
% 100.34/100.57 inference(rewrite,[status(thm)],[])).
% 100.34/100.57 tff(294,plain,
% 100.34/100.57 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))))),
% 100.34/100.57 inference(monotonicity,[status(thm)],[293])).
% 100.34/100.57 tff(295,plain,
% 100.34/100.57 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)))),
% 100.34/100.57 inference(transitivity,[status(thm)],[294, 292])).
% 100.34/100.57 tff(296,plain,
% 100.34/100.57 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)))),
% 100.34/100.57 inference(quant_inst,[status(thm)],[])).
% 100.34/100.57 tff(297,plain,
% 100.34/100.57 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))),
% 100.34/100.57 inference(modus_ponens,[status(thm)],[296, 295])).
% 100.34/100.57 tff(298,plain,
% 100.34/100.57 ($false),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[297, 18, 291, 285])).
% 100.34/100.57 tff(299,plain,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))) | (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as)))), inference(lemma,lemma(discharge,[]))).
% 100.34/100.57 tff(300,plain,
% 100.34/100.57 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[299, 263])).
% 100.34/100.57 tff(301,plain,
% 100.34/100.57 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))),
% 100.34/100.57 inference(modus_ponens,[status(thm)],[300, 262])).
% 100.34/100.57 tff(302,plain,
% 100.34/100.57 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs))),
% 100.34/100.57 inference(rewrite,[status(thm)],[])).
% 100.34/100.57 tff(303,plain,
% 100.34/100.57 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs))),
% 100.34/100.57 inference(quant_inst,[status(thm)],[])).
% 100.34/100.57 tff(304,plain,
% 100.34/100.57 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)),
% 100.34/100.57 inference(modus_ponens,[status(thm)],[303, 302])).
% 100.34/100.57 tff(305,plain,
% 100.34/100.57 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)),
% 100.34/100.57 inference(unit_resolution,[status(thm)],[304, 66, 301])).
% 100.34/100.57 tff(306,plain,
% 100.34/100.57 (((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)))) <=> ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)))),
% 100.34/100.57 inference(rewrite,[status(thm)],[])).
% 100.34/100.57 tff(307,plain,
% 100.34/100.57 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)))),
% 100.34/100.57 inference(quant_inst,[status(thm)],[])).
% 100.34/100.57 tff(308,plain,
% 100.34/100.57 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs))),
% 100.34/100.57 inference(modus_ponens,[status(thm)],[307, 306])).
% 100.34/100.57 tff(309,plain,
% 100.34/100.57 (little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))),
% 100.34/100.58 inference(unit_resolution,[status(thm)],[308, 223, 305])).
% 100.34/100.58 tff(310,plain,
% 100.34/100.58 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), universal_set))),
% 100.34/100.58 inference(rewrite,[status(thm)],[])).
% 100.34/100.58 tff(311,plain,
% 100.34/100.58 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), universal_set))),
% 100.34/100.58 inference(quant_inst,[status(thm)],[])).
% 100.34/100.58 tff(312,plain,
% 100.34/100.58 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), universal_set)),
% 100.34/100.58 inference(modus_ponens,[status(thm)],[311, 310])).
% 100.34/100.58 tff(313,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), universal_set)),
% 100.34/100.58 inference(unit_resolution,[status(thm)],[312, 237, 309])).
% 100.34/100.58 tff(314,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))),
% 100.34/100.58 inference(modus_ponens,[status(thm)],[313, 111])).
% 100.34/100.58 tff(315,plain,
% 100.34/100.58 (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(cs, as))),
% 100.34/100.58 inference(symmetry,[status(thm)],[109])).
% 100.34/100.58 tff(316,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.34/100.58 inference(monotonicity,[status(thm)],[109])).
% 100.34/100.58 tff(317,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.34/100.58 inference(symmetry,[status(thm)],[316])).
% 100.34/100.58 tff(318,assumption,(~(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))), introduced(assumption)).
% 100.34/100.58 tff(319,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(bs, universal_set), bs), as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)),
% 100.34/100.58 inference(monotonicity,[status(thm)],[255])).
% 100.34/100.58 tff(320,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.34/100.58 inference(symmetry,[status(thm)],[319])).
% 100.34/100.58 tff(321,plain,
% 100.34/100.58 (intersection(intersection(universal_set, universal_set), cs) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.34/100.58 inference(monotonicity,[status(thm)],[258])).
% 100.34/100.58 tff(322,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.34/100.58 inference(monotonicity,[status(thm)],[321])).
% 100.34/100.58 tff(323,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.34/100.58 inference(symmetry,[status(thm)],[322])).
% 100.34/100.58 tff(324,assumption,(~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))), introduced(assumption)).
% 100.34/100.58 tff(325,plain,
% 100.34/100.58 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.34/100.58 inference(rewrite,[status(thm)],[])).
% 100.34/100.58 tff(326,plain,
% 100.34/100.58 (((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.34/100.58 inference(rewrite,[status(thm)],[])).
% 100.34/100.58 tff(327,plain,
% 100.34/100.58 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))))),
% 100.34/100.58 inference(monotonicity,[status(thm)],[326])).
% 100.34/100.58 tff(328,plain,
% 100.34/100.58 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.34/100.58 inference(transitivity,[status(thm)],[327, 325])).
% 100.34/100.58 tff(329,plain,
% 100.34/100.58 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.34/100.58 inference(quant_inst,[status(thm)],[])).
% 100.34/100.58 tff(330,plain,
% 100.34/100.58 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.34/100.58 inference(modus_ponens,[status(thm)],[329, 328])).
% 100.34/100.58 tff(331,plain,
% 100.34/100.58 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.34/100.58 inference(unit_resolution,[status(thm)],[330, 35])).
% 100.34/100.58 tff(332,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.34/100.58 inference(unit_resolution,[status(thm)],[331, 324, 318])).
% 100.34/100.58 tff(333,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.34/100.58 inference(modus_ponens,[status(thm)],[332, 323])).
% 100.34/100.58 tff(334,plain,
% 100.34/100.58 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs))),
% 100.34/100.58 inference(rewrite,[status(thm)],[])).
% 100.34/100.58 tff(335,plain,
% 100.34/100.58 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs))),
% 100.34/100.58 inference(quant_inst,[status(thm)],[])).
% 100.34/100.58 tff(336,plain,
% 100.34/100.58 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)),
% 100.34/100.58 inference(modus_ponens,[status(thm)],[335, 334])).
% 100.34/100.58 tff(337,plain,
% 100.34/100.58 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)),
% 100.34/100.58 inference(unit_resolution,[status(thm)],[336, 180])).
% 100.34/100.58 tff(338,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)),
% 100.34/100.58 inference(unit_resolution,[status(thm)],[337, 333])).
% 100.34/100.58 tff(339,plain,
% 100.34/100.58 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.34/100.58 inference(modus_ponens,[status(thm)],[338, 320])).
% 100.34/100.58 tff(340,plain,
% 100.34/100.58 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set)))),
% 100.34/100.58 inference(rewrite,[status(thm)],[])).
% 100.34/100.58 tff(341,plain,
% 100.34/100.58 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set)))),
% 100.34/100.58 inference(quant_inst,[status(thm)],[])).
% 100.34/100.58 tff(342,plain,
% 100.34/100.58 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))),
% 100.34/100.59 inference(modus_ponens,[status(thm)],[341, 340])).
% 100.34/100.59 tff(343,plain,
% 100.34/100.59 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))),
% 100.34/100.59 inference(unit_resolution,[status(thm)],[342, 66])).
% 100.34/100.59 tff(344,plain,
% 100.34/100.59 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))),
% 100.34/100.59 inference(unit_resolution,[status(thm)],[343, 333])).
% 100.34/100.59 tff(345,plain,
% 100.34/100.59 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))))),
% 100.34/100.59 inference(monotonicity,[status(thm)],[317])).
% 100.34/100.59 tff(346,plain,
% 100.34/100.59 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.34/100.59 inference(modus_ponens,[status(thm)],[324, 345])).
% 100.34/100.59 tff(347,plain,
% 100.34/100.59 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))))),
% 100.34/100.59 inference(rewrite,[status(thm)],[])).
% 100.34/100.59 tff(348,plain,
% 100.34/100.59 ((member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set)))) <=> ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))))),
% 100.34/100.59 inference(rewrite,[status(thm)],[])).
% 100.34/100.59 tff(349,plain,
% 100.34/100.59 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)))))),
% 100.34/100.59 inference(monotonicity,[status(thm)],[348])).
% 100.34/100.59 tff(350,plain,
% 100.34/100.59 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))))),
% 100.34/100.59 inference(transitivity,[status(thm)],[349, 347])).
% 100.34/100.59 tff(351,plain,
% 100.34/100.59 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))))),
% 100.34/100.59 inference(quant_inst,[status(thm)],[])).
% 100.34/100.59 tff(352,plain,
% 100.34/100.59 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)))),
% 100.34/100.59 inference(modus_ponens,[status(thm)],[351, 350])).
% 100.34/100.59 tff(353,plain,
% 100.34/100.59 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)))),
% 100.34/100.59 inference(unit_resolution,[status(thm)],[352, 18])).
% 100.34/100.59 tff(354,plain,
% 100.34/100.59 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))),
% 100.34/100.59 inference(unit_resolution,[status(thm)],[353, 346, 344])).
% 100.34/100.59 tff(355,plain,
% 100.34/100.59 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)))),
% 100.34/100.59 inference(rewrite,[status(thm)],[])).
% 100.34/100.59 tff(356,plain,
% 100.34/100.59 ((member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs))) <=> ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)))),
% 100.34/100.59 inference(rewrite,[status(thm)],[])).
% 100.34/100.59 tff(357,plain,
% 100.34/100.59 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as))))),
% 100.34/100.59 inference(monotonicity,[status(thm)],[356])).
% 100.34/100.59 tff(358,plain,
% 100.34/100.59 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)))),
% 100.38/100.59 inference(transitivity,[status(thm)],[357, 355])).
% 100.38/100.59 tff(359,plain,
% 100.38/100.59 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)))),
% 100.38/100.59 inference(quant_inst,[status(thm)],[])).
% 100.38/100.59 tff(360,plain,
% 100.38/100.59 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as))),
% 100.38/100.59 inference(modus_ponens,[status(thm)],[359, 358])).
% 100.38/100.59 tff(361,plain,
% 100.38/100.59 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)),
% 100.38/100.59 inference(unit_resolution,[status(thm)],[360, 18, 338, 354])).
% 100.38/100.59 tff(362,plain,
% 100.38/100.59 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as))),
% 100.38/100.59 inference(rewrite,[status(thm)],[])).
% 100.38/100.59 tff(363,plain,
% 100.38/100.59 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as))),
% 100.38/100.59 inference(quant_inst,[status(thm)],[])).
% 100.38/100.59 tff(364,plain,
% 100.38/100.59 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)),
% 100.38/100.59 inference(modus_ponens,[status(thm)],[363, 362])).
% 100.38/100.59 tff(365,plain,
% 100.38/100.59 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), as)),
% 100.38/100.59 inference(unit_resolution,[status(thm)],[364, 180])).
% 100.38/100.59 tff(366,plain,
% 100.38/100.59 ($false),
% 100.38/100.59 inference(unit_resolution,[status(thm)],[365, 361, 339])).
% 100.38/100.59 tff(367,plain,(member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))), inference(lemma,lemma(discharge,[]))).
% 100.38/100.59 tff(368,plain,
% 100.38/100.59 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.59 inference(unit_resolution,[status(thm)],[367, 318])).
% 100.38/100.59 tff(369,plain,
% 100.38/100.59 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.38/100.59 inference(modus_ponens,[status(thm)],[368, 317])).
% 100.38/100.59 tff(370,plain,
% 100.38/100.59 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set)))),
% 100.38/100.60 inference(rewrite,[status(thm)],[])).
% 100.38/100.60 tff(371,plain,
% 100.38/100.60 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set)))),
% 100.38/100.60 inference(quant_inst,[status(thm)],[])).
% 100.38/100.60 tff(372,plain,
% 100.38/100.60 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))),
% 100.38/100.60 inference(modus_ponens,[status(thm)],[371, 370])).
% 100.38/100.60 tff(373,plain,
% 100.38/100.60 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))),
% 100.38/100.60 inference(unit_resolution,[status(thm)],[372, 66])).
% 100.38/100.60 tff(374,plain,
% 100.38/100.60 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))),
% 100.38/100.60 inference(unit_resolution,[status(thm)],[373, 369])).
% 100.38/100.60 tff(375,plain,
% 100.38/100.60 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))) <=> (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)))),
% 100.38/100.60 inference(monotonicity,[status(thm)],[323])).
% 100.38/100.60 tff(376,plain,
% 100.38/100.60 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))))),
% 100.38/100.60 inference(rewrite,[status(thm)],[])).
% 100.38/100.60 tff(377,plain,
% 100.38/100.60 (((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))))),
% 100.38/100.60 inference(rewrite,[status(thm)],[])).
% 100.38/100.60 tff(378,plain,
% 100.38/100.60 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))))))),
% 100.38/100.60 inference(monotonicity,[status(thm)],[377])).
% 100.38/100.60 tff(379,plain,
% 100.38/100.60 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))))),
% 100.38/100.60 inference(transitivity,[status(thm)],[378, 376])).
% 100.38/100.60 tff(380,plain,
% 100.38/100.60 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.38/100.60 inference(quant_inst,[status(thm)],[])).
% 100.38/100.60 tff(381,plain,
% 100.38/100.60 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.38/100.60 inference(modus_ponens,[status(thm)],[380, 379])).
% 100.38/100.60 tff(382,plain,
% 100.38/100.60 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.38/100.60 inference(unit_resolution,[status(thm)],[381, 54, 318, 368])).
% 100.38/100.60 tff(383,plain,
% 100.38/100.60 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.38/100.60 inference(modus_ponens,[status(thm)],[382, 375])).
% 100.38/100.60 tff(384,plain,
% 100.38/100.60 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)))),
% 100.38/100.60 inference(rewrite,[status(thm)],[])).
% 100.38/100.60 tff(385,plain,
% 100.38/100.60 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as)))),
% 100.38/100.60 inference(quant_inst,[status(thm)],[])).
% 100.38/100.60 tff(386,plain,
% 100.38/100.60 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))),
% 100.38/100.60 inference(modus_ponens,[status(thm)],[385, 384])).
% 100.38/100.60 tff(387,plain,
% 100.38/100.60 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))),
% 100.38/100.60 inference(unit_resolution,[status(thm)],[386, 180])).
% 100.38/100.60 tff(388,plain,
% 100.38/100.60 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))),
% 100.38/100.60 inference(unit_resolution,[status(thm)],[387, 369])).
% 100.38/100.60 tff(389,plain,
% 100.38/100.60 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs))),
% 100.38/100.60 inference(rewrite,[status(thm)],[])).
% 100.38/100.60 tff(390,plain,
% 100.38/100.60 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs))),
% 100.38/100.60 inference(quant_inst,[status(thm)],[])).
% 100.38/100.60 tff(391,plain,
% 100.38/100.60 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(cs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)),
% 100.38/100.60 inference(modus_ponens,[status(thm)],[390, 389])).
% 100.38/100.60 tff(392,plain,
% 100.38/100.60 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)),
% 100.38/100.60 inference(unit_resolution,[status(thm)],[391, 66, 388])).
% 100.38/100.60 tff(393,plain,
% 100.38/100.60 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)))),
% 100.38/100.60 inference(rewrite,[status(thm)],[])).
% 100.38/100.60 tff(394,plain,
% 100.38/100.60 ((member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set)))) <=> ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)))),
% 100.38/100.60 inference(rewrite,[status(thm)],[])).
% 100.38/100.60 tff(395,plain,
% 100.38/100.60 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[394])).
% 100.38/100.61 tff(396,plain,
% 100.38/100.61 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)))),
% 100.38/100.61 inference(transitivity,[status(thm)],[395, 393])).
% 100.38/100.61 tff(397,plain,
% 100.38/100.61 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))))),
% 100.38/100.61 inference(quant_inst,[status(thm)],[])).
% 100.38/100.61 tff(398,plain,
% 100.38/100.61 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.38/100.61 inference(modus_ponens,[status(thm)],[397, 396])).
% 100.38/100.61 tff(399,plain,
% 100.38/100.61 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(universal_set, universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.38/100.61 inference(unit_resolution,[status(thm)],[398, 18])).
% 100.38/100.61 tff(400,plain,
% 100.38/100.61 ($false),
% 100.38/100.61 inference(unit_resolution,[status(thm)],[399, 392, 383, 374])).
% 100.38/100.61 tff(401,plain,(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as))), inference(lemma,lemma(discharge,[]))).
% 100.38/100.61 tff(402,plain,
% 100.38/100.61 (intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.38/100.61 inference(symmetry,[status(thm)],[401])).
% 100.38/100.61 tff(403,plain,
% 100.38/100.61 (intersection(intersection(universal_set, universal_set), cs) = intersection(intersection(universal_set, universal_set), intersection(cs, as))),
% 100.38/100.61 inference(transitivity,[status(thm)],[321, 402, 315])).
% 100.38/100.61 tff(404,plain,
% 100.38/100.61 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[403])).
% 100.38/100.61 tff(405,plain,
% 100.38/100.61 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.38/100.61 inference(symmetry,[status(thm)],[404])).
% 100.38/100.61 tff(406,plain,
% 100.38/100.61 ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))) <=> (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[405])).
% 100.38/100.61 tff(407,plain,
% 100.38/100.61 (f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) = f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[257, 315])).
% 100.38/100.61 tff(408,plain,
% 100.38/100.61 (member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[407, 315])).
% 100.38/100.61 tff(409,plain,
% 100.38/100.61 ((~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as))))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[408])).
% 100.38/100.61 tff(410,plain,
% 100.38/100.61 ((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[257, 315])).
% 100.38/100.61 tff(411,plain,
% 100.38/100.61 ((intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as))) <=> (intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.61 inference(symmetry,[status(thm)],[410])).
% 100.38/100.61 tff(412,plain,
% 100.38/100.61 ((~(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as)))) <=> (~(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[411])).
% 100.38/100.61 tff(413,plain,
% 100.38/100.61 (~(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.61 inference(modus_ponens,[status(thm)],[263, 412])).
% 100.38/100.61 tff(414,plain,
% 100.38/100.61 (member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[407, 257])).
% 100.38/100.61 tff(415,plain,
% 100.38/100.61 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.38/100.61 inference(symmetry,[status(thm)],[414])).
% 100.38/100.61 tff(416,plain,
% 100.38/100.61 (member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.38/100.61 inference(modus_ponens,[status(thm)],[300, 415])).
% 100.38/100.61 tff(417,plain,
% 100.38/100.61 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.38/100.61 inference(rewrite,[status(thm)],[])).
% 100.38/100.61 tff(418,plain,
% 100.38/100.61 (((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as))))) <=> ((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.38/100.61 inference(rewrite,[status(thm)],[])).
% 100.38/100.61 tff(419,plain,
% 100.38/100.61 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))))),
% 100.38/100.61 inference(monotonicity,[status(thm)],[418])).
% 100.38/100.61 tff(420,plain,
% 100.38/100.61 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.38/100.61 inference(transitivity,[status(thm)],[419, 417])).
% 100.38/100.61 tff(421,plain,
% 100.38/100.61 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))))),
% 100.38/100.61 inference(quant_inst,[status(thm)],[])).
% 100.38/100.61 tff(422,plain,
% 100.38/100.61 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.61 inference(modus_ponens,[status(thm)],[421, 420])).
% 100.38/100.61 tff(423,plain,
% 100.38/100.61 ((intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.61 inference(unit_resolution,[status(thm)],[422, 54])).
% 100.38/100.61 tff(424,plain,
% 100.38/100.61 (~member(f1(intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.61 inference(unit_resolution,[status(thm)],[423, 416, 413])).
% 100.38/100.61 tff(425,plain,
% 100.38/100.61 (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), intersection(cs, as)))),
% 100.38/100.61 inference(modus_ponens,[status(thm)],[424, 409])).
% 100.38/100.61 tff(426,plain,
% 100.38/100.61 (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.38/100.61 inference(modus_ponens,[status(thm)],[425, 406])).
% 100.38/100.61 tff(427,plain,
% 100.38/100.61 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)))),
% 100.38/100.61 inference(rewrite,[status(thm)],[])).
% 100.38/100.61 tff(428,plain,
% 100.38/100.61 ((member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set)))) <=> ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)))),
% 100.38/100.62 inference(rewrite,[status(thm)],[])).
% 100.38/100.62 tff(429,plain,
% 100.38/100.62 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs))))),
% 100.38/100.62 inference(monotonicity,[status(thm)],[428])).
% 100.38/100.62 tff(430,plain,
% 100.38/100.62 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)))),
% 100.38/100.62 inference(transitivity,[status(thm)],[429, 427])).
% 100.38/100.62 tff(431,plain,
% 100.38/100.62 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))))),
% 100.38/100.62 inference(quant_inst,[status(thm)],[])).
% 100.38/100.62 tff(432,plain,
% 100.38/100.62 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), cs)) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[431, 430])).
% 100.38/100.62 tff(433,plain,
% 100.38/100.62 ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(universal_set, universal_set))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(intersection(universal_set, universal_set), intersection(cs, as))), intersection(intersection(universal_set, universal_set), cs))),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[432, 18, 305])).
% 100.38/100.62 tff(434,plain,
% 100.38/100.62 ($false),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[433, 426, 314])).
% 100.38/100.62 tff(435,plain,(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as))), inference(lemma,lemma(discharge,[]))).
% 100.38/100.62 tff(436,plain,
% 100.38/100.62 (intersection(cs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.38/100.62 inference(monotonicity,[status(thm)],[258])).
% 100.38/100.62 tff(437,plain,
% 100.38/100.62 (intersection(cs, cs) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.38/100.62 inference(transitivity,[status(thm)],[259, 436, 435, 109])).
% 100.38/100.62 tff(438,plain,
% 100.38/100.62 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.62 inference(monotonicity,[status(thm)],[437])).
% 100.38/100.62 tff(439,plain,
% 100.38/100.62 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))),
% 100.38/100.62 inference(symmetry,[status(thm)],[438])).
% 100.38/100.62 tff(440,plain,
% 100.38/100.62 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)))),
% 100.38/100.62 inference(monotonicity,[status(thm)],[439])).
% 100.38/100.62 tff(441,assumption,(~(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs)), introduced(assumption)).
% 100.38/100.62 tff(442,assumption,(~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)), introduced(assumption)).
% 100.38/100.62 tff(443,plain,
% 100.38/100.62 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.62 inference(rewrite,[status(thm)],[])).
% 100.38/100.62 tff(444,plain,
% 100.38/100.62 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.62 inference(quant_inst,[status(thm)],[])).
% 100.38/100.62 tff(445,plain,
% 100.38/100.62 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[444, 443])).
% 100.38/100.62 tff(446,plain,
% 100.38/100.62 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[445, 35])).
% 100.38/100.62 tff(447,plain,
% 100.38/100.62 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[446, 442, 441])).
% 100.38/100.62 tff(448,plain,
% 100.38/100.62 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[447, 439])).
% 100.38/100.62 tff(449,plain,
% 100.38/100.62 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs))),
% 100.38/100.62 inference(rewrite,[status(thm)],[])).
% 100.38/100.62 tff(450,plain,
% 100.38/100.62 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs))),
% 100.38/100.62 inference(quant_inst,[status(thm)],[])).
% 100.38/100.62 tff(451,plain,
% 100.38/100.62 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[450, 449])).
% 100.38/100.62 tff(452,plain,
% 100.38/100.62 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[451, 66, 442])).
% 100.38/100.62 tff(453,plain,
% 100.38/100.62 ($false),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[452, 448])).
% 100.38/100.62 tff(454,plain,(member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs)), inference(lemma,lemma(discharge,[]))).
% 100.38/100.62 tff(455,plain,
% 100.38/100.62 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[454, 441])).
% 100.38/100.62 tff(456,plain,
% 100.38/100.62 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.38/100.62 inference(rewrite,[status(thm)],[])).
% 100.38/100.62 tff(457,plain,
% 100.38/100.62 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.38/100.62 inference(quant_inst,[status(thm)],[])).
% 100.38/100.62 tff(458,plain,
% 100.38/100.62 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[457, 456])).
% 100.38/100.62 tff(459,plain,
% 100.38/100.62 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[458, 54, 441, 455])).
% 100.38/100.62 tff(460,plain,
% 100.38/100.62 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[459, 440])).
% 100.38/100.62 tff(461,plain,
% 100.38/100.62 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)))),
% 100.38/100.62 inference(rewrite,[status(thm)],[])).
% 100.38/100.62 tff(462,plain,
% 100.38/100.62 ((member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs))) <=> ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)))),
% 100.38/100.62 inference(rewrite,[status(thm)],[])).
% 100.38/100.62 tff(463,plain,
% 100.38/100.62 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))))),
% 100.38/100.62 inference(monotonicity,[status(thm)],[462])).
% 100.38/100.62 tff(464,plain,
% 100.38/100.62 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)))),
% 100.38/100.62 inference(transitivity,[status(thm)],[463, 461])).
% 100.38/100.62 tff(465,plain,
% 100.38/100.62 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)))),
% 100.38/100.62 inference(quant_inst,[status(thm)],[])).
% 100.38/100.62 tff(466,plain,
% 100.38/100.62 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[465, 464])).
% 100.38/100.62 tff(467,plain,
% 100.38/100.62 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), cs), intersection(cs, cs))),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[466, 18, 455])).
% 100.38/100.62 tff(468,plain,
% 100.38/100.62 ($false),
% 100.38/100.62 inference(unit_resolution,[status(thm)],[467, 460])).
% 100.38/100.62 tff(469,plain,(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = cs), inference(lemma,lemma(discharge,[]))).
% 100.38/100.62 tff(470,plain,
% 100.38/100.62 (cs = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.38/100.62 inference(symmetry,[status(thm)],[469])).
% 100.38/100.62 tff(471,plain,
% 100.38/100.62 (intersection(as, bs) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.38/100.62 inference(transitivity,[status(thm)],[152, 470])).
% 100.38/100.62 tff(472,plain,
% 100.38/100.62 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.62 inference(monotonicity,[status(thm)],[471])).
% 100.38/100.62 tff(473,plain,
% 100.38/100.62 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs))),
% 100.38/100.62 inference(symmetry,[status(thm)],[472])).
% 100.38/100.62 tff(474,plain,
% 100.38/100.62 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)))),
% 100.38/100.62 inference(monotonicity,[status(thm)],[473])).
% 100.38/100.62 tff(475,assumption,(~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))), introduced(assumption)).
% 100.38/100.62 tff(476,plain,
% 100.38/100.62 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs))),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[475, 474])).
% 100.38/100.62 tff(477,plain,
% 100.38/100.62 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) <=> (cs = ds)),
% 100.38/100.62 inference(monotonicity,[status(thm)],[469])).
% 100.38/100.62 tff(478,plain,
% 100.38/100.62 ((cs = ds) <=> (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds)),
% 100.38/100.62 inference(symmetry,[status(thm)],[477])).
% 100.38/100.62 tff(479,plain,
% 100.38/100.62 ((~(cs = ds)) <=> (~(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds))),
% 100.38/100.62 inference(monotonicity,[status(thm)],[478])).
% 100.38/100.62 tff(480,plain,
% 100.38/100.62 ((~(cs = ds)) <=> (~(cs = ds))),
% 100.38/100.62 inference(rewrite,[status(thm)],[])).
% 100.38/100.62 tff(481,axiom,(~(cs = ds)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_c_equals_d')).
% 100.38/100.62 tff(482,plain,
% 100.38/100.62 (~(cs = ds)),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[481, 480])).
% 100.38/100.62 tff(483,plain,
% 100.38/100.62 (~(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds)),
% 100.38/100.62 inference(modus_ponens,[status(thm)],[482, 479])).
% 100.38/100.62 tff(484,plain,
% 100.38/100.62 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.62 inference(rewrite,[status(thm)],[])).
% 100.38/100.62 tff(485,plain,
% 100.38/100.62 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.63 inference(quant_inst,[status(thm)],[])).
% 100.38/100.63 tff(486,plain,
% 100.38/100.63 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.63 inference(modus_ponens,[status(thm)],[485, 484])).
% 100.38/100.63 tff(487,plain,
% 100.38/100.63 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[486, 35])).
% 100.38/100.63 tff(488,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[487, 483])).
% 100.38/100.63 tff(489,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[488, 475])).
% 100.38/100.63 tff(490,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))),
% 100.38/100.63 inference(modus_ponens,[status(thm)],[489, 5])).
% 100.38/100.63 tff(491,plain,
% 100.38/100.63 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs))),
% 100.38/100.63 inference(rewrite,[status(thm)],[])).
% 100.38/100.63 tff(492,plain,
% 100.38/100.63 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs))),
% 100.38/100.63 inference(quant_inst,[status(thm)],[])).
% 100.38/100.63 tff(493,plain,
% 100.38/100.63 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)),
% 100.38/100.63 inference(modus_ponens,[status(thm)],[492, 491])).
% 100.38/100.63 tff(494,plain,
% 100.38/100.63 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[493, 66])).
% 100.38/100.63 tff(495,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[494, 490])).
% 100.38/100.63 tff(496,plain,
% 100.38/100.63 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))),
% 100.38/100.63 inference(rewrite,[status(thm)],[])).
% 100.38/100.63 tff(497,plain,
% 100.38/100.63 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))),
% 100.38/100.63 inference(quant_inst,[status(thm)],[])).
% 100.38/100.63 tff(498,plain,
% 100.38/100.63 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)),
% 100.38/100.63 inference(modus_ponens,[status(thm)],[497, 496])).
% 100.38/100.63 tff(499,plain,
% 100.38/100.63 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[498, 180])).
% 100.38/100.63 tff(500,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[499, 490])).
% 100.38/100.63 tff(501,plain,
% 100.38/100.63 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)))),
% 100.38/100.63 inference(rewrite,[status(thm)],[])).
% 100.38/100.63 tff(502,plain,
% 100.38/100.63 ((member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))) <=> ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)))),
% 100.38/100.63 inference(rewrite,[status(thm)],[])).
% 100.38/100.63 tff(503,plain,
% 100.38/100.63 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs))))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[502])).
% 100.38/100.63 tff(504,plain,
% 100.38/100.63 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)))),
% 100.38/100.63 inference(transitivity,[status(thm)],[503, 501])).
% 100.38/100.63 tff(505,plain,
% 100.38/100.63 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)))),
% 100.38/100.63 inference(quant_inst,[status(thm)],[])).
% 100.38/100.63 tff(506,plain,
% 100.38/100.63 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs))),
% 100.38/100.63 inference(modus_ponens,[status(thm)],[505, 504])).
% 100.38/100.63 tff(507,plain,
% 100.38/100.63 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs))),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[506, 18])).
% 100.38/100.63 tff(508,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, bs))),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[507, 500, 495])).
% 100.38/100.63 tff(509,plain,
% 100.38/100.63 ($false),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[508, 476])).
% 100.38/100.63 tff(510,plain,(member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))), inference(lemma,lemma(discharge,[]))).
% 100.38/100.63 tff(511,plain,
% 100.38/100.63 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)))),
% 100.38/100.63 inference(rewrite,[status(thm)],[])).
% 100.38/100.63 tff(512,plain,
% 100.38/100.63 (((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)))),
% 100.38/100.63 inference(rewrite,[status(thm)],[])).
% 100.38/100.63 tff(513,plain,
% 100.38/100.63 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds))))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[512])).
% 100.38/100.63 tff(514,plain,
% 100.38/100.63 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)))),
% 100.38/100.63 inference(transitivity,[status(thm)],[513, 511])).
% 100.38/100.63 tff(515,plain,
% 100.38/100.63 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.38/100.63 inference(quant_inst,[status(thm)],[])).
% 100.38/100.63 tff(516,plain,
% 100.38/100.63 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = ds) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds))),
% 100.38/100.63 inference(modus_ponens,[status(thm)],[515, 514])).
% 100.38/100.63 tff(517,plain,
% 100.38/100.63 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), ds)),
% 100.38/100.63 inference(unit_resolution,[status(thm)],[516, 54, 483, 510])).
% 100.38/100.63 tff(518,plain,
% 100.38/100.63 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))),
% 100.38/100.63 inference(modus_ponens,[status(thm)],[517, 6])).
% 100.38/100.63 tff(519,plain,
% 100.38/100.63 (intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) = intersection(as, cs)),
% 100.38/100.63 inference(monotonicity,[status(thm)],[469])).
% 100.38/100.63 tff(520,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[519])).
% 100.38/100.63 tff(521,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.38/100.63 inference(symmetry,[status(thm)],[520])).
% 100.38/100.63 tff(522,assumption,(~(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs))), introduced(assumption)).
% 100.38/100.63 tff(523,plain,
% 100.38/100.63 ((cs = intersection(cs, as)) <=> (intersection(cs, as) = cs)),
% 100.38/100.63 inference(commutativity,[status(thm)],[])).
% 100.38/100.63 tff(524,plain,
% 100.38/100.63 ((intersection(cs, as) = cs) <=> (cs = intersection(cs, as))),
% 100.38/100.63 inference(symmetry,[status(thm)],[523])).
% 100.38/100.63 tff(525,plain,
% 100.38/100.63 ((intersection(cs, as) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(cs, as))),
% 100.38/100.63 inference(commutativity,[status(thm)],[])).
% 100.38/100.63 tff(526,plain,
% 100.38/100.63 ((intersection(cs, as) = cs) <=> (intersection(cs, as) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[470])).
% 100.38/100.63 tff(527,plain,
% 100.38/100.63 ((intersection(cs, as) = cs) <=> (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(cs, as))),
% 100.38/100.63 inference(transitivity,[status(thm)],[526, 525])).
% 100.38/100.63 tff(528,plain,
% 100.38/100.63 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(cs, as)) <=> (intersection(cs, as) = cs)),
% 100.38/100.63 inference(symmetry,[status(thm)],[527])).
% 100.38/100.63 tff(529,plain,
% 100.38/100.63 (intersection(intersection(universal_set, universal_set), intersection(cs, as)) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.38/100.63 inference(symmetry,[status(thm)],[435])).
% 100.38/100.63 tff(530,plain,
% 100.38/100.63 (cs = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.38/100.63 inference(transitivity,[status(thm)],[470, 315, 529])).
% 100.38/100.63 tff(531,plain,
% 100.38/100.63 (intersection(cs, as) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)),
% 100.38/100.63 inference(monotonicity,[status(thm)],[530])).
% 100.38/100.63 tff(532,plain,
% 100.38/100.63 (intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as) = intersection(cs, as)),
% 100.38/100.63 inference(symmetry,[status(thm)],[531])).
% 100.38/100.63 tff(533,plain,
% 100.38/100.63 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) <=> (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(cs, as))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[532])).
% 100.38/100.63 tff(534,plain,
% 100.38/100.63 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) <=> (cs = intersection(cs, as))),
% 100.38/100.63 inference(transitivity,[status(thm)],[533, 528, 524])).
% 100.38/100.63 tff(535,plain,
% 100.38/100.63 (f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) = f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[532])).
% 100.38/100.63 tff(536,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[535])).
% 100.38/100.63 tff(537,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.63 inference(symmetry,[status(thm)],[536])).
% 100.38/100.63 tff(538,plain,
% 100.38/100.63 (f1(cs, intersection(cs, as)) = f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[470])).
% 100.38/100.63 tff(539,plain,
% 100.38/100.63 (member(f1(cs, intersection(cs, as)), cs) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.38/100.63 inference(monotonicity,[status(thm)],[538, 470])).
% 100.38/100.63 tff(540,assumption,(~(cs = intersection(cs, as))), introduced(assumption)).
% 100.38/100.63 tff(541,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(cs, intersection(cs, as)), cs)),
% 100.38/100.63 inference(symmetry,[status(thm)],[539])).
% 100.38/100.63 tff(542,plain,
% 100.38/100.63 (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.38/100.63 inference(transitivity,[status(thm)],[315, 529])).
% 100.38/100.63 tff(543,plain,
% 100.38/100.63 (intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)),
% 100.38/100.63 inference(monotonicity,[status(thm)],[542])).
% 100.38/100.63 tff(544,plain,
% 100.38/100.63 (intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as) = intersection(cs, as)),
% 100.38/100.63 inference(transitivity,[status(thm)],[543, 532])).
% 100.38/100.63 tff(545,plain,
% 100.38/100.63 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(cs, as))),
% 100.38/100.64 inference(monotonicity,[status(thm)],[544])).
% 100.38/100.64 tff(546,plain,
% 100.38/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(cs, as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))),
% 100.38/100.64 inference(symmetry,[status(thm)],[545])).
% 100.38/100.64 tff(547,plain,
% 100.38/100.64 (member(f1(cs, intersection(cs, as)), intersection(cs, as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(cs, as))),
% 100.38/100.64 inference(monotonicity,[status(thm)],[538])).
% 100.38/100.64 tff(548,assumption,(~member(f1(cs, intersection(cs, as)), cs)), introduced(assumption)).
% 100.38/100.64 tff(549,plain,
% 100.38/100.64 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (member(f1(cs, intersection(cs, as)), intersection(cs, as)) | (cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(cs, intersection(cs, as)), intersection(cs, as)) | (cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs))),
% 100.38/100.64 inference(rewrite,[status(thm)],[])).
% 100.38/100.64 tff(550,plain,
% 100.38/100.64 (((cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs)) <=> (member(f1(cs, intersection(cs, as)), intersection(cs, as)) | (cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs))),
% 100.38/100.64 inference(rewrite,[status(thm)],[])).
% 100.38/100.64 tff(551,plain,
% 100.38/100.64 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (member(f1(cs, intersection(cs, as)), intersection(cs, as)) | (cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs)))),
% 100.38/100.64 inference(monotonicity,[status(thm)],[550])).
% 100.38/100.64 tff(552,plain,
% 100.38/100.64 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(cs, intersection(cs, as)), intersection(cs, as)) | (cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs))),
% 100.38/100.64 inference(transitivity,[status(thm)],[551, 549])).
% 100.38/100.64 tff(553,plain,
% 100.38/100.64 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs))),
% 100.38/100.64 inference(quant_inst,[status(thm)],[])).
% 100.38/100.64 tff(554,plain,
% 100.38/100.64 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | member(f1(cs, intersection(cs, as)), intersection(cs, as)) | (cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs)),
% 100.38/100.64 inference(modus_ponens,[status(thm)],[553, 552])).
% 100.38/100.64 tff(555,plain,
% 100.38/100.64 (member(f1(cs, intersection(cs, as)), intersection(cs, as)) | (cs = intersection(cs, as)) | member(f1(cs, intersection(cs, as)), cs)),
% 100.38/100.64 inference(unit_resolution,[status(thm)],[554, 35])).
% 100.38/100.64 tff(556,plain,
% 100.38/100.64 (member(f1(cs, intersection(cs, as)), intersection(cs, as))),
% 100.38/100.64 inference(unit_resolution,[status(thm)],[555, 548, 540])).
% 100.38/100.64 tff(557,plain,
% 100.38/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(cs, as))),
% 100.42/100.64 inference(modus_ponens,[status(thm)],[556, 547])).
% 100.42/100.64 tff(558,plain,
% 100.42/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))),
% 100.42/100.64 inference(modus_ponens,[status(thm)],[557, 546])).
% 100.42/100.64 tff(559,plain,
% 100.42/100.64 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.42/100.64 inference(rewrite,[status(thm)],[])).
% 100.42/100.64 tff(560,plain,
% 100.42/100.64 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.42/100.64 inference(quant_inst,[status(thm)],[])).
% 100.42/100.64 tff(561,plain,
% 100.42/100.64 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.42/100.64 inference(modus_ponens,[status(thm)],[560, 559])).
% 100.42/100.64 tff(562,plain,
% 100.42/100.64 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.42/100.64 inference(unit_resolution,[status(thm)],[561, 66])).
% 100.42/100.64 tff(563,plain,
% 100.42/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.42/100.64 inference(unit_resolution,[status(thm)],[562, 558])).
% 100.42/100.64 tff(564,plain,
% 100.42/100.64 (member(f1(cs, intersection(cs, as)), cs)),
% 100.42/100.64 inference(modus_ponens,[status(thm)],[563, 541])).
% 100.42/100.64 tff(565,plain,
% 100.42/100.64 ($false),
% 100.42/100.64 inference(unit_resolution,[status(thm)],[548, 564])).
% 100.42/100.64 tff(566,plain,(member(f1(cs, intersection(cs, as)), cs) | (cs = intersection(cs, as))), inference(lemma,lemma(discharge,[]))).
% 100.42/100.64 tff(567,plain,
% 100.42/100.64 (member(f1(cs, intersection(cs, as)), cs)),
% 100.42/100.64 inference(unit_resolution,[status(thm)],[566, 540])).
% 100.42/100.64 tff(568,plain,
% 100.42/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.42/100.64 inference(modus_ponens,[status(thm)],[567, 539])).
% 100.42/100.64 tff(569,plain,
% 100.42/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.42/100.64 inference(modus_ponens,[status(thm)],[568, 537])).
% 100.42/100.64 tff(570,plain,
% 100.42/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(cs, as))),
% 100.42/100.64 inference(monotonicity,[status(thm)],[535, 532])).
% 100.42/100.64 tff(571,plain,
% 100.42/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(cs, as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))),
% 100.42/100.64 inference(symmetry,[status(thm)],[570])).
% 100.42/100.64 tff(572,plain,
% 100.42/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(cs, as))),
% 100.42/100.64 inference(monotonicity,[status(thm)],[532])).
% 100.42/100.64 tff(573,plain,
% 100.42/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))),
% 100.42/100.64 inference(transitivity,[status(thm)],[572, 571])).
% 100.42/100.64 tff(574,plain,
% 100.42/100.64 (intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) = intersection(intersection(universal_set, universal_set), intersection(cs, as))),
% 100.43/100.64 inference(monotonicity,[status(thm)],[532])).
% 100.43/100.64 tff(575,plain,
% 100.43/100.64 (intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.43/100.64 inference(transitivity,[status(thm)],[574, 109])).
% 100.43/100.64 tff(576,plain,
% 100.43/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.64 inference(monotonicity,[status(thm)],[575])).
% 100.43/100.64 tff(577,plain,
% 100.43/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))),
% 100.43/100.64 inference(symmetry,[status(thm)],[576])).
% 100.43/100.64 tff(578,plain,
% 100.43/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))),
% 100.43/100.64 inference(modus_ponens,[status(thm)],[568, 577])).
% 100.43/100.64 tff(579,plain,
% 100.43/100.64 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))),
% 100.43/100.64 inference(rewrite,[status(thm)],[])).
% 100.43/100.64 tff(580,plain,
% 100.43/100.64 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))),
% 100.43/100.64 inference(quant_inst,[status(thm)],[])).
% 100.43/100.64 tff(581,plain,
% 100.43/100.64 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))),
% 100.43/100.64 inference(modus_ponens,[status(thm)],[580, 579])).
% 100.43/100.64 tff(582,plain,
% 100.43/100.64 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(universal_set, universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))),
% 100.43/100.64 inference(unit_resolution,[status(thm)],[581, 180])).
% 100.43/100.64 tff(583,plain,
% 100.43/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(cs, as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))),
% 100.43/100.64 inference(unit_resolution,[status(thm)],[582, 578])).
% 100.43/100.64 tff(584,plain,
% 100.43/100.64 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))),
% 100.43/100.64 inference(modus_ponens,[status(thm)],[583, 573])).
% 100.43/100.64 tff(585,plain,
% 100.43/100.64 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))))),
% 100.43/100.64 inference(rewrite,[status(thm)],[])).
% 100.43/100.64 tff(586,plain,
% 100.43/100.64 (((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))))),
% 100.43/100.64 inference(rewrite,[status(thm)],[])).
% 100.43/100.64 tff(587,plain,
% 100.43/100.64 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))))),
% 100.43/100.64 inference(monotonicity,[status(thm)],[586])).
% 100.43/100.64 tff(588,plain,
% 100.43/100.64 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))))),
% 100.43/100.65 inference(transitivity,[status(thm)],[587, 585])).
% 100.43/100.65 tff(589,plain,
% 100.43/100.65 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.65 inference(quant_inst,[status(thm)],[])).
% 100.43/100.65 tff(590,plain,
% 100.43/100.65 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[589, 588])).
% 100.43/100.65 tff(591,plain,
% 100.43/100.65 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)), intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)))),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[590, 54])).
% 100.43/100.65 tff(592,plain,
% 100.43/100.65 (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as)),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[591, 584, 569])).
% 100.43/100.65 tff(593,plain,
% 100.43/100.65 (cs = intersection(cs, as)),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[592, 534])).
% 100.43/100.65 tff(594,plain,
% 100.43/100.65 ($false),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[540, 593])).
% 100.43/100.65 tff(595,plain,(cs = intersection(cs, as)), inference(lemma,lemma(discharge,[]))).
% 100.43/100.65 tff(596,plain,
% 100.43/100.65 (intersection(cs, as) = cs),
% 100.43/100.65 inference(symmetry,[status(thm)],[595])).
% 100.43/100.65 tff(597,plain,
% 100.43/100.65 (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = cs),
% 100.43/100.65 inference(transitivity,[status(thm)],[435, 109, 469])).
% 100.43/100.65 tff(598,plain,
% 100.43/100.65 (intersection(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), as) = intersection(cs, as)),
% 100.43/100.65 inference(monotonicity,[status(thm)],[597])).
% 100.43/100.65 tff(599,plain,
% 100.43/100.65 (intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.43/100.65 inference(transitivity,[status(thm)],[543, 598, 596, 470])).
% 100.43/100.65 tff(600,plain,
% 100.43/100.65 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.65 inference(monotonicity,[status(thm)],[599])).
% 100.43/100.65 tff(601,plain,
% 100.43/100.65 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))),
% 100.43/100.65 inference(symmetry,[status(thm)],[600])).
% 100.43/100.65 tff(602,assumption,(~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))), introduced(assumption)).
% 100.43/100.65 tff(603,plain,
% 100.43/100.65 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.65 inference(rewrite,[status(thm)],[])).
% 100.43/100.65 tff(604,plain,
% 100.43/100.65 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.65 inference(quant_inst,[status(thm)],[])).
% 100.43/100.65 tff(605,plain,
% 100.43/100.65 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[604, 603])).
% 100.43/100.65 tff(606,plain,
% 100.43/100.65 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[605, 35, 522, 602])).
% 100.43/100.65 tff(607,plain,
% 100.43/100.65 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[606, 601])).
% 100.43/100.65 tff(608,plain,
% 100.43/100.65 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))) <=> (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.65 inference(monotonicity,[status(thm)],[521])).
% 100.43/100.65 tff(609,plain,
% 100.43/100.65 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[602, 608])).
% 100.43/100.65 tff(610,plain,
% 100.43/100.65 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.65 inference(rewrite,[status(thm)],[])).
% 100.43/100.65 tff(611,plain,
% 100.43/100.65 ((member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as))) <=> ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.65 inference(rewrite,[status(thm)],[])).
% 100.43/100.65 tff(612,plain,
% 100.43/100.65 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))))),
% 100.43/100.65 inference(monotonicity,[status(thm)],[611])).
% 100.43/100.65 tff(613,plain,
% 100.43/100.65 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.65 inference(transitivity,[status(thm)],[612, 610])).
% 100.43/100.65 tff(614,plain,
% 100.43/100.65 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)))),
% 100.43/100.65 inference(quant_inst,[status(thm)],[])).
% 100.43/100.65 tff(615,plain,
% 100.43/100.65 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[614, 613])).
% 100.43/100.65 tff(616,plain,
% 100.43/100.65 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[615, 18])).
% 100.43/100.65 tff(617,plain,
% 100.43/100.65 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[616, 609, 606])).
% 100.43/100.65 tff(618,plain,
% 100.43/100.65 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as))),
% 100.43/100.65 inference(rewrite,[status(thm)],[])).
% 100.43/100.65 tff(619,plain,
% 100.43/100.65 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as))),
% 100.43/100.65 inference(quant_inst,[status(thm)],[])).
% 100.43/100.65 tff(620,plain,
% 100.43/100.65 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[619, 618])).
% 100.43/100.65 tff(621,plain,
% 100.43/100.65 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), as)),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[620, 180])).
% 100.43/100.65 tff(622,plain,
% 100.43/100.65 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), as))),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[621, 617])).
% 100.43/100.65 tff(623,plain,
% 100.43/100.65 ($false),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[622, 607])).
% 100.43/100.65 tff(624,plain,(member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs)) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs))), inference(lemma,lemma(discharge,[]))).
% 100.43/100.65 tff(625,plain,
% 100.43/100.65 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))),
% 100.43/100.65 inference(unit_resolution,[status(thm)],[624, 522])).
% 100.43/100.65 tff(626,plain,
% 100.43/100.65 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[625, 521])).
% 100.43/100.65 tff(627,plain,
% 100.43/100.65 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.65 inference(rewrite,[status(thm)],[])).
% 100.43/100.65 tff(628,plain,
% 100.43/100.65 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.65 inference(quant_inst,[status(thm)],[])).
% 100.43/100.65 tff(629,plain,
% 100.43/100.65 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.65 inference(modus_ponens,[status(thm)],[628, 627])).
% 100.43/100.65 tff(630,plain,
% 100.43/100.65 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, cs))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(unit_resolution,[status(thm)],[629, 54])).
% 100.43/100.66 tff(631,plain,
% 100.43/100.66 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.66 inference(unit_resolution,[status(thm)],[630, 625, 522])).
% 100.43/100.66 tff(632,plain,
% 100.43/100.66 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(rewrite,[status(thm)],[])).
% 100.43/100.66 tff(633,plain,
% 100.43/100.66 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(quant_inst,[status(thm)],[])).
% 100.43/100.66 tff(634,plain,
% 100.43/100.66 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.66 inference(modus_ponens,[status(thm)],[633, 632])).
% 100.43/100.66 tff(635,plain,
% 100.43/100.66 (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(as, cs)), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(unit_resolution,[status(thm)],[634, 180, 631])).
% 100.43/100.66 tff(636,plain,
% 100.43/100.66 ($false),
% 100.43/100.66 inference(unit_resolution,[status(thm)],[635, 626])).
% 100.43/100.66 tff(637,plain,(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(as, cs)), inference(lemma,lemma(discharge,[]))).
% 100.43/100.66 tff(638,plain,
% 100.43/100.66 (intersection(as, cs) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.43/100.66 inference(symmetry,[status(thm)],[637])).
% 100.43/100.66 tff(639,plain,
% 100.43/100.66 (intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.43/100.66 inference(transitivity,[status(thm)],[519, 638])).
% 100.43/100.66 tff(640,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.66 inference(monotonicity,[status(thm)],[639])).
% 100.43/100.66 tff(641,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(symmetry,[status(thm)],[640])).
% 100.43/100.66 tff(642,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(modus_ponens,[status(thm)],[510, 641])).
% 100.43/100.66 tff(643,plain,
% 100.43/100.66 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))),
% 100.43/100.66 inference(rewrite,[status(thm)],[])).
% 100.43/100.66 tff(644,plain,
% 100.43/100.66 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))),
% 100.43/100.66 inference(quant_inst,[status(thm)],[])).
% 100.43/100.66 tff(645,plain,
% 100.43/100.66 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)),
% 100.43/100.66 inference(modus_ponens,[status(thm)],[644, 643])).
% 100.43/100.66 tff(646,plain,
% 100.43/100.66 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(as, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)),
% 100.43/100.66 inference(unit_resolution,[status(thm)],[645, 66])).
% 100.43/100.66 tff(647,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)),
% 100.43/100.66 inference(unit_resolution,[status(thm)],[646, 642])).
% 100.43/100.66 tff(648,plain,
% 100.43/100.66 ((intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) <=> (intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(commutativity,[status(thm)],[])).
% 100.43/100.66 tff(649,plain,
% 100.43/100.66 ((intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))) <=> (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(symmetry,[status(thm)],[648])).
% 100.43/100.66 tff(650,plain,
% 100.43/100.66 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) <=> (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(monotonicity,[status(thm)],[542])).
% 100.43/100.66 tff(651,plain,
% 100.43/100.66 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) <=> (intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(transitivity,[status(thm)],[650, 648])).
% 100.43/100.66 tff(652,plain,
% 100.43/100.66 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) <=> (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(transitivity,[status(thm)],[651, 649])).
% 100.43/100.66 tff(653,plain,
% 100.43/100.66 (f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) = f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(monotonicity,[status(thm)],[542])).
% 100.43/100.66 tff(654,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(monotonicity,[status(thm)],[653, 542])).
% 100.43/100.66 tff(655,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.66 inference(symmetry,[status(thm)],[654])).
% 100.43/100.66 tff(656,assumption,(~(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))), introduced(assumption)).
% 100.43/100.66 tff(657,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(monotonicity,[status(thm)],[542])).
% 100.43/100.66 tff(658,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.66 inference(symmetry,[status(thm)],[657])).
% 100.43/100.66 tff(659,plain,
% 100.43/100.66 ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))) <=> (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(monotonicity,[status(thm)],[658])).
% 100.43/100.66 tff(660,assumption,(~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))), introduced(assumption)).
% 100.43/100.66 tff(661,plain,
% 100.43/100.66 (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.66 inference(modus_ponens,[status(thm)],[660, 659])).
% 100.43/100.66 tff(662,plain,
% 100.43/100.66 (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(intersection(intersection(bs, universal_set), bs), as)),
% 100.43/100.66 inference(transitivity,[status(thm)],[469, 258])).
% 100.43/100.66 tff(663,plain,
% 100.43/100.66 (intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.43/100.66 inference(monotonicity,[status(thm)],[662])).
% 100.43/100.66 tff(664,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(monotonicity,[status(thm)],[663])).
% 100.43/100.66 tff(665,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(symmetry,[status(thm)],[664])).
% 100.43/100.66 tff(666,plain,
% 100.43/100.66 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.43/100.66 inference(rewrite,[status(thm)],[])).
% 100.43/100.66 tff(667,plain,
% 100.43/100.66 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.43/100.66 inference(quant_inst,[status(thm)],[])).
% 100.43/100.66 tff(668,plain,
% 100.43/100.66 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(modus_ponens,[status(thm)],[667, 666])).
% 100.43/100.66 tff(669,plain,
% 100.43/100.66 ((intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(unit_resolution,[status(thm)],[668, 35])).
% 100.43/100.66 tff(670,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.66 inference(unit_resolution,[status(thm)],[669, 660, 656])).
% 100.43/100.66 tff(671,plain,
% 100.43/100.66 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(modus_ponens,[status(thm)],[670, 665])).
% 100.43/100.66 tff(672,plain,
% 100.43/100.66 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(rewrite,[status(thm)],[])).
% 100.43/100.66 tff(673,plain,
% 100.43/100.66 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.66 inference(quant_inst,[status(thm)],[])).
% 100.43/100.66 tff(674,plain,
% 100.43/100.66 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.67 inference(modus_ponens,[status(thm)],[673, 672])).
% 100.43/100.67 tff(675,plain,
% 100.43/100.67 ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.67 inference(unit_resolution,[status(thm)],[674, 180])).
% 100.43/100.67 tff(676,plain,
% 100.43/100.67 ($false),
% 100.43/100.67 inference(unit_resolution,[status(thm)],[675, 671, 661])).
% 100.43/100.67 tff(677,plain,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))) | (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))), inference(lemma,lemma(discharge,[]))).
% 100.43/100.67 tff(678,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.67 inference(unit_resolution,[status(thm)],[677, 656])).
% 100.43/100.67 tff(679,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.67 inference(modus_ponens,[status(thm)],[678, 655])).
% 100.43/100.67 tff(680,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.67 inference(monotonicity,[status(thm)],[653])).
% 100.43/100.67 tff(681,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.67 inference(symmetry,[status(thm)],[680])).
% 100.43/100.67 tff(682,plain,
% 100.43/100.67 (intersection(as, bs) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.43/100.67 inference(transitivity,[status(thm)],[152, 470, 315, 529])).
% 100.43/100.67 tff(683,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(as, bs)) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.67 inference(monotonicity,[status(thm)],[682])).
% 100.43/100.67 tff(684,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))) <=> member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(as, bs))),
% 100.43/100.67 inference(symmetry,[status(thm)],[683])).
% 100.43/100.67 tff(685,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(as, bs))),
% 100.43/100.67 inference(modus_ponens,[status(thm)],[678, 684])).
% 100.43/100.67 tff(686,plain,
% 100.43/100.67 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(as, bs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(as, bs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs))),
% 100.43/100.67 inference(rewrite,[status(thm)],[])).
% 100.43/100.67 tff(687,plain,
% 100.43/100.67 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(as, bs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs))),
% 100.43/100.67 inference(quant_inst,[status(thm)],[])).
% 100.43/100.67 tff(688,plain,
% 100.43/100.67 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(as, bs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)),
% 100.43/100.67 inference(modus_ponens,[status(thm)],[687, 686])).
% 100.43/100.67 tff(689,plain,
% 100.43/100.67 ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(as, bs))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)),
% 100.43/100.67 inference(unit_resolution,[status(thm)],[688, 180])).
% 100.43/100.67 tff(690,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)),
% 100.43/100.67 inference(unit_resolution,[status(thm)],[689, 685])).
% 100.43/100.67 tff(691,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.67 inference(modus_ponens,[status(thm)],[678, 658])).
% 100.43/100.67 tff(692,assumption,(~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))), introduced(assumption)).
% 100.43/100.67 tff(693,assumption,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)), introduced(assumption)).
% 100.43/100.67 tff(694,assumption,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))), introduced(assumption)).
% 100.43/100.67 tff(695,plain,
% 100.43/100.67 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.67 inference(rewrite,[status(thm)],[])).
% 100.43/100.67 tff(696,plain,
% 100.43/100.67 ((member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs))) <=> ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.67 inference(rewrite,[status(thm)],[])).
% 100.43/100.67 tff(697,plain,
% 100.43/100.67 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))))),
% 100.43/100.67 inference(monotonicity,[status(thm)],[696])).
% 100.43/100.67 tff(698,plain,
% 100.43/100.67 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.67 inference(transitivity,[status(thm)],[697, 695])).
% 100.43/100.67 tff(699,plain,
% 100.43/100.67 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)))),
% 100.43/100.67 inference(quant_inst,[status(thm)],[])).
% 100.43/100.67 tff(700,plain,
% 100.43/100.67 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs)) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.67 inference(modus_ponens,[status(thm)],[699, 698])).
% 100.43/100.67 tff(701,plain,
% 100.43/100.67 ($false),
% 100.43/100.67 inference(unit_resolution,[status(thm)],[700, 18, 694, 693, 692])).
% 100.43/100.67 tff(702,plain,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), bs))), inference(lemma,lemma(discharge,[]))).
% 100.43/100.67 tff(703,plain,
% 100.43/100.67 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.67 inference(unit_resolution,[status(thm)],[702, 691, 690])).
% 100.43/100.67 tff(704,plain,
% 100.43/100.67 ((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))) <=> (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.68 inference(monotonicity,[status(thm)],[665])).
% 100.43/100.68 tff(705,assumption,(~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))), introduced(assumption)).
% 100.43/100.68 tff(706,plain,
% 100.43/100.68 (~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.68 inference(modus_ponens,[status(thm)],[705, 704])).
% 100.43/100.68 tff(707,assumption,(member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))), introduced(assumption)).
% 100.43/100.68 tff(708,plain,
% 100.43/100.68 ($false),
% 100.43/100.68 inference(unit_resolution,[status(thm)],[707, 706])).
% 100.43/100.68 tff(709,plain,((~member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))), inference(lemma,lemma(discharge,[]))).
% 100.43/100.68 tff(710,plain,
% 100.43/100.68 (member(f1(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.68 inference(unit_resolution,[status(thm)],[709, 703])).
% 100.43/100.68 tff(711,plain,
% 100.43/100.68 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))),
% 100.43/100.68 inference(modus_ponens,[status(thm)],[710, 681])).
% 100.43/100.68 tff(712,plain,
% 100.43/100.68 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))))),
% 100.43/100.68 inference(rewrite,[status(thm)],[])).
% 100.43/100.68 tff(713,plain,
% 100.43/100.68 (((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) <=> ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))))),
% 100.43/100.68 inference(rewrite,[status(thm)],[])).
% 100.43/100.68 tff(714,plain,
% 100.43/100.68 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))))))),
% 100.43/100.68 inference(monotonicity,[status(thm)],[713])).
% 100.43/100.68 tff(715,plain,
% 100.43/100.68 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))))),
% 100.43/100.68 inference(transitivity,[status(thm)],[714, 712])).
% 100.43/100.68 tff(716,plain,
% 100.43/100.68 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))))),
% 100.43/100.68 inference(quant_inst,[status(thm)],[])).
% 100.43/100.68 tff(717,plain,
% 100.43/100.68 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.43/100.68 inference(modus_ponens,[status(thm)],[716, 715])).
% 100.43/100.68 tff(718,plain,
% 100.43/100.68 ((intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))))),
% 100.43/100.68 inference(unit_resolution,[status(thm)],[717, 54])).
% 100.43/100.68 tff(719,plain,
% 100.43/100.68 (intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.43/100.68 inference(unit_resolution,[status(thm)],[718, 711, 679])).
% 100.43/100.68 tff(720,plain,
% 100.43/100.68 (intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.43/100.68 inference(modus_ponens,[status(thm)],[719, 652])).
% 100.43/100.68 tff(721,plain,
% 100.43/100.68 ($false),
% 100.43/100.68 inference(unit_resolution,[status(thm)],[656, 720])).
% 100.43/100.68 tff(722,plain,(intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as))), inference(lemma,lemma(discharge,[]))).
% 100.43/100.68 tff(723,plain,
% 100.43/100.68 (intersection(bs, intersection(intersection(intersection(bs, universal_set), bs), as)) = intersection(intersection(intersection(intersection(bs, universal_set), bs), as), intersection(intersection(intersection(bs, universal_set), bs), as))),
% 100.43/100.68 inference(symmetry,[status(thm)],[722])).
% 100.43/100.68 tff(724,plain,
% 100.43/100.68 (intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) = intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)),
% 100.43/100.68 inference(transitivity,[status(thm)],[663, 723, 435, 109])).
% 100.43/100.68 tff(725,plain,
% 100.43/100.68 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set))),
% 100.43/100.68 inference(monotonicity,[status(thm)],[724])).
% 100.43/100.68 tff(726,plain,
% 100.43/100.68 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)) <=> member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.68 inference(symmetry,[status(thm)],[725])).
% 100.43/100.68 tff(727,plain,
% 100.43/100.68 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))),
% 100.43/100.68 inference(modus_ponens,[status(thm)],[510, 726])).
% 100.43/100.68 tff(728,plain,
% 100.43/100.68 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs))),
% 100.43/100.68 inference(rewrite,[status(thm)],[])).
% 100.43/100.68 tff(729,plain,
% 100.43/100.68 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs))),
% 100.43/100.68 inference(quant_inst,[status(thm)],[])).
% 100.43/100.68 tff(730,plain,
% 100.43/100.68 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)),
% 100.43/100.68 inference(modus_ponens,[status(thm)],[729, 728])).
% 100.43/100.68 tff(731,plain,
% 100.43/100.68 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set)))) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)),
% 100.43/100.68 inference(unit_resolution,[status(thm)],[730, 66])).
% 100.43/100.68 tff(732,plain,
% 100.43/100.68 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)),
% 100.43/100.68 inference(unit_resolution,[status(thm)],[731, 727])).
% 100.43/100.68 tff(733,plain,
% 100.43/100.68 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)))),
% 100.43/100.68 inference(rewrite,[status(thm)],[])).
% 100.43/100.68 tff(734,plain,
% 100.43/100.68 ((member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs))) <=> ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)))),
% 100.43/100.68 inference(rewrite,[status(thm)],[])).
% 100.43/100.68 tff(735,plain,
% 100.43/100.68 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))))),
% 100.43/100.68 inference(monotonicity,[status(thm)],[734])).
% 100.43/100.68 tff(736,plain,
% 100.43/100.68 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)))),
% 100.43/100.68 inference(transitivity,[status(thm)],[735, 733])).
% 100.43/100.68 tff(737,plain,
% 100.43/100.68 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)))),
% 100.43/100.68 inference(quant_inst,[status(thm)],[])).
% 100.43/100.68 tff(738,plain,
% 100.43/100.68 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))),
% 100.43/100.69 inference(modus_ponens,[status(thm)],[737, 736])).
% 100.43/100.69 tff(739,plain,
% 100.43/100.69 ((~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), bs)) | member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as)) | (~member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), as))),
% 100.43/100.69 inference(unit_resolution,[status(thm)],[738, 18])).
% 100.43/100.69 tff(740,plain,
% 100.43/100.69 (member(f1(intersection(intersection(intersection(universal_set, universal_set), intersection(cs, as)), universal_set), ds), intersection(bs, as))),
% 100.43/100.69 inference(unit_resolution,[status(thm)],[739, 732, 647])).
% 100.43/100.69 tff(741,plain,
% 100.43/100.69 ($false),
% 100.43/100.69 inference(unit_resolution,[status(thm)],[740, 518])).
% 100.43/100.69 % SZS output end Proof
% 100.43/100.69 % E exiting
%------------------------------------------------------------------------------