%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET637+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:26:04 AM UTC 2025
% Result : Theorem 0.21s 0.60s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET637+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 05:32:24 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.21/0.60 % SZS status Theorem
% 0.21/0.60 % SZS output start Proof
% 0.21/0.60 tff(empty_set_type, type, (
% 0.21/0.60 empty_set: $i)).
% 0.21/0.60 tff(intersection_type, type, (
% 0.21/0.60 intersection: ( $i * $i ) > $i)).
% 0.21/0.60 tff(tptp_fun_C_3_type, type, (
% 0.21/0.60 tptp_fun_C_3: $i)).
% 0.21/0.60 tff(tptp_fun_B_4_type, type, (
% 0.21/0.60 tptp_fun_B_4: $i)).
% 0.21/0.60 tff(member_type, type, (
% 0.21/0.60 member: ( $i * $i ) > $o)).
% 0.21/0.60 tff(tptp_fun_D_1_type, type, (
% 0.21/0.60 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.21/0.60 tff(tptp_fun_D_0_type, type, (
% 0.21/0.60 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.21/0.60 tff(empty_type, type, (
% 0.21/0.60 empty: $i > $o)).
% 0.21/0.60 tff(tptp_fun_C_2_type, type, (
% 0.21/0.60 tptp_fun_C_2: $i > $i)).
% 0.21/0.60 tff(intersect_type, type, (
% 0.21/0.60 intersect: ( $i * $i ) > $o)).
% 0.21/0.60 tff(not_equal_type, type, (
% 0.21/0.60 not_equal: ( $i * $i ) > $o)).
% 0.21/0.60 tff(1,plain,
% 0.21/0.60 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(2,plain,
% 0.21/0.60 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.60 tff(3,plain,
% 0.21/0.60 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, C)) | (~member(D, B))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(4,plain,
% 0.21/0.60 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.60 tff(5,plain,
% 0.21/0.60 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.21/0.60 tff(7,plain,
% 0.21/0.60 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.60 tff(8,plain,(
% 0.21/0.60 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.21/0.60 inference(skolemize,[status(sab)],[7])).
% 0.21/0.60 tff(9,plain,
% 0.21/0.60 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.60 tff(10,plain,
% 0.21/0.60 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.60 tff(11,plain,
% 0.21/0.60 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), C!3))) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set))))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(12,plain,
% 0.21/0.60 (~(((~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), C!3))) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)))),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.60 tff(13,assumption,(~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set))), introduced(assumption)).
% 0.21/0.60 tff(14,plain,
% 0.21/0.60 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(15,plain,
% 0.21/0.60 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.60 tff(16,plain,
% 0.21/0.60 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(17,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.21/0.60 tff(18,plain,
% 0.21/0.60 (![B: $i] : (~member(B, empty_set))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.60 tff(19,plain,(
% 0.21/0.60 ![B: $i] : (~member(B, empty_set))),
% 0.21/0.60 inference(skolemize,[status(sab)],[18])).
% 0.21/0.60 tff(20,plain,
% 0.21/0.60 (![B: $i] : (~member(B, empty_set))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.60 tff(21,plain,
% 0.21/0.60 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(22,plain,
% 0.21/0.60 (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.60 tff(23,plain,
% 0.21/0.60 ((member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)) | member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) | member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)),
% 0.21/0.60 inference(tautology,[status(thm)],[])).
% 0.21/0.60 tff(24,plain,
% 0.21/0.60 (member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set))),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[23, 22, 13])).
% 0.21/0.60 tff(25,plain,
% 0.21/0.60 (((~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), C!3))) | member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)),
% 0.21/0.60 inference(tautology,[status(thm)],[])).
% 0.21/0.60 tff(26,plain,
% 0.21/0.60 ((~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), C!3))),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.21/0.60 tff(27,plain,
% 0.21/0.60 ((((~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), C!3))) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set))) | (~((~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), C!3)))) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)))),
% 0.21/0.60 inference(tautology,[status(thm)],[])).
% 0.21/0.60 tff(28,plain,
% 0.21/0.60 ((((~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), C!3))) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set))) | (~member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)))),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.21/0.60 tff(29,plain,
% 0.21/0.60 ($false),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[28, 24, 12])).
% 0.21/0.60 tff(30,plain,(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.60 tff(31,plain,
% 0.21/0.60 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(32,plain,
% 0.21/0.60 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.60 tff(33,plain,
% 0.21/0.60 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.21/0.60 inference(pull_quant,[status(thm)],[])).
% 0.21/0.60 tff(34,plain,
% 0.21/0.60 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(35,plain,
% 0.21/0.60 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.60 tff(36,plain,
% 0.21/0.60 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[35, 33])).
% 0.45/0.61 tff(37,plain,
% 0.45/0.61 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[36, 32])).
% 0.45/0.61 tff(38,plain,
% 0.45/0.61 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(39,plain,
% 0.45/0.61 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[38])).
% 0.45/0.61 tff(40,plain,
% 0.45/0.61 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[39, 37])).
% 0.45/0.61 tff(41,plain,
% 0.45/0.61 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), trans(monotonicity(rewrite((~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))) <=> (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(42,plain,
% 0.45/0.61 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[41])).
% 0.45/0.61 tff(43,plain,
% 0.45/0.61 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(44,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 0.45/0.61 tff(45,plain,
% 0.45/0.61 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.45/0.61 tff(46,plain,(
% 0.45/0.61 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.45/0.61 inference(skolemize,[status(sab)],[45])).
% 0.45/0.61 tff(47,plain,
% 0.45/0.61 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.45/0.61 tff(48,plain,
% 0.45/0.61 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.45/0.61 tff(49,plain,
% 0.45/0.61 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(C!3, empty_set) = empty_set)) | (member(tptp_fun_D_1(tptp_fun_D_0(B!4, C!3), intersection(tptp_fun_D_1(B!4, C!3), C!3)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(tptp_fun_D_0(B!4, C!3), intersection(tptp_fun_D_1(B!4, C!3), C!3)), empty_set)))) | (~((intersection(C!3, empty_set) = empty_set) | (~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)))))))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(50,plain,
% 0.45/0.61 (~((~((~(intersection(C!3, empty_set) = empty_set)) | (member(tptp_fun_D_1(tptp_fun_D_0(B!4, C!3), intersection(tptp_fun_D_1(B!4, C!3), C!3)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(tptp_fun_D_0(B!4, C!3), intersection(tptp_fun_D_1(B!4, C!3), C!3)), empty_set)))) | (~((intersection(C!3, empty_set) = empty_set) | (~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set))))))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.45/0.61 tff(51,plain,
% 0.45/0.61 (((~((~(intersection(C!3, empty_set) = empty_set)) | (member(tptp_fun_D_1(tptp_fun_D_0(B!4, C!3), intersection(tptp_fun_D_1(B!4, C!3), C!3)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(tptp_fun_D_0(B!4, C!3), intersection(tptp_fun_D_1(B!4, C!3), C!3)), empty_set)))) | (~((intersection(C!3, empty_set) = empty_set) | (~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)))))) | ((intersection(C!3, empty_set) = empty_set) | (~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set))))),
% 0.45/0.61 inference(tautology,[status(thm)],[])).
% 0.45/0.61 tff(52,plain,
% 0.45/0.61 ((intersection(C!3, empty_set) = empty_set) | (~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.45/0.61 tff(53,plain,
% 0.45/0.61 ((~((intersection(C!3, empty_set) = empty_set) | (~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set))))) | (intersection(C!3, empty_set) = empty_set) | (~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)))),
% 0.45/0.61 inference(tautology,[status(thm)],[])).
% 0.45/0.61 tff(54,plain,
% 0.45/0.61 ((intersection(C!3, empty_set) = empty_set) | (~(member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), intersection(C!3, empty_set)) <=> member(tptp_fun_D_1(empty_set, intersection(C!3, empty_set)), empty_set)))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.45/0.61 tff(55,plain,
% 0.45/0.61 (intersection(C!3, empty_set) = empty_set),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[54, 30])).
% 0.45/0.61 tff(56,plain,
% 0.45/0.61 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(57,plain,
% 0.45/0.61 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[56])).
% 0.45/0.61 tff(58,plain,
% 0.45/0.61 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(59,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.45/0.61 tff(60,plain,
% 0.45/0.61 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.45/0.61 tff(61,plain,(
% 0.45/0.61 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.45/0.61 inference(skolemize,[status(sab)],[60])).
% 0.45/0.61 tff(62,plain,
% 0.45/0.61 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.45/0.61 tff(63,plain,
% 0.45/0.61 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, empty_set) = intersection(empty_set, C!3))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(64,plain,
% 0.45/0.61 (intersection(C!3, empty_set) = intersection(empty_set, C!3)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.45/0.61 tff(65,plain,
% 0.45/0.61 (intersection(empty_set, C!3) = intersection(C!3, empty_set)),
% 0.45/0.61 inference(symmetry,[status(thm)],[64])).
% 0.45/0.61 tff(66,plain,
% 0.45/0.61 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(empty_set, C!3))) | (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))))) | (~((intersection(C!3, B!4) = intersection(empty_set, C!3)) | (~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))))))))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(67,plain,
% 0.45/0.61 (~((~((~(intersection(C!3, B!4) = intersection(empty_set, C!3))) | (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))))) | (~((intersection(C!3, B!4) = intersection(empty_set, C!3)) | (~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3)))))))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[66, 48])).
% 0.45/0.61 tff(68,plain,
% 0.45/0.61 (((~((~(intersection(C!3, B!4) = intersection(empty_set, C!3))) | (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))))) | (~((intersection(C!3, B!4) = intersection(empty_set, C!3)) | (~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))))))) | ((intersection(C!3, B!4) = intersection(empty_set, C!3)) | (~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3)))))),
% 0.45/0.61 inference(tautology,[status(thm)],[])).
% 0.45/0.61 tff(69,plain,
% 0.45/0.61 ((intersection(C!3, B!4) = intersection(empty_set, C!3)) | (~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.45/0.61 tff(70,assumption,(~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))), introduced(assumption)).
% 0.45/0.61 tff(71,plain,
% 0.45/0.61 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(72,plain,
% 0.45/0.61 ((~(~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))) <=> (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(73,plain,
% 0.45/0.61 ((~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) <=> (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(74,plain,
% 0.45/0.61 (((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) <=> (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(75,plain,
% 0.45/0.61 (((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(76,plain,
% 0.45/0.61 ((((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) <=> ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[75])).
% 0.45/0.61 tff(77,plain,
% 0.45/0.61 ((((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) <=> (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[76, 74])).
% 0.45/0.61 tff(78,plain,
% 0.45/0.61 ((((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) <=> (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[77, 73])).
% 0.45/0.61 tff(79,plain,
% 0.45/0.61 ((~(((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) <=> (~(~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[78])).
% 0.45/0.61 tff(80,plain,
% 0.45/0.61 ((~(((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) <=> (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 0.45/0.61 inference(transitivity,[status(thm)],[79, 72])).
% 0.45/0.61 tff(81,plain,
% 0.45/0.61 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[80])).
% 0.45/0.61 tff(82,plain,
% 0.45/0.61 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[81, 71])).
% 0.45/0.61 tff(83,plain,
% 0.45/0.61 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(84,plain,
% 0.45/0.61 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.45/0.61 tff(85,plain,
% 0.45/0.61 ($false),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[84, 10, 70])).
% 0.45/0.61 tff(86,plain,(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.61 tff(87,plain,
% 0.45/0.61 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_D_1(C!3, B!4), B!4) <=> member(tptp_fun_D_1(C!3, B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))))))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(88,plain,
% 0.45/0.61 (~((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_D_1(C!3, B!4), B!4) <=> member(tptp_fun_D_1(C!3, B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[87, 48])).
% 0.45/0.61 tff(89,plain,
% 0.45/0.61 (((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_D_1(C!3, B!4), B!4) <=> member(tptp_fun_D_1(C!3, B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))))) | ((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(90,plain,
% 0.45/0.62 ((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.45/0.62 tff(91,plain,
% 0.45/0.62 ((~((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))) | (B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(92,plain,
% 0.45/0.62 ((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.45/0.62 tff(93,plain,
% 0.45/0.62 (B!4 = intersection(B!4, B!4)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[92, 86])).
% 0.45/0.62 tff(94,plain,
% 0.45/0.62 (intersection(B!4, B!4) = B!4),
% 0.45/0.62 inference(symmetry,[status(thm)],[93])).
% 0.45/0.62 tff(95,assumption,(~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))), introduced(assumption)).
% 0.45/0.62 tff(96,plain,
% 0.45/0.62 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(97,plain,
% 0.45/0.62 ((~(~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(98,plain,
% 0.45/0.62 ((~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(99,plain,
% 0.45/0.62 (((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(100,plain,
% 0.45/0.62 (((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(101,plain,
% 0.45/0.62 ((((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> ((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[100])).
% 0.45/0.62 tff(102,plain,
% 0.45/0.62 ((((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[101, 99])).
% 0.45/0.62 tff(103,plain,
% 0.45/0.62 ((((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[102, 98])).
% 0.45/0.62 tff(104,plain,
% 0.45/0.62 ((~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (~(~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[103])).
% 0.45/0.62 tff(105,plain,
% 0.45/0.62 ((~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.45/0.62 inference(transitivity,[status(thm)],[104, 97])).
% 0.45/0.62 tff(106,plain,
% 0.45/0.62 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[105])).
% 0.45/0.62 tff(107,plain,
% 0.45/0.62 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[106, 96])).
% 0.45/0.62 tff(108,plain,
% 0.45/0.62 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(109,plain,
% 0.45/0.62 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.45/0.62 tff(110,plain,
% 0.45/0.62 ($false),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[109, 10, 95])).
% 0.45/0.62 tff(111,plain,(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.62 tff(112,plain,
% 0.45/0.62 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(tptp_fun_D_1(B!4, C!3), C!3), C!3) <=> member(tptp_fun_D_1(tptp_fun_D_1(B!4, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(113,plain,
% 0.45/0.62 (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(tptp_fun_D_1(B!4, C!3), C!3), C!3) <=> member(tptp_fun_D_1(tptp_fun_D_1(B!4, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[112, 48])).
% 0.45/0.62 tff(114,plain,
% 0.45/0.62 (((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(tptp_fun_D_1(B!4, C!3), C!3), C!3) <=> member(tptp_fun_D_1(tptp_fun_D_1(B!4, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))) | ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(115,plain,
% 0.45/0.62 ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.45/0.62 tff(116,plain,
% 0.45/0.62 ((~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))) | (C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(117,plain,
% 0.45/0.62 ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.45/0.62 tff(118,plain,
% 0.45/0.62 (C!3 = intersection(C!3, C!3)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[117, 111])).
% 0.45/0.62 tff(119,plain,
% 0.45/0.62 (intersection(C!3, C!3) = C!3),
% 0.45/0.62 inference(symmetry,[status(thm)],[118])).
% 0.45/0.62 tff(120,plain,
% 0.45/0.62 (intersection(intersection(C!3, C!3), intersection(B!4, B!4)) = intersection(C!3, B!4)),
% 0.45/0.62 inference(monotonicity,[status(thm)],[119, 94])).
% 0.45/0.62 tff(121,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[120])).
% 0.45/0.62 tff(122,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4)))),
% 0.45/0.62 inference(symmetry,[status(thm)],[121])).
% 0.45/0.62 tff(123,assumption,(~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3)))), introduced(assumption)).
% 0.45/0.62 tff(124,plain,
% 0.45/0.62 (empty_set = intersection(C!3, empty_set)),
% 0.45/0.62 inference(symmetry,[status(thm)],[55])).
% 0.45/0.62 tff(125,plain,
% 0.45/0.62 (empty_set = intersection(empty_set, C!3)),
% 0.45/0.62 inference(transitivity,[status(thm)],[124, 64])).
% 0.45/0.62 tff(126,plain,
% 0.45/0.62 (member(tptp_fun_C_2(intersection(empty_set, C!3)), empty_set) <=> member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[125])).
% 0.45/0.62 tff(127,plain,
% 0.45/0.62 (member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3)) <=> member(tptp_fun_C_2(intersection(empty_set, C!3)), empty_set)),
% 0.45/0.62 inference(symmetry,[status(thm)],[126])).
% 0.45/0.62 tff(128,assumption,(member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3))), introduced(assumption)).
% 0.45/0.62 tff(129,plain,
% 0.45/0.62 (member(tptp_fun_C_2(intersection(empty_set, C!3)), empty_set)),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.45/0.62 tff(130,plain,
% 0.45/0.62 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_C_2(intersection(empty_set, C!3)), empty_set))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(131,plain,
% 0.45/0.62 (~member(tptp_fun_C_2(intersection(empty_set, C!3)), empty_set)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[130, 20])).
% 0.45/0.62 tff(132,plain,
% 0.45/0.62 ($false),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[131, 129])).
% 0.45/0.62 tff(133,plain,(~member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.62 tff(134,plain,
% 0.45/0.62 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B)))))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(135,plain,
% 0.45/0.62 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[134])).
% 0.45/0.62 tff(136,plain,
% 0.45/0.62 (^[B: $i] : refl((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(137,plain,
% 0.45/0.62 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[136])).
% 0.45/0.62 tff(138,plain,
% 0.45/0.62 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(139,plain,
% 0.45/0.62 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[138])).
% 0.45/0.62 tff(140,plain,
% 0.45/0.62 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[139, 137])).
% 0.45/0.62 tff(141,plain,
% 0.45/0.62 (^[B: $i] : trans(monotonicity(rewrite(((~empty(B)) | ![C: $i] : (~member(C, B))) <=> ((~empty(B)) | ![C: $i] : (~member(C, B)))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))))), rewrite((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(142,plain,
% 0.45/0.62 (![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[141])).
% 0.45/0.62 tff(143,plain,
% 0.45/0.62 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B))) <=> ![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(144,axiom,(![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_defn')).
% 0.45/0.62 tff(145,plain,
% 0.45/0.62 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.45/0.62 tff(146,plain,(
% 0.45/0.62 ![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B)))),
% 0.45/0.62 inference(skolemize,[status(sab)],[145])).
% 0.45/0.62 tff(147,plain,
% 0.45/0.62 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.45/0.62 tff(148,plain,
% 0.45/0.62 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.45/0.62 tff(149,plain,
% 0.45/0.62 (![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[148, 135])).
% 0.45/0.62 tff(150,plain,
% 0.45/0.62 ((~![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))) | (~((~(empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3)))) | (~((~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3)))))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(151,plain,
% 0.45/0.62 (~((~(empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3)))) | (~((~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3))))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.45/0.62 tff(152,plain,
% 0.45/0.62 (((~(empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3)))) | (~((~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3)))))) | (empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3)))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(153,plain,
% 0.45/0.62 (empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.45/0.62 tff(154,plain,
% 0.45/0.62 ((~(empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3)))) | empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(155,plain,
% 0.45/0.62 (empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.45/0.62 tff(156,plain,
% 0.45/0.62 (empty(intersection(empty_set, C!3))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[155, 133])).
% 0.45/0.62 tff(157,plain,
% 0.45/0.62 (((~(empty(intersection(empty_set, C!3)) | member(tptp_fun_C_2(intersection(empty_set, C!3)), intersection(empty_set, C!3)))) | (~((~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3)))))) | ((~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3))))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(158,plain,
% 0.45/0.62 ((~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[157, 151])).
% 0.45/0.62 tff(159,plain,
% 0.45/0.62 ((~((~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3))))) | (~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3)))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(160,plain,
% 0.45/0.62 ((~empty(intersection(empty_set, C!3))) | ![C: $i] : (~member(C, intersection(empty_set, C!3)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.45/0.62 tff(161,plain,
% 0.45/0.62 (![C: $i] : (~member(C, intersection(empty_set, C!3)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[160, 156])).
% 0.45/0.62 tff(162,plain,
% 0.45/0.62 ((~![C: $i] : (~member(C, intersection(empty_set, C!3)))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3)))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(163,plain,
% 0.45/0.62 (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.45/0.62 tff(164,plain,
% 0.45/0.62 ((member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))) | member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) | member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(165,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[164, 163, 123])).
% 0.45/0.62 tff(166,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[165, 122])).
% 0.45/0.62 tff(167,plain,
% 0.45/0.62 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4)))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(168,plain,
% 0.45/0.62 (~(((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[167, 10])).
% 0.45/0.62 tff(169,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[118])).
% 0.45/0.62 tff(170,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)),
% 0.45/0.62 inference(symmetry,[status(thm)],[169])).
% 0.45/0.62 tff(171,assumption,(~((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3))))), introduced(assumption)).
% 0.45/0.62 tff(172,plain,
% 0.45/0.62 (((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(173,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.45/0.62 tff(174,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[173, 170])).
% 0.45/0.62 tff(175,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[93])).
% 0.45/0.62 tff(176,plain,
% 0.45/0.62 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)),
% 0.45/0.62 inference(symmetry,[status(thm)],[175])).
% 0.45/0.63 tff(177,plain,
% 0.45/0.63 (((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))),
% 0.45/0.63 inference(tautology,[status(thm)],[])).
% 0.45/0.63 tff(178,plain,
% 0.45/0.63 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[177, 171])).
% 0.45/0.63 tff(179,plain,
% 0.45/0.63 (member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[178, 176])).
% 0.45/0.63 tff(180,assumption,(~not_equal(intersection(B!4, C!3), empty_set)), introduced(assumption)).
% 0.45/0.63 tff(181,plain,
% 0.45/0.63 (^[B: $i, C: $i] : refl((~((B = C) <=> not_equal(B, C))) <=> (~((B = C) <=> not_equal(B, C))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(182,plain,
% 0.45/0.63 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C))) <=> ![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[181])).
% 0.45/0.63 tff(183,plain,
% 0.45/0.63 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C))) <=> ![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(184,plain,
% 0.45/0.63 (^[B: $i, C: $i] : trans(rewrite((not_equal(B, C) <=> (~(B = C))) <=> (~((B = C) <=> not_equal(B, C)))), rewrite((~((B = C) <=> not_equal(B, C))) <=> (~((B = C) <=> not_equal(B, C)))), ((not_equal(B, C) <=> (~(B = C))) <=> (~((B = C) <=> not_equal(B, C)))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(185,plain,
% 0.45/0.63 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C))) <=> ![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[184])).
% 0.45/0.63 tff(186,axiom,(![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_defn')).
% 0.45/0.63 tff(187,plain,
% 0.45/0.63 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.45/0.63 tff(188,plain,
% 0.45/0.63 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.45/0.63 tff(189,plain,(
% 0.45/0.63 ![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.45/0.63 inference(skolemize,[status(sab)],[188])).
% 0.45/0.63 tff(190,plain,
% 0.45/0.63 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.45/0.63 tff(191,plain,
% 0.45/0.63 ((~![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))) | (~((intersection(B!4, C!3) = empty_set) <=> not_equal(intersection(B!4, C!3), empty_set)))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(192,plain,
% 0.45/0.63 (~((intersection(B!4, C!3) = empty_set) <=> not_equal(intersection(B!4, C!3), empty_set))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.45/0.63 tff(193,plain,
% 0.45/0.63 (((intersection(B!4, C!3) = empty_set) <=> not_equal(intersection(B!4, C!3), empty_set)) | (intersection(B!4, C!3) = empty_set) | not_equal(intersection(B!4, C!3), empty_set)),
% 0.45/0.63 inference(tautology,[status(thm)],[])).
% 0.45/0.63 tff(194,plain,
% 0.45/0.63 ((intersection(B!4, C!3) = empty_set) | not_equal(intersection(B!4, C!3), empty_set)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.45/0.63 tff(195,plain,
% 0.45/0.63 (intersection(B!4, C!3) = empty_set),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[194, 180])).
% 0.45/0.63 tff(196,plain,
% 0.45/0.63 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, C!3) = intersection(C!3, B!4))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(197,plain,
% 0.45/0.63 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[196, 62])).
% 0.45/0.63 tff(198,plain,
% 0.45/0.63 (intersection(C!3, B!4) = intersection(B!4, C!3)),
% 0.45/0.63 inference(symmetry,[status(thm)],[197])).
% 0.45/0.63 tff(199,plain,
% 0.45/0.63 (intersection(C!3, B!4) = empty_set),
% 0.45/0.63 inference(transitivity,[status(thm)],[198, 195])).
% 0.45/0.63 tff(200,plain,
% 0.45/0.63 (member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(C!3, B!4), empty_set)),
% 0.45/0.63 inference(monotonicity,[status(thm)],[199])).
% 0.45/0.63 tff(201,plain,
% 0.45/0.63 (member(tptp_fun_D_0(C!3, B!4), empty_set) <=> member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 0.45/0.63 inference(symmetry,[status(thm)],[200])).
% 0.45/0.63 tff(202,plain,
% 0.45/0.63 ((~member(tptp_fun_D_0(C!3, B!4), empty_set)) <=> (~member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[201])).
% 0.45/0.63 tff(203,plain,
% 0.45/0.63 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(C!3, B!4), empty_set))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(204,plain,
% 0.45/0.63 (~member(tptp_fun_D_0(C!3, B!4), empty_set)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[203, 20])).
% 0.45/0.63 tff(205,plain,
% 0.45/0.63 (~member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[204, 202])).
% 0.45/0.63 tff(206,plain,
% 0.45/0.63 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))) <=> member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(207,plain,
% 0.45/0.63 (~(((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))) <=> member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[206, 10])).
% 0.45/0.63 tff(208,plain,
% 0.45/0.63 ((~(intersect(B!4, C!3) <=> not_equal(intersection(B!4, C!3), empty_set))) <=> (~(intersect(B!4, C!3) <=> not_equal(intersection(B!4, C!3), empty_set)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(209,plain,
% 0.45/0.63 ((~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))) <=> (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(210,axiom,(~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th119')).
% 0.45/0.63 tff(211,plain,
% 0.45/0.63 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.45/0.63 tff(212,plain,
% 0.45/0.63 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[211, 209])).
% 0.45/0.63 tff(213,plain,
% 0.45/0.63 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[212, 209])).
% 0.45/0.63 tff(214,plain,
% 0.45/0.63 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.45/0.63 tff(215,plain,(
% 0.45/0.63 ~(intersect(B!4, C!3) <=> not_equal(intersection(B!4, C!3), empty_set))),
% 0.45/0.63 inference(skolemize,[status(sab)],[214])).
% 0.45/0.63 tff(216,plain,
% 0.45/0.63 (~(intersect(B!4, C!3) <=> not_equal(intersection(B!4, C!3), empty_set))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.45/0.63 tff(217,plain,
% 0.45/0.63 ((intersect(B!4, C!3) <=> not_equal(intersection(B!4, C!3), empty_set)) | intersect(B!4, C!3) | not_equal(intersection(B!4, C!3), empty_set)),
% 0.45/0.63 inference(tautology,[status(thm)],[])).
% 0.45/0.63 tff(218,plain,
% 0.45/0.63 (intersect(B!4, C!3) | not_equal(intersection(B!4, C!3), empty_set)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.45/0.63 tff(219,plain,
% 0.45/0.63 (intersect(B!4, C!3)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[218, 180])).
% 0.45/0.63 tff(220,plain,
% 0.45/0.63 (^[B: $i, C: $i] : refl((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(221,plain,
% 0.45/0.63 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[220])).
% 0.45/0.63 tff(222,plain,
% 0.45/0.63 (^[B: $i, C: $i] : rewrite((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(223,plain,
% 0.45/0.63 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[222])).
% 0.45/0.63 tff(224,plain,
% 0.45/0.63 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.45/0.63 inference(transitivity,[status(thm)],[223, 221])).
% 0.45/0.63 tff(225,plain,
% 0.45/0.63 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) <=> ((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))), rewrite((intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))) <=> (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))), rewrite((((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(226,plain,
% 0.48/0.63 (![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[225])).
% 0.48/0.63 tff(227,plain,
% 0.48/0.63 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C))) <=> ![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(228,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_defn')).
% 0.48/0.63 tff(229,plain,
% 0.48/0.63 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.48/0.63 tff(230,plain,(
% 0.48/0.63 ![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))))),
% 0.48/0.63 inference(skolemize,[status(sab)],[229])).
% 0.48/0.63 tff(231,plain,
% 0.48/0.63 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.48/0.63 tff(232,plain,
% 0.48/0.63 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.48/0.63 tff(233,plain,
% 0.48/0.63 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(234,plain,
% 0.48/0.63 ((~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))))) <=> (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(235,plain,
% 0.48/0.63 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[234])).
% 0.48/0.63 tff(236,plain,
% 0.48/0.63 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[235, 233])).
% 0.48/0.63 tff(237,plain,
% 0.48/0.63 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(238,plain,
% 0.48/0.63 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.48/0.63 tff(239,plain,
% 0.48/0.63 (~((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[238, 232])).
% 0.48/0.63 tff(240,plain,
% 0.48/0.63 (((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))) | ((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(241,plain,
% 0.48/0.63 ((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.48/0.63 tff(242,plain,
% 0.48/0.63 ((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(243,plain,
% 0.48/0.63 ((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.48/0.63 tff(244,plain,
% 0.48/0.63 (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[243, 219])).
% 0.48/0.63 tff(245,plain,
% 0.48/0.63 ((((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))) <=> member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))) | ((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))) | member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(246,plain,
% 0.48/0.63 ((((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))) <=> member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))) | member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.48/0.63 tff(247,plain,
% 0.48/0.63 (member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[246, 207])).
% 0.48/0.63 tff(248,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[247, 205])).
% 0.48/0.63 tff(249,plain,(not_equal(intersection(B!4, C!3), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(250,plain,
% 0.48/0.63 ((intersect(B!4, C!3) <=> not_equal(intersection(B!4, C!3), empty_set)) | (~intersect(B!4, C!3)) | (~not_equal(intersection(B!4, C!3), empty_set))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(251,plain,
% 0.48/0.63 ((~intersect(B!4, C!3)) | (~not_equal(intersection(B!4, C!3), empty_set))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[250, 216])).
% 0.48/0.63 tff(252,plain,
% 0.48/0.63 (~intersect(B!4, C!3)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[251, 249])).
% 0.48/0.63 tff(253,plain,
% 0.48/0.63 (((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))))) | (intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(254,plain,
% 0.48/0.63 (intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[253, 239])).
% 0.48/0.63 tff(255,plain,
% 0.48/0.63 ((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(256,plain,
% 0.48/0.63 (intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.48/0.63 tff(257,plain,
% 0.48/0.63 (![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[256, 252])).
% 0.48/0.63 tff(258,plain,
% 0.48/0.63 (((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | ((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)))) <=> ((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(259,plain,
% 0.48/0.63 (((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4))) <=> ((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(260,plain,
% 0.48/0.63 (((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | ((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)))) <=> ((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | ((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[259])).
% 0.48/0.63 tff(261,plain,
% 0.48/0.63 (((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | ((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)))) <=> ((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[260, 258])).
% 0.48/0.63 tff(262,plain,
% 0.48/0.63 ((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | ((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(263,plain,
% 0.48/0.63 ((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.48/0.63 tff(264,plain,
% 0.48/0.63 (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), C!3)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[263, 257, 179])).
% 0.48/0.63 tff(265,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[264, 174])).
% 0.48/0.63 tff(266,plain,((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(267,plain,
% 0.48/0.63 ((((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4)))) | (~((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3))))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4))))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(268,plain,
% 0.48/0.64 ((((~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4)))) | (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.48/0.64 tff(269,plain,
% 0.48/0.64 (~member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), intersection(B!4, B!4)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[268, 168])).
% 0.48/0.64 tff(270,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[269, 166])).
% 0.48/0.64 tff(271,plain,(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(272,plain,
% 0.48/0.64 ((~((intersection(C!3, B!4) = intersection(empty_set, C!3)) | (~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3)))))) | (intersection(C!3, B!4) = intersection(empty_set, C!3)) | (~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3))))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(273,plain,
% 0.48/0.64 ((~((intersection(C!3, B!4) = intersection(empty_set, C!3)) | (~(member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, C!3), intersection(C!3, B!4)), intersection(empty_set, C!3)))))) | (intersection(C!3, B!4) = intersection(empty_set, C!3))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.48/0.64 tff(274,plain,
% 0.48/0.64 (intersection(C!3, B!4) = intersection(empty_set, C!3)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[273, 69])).
% 0.48/0.64 tff(275,plain,
% 0.48/0.64 (intersection(B!4, C!3) = empty_set),
% 0.48/0.64 inference(transitivity,[status(thm)],[197, 274, 65, 55])).
% 0.48/0.64 tff(276,plain,
% 0.48/0.64 (((intersection(B!4, C!3) = empty_set) <=> not_equal(intersection(B!4, C!3), empty_set)) | (~(intersection(B!4, C!3) = empty_set)) | (~not_equal(intersection(B!4, C!3), empty_set))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(277,plain,
% 0.48/0.64 ((~(intersection(B!4, C!3) = empty_set)) | (~not_equal(intersection(B!4, C!3), empty_set))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[276, 192])).
% 0.48/0.64 tff(278,plain,
% 0.48/0.64 (~(intersection(B!4, C!3) = empty_set)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[277, 249])).
% 0.48/0.64 tff(279,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[278, 275])).
% 0.48/0.64 % SZS output end Proof
% 0.48/0.64 % E exiting
%------------------------------------------------------------------------------