%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET578+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:25:53 AM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET578+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:28:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(member_type, type, (
% 0.20/0.42 member: ( $i * $i ) > $o)).
% 0.20/0.42 tff(intersection_type, type, (
% 0.20/0.42 intersection: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_D_2_type, type, (
% 0.20/0.42 tptp_fun_D_2: $i)).
% 0.20/0.42 tff(tptp_fun_C_3_type, type, (
% 0.20/0.42 tptp_fun_C_3: $i)).
% 0.20/0.42 tff(tptp_fun_D_1_type, type, (
% 0.20/0.42 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_B_4_type, type, (
% 0.20/0.42 tptp_fun_B_4: $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(4,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.42 tff(6,plain,(
% 0.20/0.42 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.42 inference(skolemize,[status(sab)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, D!2) = intersection(D!2, C!3))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.42 tff(10,assumption,(~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))), introduced(assumption)).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, B)) | (~member(D, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![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, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(16,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')).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.42 tff(18,plain,(
% 0.20/0.42 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~(~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))) <=> (member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))) <=> (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))) <=> (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 ((((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))) <=> ((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 ((((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))) <=> (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 ((((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))) <=> (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[27, 23])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ((~(((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))) <=> (~(~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((~(((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))) <=> (member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[29, 22])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[31, 21])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[34, 20, 10])).
% 0.20/0.43 tff(36,plain,(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (^[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))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(pull_quant,[status(thm)],[])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (^[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)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[42, 38])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (^[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))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (^[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)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(50,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')).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.43 tff(52,plain,(
% 0.20/0.43 ![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)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[51])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (![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)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((~![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)))))))) | (~((~((~(D!2 = intersection(D!2, D!2))) | (member(tptp_fun_D_1(D!2, C!3), D!2) <=> member(tptp_fun_D_1(D!2, C!3), intersection(D!2, D!2))))) | (~((D!2 = intersection(D!2, D!2)) | (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (~((~((~(D!2 = intersection(D!2, D!2))) | (member(tptp_fun_D_1(D!2, C!3), D!2) <=> member(tptp_fun_D_1(D!2, C!3), intersection(D!2, D!2))))) | (~((D!2 = intersection(D!2, D!2)) | (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (((~((~(D!2 = intersection(D!2, D!2))) | (member(tptp_fun_D_1(D!2, C!3), D!2) <=> member(tptp_fun_D_1(D!2, C!3), intersection(D!2, D!2))))) | (~((D!2 = intersection(D!2, D!2)) | (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))))) | ((D!2 = intersection(D!2, D!2)) | (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 ((D!2 = intersection(D!2, D!2)) | (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 ((~((D!2 = intersection(D!2, D!2)) | (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2)))))) | (D!2 = intersection(D!2, D!2)) | (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 ((D!2 = intersection(D!2, D!2)) | (~(member(tptp_fun_D_1(intersection(D!2, D!2), D!2), D!2) <=> member(tptp_fun_D_1(intersection(D!2, D!2), D!2), intersection(D!2, D!2))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (D!2 = intersection(D!2, D!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[60, 36])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (intersection(D!2, D!2) = D!2),
% 0.20/0.43 inference(symmetry,[status(thm)],[61])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (intersection(C!3, intersection(D!2, D!2)) = intersection(C!3, D!2)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (intersection(C!3, intersection(D!2, D!2)) = intersection(D!2, C!3)),
% 0.20/0.43 inference(transitivity,[status(thm)],[63, 9])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[65])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) <=> (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.43 tff(68,assumption,(~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)), introduced(assumption)).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 ((~![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(D!2, C!3) = B!4)) | (member(tptp_fun_D_1(C!3, D!2), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(C!3, D!2), B!4)))) | (~((intersection(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (~((~((~(intersection(D!2, C!3) = B!4)) | (member(tptp_fun_D_1(C!3, D!2), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(C!3, D!2), B!4)))) | (~((intersection(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[69, 54])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (((~((~(intersection(D!2, C!3) = B!4)) | (member(tptp_fun_D_1(C!3, D!2), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(C!3, D!2), B!4)))) | (~((intersection(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)))))) | ((intersection(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 ((intersection(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 ((intersection(C!3, D!2) = B!4) <=> (B!4 = intersection(C!3, D!2))),
% 0.20/0.44 inference(commutativity,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 0.20/0.44 inference(symmetry,[status(thm)],[9])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 ((intersection(D!2, C!3) = B!4) <=> (intersection(C!3, D!2) = B!4)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 ((intersection(D!2, C!3) = B!4) <=> (B!4 = intersection(C!3, D!2))),
% 0.20/0.44 inference(transitivity,[status(thm)],[75, 73])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 ((B!4 = intersection(C!3, D!2)) <=> (intersection(D!2, C!3) = B!4)),
% 0.20/0.44 inference(symmetry,[status(thm)],[76])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ((~(B!4 = intersection(C!3, D!2))) <=> (~(intersection(D!2, C!3) = B!4))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 ((![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) & (~(B!4 = intersection(C!3, D!2)))) <=> (![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) & (~(B!4 = intersection(C!3, D!2))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ((~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 ((~![B: $i, C: $i, D: $i] : (![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D))) => (B = intersection(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(82,axiom,(~![B: $i, C: $i, D: $i] : (![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D))) => (B = intersection(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th19')).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, C) & member(E, D)))) | (B = intersection(C, D)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[85, 80])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) & (~(B!4 = intersection(C!3, D!2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (~(B!4 = intersection(C!3, D!2))),
% 0.20/0.44 inference(and_elim,[status(thm)],[87])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (~(intersection(D!2, C!3) = B!4)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[88, 78])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 ((~((intersection(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))))) | (intersection(D!2, C!3) = B!4) | (~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (~(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[90, 89, 72])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 ((member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[93, 68])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[94, 66])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (intersection(intersection(D!2, D!2), C!3) = intersection(D!2, C!3)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))) <=> (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[98])).
% 0.20/0.44 tff(100,assumption,(~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))), introduced(assumption)).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 ((~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))) <=> (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ((((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))) <=> (((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 ((~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))) <=> (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 ((~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))) <=> (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[106, 104])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[108, 103])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[111, 20])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 ((((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))) | (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 ((~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(intersection(D!2, D!2), C!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[114, 102])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[115, 99])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[93, 116])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))) <=> (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[100, 118])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (^[E: $i] : refl((~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4))) <=> (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 (![E: $i] : (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4))) <=> ![E: $i] : (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (^[E: $i] : trans(trans(monotonicity(rewrite((member(E, C!3) & member(E, D!2)) <=> (~((~member(E, C!3)) | (~member(E, D!2))))), ((member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) <=> (member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2))))))), rewrite((member(E, B!4) <=> (~((~member(E, C!3)) | (~member(E, D!2))))) <=> (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4)))), ((member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) <=> (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4))))), rewrite((~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4))) <=> (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4)))), ((member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) <=> (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2))) <=> ![E: $i] : (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (![E: $i] : (member(E, B!4) <=> (member(E, C!3) & member(E, D!2)))),
% 0.20/0.45 inference(and_elim,[status(thm)],[87])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 (![E: $i] : (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (![E: $i] : (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 ((~![E: $i] : (~(((~member(E, C!3)) | (~member(E, D!2))) <=> member(E, B!4)))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 ((((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)) | (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 ((~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 121, 117])).
% 0.20/0.45 tff(134,plain,(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[134, 96])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 ((((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[136, 130])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[137, 68])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[139, 138, 135])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (~(((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[143, 20])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ((((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))) | (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 ((~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[146, 142])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[147, 95])).
% 0.20/0.45 tff(149,plain,(member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 ((member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), B!4))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[150, 91])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[151, 149])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[152, 67])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 149])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), D!2))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 ((~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))))) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (~((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[157, 156, 134])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 ((((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) <=> member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))) | ((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (((~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(D!2, D!2)))) | member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[159, 144])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (member(tptp_fun_D_1(B!4, intersection(D!2, C!3)), intersection(C!3, intersection(D!2, D!2)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[160, 158])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[161, 153])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------