%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU328+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:27:37 AM UTC 2025
% Result : Theorem 264.51s 264.73s
% Output : Proof 264.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU328+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 06:47:01 EDT 2025
% 0.12/0.34 % CPUTime :
% 264.51/264.73 % SZS status Theorem
% 264.51/264.73 % SZS output start Proof
% 264.51/264.73 tff(element_type, type, (
% 264.51/264.73 element: ( $i * $i ) > $o)).
% 264.51/264.73 tff(powerset_type, type, (
% 264.51/264.73 powerset: $i > $i)).
% 264.51/264.73 tff(tptp_fun_A_219_type, type, (
% 264.51/264.73 tptp_fun_A_219: $i)).
% 264.51/264.73 tff(meet_of_subsets_type, type, (
% 264.51/264.73 meet_of_subsets: ( $i * $i ) > $i)).
% 264.51/264.73 tff(complements_of_subsets_type, type, (
% 264.51/264.73 complements_of_subsets: ( $i * $i ) > $i)).
% 264.51/264.73 tff(tptp_fun_B_218_type, type, (
% 264.51/264.73 tptp_fun_B_218: $i)).
% 264.51/264.73 tff(subset_complement_type, type, (
% 264.51/264.73 subset_complement: ( $i * $i ) > $i)).
% 264.51/264.73 tff(union_of_subsets_type, type, (
% 264.51/264.73 union_of_subsets: ( $i * $i ) > $i)).
% 264.51/264.73 tff(empty_set_type, type, (
% 264.51/264.73 empty_set: $i)).
% 264.51/264.73 tff(set_difference_type, type, (
% 264.51/264.73 set_difference: ( $i * $i ) > $i)).
% 264.51/264.73 tff(cast_to_subset_type, type, (
% 264.51/264.73 cast_to_subset: $i > $i)).
% 264.51/264.73 tff(subset_difference_type, type, (
% 264.51/264.73 subset_difference: ( $i * $i * $i ) > $i)).
% 264.51/264.73 tff(1,plain,
% 264.51/264.73 ((~((B!218 = empty_set) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218))) | (~element(B!218, powerset(powerset(A!219)))))) <=> (~((B!218 = empty_set) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218))) | (~element(B!218, powerset(powerset(A!219))))))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(2,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) <=> (~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A))))))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(3,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : (element(B, powerset(powerset(A))) => ((~(B = empty_set)) => (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B)))))) <=> (~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A))))))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(4,axiom,(~![A: $i, B: $i] : (element(B, powerset(powerset(A))) => ((~(B = empty_set)) => (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_tops_2')).
% 264.51/264.73 tff(5,plain,
% 264.51/264.73 (~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[4, 3])).
% 264.51/264.73 tff(6,plain,
% 264.51/264.73 (~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[5, 2])).
% 264.51/264.73 tff(7,plain,
% 264.51/264.73 (~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[6, 2])).
% 264.51/264.73 tff(8,plain,
% 264.51/264.73 (~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_complement(A, meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[7, 2])).
% 264.51/264.73 tff(9,plain,(
% 264.51/264.73 ~((B!218 = empty_set) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218))) | (~element(B!218, powerset(powerset(A!219)))))),
% 264.51/264.73 inference(skolemize,[status(sab)],[8])).
% 264.51/264.73 tff(10,plain,
% 264.51/264.73 (~((B!218 = empty_set) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218))) | (~element(B!218, powerset(powerset(A!219)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[9, 1])).
% 264.51/264.73 tff(11,plain,
% 264.51/264.73 (element(B!218, powerset(powerset(A!219)))),
% 264.51/264.73 inference(or_elim,[status(thm)],[10])).
% 264.51/264.73 tff(12,plain,
% 264.51/264.73 (^[A: $i, B: $i] : refl(((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(13,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[12])).
% 264.51/264.73 tff(14,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(15,plain,
% 264.51/264.73 (^[A: $i, B: $i] : rewrite((element(B, powerset(powerset(A))) => (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(16,plain,
% 264.51/264.73 (![A: $i, B: $i] : (element(B, powerset(powerset(A))) => (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[15])).
% 264.51/264.73 tff(17,axiom,(![A: $i, B: $i] : (element(B, powerset(powerset(A))) => (complements_of_subsets(A, complements_of_subsets(A, B)) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','involutiveness_k7_setfam_1')).
% 264.51/264.73 tff(18,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[17, 16])).
% 264.51/264.73 tff(19,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[18, 14])).
% 264.51/264.73 tff(20,plain,(
% 264.51/264.73 ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 264.51/264.73 inference(skolemize,[status(sab)],[19])).
% 264.51/264.73 tff(21,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[20, 13])).
% 264.51/264.73 tff(22,plain,
% 264.51/264.73 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))) | ((~element(B!218, powerset(powerset(A!219)))) | (complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = B!218))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))) | (~element(B!218, powerset(powerset(A!219)))) | (complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = B!218))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(23,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))) | ((~element(B!218, powerset(powerset(A!219)))) | (complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = B!218))),
% 264.51/264.73 inference(quant_inst,[status(thm)],[])).
% 264.51/264.73 tff(24,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))) | (~element(B!218, powerset(powerset(A!219)))) | (complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = B!218)),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[23, 22])).
% 264.51/264.73 tff(25,plain,
% 264.51/264.73 (complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = B!218),
% 264.51/264.73 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 264.51/264.73 tff(26,plain,
% 264.51/264.73 (B!218 = complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(symmetry,[status(thm)],[25])).
% 264.51/264.73 tff(27,plain,
% 264.51/264.73 (meet_of_subsets(A!219, B!218) = meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))),
% 264.51/264.73 inference(monotonicity,[status(thm)],[26])).
% 264.51/264.73 tff(28,plain,
% 264.51/264.73 (meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))) = meet_of_subsets(A!219, B!218)),
% 264.51/264.73 inference(symmetry,[status(thm)],[27])).
% 264.51/264.73 tff(29,plain,
% 264.51/264.73 (element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219)) <=> element(meet_of_subsets(A!219, B!218), powerset(A!219))),
% 264.51/264.73 inference(monotonicity,[status(thm)],[28])).
% 264.51/264.73 tff(30,plain,
% 264.51/264.73 (element(meet_of_subsets(A!219, B!218), powerset(A!219)) <=> element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))),
% 264.51/264.73 inference(symmetry,[status(thm)],[29])).
% 264.51/264.73 tff(31,plain,
% 264.51/264.73 (^[A: $i, B: $i] : refl(((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A))) <=> ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(32,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[31])).
% 264.51/264.73 tff(33,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(34,plain,
% 264.51/264.73 (^[A: $i, B: $i] : rewrite((element(B, powerset(powerset(A))) => element(meet_of_subsets(A, B), powerset(A))) <=> ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(35,plain,
% 264.51/264.73 (![A: $i, B: $i] : (element(B, powerset(powerset(A))) => element(meet_of_subsets(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[34])).
% 264.51/264.73 tff(36,axiom,(![A: $i, B: $i] : (element(B, powerset(powerset(A))) => element(meet_of_subsets(A, B), powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_setfam_1')).
% 264.51/264.73 tff(37,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[36, 35])).
% 264.51/264.73 tff(38,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[37, 33])).
% 264.51/264.73 tff(39,plain,(
% 264.51/264.73 ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))),
% 264.51/264.73 inference(skolemize,[status(sab)],[38])).
% 264.51/264.73 tff(40,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[39, 32])).
% 264.51/264.73 tff(41,plain,
% 264.51/264.73 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))) | ((~element(B!218, powerset(powerset(A!219)))) | element(meet_of_subsets(A!219, B!218), powerset(A!219)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))) | (~element(B!218, powerset(powerset(A!219)))) | element(meet_of_subsets(A!219, B!218), powerset(A!219)))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(42,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))) | ((~element(B!218, powerset(powerset(A!219)))) | element(meet_of_subsets(A!219, B!218), powerset(A!219)))),
% 264.51/264.73 inference(quant_inst,[status(thm)],[])).
% 264.51/264.73 tff(43,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(meet_of_subsets(A, B), powerset(A)))) | (~element(B!218, powerset(powerset(A!219)))) | element(meet_of_subsets(A!219, B!218), powerset(A!219))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[42, 41])).
% 264.51/264.73 tff(44,plain,
% 264.51/264.73 (element(meet_of_subsets(A!219, B!218), powerset(A!219))),
% 264.51/264.73 inference(unit_resolution,[status(thm)],[43, 40, 11])).
% 264.51/264.73 tff(45,plain,
% 264.51/264.73 (element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[44, 30])).
% 264.51/264.73 tff(46,plain,
% 264.51/264.73 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(47,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[46])).
% 264.51/264.73 tff(48,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(49,plain,
% 264.51/264.73 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(50,plain,
% 264.51/264.73 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[49])).
% 264.51/264.73 tff(51,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_subset_1')).
% 264.51/264.73 tff(52,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[51, 50])).
% 264.51/264.73 tff(53,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[52, 48])).
% 264.51/264.73 tff(54,plain,(
% 264.51/264.73 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 264.51/264.73 inference(skolemize,[status(sab)],[53])).
% 264.51/264.73 tff(55,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[54, 47])).
% 264.51/264.73 tff(56,plain,
% 264.51/264.73 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(meet_of_subsets(A!219, B!218), powerset(A!219))) | (subset_complement(A!219, meet_of_subsets(A!219, B!218)) = set_difference(A!219, meet_of_subsets(A!219, B!218))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(meet_of_subsets(A!219, B!218), powerset(A!219))) | (subset_complement(A!219, meet_of_subsets(A!219, B!218)) = set_difference(A!219, meet_of_subsets(A!219, B!218))))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(57,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(meet_of_subsets(A!219, B!218), powerset(A!219))) | (subset_complement(A!219, meet_of_subsets(A!219, B!218)) = set_difference(A!219, meet_of_subsets(A!219, B!218))))),
% 264.51/264.73 inference(quant_inst,[status(thm)],[])).
% 264.51/264.73 tff(58,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(meet_of_subsets(A!219, B!218), powerset(A!219))) | (subset_complement(A!219, meet_of_subsets(A!219, B!218)) = set_difference(A!219, meet_of_subsets(A!219, B!218)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[57, 56])).
% 264.51/264.73 tff(59,plain,
% 264.51/264.73 (subset_complement(A!219, meet_of_subsets(A!219, B!218)) = set_difference(A!219, meet_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(unit_resolution,[status(thm)],[58, 55, 44])).
% 264.51/264.73 tff(60,plain,
% 264.51/264.73 (set_difference(A!219, meet_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(symmetry,[status(thm)],[59])).
% 264.51/264.73 tff(61,plain,
% 264.51/264.73 (^[A: $i] : refl((cast_to_subset(A) = A) <=> (cast_to_subset(A) = A))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(62,plain,
% 264.51/264.73 (![A: $i] : (cast_to_subset(A) = A) <=> ![A: $i] : (cast_to_subset(A) = A)),
% 264.51/264.73 inference(quant_intro,[status(thm)],[61])).
% 264.51/264.73 tff(63,plain,
% 264.51/264.73 (![A: $i] : (cast_to_subset(A) = A) <=> ![A: $i] : (cast_to_subset(A) = A)),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(64,axiom,(![A: $i] : (cast_to_subset(A) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_subset_1')).
% 264.51/264.73 tff(65,plain,
% 264.51/264.73 (![A: $i] : (cast_to_subset(A) = A)),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[64, 63])).
% 264.51/264.73 tff(66,plain,(
% 264.51/264.73 ![A: $i] : (cast_to_subset(A) = A)),
% 264.51/264.73 inference(skolemize,[status(sab)],[65])).
% 264.51/264.73 tff(67,plain,
% 264.51/264.73 (![A: $i] : (cast_to_subset(A) = A)),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[66, 62])).
% 264.51/264.73 tff(68,plain,
% 264.51/264.73 ((~![A: $i] : (cast_to_subset(A) = A)) | (cast_to_subset(A!219) = A!219)),
% 264.51/264.73 inference(quant_inst,[status(thm)],[])).
% 264.51/264.73 tff(69,plain,
% 264.51/264.73 (cast_to_subset(A!219) = A!219),
% 264.51/264.73 inference(unit_resolution,[status(thm)],[68, 67])).
% 264.51/264.73 tff(70,plain,
% 264.51/264.73 (set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(A!219, meet_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(monotonicity,[status(thm)],[69, 28])).
% 264.51/264.73 tff(71,plain,
% 264.51/264.73 (set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = subset_complement(A!219, meet_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(transitivity,[status(thm)],[70, 60])).
% 264.51/264.73 tff(72,plain,
% 264.51/264.73 (^[A: $i, B: $i] : refl(((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A))))) <=> ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A))))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(73,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A))))) <=> ![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[72])).
% 264.51/264.73 tff(74,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A))))) <=> ![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(75,plain,
% 264.51/264.73 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = empty_set)) => (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B)))) <=> ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))))), ((element(B, powerset(powerset(A))) => ((~(B = empty_set)) => (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))))) <=> (element(B, powerset(powerset(A))) => ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))))))), rewrite((element(B, powerset(powerset(A))) => ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))))) <=> ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))), ((element(B, powerset(powerset(A))) => ((~(B = empty_set)) => (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))))) <=> ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(76,plain,
% 264.51/264.73 (![A: $i, B: $i] : (element(B, powerset(powerset(A))) => ((~(B = empty_set)) => (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))))) <=> ![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[75])).
% 264.51/264.73 tff(77,axiom,(![A: $i, B: $i] : (element(B, powerset(powerset(A))) => ((~(B = empty_set)) => (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t48_setfam_1')).
% 264.51/264.73 tff(78,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[77, 76])).
% 264.51/264.73 tff(79,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[78, 74])).
% 264.51/264.73 tff(80,plain,(
% 264.51/264.73 ![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(skolemize,[status(sab)],[79])).
% 264.51/264.73 tff(81,plain,
% 264.51/264.73 (![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[80, 73])).
% 264.51/264.73 tff(82,plain,
% 264.51/264.73 (~(B!218 = empty_set)),
% 264.51/264.73 inference(or_elim,[status(thm)],[10])).
% 264.51/264.73 tff(83,plain,
% 264.51/264.73 (((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) | ((B!218 = empty_set) | (~element(B!218, powerset(powerset(A!219)))) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))))) <=> ((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) | (B!218 = empty_set) | (~element(B!218, powerset(powerset(A!219)))) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(84,plain,
% 264.51/264.73 (((B!218 = empty_set) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))) | (~element(B!218, powerset(powerset(A!219))))) <=> ((B!218 = empty_set) | (~element(B!218, powerset(powerset(A!219)))) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(85,plain,
% 264.51/264.73 (((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) | ((B!218 = empty_set) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))) | (~element(B!218, powerset(powerset(A!219)))))) <=> ((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) | ((B!218 = empty_set) | (~element(B!218, powerset(powerset(A!219)))) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218)))))),
% 264.51/264.73 inference(monotonicity,[status(thm)],[84])).
% 264.51/264.73 tff(86,plain,
% 264.51/264.73 (((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) | ((B!218 = empty_set) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))) | (~element(B!218, powerset(powerset(A!219)))))) <=> ((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) | (B!218 = empty_set) | (~element(B!218, powerset(powerset(A!219)))) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))))),
% 264.51/264.73 inference(transitivity,[status(thm)],[85, 83])).
% 264.51/264.73 tff(87,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) | ((B!218 = empty_set) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))) | (~element(B!218, powerset(powerset(A!219)))))),
% 264.51/264.73 inference(quant_inst,[status(thm)],[])).
% 264.51/264.73 tff(88,plain,
% 264.51/264.73 ((~![A: $i, B: $i] : ((B = empty_set) | (union_of_subsets(A, complements_of_subsets(A, B)) = subset_difference(A, cast_to_subset(A), meet_of_subsets(A, B))) | (~element(B, powerset(powerset(A)))))) | (B!218 = empty_set) | (~element(B!218, powerset(powerset(A!219)))) | (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[87, 86])).
% 264.51/264.73 tff(89,plain,
% 264.51/264.73 (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(unit_resolution,[status(thm)],[88, 82, 11, 81])).
% 264.51/264.73 tff(90,plain,
% 264.51/264.73 (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218)) = union_of_subsets(A!219, complements_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(symmetry,[status(thm)],[89])).
% 264.51/264.73 tff(91,plain,
% 264.51/264.73 (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(monotonicity,[status(thm)],[28])).
% 264.51/264.73 tff(92,plain,
% 264.51/264.73 (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = union_of_subsets(A!219, complements_of_subsets(A!219, B!218))),
% 264.51/264.73 inference(transitivity,[status(thm)],[91, 90])).
% 264.51/264.73 tff(93,plain,
% 264.51/264.73 ((subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))) <=> (union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218)))),
% 264.51/264.73 inference(monotonicity,[status(thm)],[92, 71])).
% 264.51/264.73 tff(94,plain,
% 264.51/264.73 ((union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218))) <=> (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))))),
% 264.51/264.73 inference(symmetry,[status(thm)],[93])).
% 264.51/264.73 tff(95,plain,
% 264.51/264.73 ((~(union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218)))) <=> (~(subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))))),
% 264.51/264.73 inference(monotonicity,[status(thm)],[94])).
% 264.51/264.73 tff(96,plain,
% 264.51/264.73 (~(union_of_subsets(A!219, complements_of_subsets(A!219, B!218)) = subset_complement(A!219, meet_of_subsets(A!219, B!218)))),
% 264.51/264.73 inference(or_elim,[status(thm)],[10])).
% 264.51/264.73 tff(97,plain,
% 264.51/264.73 (~(subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[96, 95])).
% 264.51/264.73 tff(98,plain,
% 264.51/264.73 (^[A: $i] : refl(element(cast_to_subset(A), powerset(A)) <=> element(cast_to_subset(A), powerset(A)))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(99,plain,
% 264.51/264.73 (![A: $i] : element(cast_to_subset(A), powerset(A)) <=> ![A: $i] : element(cast_to_subset(A), powerset(A))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[98])).
% 264.51/264.73 tff(100,plain,
% 264.51/264.73 (![A: $i] : element(cast_to_subset(A), powerset(A)) <=> ![A: $i] : element(cast_to_subset(A), powerset(A))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(101,axiom,(![A: $i] : element(cast_to_subset(A), powerset(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_subset_1')).
% 264.51/264.73 tff(102,plain,
% 264.51/264.73 (![A: $i] : element(cast_to_subset(A), powerset(A))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[101, 100])).
% 264.51/264.73 tff(103,plain,(
% 264.51/264.73 ![A: $i] : element(cast_to_subset(A), powerset(A))),
% 264.51/264.73 inference(skolemize,[status(sab)],[102])).
% 264.51/264.73 tff(104,plain,
% 264.51/264.73 (![A: $i] : element(cast_to_subset(A), powerset(A))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[103, 99])).
% 264.51/264.73 tff(105,plain,
% 264.51/264.73 ((~![A: $i] : element(cast_to_subset(A), powerset(A))) | element(cast_to_subset(A!219), powerset(A!219))),
% 264.51/264.73 inference(quant_inst,[status(thm)],[])).
% 264.51/264.73 tff(106,plain,
% 264.51/264.73 (element(cast_to_subset(A!219), powerset(A!219))),
% 264.51/264.73 inference(unit_resolution,[status(thm)],[105, 104])).
% 264.51/264.73 tff(107,plain,
% 264.51/264.73 (^[A: $i, B: $i, C: $i] : refl(((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(108,plain,
% 264.51/264.73 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[107])).
% 264.51/264.73 tff(109,plain,
% 264.51/264.73 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(C, powerset(A))) | (~element(B, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))))), rewrite((~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A)))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> (((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))))), rewrite((((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(110,plain,
% 264.51/264.73 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[109])).
% 264.51/264.73 tff(111,plain,
% 264.51/264.73 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 264.51/264.73 inference(rewrite,[status(thm)],[])).
% 264.51/264.73 tff(112,plain,
% 264.51/264.73 (^[A: $i, B: $i, C: $i] : rewrite(((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C))) <=> ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))))),
% 264.51/264.73 inference(bind,[status(th)],[])).
% 264.51/264.73 tff(113,plain,
% 264.51/264.73 (![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 264.51/264.73 inference(quant_intro,[status(thm)],[112])).
% 264.51/264.73 tff(114,axiom,(![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k6_subset_1')).
% 264.51/264.73 tff(115,plain,
% 264.51/264.73 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[114, 113])).
% 264.51/264.73 tff(116,plain,
% 264.51/264.73 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[115, 111])).
% 264.51/264.73 tff(117,plain,(
% 264.51/264.73 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 264.51/264.73 inference(skolemize,[status(sab)],[116])).
% 264.51/264.73 tff(118,plain,
% 264.51/264.73 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[117, 110])).
% 264.51/264.73 tff(119,plain,
% 264.51/264.73 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 264.51/264.73 inference(modus_ponens,[status(thm)],[118, 108])).
% 264.51/264.73 tff(120,plain,
% 264.51/264.73 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(cast_to_subset(A!219), powerset(A!219))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(cast_to_subset(A!219), powerset(A!219))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))))),
% 264.51/264.74 inference(rewrite,[status(thm)],[])).
% 264.51/264.74 tff(121,plain,
% 264.51/264.74 (((subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (~element(cast_to_subset(A!219), powerset(A!219)))) <=> ((~element(cast_to_subset(A!219), powerset(A!219))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))))),
% 264.51/264.74 inference(rewrite,[status(thm)],[])).
% 264.51/264.74 tff(122,plain,
% 264.51/264.74 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (~element(cast_to_subset(A!219), powerset(A!219))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(cast_to_subset(A!219), powerset(A!219))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))))))),
% 264.51/264.74 inference(monotonicity,[status(thm)],[121])).
% 264.51/264.74 tff(123,plain,
% 264.51/264.74 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (~element(cast_to_subset(A!219), powerset(A!219))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(cast_to_subset(A!219), powerset(A!219))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))))),
% 264.51/264.74 inference(transitivity,[status(thm)],[122, 120])).
% 264.51/264.74 tff(124,plain,
% 264.51/264.74 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (~element(cast_to_subset(A!219), powerset(A!219))))),
% 264.74/264.96 inference(quant_inst,[status(thm)],[])).
% 264.74/264.96 tff(125,plain,
% 264.74/264.96 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(cast_to_subset(A!219), powerset(A!219))) | (~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))))),
% 264.74/264.96 inference(modus_ponens,[status(thm)],[124, 123])).
% 264.74/264.96 tff(126,plain,
% 264.74/264.96 ((~element(meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218))), powerset(A!219))) | (subset_difference(A!219, cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))) = set_difference(cast_to_subset(A!219), meet_of_subsets(A!219, complements_of_subsets(A!219, complements_of_subsets(A!219, B!218)))))),
% 264.74/264.96 inference(unit_resolution,[status(thm)],[125, 119, 106])).
% 264.74/264.96 tff(127,plain,
% 264.74/264.96 ($false),
% 264.74/264.96 inference(unit_resolution,[status(thm)],[126, 97, 45])).
% 264.74/264.96 % SZS output end Proof
% 265.17/265.44 % E exiting
%------------------------------------------------------------------------------