%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET014-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:24:47 AM UTC 2025
% Result : Unsatisfiable 10.68s 10.87s
% Output : Proof 10.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET014-3 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.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 04:00:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 10.68/10.87 % SZS status Unsatisfiable
% 10.68/10.87 % SZS output start Proof
% 10.68/10.87 tff(member_type, type, (
% 10.68/10.87 member: ( $i * $i ) > $o)).
% 10.68/10.87 tff(bs_type, type, (
% 10.68/10.87 bs: $i)).
% 10.68/10.87 tff(f17_type, type, (
% 10.68/10.87 f17: ( $i * $i ) > $i)).
% 10.68/10.87 tff(cs_type, type, (
% 10.68/10.87 cs: $i)).
% 10.68/10.87 tff(union_type, type, (
% 10.68/10.87 union: ( $i * $i ) > $i)).
% 10.68/10.87 tff(as_type, type, (
% 10.68/10.87 as: $i)).
% 10.68/10.87 tff(subset_type, type, (
% 10.68/10.87 subset: ( $i * $i ) > $o)).
% 10.68/10.87 tff(complement_type, type, (
% 10.68/10.87 complement: $i > $i)).
% 10.68/10.87 tff(little_set_type, type, (
% 10.68/10.87 little_set: $i > $o)).
% 10.68/10.87 tff(intersection_type, type, (
% 10.68/10.87 intersection: ( $i * $i ) > $i)).
% 10.68/10.87 tff(1,assumption,(member(f17(union(as, bs), cs), bs)), introduced(assumption)).
% 10.68/10.87 tff(2,plain,
% 10.68/10.87 ((~subset(union(as, bs), cs)) <=> (~subset(union(as, bs), cs))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(3,axiom,(~subset(union(as, bs), cs)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_a_union_b_subset_of_c')).
% 10.68/10.87 tff(4,plain,
% 10.68/10.87 (~subset(union(as, bs), cs)),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[3, 2])).
% 10.68/10.87 tff(5,plain,
% 10.68/10.87 (^[Y: $i, X: $i] : refl((subset(X, Y) | (~member(f17(X, Y), Y))) <=> (subset(X, Y) | (~member(f17(X, Y), Y))))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(6,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y))) <=> ![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[5])).
% 10.68/10.87 tff(7,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y))) <=> ![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(8,axiom,(![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','subset3')).
% 10.68/10.87 tff(9,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[8, 7])).
% 10.68/10.87 tff(10,plain,(
% 10.68/10.87 ![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 10.68/10.87 inference(skolemize,[status(sab)],[9])).
% 10.68/10.87 tff(11,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[10, 6])).
% 10.68/10.87 tff(12,plain,
% 10.68/10.87 (((~![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))) | (subset(union(as, bs), cs) | (~member(f17(union(as, bs), cs), cs)))) <=> ((~![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))) | subset(union(as, bs), cs) | (~member(f17(union(as, bs), cs), cs)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(13,plain,
% 10.68/10.87 ((~![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))) | (subset(union(as, bs), cs) | (~member(f17(union(as, bs), cs), cs)))),
% 10.68/10.87 inference(quant_inst,[status(thm)],[])).
% 10.68/10.87 tff(14,plain,
% 10.68/10.87 ((~![Y: $i, X: $i] : (subset(X, Y) | (~member(f17(X, Y), Y)))) | subset(union(as, bs), cs) | (~member(f17(union(as, bs), cs), cs))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[13, 12])).
% 10.68/10.87 tff(15,plain,
% 10.68/10.87 (~member(f17(union(as, bs), cs), cs)),
% 10.68/10.87 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 10.68/10.87 tff(16,plain,
% 10.68/10.87 (subset(bs, cs) <=> subset(bs, cs)),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(17,axiom,(subset(bs, cs)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_subset_of_c')).
% 10.68/10.87 tff(18,plain,
% 10.68/10.87 (subset(bs, cs)),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[17, 16])).
% 10.68/10.87 tff(19,plain,
% 10.68/10.87 (^[Y: $i, U: $i, X: $i] : refl(((~member(U, X)) | member(U, Y) | (~subset(X, Y))) <=> ((~member(U, X)) | member(U, Y) | (~subset(X, Y))))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(20,plain,
% 10.68/10.87 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y))) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[19])).
% 10.68/10.87 tff(21,plain,
% 10.68/10.87 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y))) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(22,plain,
% 10.68/10.87 (^[Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~subset(X, Y)) | (~member(U, X))) <=> ((~member(U, X)) | (~subset(X, Y)))), ((((~subset(X, Y)) | (~member(U, X))) | member(U, Y)) <=> (((~member(U, X)) | (~subset(X, Y))) | member(U, Y)))), rewrite((((~member(U, X)) | (~subset(X, Y))) | member(U, Y)) <=> ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))), ((((~subset(X, Y)) | (~member(U, X))) | member(U, Y)) <=> ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(23,plain,
% 10.68/10.87 (![Y: $i, U: $i, X: $i] : (((~subset(X, Y)) | (~member(U, X))) | member(U, Y)) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[22])).
% 10.68/10.87 tff(24,axiom,(![Y: $i, U: $i, X: $i] : (((~subset(X, Y)) | (~member(U, X))) | member(U, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','subset1')).
% 10.68/10.87 tff(25,plain,
% 10.68/10.87 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[24, 23])).
% 10.68/10.87 tff(26,plain,
% 10.68/10.87 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[25, 21])).
% 10.68/10.87 tff(27,plain,(
% 10.68/10.87 ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 10.68/10.87 inference(skolemize,[status(sab)],[26])).
% 10.68/10.87 tff(28,plain,
% 10.68/10.87 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[27, 20])).
% 10.68/10.87 tff(29,plain,
% 10.68/10.87 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~subset(bs, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (~subset(bs, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(30,plain,
% 10.68/10.87 (((~member(f17(union(as, bs), cs), bs)) | member(f17(union(as, bs), cs), cs) | (~subset(bs, cs))) <=> ((~subset(bs, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(31,plain,
% 10.68/10.87 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), bs)) | member(f17(union(as, bs), cs), cs) | (~subset(bs, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~subset(bs, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs))))),
% 10.68/10.87 inference(monotonicity,[status(thm)],[30])).
% 10.68/10.87 tff(32,plain,
% 10.68/10.87 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), bs)) | member(f17(union(as, bs), cs), cs) | (~subset(bs, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (~subset(bs, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs)))),
% 10.68/10.87 inference(transitivity,[status(thm)],[31, 29])).
% 10.68/10.87 tff(33,plain,
% 10.68/10.87 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), bs)) | member(f17(union(as, bs), cs), cs) | (~subset(bs, cs)))),
% 10.68/10.87 inference(quant_inst,[status(thm)],[])).
% 10.68/10.87 tff(34,plain,
% 10.68/10.87 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (~subset(bs, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), bs))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[33, 32])).
% 10.68/10.87 tff(35,plain,
% 10.68/10.87 ($false),
% 10.68/10.87 inference(unit_resolution,[status(thm)],[34, 28, 18, 15, 1])).
% 10.68/10.87 tff(36,plain,(~member(f17(union(as, bs), cs), bs)), inference(lemma,lemma(discharge,[]))).
% 10.68/10.87 tff(37,assumption,(member(f17(union(as, bs), cs), as)), introduced(assumption)).
% 10.68/10.87 tff(38,plain,
% 10.68/10.87 (subset(as, cs) <=> subset(as, cs)),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(39,axiom,(subset(as, cs)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_subset_of_c')).
% 10.68/10.87 tff(40,plain,
% 10.68/10.87 (subset(as, cs)),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[39, 38])).
% 10.68/10.87 tff(41,plain,
% 10.68/10.87 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~subset(as, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (~subset(as, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(42,plain,
% 10.68/10.87 (((~member(f17(union(as, bs), cs), as)) | member(f17(union(as, bs), cs), cs) | (~subset(as, cs))) <=> ((~subset(as, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(43,plain,
% 10.68/10.87 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), as)) | member(f17(union(as, bs), cs), cs) | (~subset(as, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~subset(as, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as))))),
% 10.68/10.87 inference(monotonicity,[status(thm)],[42])).
% 10.68/10.87 tff(44,plain,
% 10.68/10.87 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), as)) | member(f17(union(as, bs), cs), cs) | (~subset(as, cs)))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (~subset(as, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as)))),
% 10.68/10.87 inference(transitivity,[status(thm)],[43, 41])).
% 10.68/10.87 tff(45,plain,
% 10.68/10.87 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | ((~member(f17(union(as, bs), cs), as)) | member(f17(union(as, bs), cs), cs) | (~subset(as, cs)))),
% 10.68/10.87 inference(quant_inst,[status(thm)],[])).
% 10.68/10.87 tff(46,plain,
% 10.68/10.87 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(U, Y) | (~subset(X, Y)))) | (~subset(as, cs)) | member(f17(union(as, bs), cs), cs) | (~member(f17(union(as, bs), cs), as))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[45, 44])).
% 10.68/10.87 tff(47,plain,
% 10.68/10.87 ($false),
% 10.68/10.87 inference(unit_resolution,[status(thm)],[46, 28, 40, 15, 37])).
% 10.68/10.87 tff(48,plain,(~member(f17(union(as, bs), cs), as)), inference(lemma,lemma(discharge,[]))).
% 10.68/10.87 tff(49,assumption,(~member(f17(union(as, bs), cs), complement(as))), introduced(assumption)).
% 10.68/10.87 tff(50,plain,
% 10.68/10.87 (^[Y: $i, X: $i] : refl((union(X, Y) = complement(intersection(complement(X), complement(Y)))) <=> (union(X, Y) = complement(intersection(complement(X), complement(Y)))))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(51,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y)))) <=> ![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[50])).
% 10.68/10.87 tff(52,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y)))) <=> ![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(53,axiom,(![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','union')).
% 10.68/10.87 tff(54,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[53, 52])).
% 10.68/10.87 tff(55,plain,(
% 10.68/10.87 ![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 10.68/10.87 inference(skolemize,[status(sab)],[54])).
% 10.68/10.87 tff(56,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[55, 51])).
% 10.68/10.87 tff(57,plain,
% 10.68/10.87 ((~![Y: $i, X: $i] : (union(X, Y) = complement(intersection(complement(X), complement(Y))))) | (union(as, bs) = complement(intersection(complement(as), complement(bs))))),
% 10.68/10.87 inference(quant_inst,[status(thm)],[])).
% 10.68/10.87 tff(58,plain,
% 10.68/10.87 (union(as, bs) = complement(intersection(complement(as), complement(bs)))),
% 10.68/10.87 inference(unit_resolution,[status(thm)],[57, 56])).
% 10.68/10.87 tff(59,plain,
% 10.68/10.87 (complement(intersection(complement(as), complement(bs))) = union(as, bs)),
% 10.68/10.87 inference(symmetry,[status(thm)],[58])).
% 10.68/10.87 tff(60,plain,
% 10.68/10.87 (member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))) <=> member(f17(union(as, bs), cs), union(as, bs))),
% 10.68/10.87 inference(monotonicity,[status(thm)],[59])).
% 10.68/10.87 tff(61,plain,
% 10.68/10.87 (member(f17(union(as, bs), cs), union(as, bs)) <=> member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))),
% 10.68/10.87 inference(symmetry,[status(thm)],[60])).
% 10.68/10.87 tff(62,plain,
% 10.68/10.87 (^[Y: $i, X: $i] : refl((subset(X, Y) | member(f17(X, Y), X)) <=> (subset(X, Y) | member(f17(X, Y), X)))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(63,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X)) <=> ![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[62])).
% 10.68/10.87 tff(64,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X)) <=> ![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(65,axiom,(![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','subset2')).
% 10.68/10.87 tff(66,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[65, 64])).
% 10.68/10.87 tff(67,plain,(
% 10.68/10.87 ![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 10.68/10.87 inference(skolemize,[status(sab)],[66])).
% 10.68/10.87 tff(68,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[67, 63])).
% 10.68/10.87 tff(69,plain,
% 10.68/10.87 (((~![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))) | (subset(union(as, bs), cs) | member(f17(union(as, bs), cs), union(as, bs)))) <=> ((~![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))) | subset(union(as, bs), cs) | member(f17(union(as, bs), cs), union(as, bs)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(70,plain,
% 10.68/10.87 ((~![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))) | (subset(union(as, bs), cs) | member(f17(union(as, bs), cs), union(as, bs)))),
% 10.68/10.87 inference(quant_inst,[status(thm)],[])).
% 10.68/10.87 tff(71,plain,
% 10.68/10.87 ((~![Y: $i, X: $i] : (subset(X, Y) | member(f17(X, Y), X))) | subset(union(as, bs), cs) | member(f17(union(as, bs), cs), union(as, bs))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[70, 69])).
% 10.68/10.87 tff(72,plain,
% 10.68/10.87 (member(f17(union(as, bs), cs), union(as, bs))),
% 10.68/10.87 inference(unit_resolution,[status(thm)],[71, 68, 4])).
% 10.68/10.87 tff(73,plain,
% 10.68/10.87 (member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[72, 61])).
% 10.68/10.87 tff(74,plain,
% 10.68/10.87 (^[Y: $i, X: $i] : refl((little_set(X) | (~member(X, Y))) <=> (little_set(X) | (~member(X, Y))))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(75,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[74])).
% 10.68/10.87 tff(76,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(77,plain,
% 10.68/10.87 (^[Y: $i, X: $i] : rewrite(((~member(X, Y)) | little_set(X)) <=> (little_set(X) | (~member(X, Y))))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(78,plain,
% 10.68/10.87 (![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X)) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[77])).
% 10.68/10.87 tff(79,axiom,(![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','a2')).
% 10.68/10.87 tff(80,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[79, 78])).
% 10.68/10.87 tff(81,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[80, 76])).
% 10.68/10.87 tff(82,plain,(
% 10.68/10.87 ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 10.68/10.87 inference(skolemize,[status(sab)],[81])).
% 10.68/10.87 tff(83,plain,
% 10.68/10.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[82, 75])).
% 10.68/10.87 tff(84,plain,
% 10.68/10.87 (((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))) <=> ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(85,plain,
% 10.68/10.87 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))),
% 10.68/10.87 inference(quant_inst,[status(thm)],[])).
% 10.68/10.87 tff(86,plain,
% 10.68/10.87 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[85, 84])).
% 10.68/10.87 tff(87,plain,
% 10.68/10.87 (little_set(f17(union(as, bs), cs)) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))))),
% 10.68/10.87 inference(unit_resolution,[status(thm)],[86, 83])).
% 10.68/10.87 tff(88,plain,
% 10.68/10.87 (little_set(f17(union(as, bs), cs))),
% 10.68/10.87 inference(unit_resolution,[status(thm)],[87, 73])).
% 10.68/10.87 tff(89,plain,
% 10.68/10.87 (^[Z: $i, X: $i] : refl(((~little_set(Z)) | member(Z, X) | member(Z, complement(X))) <=> ((~little_set(Z)) | member(Z, X) | member(Z, complement(X))))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(90,plain,
% 10.68/10.87 (![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X))) <=> ![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[89])).
% 10.68/10.87 tff(91,plain,
% 10.68/10.87 (![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X))) <=> ![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(92,plain,
% 10.68/10.87 (^[Z: $i, X: $i] : trans(monotonicity(rewrite((member(Z, complement(X)) | (~little_set(Z))) <=> ((~little_set(Z)) | member(Z, complement(X)))), (((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> (((~little_set(Z)) | member(Z, complement(X))) | member(Z, X)))), rewrite((((~little_set(Z)) | member(Z, complement(X))) | member(Z, X)) <=> ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))), (((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))))),
% 10.68/10.87 inference(bind,[status(th)],[])).
% 10.68/10.87 tff(93,plain,
% 10.68/10.87 (![Z: $i, X: $i] : ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> ![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))),
% 10.68/10.87 inference(quant_intro,[status(thm)],[92])).
% 10.68/10.87 tff(94,axiom,(![Z: $i, X: $i] : ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','complement2')).
% 10.68/10.87 tff(95,plain,
% 10.68/10.87 (![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[94, 93])).
% 10.68/10.87 tff(96,plain,
% 10.68/10.87 (![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[95, 91])).
% 10.68/10.87 tff(97,plain,(
% 10.68/10.87 ![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))),
% 10.68/10.87 inference(skolemize,[status(sab)],[96])).
% 10.68/10.87 tff(98,plain,
% 10.68/10.87 (![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))),
% 10.68/10.87 inference(modus_ponens,[status(thm)],[97, 90])).
% 10.68/10.87 tff(99,plain,
% 10.68/10.87 (((~![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))) | ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), as) | member(f17(union(as, bs), cs), complement(as)))) <=> ((~![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), as) | member(f17(union(as, bs), cs), complement(as)))),
% 10.68/10.87 inference(rewrite,[status(thm)],[])).
% 10.68/10.87 tff(100,plain,
% 10.68/10.87 ((~![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))) | ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), as) | member(f17(union(as, bs), cs), complement(as)))),
% 10.68/10.88 inference(quant_inst,[status(thm)],[])).
% 10.68/10.88 tff(101,plain,
% 10.68/10.88 ((~![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), as) | member(f17(union(as, bs), cs), complement(as))),
% 10.68/10.88 inference(modus_ponens,[status(thm)],[100, 99])).
% 10.68/10.88 tff(102,plain,
% 10.68/10.88 ($false),
% 10.68/10.88 inference(unit_resolution,[status(thm)],[101, 98, 88, 49, 48])).
% 10.68/10.88 tff(103,plain,(member(f17(union(as, bs), cs), complement(as))), inference(lemma,lemma(discharge,[]))).
% 10.68/10.88 tff(104,plain,
% 10.68/10.88 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 10.68/10.88 inference(bind,[status(th)],[])).
% 10.68/10.88 tff(105,plain,
% 10.68/10.88 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 10.68/10.88 inference(quant_intro,[status(thm)],[104])).
% 10.68/10.88 tff(106,plain,
% 10.68/10.88 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 10.68/10.88 inference(rewrite,[status(thm)],[])).
% 10.68/10.88 tff(107,plain,
% 10.68/10.88 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 10.68/10.88 inference(bind,[status(th)],[])).
% 10.68/10.88 tff(108,plain,
% 10.68/10.88 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 10.68/10.88 inference(quant_intro,[status(thm)],[107])).
% 10.68/10.88 tff(109,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','complement1')).
% 10.68/10.88 tff(110,plain,
% 10.68/10.88 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 10.68/10.88 inference(modus_ponens,[status(thm)],[109, 108])).
% 10.68/10.88 tff(111,plain,
% 10.68/10.88 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 10.68/10.88 inference(modus_ponens,[status(thm)],[110, 106])).
% 10.68/10.88 tff(112,plain,(
% 10.68/10.88 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 10.68/10.88 inference(skolemize,[status(sab)],[111])).
% 10.68/10.88 tff(113,plain,
% 10.68/10.88 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 10.68/10.88 inference(modus_ponens,[status(thm)],[112, 105])).
% 10.68/10.88 tff(114,plain,
% 10.68/10.88 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))),
% 10.68/10.88 inference(rewrite,[status(thm)],[])).
% 10.68/10.88 tff(115,plain,
% 10.68/10.88 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs))))))),
% 10.68/10.88 inference(quant_inst,[status(thm)],[])).
% 10.68/10.88 tff(116,plain,
% 10.68/10.88 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))))),
% 10.68/10.88 inference(modus_ponens,[status(thm)],[115, 114])).
% 10.68/10.88 tff(117,plain,
% 10.68/10.88 ((~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))) | (~member(f17(union(as, bs), cs), complement(intersection(complement(as), complement(bs)))))),
% 10.68/10.88 inference(unit_resolution,[status(thm)],[116, 113])).
% 10.68/10.88 tff(118,plain,
% 10.68/10.88 (~member(f17(union(as, bs), cs), intersection(complement(as), complement(bs)))),
% 10.68/10.88 inference(unit_resolution,[status(thm)],[117, 73])).
% 10.68/10.88 tff(119,plain,
% 10.68/10.88 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X))) <=> ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X))))),
% 10.68/10.88 inference(bind,[status(th)],[])).
% 10.68/10.88 tff(120,plain,
% 10.72/10.88 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))),
% 10.72/10.88 inference(quant_intro,[status(thm)],[119])).
% 10.72/10.88 tff(121,plain,
% 10.72/10.88 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))),
% 10.72/10.88 inference(rewrite,[status(thm)],[])).
% 10.72/10.88 tff(122,plain,
% 10.72/10.88 (^[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, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))), (((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y))) <=> ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))))),
% 10.72/10.88 inference(bind,[status(th)],[])).
% 10.72/10.88 tff(123,plain,
% 10.72/10.88 (![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, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))),
% 10.72/10.88 inference(quant_intro,[status(thm)],[122])).
% 10.72/10.88 tff(124,axiom,(![Z: $i, Y: $i, X: $i] : ((member(Z, intersection(X, Y)) | (~member(Z, X))) | (~member(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','intersection3')).
% 10.72/10.88 tff(125,plain,
% 10.72/10.88 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))),
% 10.72/10.88 inference(modus_ponens,[status(thm)],[124, 123])).
% 10.72/10.88 tff(126,plain,
% 10.72/10.88 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))),
% 10.72/10.88 inference(modus_ponens,[status(thm)],[125, 121])).
% 10.72/10.88 tff(127,plain,(
% 10.72/10.88 ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))),
% 10.72/10.88 inference(skolemize,[status(sab)],[126])).
% 10.72/10.88 tff(128,plain,
% 10.72/10.88 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))),
% 10.72/10.88 inference(modus_ponens,[status(thm)],[127, 120])).
% 10.72/10.88 tff(129,plain,
% 10.72/10.88 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))) | (member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))),
% 10.72/10.88 inference(rewrite,[status(thm)],[])).
% 10.72/10.88 tff(130,plain,
% 10.72/10.88 (((~member(f17(union(as, bs), cs), complement(bs))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as)))) <=> (member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))),
% 10.72/10.88 inference(rewrite,[status(thm)],[])).
% 10.72/10.88 tff(131,plain,
% 10.72/10.88 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))) | ((~member(f17(union(as, bs), cs), complement(bs))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))) | (member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as)))))),
% 10.72/10.88 inference(monotonicity,[status(thm)],[130])).
% 10.72/10.88 tff(132,plain,
% 10.72/10.88 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))) | ((~member(f17(union(as, bs), cs), complement(bs))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))),
% 10.72/10.89 inference(transitivity,[status(thm)],[131, 129])).
% 10.72/10.89 tff(133,plain,
% 10.72/10.89 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))) | ((~member(f17(union(as, bs), cs), complement(bs))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as))))),
% 10.72/10.89 inference(quant_inst,[status(thm)],[])).
% 10.72/10.89 tff(134,plain,
% 10.72/10.89 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | member(Z, intersection(X, Y)) | (~member(Z, X)))) | member(f17(union(as, bs), cs), intersection(complement(as), complement(bs))) | (~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as)))),
% 10.72/10.89 inference(modus_ponens,[status(thm)],[133, 132])).
% 10.72/10.89 tff(135,plain,
% 10.72/10.89 ((~member(f17(union(as, bs), cs), complement(bs))) | (~member(f17(union(as, bs), cs), complement(as)))),
% 10.72/10.89 inference(unit_resolution,[status(thm)],[134, 128, 118])).
% 10.72/10.89 tff(136,plain,
% 10.72/10.89 (~member(f17(union(as, bs), cs), complement(bs))),
% 10.72/10.89 inference(unit_resolution,[status(thm)],[135, 103])).
% 10.72/10.89 tff(137,plain,
% 10.72/10.89 (((~![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))) | ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), bs) | member(f17(union(as, bs), cs), complement(bs)))) <=> ((~![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), bs) | member(f17(union(as, bs), cs), complement(bs)))),
% 10.72/10.89 inference(rewrite,[status(thm)],[])).
% 10.72/10.89 tff(138,plain,
% 10.72/10.89 ((~![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))) | ((~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), bs) | member(f17(union(as, bs), cs), complement(bs)))),
% 10.72/10.89 inference(quant_inst,[status(thm)],[])).
% 10.72/10.89 tff(139,plain,
% 10.72/10.89 ((~![Z: $i, X: $i] : ((~little_set(Z)) | member(Z, X) | member(Z, complement(X)))) | (~little_set(f17(union(as, bs), cs))) | member(f17(union(as, bs), cs), bs) | member(f17(union(as, bs), cs), complement(bs))),
% 10.72/10.89 inference(modus_ponens,[status(thm)],[138, 137])).
% 10.72/10.89 tff(140,plain,
% 10.72/10.89 ($false),
% 10.72/10.89 inference(unit_resolution,[status(thm)],[139, 98, 88, 136, 36])).
% 10.72/10.89 % SZS output end Proof
% 10.72/10.90 % E exiting
%------------------------------------------------------------------------------