%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET171+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:25:24 AM UTC 2025
% Result : Theorem 80.74s 80.93s
% Output : Proof 80.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET171+3 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:29:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 80.74/80.93 % SZS status Theorem
% 80.74/80.93 % SZS output start Proof
% 80.74/80.93 tff(member_type, type, (
% 80.74/80.93 member: ( $i * $i ) > $o)).
% 80.74/80.93 tff(intersection_type, type, (
% 80.74/80.93 intersection: ( $i * $i ) > $i)).
% 80.74/80.93 tff(tptp_fun_C_3_type, type, (
% 80.74/80.93 tptp_fun_C_3: $i)).
% 80.74/80.93 tff(tptp_fun_D_2_type, type, (
% 80.74/80.93 tptp_fun_D_2: $i)).
% 80.74/80.93 tff(tptp_fun_D_1_type, type, (
% 80.74/80.93 tptp_fun_D_1: ( $i * $i ) > $i)).
% 80.74/80.93 tff(union_type, type, (
% 80.74/80.93 union: ( $i * $i ) > $i)).
% 80.74/80.93 tff(tptp_fun_B_4_type, type, (
% 80.74/80.93 tptp_fun_B_4: $i)).
% 80.74/80.93 tff(subset_type, type, (
% 80.74/80.93 subset: ( $i * $i ) > $o)).
% 80.74/80.93 tff(tptp_fun_D_0_type, type, (
% 80.74/80.93 tptp_fun_D_0: ( $i * $i ) > $i)).
% 80.74/80.93 tff(1,assumption,(~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))), introduced(assumption)).
% 80.74/80.93 tff(2,plain,
% 80.74/80.93 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 80.74/80.93 inference(bind,[status(th)],[])).
% 80.74/80.93 tff(3,plain,
% 80.74/80.93 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 80.74/80.93 inference(quant_intro,[status(thm)],[2])).
% 80.74/80.93 tff(4,plain,
% 80.74/80.93 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 80.74/80.93 inference(rewrite,[status(thm)],[])).
% 80.74/80.93 tff(5,plain,
% 80.74/80.93 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 80.74/80.93 inference(bind,[status(th)],[])).
% 80.74/80.93 tff(6,plain,
% 80.74/80.93 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 80.74/80.93 inference(quant_intro,[status(thm)],[5])).
% 80.74/80.93 tff(7,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 80.74/80.93 tff(8,plain,
% 80.74/80.93 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 80.74/80.93 inference(modus_ponens,[status(thm)],[7, 6])).
% 80.74/80.93 tff(9,plain,
% 80.74/80.93 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 80.74/80.93 inference(modus_ponens,[status(thm)],[8, 4])).
% 80.74/80.93 tff(10,plain,(
% 80.74/80.93 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 80.74/80.93 inference(skolemize,[status(sab)],[9])).
% 80.74/80.93 tff(11,plain,
% 80.74/80.93 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 80.74/80.93 inference(modus_ponens,[status(thm)],[10, 3])).
% 80.74/80.93 tff(12,plain,
% 80.74/80.93 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))),
% 80.74/80.93 inference(quant_inst,[status(thm)],[])).
% 80.74/80.93 tff(13,plain,
% 80.74/80.93 ($false),
% 80.74/80.93 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 80.74/80.93 tff(14,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))), inference(lemma,lemma(discharge,[]))).
% 80.74/80.93 tff(15,assumption,((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))))), introduced(assumption)).
% 80.74/80.93 tff(16,plain,
% 80.74/80.93 (^[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))))))))),
% 80.74/80.93 inference(bind,[status(th)],[])).
% 80.74/80.93 tff(17,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(quant_intro,[status(thm)],[16])).
% 80.74/80.93 tff(18,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(pull_quant,[status(thm)],[])).
% 80.74/80.93 tff(19,plain,
% 80.74/80.93 (^[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)))))))))),
% 80.74/80.93 inference(bind,[status(th)],[])).
% 80.74/80.93 tff(20,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(quant_intro,[status(thm)],[19])).
% 80.74/80.93 tff(21,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(transitivity,[status(thm)],[20, 18])).
% 80.74/80.93 tff(22,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(transitivity,[status(thm)],[21, 17])).
% 80.74/80.93 tff(23,plain,
% 80.74/80.93 (^[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))))))))),
% 80.74/80.93 inference(bind,[status(th)],[])).
% 80.74/80.93 tff(24,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(quant_intro,[status(thm)],[23])).
% 80.74/80.93 tff(25,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(transitivity,[status(thm)],[24, 22])).
% 80.74/80.93 tff(26,plain,
% 80.74/80.93 (^[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)))))))))),
% 80.74/80.93 inference(bind,[status(th)],[])).
% 80.74/80.93 tff(27,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(quant_intro,[status(thm)],[26])).
% 80.74/80.93 tff(28,plain,
% 80.74/80.93 (![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)))),
% 80.74/80.93 inference(rewrite,[status(thm)],[])).
% 80.74/80.93 tff(29,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')).
% 80.74/80.93 tff(30,plain,
% 80.74/80.93 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 80.74/80.93 inference(modus_ponens,[status(thm)],[29, 28])).
% 80.74/80.93 tff(31,plain,(
% 80.74/80.93 ![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)))))),
% 80.74/80.93 inference(skolemize,[status(sab)],[30])).
% 80.74/80.93 tff(32,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(modus_ponens,[status(thm)],[31, 27])).
% 80.74/80.93 tff(33,plain,
% 80.74/80.93 (![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)))))))),
% 80.74/80.93 inference(modus_ponens,[status(thm)],[32, 25])).
% 80.74/80.93 tff(34,plain,
% 80.74/80.93 (((~![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(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))))))) <=> ((~![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(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))))))),
% 80.74/80.94 inference(rewrite,[status(thm)],[])).
% 80.74/80.94 tff(35,plain,
% 80.74/80.94 ((~((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))))))) <=> (~((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))))))),
% 80.74/80.94 inference(rewrite,[status(thm)],[])).
% 80.74/80.94 tff(36,plain,
% 80.74/80.94 (((~![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(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))))))) <=> ((~![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(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))))))),
% 80.74/80.94 inference(monotonicity,[status(thm)],[35])).
% 80.74/80.94 tff(37,plain,
% 80.74/80.94 (((~![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(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))))))) <=> ((~![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(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))))))),
% 80.74/80.94 inference(transitivity,[status(thm)],[36, 34])).
% 80.74/80.94 tff(38,plain,
% 80.74/80.94 ((~![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(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))))))),
% 80.74/80.94 inference(quant_inst,[status(thm)],[])).
% 80.74/80.94 tff(39,plain,
% 80.74/80.94 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))))))),
% 80.74/80.94 inference(modus_ponens,[status(thm)],[38, 37])).
% 80.74/80.94 tff(40,plain,
% 80.74/80.94 ($false),
% 80.74/80.94 inference(unit_resolution,[status(thm)],[39, 33, 15])).
% 80.74/80.94 tff(41,plain,(~((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))))), inference(lemma,lemma(discharge,[]))).
% 80.79/80.94 tff(42,plain,
% 80.79/80.94 (((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))))) | ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))),
% 80.79/80.94 inference(tautology,[status(thm)],[])).
% 80.79/80.94 tff(43,plain,
% 80.79/80.94 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[42, 41])).
% 80.79/80.94 tff(44,plain,
% 80.79/80.94 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 80.79/80.94 inference(bind,[status(th)],[])).
% 80.79/80.94 tff(45,plain,
% 80.79/80.94 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 80.79/80.94 inference(quant_intro,[status(thm)],[44])).
% 80.79/80.94 tff(46,plain,
% 80.79/80.94 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 80.79/80.94 inference(rewrite,[status(thm)],[])).
% 80.79/80.94 tff(47,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 80.79/80.94 tff(48,plain,
% 80.79/80.94 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[47, 46])).
% 80.79/80.94 tff(49,plain,(
% 80.79/80.94 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 80.79/80.94 inference(skolemize,[status(sab)],[48])).
% 80.79/80.94 tff(50,plain,
% 80.79/80.94 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[49, 45])).
% 80.79/80.94 tff(51,plain,
% 80.79/80.94 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(union(B!4, C!3), union(B!4, D!2)) = intersection(union(B!4, D!2), union(B!4, C!3)))),
% 80.79/80.94 inference(quant_inst,[status(thm)],[])).
% 80.79/80.94 tff(52,plain,
% 80.79/80.94 (intersection(union(B!4, C!3), union(B!4, D!2)) = intersection(union(B!4, D!2), union(B!4, C!3))),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[51, 50])).
% 80.79/80.94 tff(53,plain,
% 80.79/80.94 (intersection(union(B!4, D!2), union(B!4, C!3)) = intersection(union(B!4, C!3), union(B!4, D!2))),
% 80.79/80.94 inference(symmetry,[status(thm)],[52])).
% 80.79/80.94 tff(54,assumption,(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)), introduced(assumption)).
% 80.79/80.94 tff(55,plain,
% 80.79/80.94 (union(intersection(C!3, D!2), B!4) = intersection(union(B!4, D!2), union(B!4, C!3))),
% 80.79/80.94 inference(symmetry,[status(thm)],[54])).
% 80.79/80.94 tff(56,plain,
% 80.79/80.94 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 80.79/80.94 inference(bind,[status(th)],[])).
% 80.79/80.94 tff(57,plain,
% 80.79/80.94 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 80.79/80.94 inference(quant_intro,[status(thm)],[56])).
% 80.79/80.94 tff(58,plain,
% 80.79/80.94 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 80.79/80.94 inference(rewrite,[status(thm)],[])).
% 80.79/80.94 tff(59,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 80.79/80.94 tff(60,plain,
% 80.79/80.94 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[59, 58])).
% 80.79/80.94 tff(61,plain,(
% 80.79/80.94 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 80.79/80.94 inference(skolemize,[status(sab)],[60])).
% 80.79/80.94 tff(62,plain,
% 80.79/80.94 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[61, 57])).
% 80.79/80.94 tff(63,plain,
% 80.79/80.94 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, intersection(C!3, D!2)) = union(intersection(C!3, D!2), B!4))),
% 80.79/80.94 inference(quant_inst,[status(thm)],[])).
% 80.79/80.94 tff(64,plain,
% 80.79/80.94 (union(B!4, intersection(C!3, D!2)) = union(intersection(C!3, D!2), B!4)),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[63, 62])).
% 80.79/80.94 tff(65,plain,
% 80.79/80.94 (union(B!4, intersection(C!3, D!2)) = intersection(union(B!4, C!3), union(B!4, D!2))),
% 80.79/80.94 inference(transitivity,[status(thm)],[64, 55, 53])).
% 80.79/80.94 tff(66,plain,
% 80.79/80.94 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) <=> (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D))))),
% 80.79/80.94 inference(rewrite,[status(thm)],[])).
% 80.79/80.94 tff(67,axiom,(~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_union_distributes_over_intersection')).
% 80.79/80.94 tff(68,plain,
% 80.79/80.94 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[67, 66])).
% 80.79/80.94 tff(69,plain,
% 80.79/80.94 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[68, 66])).
% 80.79/80.94 tff(70,plain,
% 80.79/80.94 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[69, 66])).
% 80.79/80.94 tff(71,plain,
% 80.79/80.94 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[70, 66])).
% 80.79/80.94 tff(72,plain,(
% 80.79/80.94 ~(union(B!4, intersection(C!3, D!2)) = intersection(union(B!4, C!3), union(B!4, D!2)))),
% 80.79/80.94 inference(skolemize,[status(sab)],[71])).
% 80.79/80.94 tff(73,plain,
% 80.79/80.94 ($false),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[72, 65])).
% 80.79/80.94 tff(74,plain,(~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))), inference(lemma,lemma(discharge,[]))).
% 80.79/80.94 tff(75,plain,
% 80.79/80.94 ((~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))),
% 80.79/80.94 inference(tautology,[status(thm)],[])).
% 80.79/80.94 tff(76,plain,
% 80.79/80.94 ((~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[75, 74])).
% 80.79/80.94 tff(77,plain,
% 80.79/80.94 (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[76, 43])).
% 80.79/80.94 tff(78,plain,
% 80.79/80.94 (~((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))))),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[39, 33])).
% 80.79/80.94 tff(79,plain,
% 80.79/80.94 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[42, 78])).
% 80.79/80.94 tff(80,plain,
% 80.79/80.94 ((intersection(union(B!4, C!3), union(B!4, D!2)) = union(B!4, intersection(C!3, D!2))) <=> (union(B!4, intersection(C!3, D!2)) = intersection(union(B!4, C!3), union(B!4, D!2)))),
% 80.79/80.94 inference(commutativity,[status(thm)],[])).
% 80.79/80.94 tff(81,plain,
% 80.79/80.94 (union(intersection(C!3, D!2), B!4) = union(B!4, intersection(C!3, D!2))),
% 80.79/80.94 inference(symmetry,[status(thm)],[64])).
% 80.79/80.94 tff(82,plain,
% 80.79/80.94 ((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) <=> (intersection(union(B!4, C!3), union(B!4, D!2)) = union(B!4, intersection(C!3, D!2)))),
% 80.79/80.94 inference(monotonicity,[status(thm)],[53, 81])).
% 80.79/80.94 tff(83,plain,
% 80.79/80.94 ((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) <=> (union(B!4, intersection(C!3, D!2)) = intersection(union(B!4, C!3), union(B!4, D!2)))),
% 80.79/80.94 inference(transitivity,[status(thm)],[82, 80])).
% 80.79/80.94 tff(84,plain,
% 80.79/80.94 ((union(B!4, intersection(C!3, D!2)) = intersection(union(B!4, C!3), union(B!4, D!2))) <=> (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))),
% 80.79/80.94 inference(symmetry,[status(thm)],[83])).
% 80.79/80.94 tff(85,plain,
% 80.79/80.94 ((~(union(B!4, intersection(C!3, D!2)) = intersection(union(B!4, C!3), union(B!4, D!2)))) <=> (~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)))),
% 80.79/80.94 inference(monotonicity,[status(thm)],[84])).
% 80.79/80.94 tff(86,plain,
% 80.79/80.94 (~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))),
% 80.79/80.94 inference(modus_ponens,[status(thm)],[72, 85])).
% 80.79/80.94 tff(87,plain,
% 80.79/80.94 (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 80.79/80.94 inference(unit_resolution,[status(thm)],[75, 86, 79])).
% 80.79/80.94 tff(88,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))), introduced(assumption)).
% 80.79/80.95 tff(89,plain,
% 80.79/80.95 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 80.79/80.95 inference(tautology,[status(thm)],[])).
% 80.79/80.95 tff(90,plain,
% 80.79/80.95 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 80.79/80.95 inference(unit_resolution,[status(thm)],[89, 88, 87])).
% 80.79/80.95 tff(91,plain,
% 80.79/80.95 ((~![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(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3))) | (member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))) | (~((intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)) | (~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))))))),
% 80.79/80.95 inference(quant_inst,[status(thm)],[])).
% 80.79/80.95 tff(92,plain,
% 80.79/80.95 (~((~((~(intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3))) | (member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))) | (~((intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)) | (~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))))))),
% 80.79/80.95 inference(unit_resolution,[status(thm)],[91, 33])).
% 80.79/80.95 tff(93,plain,
% 80.79/80.95 (((~((~(intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3))) | (member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))) | (~((intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)) | (~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))))) | ((intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)) | (~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))))),
% 80.79/80.95 inference(tautology,[status(thm)],[])).
% 80.79/80.95 tff(94,plain,
% 80.79/80.95 ((intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)) | (~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.79/80.95 inference(unit_resolution,[status(thm)],[93, 92])).
% 80.79/80.95 tff(95,plain,
% 80.79/80.95 (^[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)))))),
% 80.79/80.95 inference(bind,[status(th)],[])).
% 80.79/80.95 tff(96,plain,
% 80.79/80.95 (![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))))),
% 80.79/80.95 inference(quant_intro,[status(thm)],[95])).
% 80.79/80.95 tff(97,plain,
% 80.79/80.95 (^[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))))))),
% 80.79/80.95 inference(bind,[status(th)],[])).
% 80.79/80.95 tff(98,plain,
% 80.79/80.95 (![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))))),
% 80.79/80.95 inference(quant_intro,[status(thm)],[97])).
% 80.79/80.95 tff(99,plain,
% 80.79/80.95 (![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)))),
% 80.79/80.95 inference(rewrite,[status(thm)],[])).
% 80.79/80.95 tff(100,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')).
% 80.79/80.95 tff(101,plain,
% 80.79/80.95 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 80.79/80.95 inference(modus_ponens,[status(thm)],[100, 99])).
% 80.79/80.95 tff(102,plain,(
% 80.79/80.95 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 80.79/80.95 inference(skolemize,[status(sab)],[101])).
% 80.79/80.95 tff(103,plain,
% 80.79/80.95 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 80.79/80.95 inference(modus_ponens,[status(thm)],[102, 98])).
% 80.79/80.95 tff(104,plain,
% 80.79/80.95 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 80.79/80.95 inference(modus_ponens,[status(thm)],[103, 96])).
% 80.79/80.95 tff(105,plain,
% 80.79/80.95 (((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(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(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))))),
% 80.80/80.95 inference(rewrite,[status(thm)],[])).
% 80.80/80.95 tff(106,plain,
% 80.80/80.95 ((~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))))),
% 80.80/80.95 inference(rewrite,[status(thm)],[])).
% 80.80/80.95 tff(107,plain,
% 80.80/80.95 ((((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))) <=> (((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))),
% 80.80/80.95 inference(rewrite,[status(thm)],[])).
% 80.80/80.95 tff(108,plain,
% 80.80/80.95 ((~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))))),
% 80.80/80.95 inference(monotonicity,[status(thm)],[107])).
% 80.80/80.95 tff(109,plain,
% 80.80/80.95 ((~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))))),
% 80.80/80.95 inference(transitivity,[status(thm)],[108, 106])).
% 80.80/80.95 tff(110,plain,
% 80.80/80.95 (((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(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(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))))),
% 80.80/80.95 inference(monotonicity,[status(thm)],[109])).
% 80.80/80.95 tff(111,plain,
% 80.80/80.95 (((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(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(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))))),
% 80.80/80.95 inference(transitivity,[status(thm)],[110, 105])).
% 80.80/80.95 tff(112,plain,
% 80.80/80.95 ((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))))),
% 80.80/80.95 inference(quant_inst,[status(thm)],[])).
% 80.80/80.95 tff(113,plain,
% 80.80/80.95 ((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))))),
% 80.80/80.95 inference(modus_ponens,[status(thm)],[112, 111])).
% 80.80/80.95 tff(114,plain,
% 80.80/80.95 (~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[113, 104])).
% 80.80/80.95 tff(115,assumption,(~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))), introduced(assumption)).
% 80.80/80.95 tff(116,assumption,(~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))), introduced(assumption)).
% 80.80/80.95 tff(117,plain,
% 80.80/80.95 ((member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))),
% 80.80/80.95 inference(tautology,[status(thm)],[])).
% 80.80/80.95 tff(118,plain,
% 80.80/80.95 (member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[117, 116, 115])).
% 80.80/80.95 tff(119,plain,
% 80.80/80.95 (((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))),
% 80.80/80.95 inference(tautology,[status(thm)],[])).
% 80.80/80.95 tff(120,plain,
% 80.80/80.95 ((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[119, 116])).
% 80.80/80.95 tff(121,plain,
% 80.80/80.95 ((((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))) | (~((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))))),
% 80.80/80.95 inference(tautology,[status(thm)],[])).
% 80.80/80.95 tff(122,plain,
% 80.80/80.95 ($false),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[121, 120, 118, 114])).
% 80.80/80.95 tff(123,plain,(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)) | (member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.95 tff(124,plain,
% 80.80/80.95 (member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[123, 115])).
% 80.80/80.95 tff(125,plain,
% 80.80/80.95 ((member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.95 inference(tautology,[status(thm)],[])).
% 80.80/80.95 tff(126,plain,
% 80.80/80.95 (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[125, 124, 115])).
% 80.80/80.95 tff(127,plain,
% 80.80/80.95 ((((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))) | ((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))),
% 80.80/80.95 inference(tautology,[status(thm)],[])).
% 80.80/80.95 tff(128,plain,
% 80.80/80.95 ((((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3)))) | ((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[127, 126])).
% 80.80/80.95 tff(129,plain,
% 80.80/80.95 ((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[128, 114])).
% 80.80/80.95 tff(130,plain,
% 80.80/80.95 ((~((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))),
% 80.80/80.95 inference(tautology,[status(thm)],[])).
% 80.80/80.95 tff(131,plain,
% 80.80/80.95 ((~((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[130, 124])).
% 80.80/80.95 tff(132,plain,
% 80.80/80.95 (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))),
% 80.80/80.95 inference(unit_resolution,[status(thm)],[131, 129])).
% 80.80/80.95 tff(133,plain,
% 80.80/80.95 (((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(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(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))))),
% 80.80/80.96 inference(rewrite,[status(thm)],[])).
% 80.80/80.96 tff(134,plain,
% 80.80/80.96 ((~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.96 inference(rewrite,[status(thm)],[])).
% 80.80/80.96 tff(135,plain,
% 80.80/80.96 ((((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) <=> (((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.96 inference(rewrite,[status(thm)],[])).
% 80.80/80.96 tff(136,plain,
% 80.80/80.96 ((~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.96 inference(monotonicity,[status(thm)],[135])).
% 80.80/80.96 tff(137,plain,
% 80.80/80.96 ((~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.96 inference(transitivity,[status(thm)],[136, 134])).
% 80.80/80.96 tff(138,plain,
% 80.80/80.96 (((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(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(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))))),
% 80.80/80.96 inference(monotonicity,[status(thm)],[137])).
% 80.80/80.96 tff(139,plain,
% 80.80/80.96 (((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(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(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))))),
% 80.80/80.96 inference(transitivity,[status(thm)],[138, 133])).
% 80.80/80.96 tff(140,plain,
% 80.80/80.96 ((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.96 inference(quant_inst,[status(thm)],[])).
% 80.80/80.96 tff(141,plain,
% 80.80/80.96 ((~![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, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.96 inference(modus_ponens,[status(thm)],[140, 139])).
% 80.80/80.96 tff(142,plain,
% 80.80/80.96 (~(((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.96 inference(unit_resolution,[status(thm)],[141, 104])).
% 80.80/80.96 tff(143,plain,
% 80.80/80.96 ((((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.96 inference(tautology,[status(thm)],[])).
% 80.80/80.96 tff(144,plain,
% 80.80/80.96 ((((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))) | (~((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))))),
% 80.80/80.96 inference(unit_resolution,[status(thm)],[143, 124])).
% 80.80/80.96 tff(145,plain,
% 80.80/80.96 (~((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)))),
% 80.80/80.96 inference(unit_resolution,[status(thm)],[144, 142])).
% 80.80/80.96 tff(146,plain,
% 80.80/80.96 (((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), C!3)) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2))) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)),
% 80.80/80.96 inference(tautology,[status(thm)],[])).
% 80.80/80.96 tff(147,plain,
% 80.80/80.96 (member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)),
% 80.80/80.96 inference(unit_resolution,[status(thm)],[146, 145])).
% 80.80/80.96 tff(148,plain,
% 80.80/80.96 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 80.80/80.96 inference(bind,[status(th)],[])).
% 80.80/80.96 tff(149,plain,
% 80.80/80.96 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 80.80/80.96 inference(quant_intro,[status(thm)],[148])).
% 80.80/80.96 tff(150,plain,
% 80.80/80.96 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 80.80/80.96 inference(bind,[status(th)],[])).
% 80.80/80.96 tff(151,plain,
% 80.80/80.96 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 80.80/80.96 inference(quant_intro,[status(thm)],[150])).
% 80.80/80.96 tff(152,plain,
% 80.80/80.96 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 80.80/80.96 inference(transitivity,[status(thm)],[151, 149])).
% 80.80/80.96 tff(153,plain,
% 80.80/80.96 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 80.80/80.96 inference(bind,[status(th)],[])).
% 80.80/80.96 tff(154,plain,
% 80.80/80.96 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 80.80/80.96 inference(quant_intro,[status(thm)],[153])).
% 80.80/80.96 tff(155,plain,
% 80.80/80.96 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 80.80/80.96 inference(rewrite,[status(thm)],[])).
% 80.80/80.96 tff(156,plain,
% 80.80/80.96 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 80.80/80.96 inference(bind,[status(th)],[])).
% 80.80/80.96 tff(157,plain,
% 80.80/80.96 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 80.80/80.96 inference(quant_intro,[status(thm)],[156])).
% 80.80/80.96 tff(158,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 80.80/80.96 tff(159,plain,
% 80.80/80.96 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 80.80/80.96 inference(modus_ponens,[status(thm)],[158, 157])).
% 80.80/80.96 tff(160,plain,
% 80.80/80.96 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 80.80/80.96 inference(modus_ponens,[status(thm)],[159, 155])).
% 80.80/80.96 tff(161,plain,(
% 80.80/80.96 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 80.80/80.96 inference(skolemize,[status(sab)],[160])).
% 80.80/80.96 tff(162,plain,
% 80.80/80.96 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 80.80/80.96 inference(modus_ponens,[status(thm)],[161, 154])).
% 80.80/80.96 tff(163,plain,
% 80.80/80.96 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 80.80/80.96 inference(modus_ponens,[status(thm)],[162, 152])).
% 80.80/80.96 tff(164,plain,
% 80.80/80.96 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(D!2, union(D!2, B!4))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4))))) | (~(subset(D!2, union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), D!2), D!2)) | member(tptp_fun_D_0(union(D!2, B!4), D!2), union(D!2, B!4))))))))),
% 80.80/80.96 inference(quant_inst,[status(thm)],[])).
% 80.80/80.96 tff(165,plain,
% 80.80/80.96 (~((~((~subset(D!2, union(D!2, B!4))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4))))) | (~(subset(D!2, union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), D!2), D!2)) | member(tptp_fun_D_0(union(D!2, B!4), D!2), union(D!2, B!4)))))))),
% 80.80/80.96 inference(unit_resolution,[status(thm)],[164, 163])).
% 80.80/80.96 tff(166,plain,
% 80.80/80.96 (((~((~subset(D!2, union(D!2, B!4))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4))))) | (~(subset(D!2, union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), D!2), D!2)) | member(tptp_fun_D_0(union(D!2, B!4), D!2), union(D!2, B!4))))))) | ((~subset(D!2, union(D!2, B!4))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4))))),
% 80.80/80.96 inference(tautology,[status(thm)],[])).
% 80.80/80.96 tff(167,plain,
% 80.80/80.96 ((~subset(D!2, union(D!2, B!4))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4)))),
% 80.80/80.96 inference(unit_resolution,[status(thm)],[166, 165])).
% 80.80/80.96 tff(168,assumption,((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2)))), introduced(assumption)).
% 80.80/80.96 tff(169,plain,
% 80.80/80.96 (((~![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)))))))) | (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2)))))) <=> ((~![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)))))))) | (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2))))))),
% 80.80/80.96 inference(rewrite,[status(thm)],[])).
% 80.80/80.96 tff(170,plain,
% 80.80/80.96 ((~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((union(D!2, intersection(D!2, C!3)) = D!2) | (~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))))))) <=> (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2)))))),
% 80.80/80.96 inference(rewrite,[status(thm)],[])).
% 80.80/80.96 tff(171,plain,
% 80.80/80.96 (((~![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)))))))) | (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((union(D!2, intersection(D!2, C!3)) = D!2) | (~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)))))))) <=> ((~![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)))))))) | (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2))))))),
% 80.80/80.96 inference(monotonicity,[status(thm)],[170])).
% 80.80/80.96 tff(172,plain,
% 80.80/80.96 (((~![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)))))))) | (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((union(D!2, intersection(D!2, C!3)) = D!2) | (~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)))))))) <=> ((~![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)))))))) | (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2))))))),
% 80.80/80.96 inference(transitivity,[status(thm)],[171, 169])).
% 80.80/80.96 tff(173,plain,
% 80.80/80.96 ((~![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)))))))) | (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((union(D!2, intersection(D!2, C!3)) = D!2) | (~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)))))))),
% 80.80/80.96 inference(quant_inst,[status(thm)],[])).
% 80.80/80.96 tff(174,plain,
% 80.80/80.96 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2)))))),
% 80.80/80.96 inference(modus_ponens,[status(thm)],[173, 172])).
% 80.80/80.96 tff(175,plain,
% 80.80/80.96 ($false),
% 80.80/80.96 inference(unit_resolution,[status(thm)],[174, 33, 168])).
% 80.80/80.96 tff(176,plain,(~((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2))))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.96 tff(177,plain,
% 80.80/80.96 (((~((~(union(D!2, intersection(D!2, C!3)) = D!2)) | (member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), D!2)))) | (~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2)))) | ((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2))),
% 80.80/80.96 inference(tautology,[status(thm)],[])).
% 80.80/80.96 tff(178,plain,
% 80.80/80.96 ((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2)),
% 80.80/80.96 inference(unit_resolution,[status(thm)],[177, 176])).
% 80.80/80.96 tff(179,assumption,(~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))), introduced(assumption)).
% 80.80/80.97 tff(180,assumption,(~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))), introduced(assumption)).
% 80.80/80.97 tff(181,plain,
% 80.80/80.97 ((member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(182,plain,
% 80.80/80.97 (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[181, 180, 179])).
% 80.80/80.97 tff(183,plain,
% 80.80/80.97 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))))),
% 80.80/80.97 inference(rewrite,[status(thm)],[])).
% 80.80/80.97 tff(184,plain,
% 80.80/80.97 ((member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.97 inference(rewrite,[status(thm)],[])).
% 80.80/80.97 tff(185,plain,
% 80.80/80.97 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))))),
% 80.80/80.97 inference(monotonicity,[status(thm)],[184])).
% 80.80/80.97 tff(186,plain,
% 80.80/80.97 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))))),
% 80.80/80.97 inference(transitivity,[status(thm)],[185, 183])).
% 80.80/80.97 tff(187,plain,
% 80.80/80.97 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)))),
% 80.80/80.97 inference(quant_inst,[status(thm)],[])).
% 80.80/80.97 tff(188,plain,
% 80.80/80.97 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.97 inference(modus_ponens,[status(thm)],[187, 186])).
% 80.80/80.97 tff(189,plain,
% 80.80/80.97 (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[188, 11])).
% 80.80/80.97 tff(190,plain,
% 80.80/80.97 ((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))))) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) | (~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(191,plain,
% 80.80/80.97 (~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[190, 180, 189])).
% 80.80/80.97 tff(192,plain,
% 80.80/80.97 ((member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(193,plain,
% 80.80/80.97 ($false),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[192, 191, 182])).
% 80.80/80.97 tff(194,plain,(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.97 tff(195,plain,
% 80.80/80.97 (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[194, 179])).
% 80.80/80.97 tff(196,plain,
% 80.80/80.97 ((member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(197,plain,
% 80.80/80.97 (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[196, 195, 179])).
% 80.80/80.97 tff(198,plain,
% 80.80/80.97 (((~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), C!3))) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(199,plain,
% 80.80/80.97 ((~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), C!3))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[198, 197])).
% 80.80/80.97 tff(200,assumption,(~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))))), introduced(assumption)).
% 80.80/80.97 tff(201,plain,
% 80.80/80.97 ($false),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[188, 11, 200])).
% 80.80/80.97 tff(202,plain,(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.97 tff(203,plain,
% 80.80/80.97 ((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))))) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(204,plain,
% 80.80/80.97 (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[203, 195, 202])).
% 80.80/80.97 tff(205,plain,
% 80.80/80.97 ((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2) | member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(206,plain,
% 80.80/80.97 (member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[205, 197, 204])).
% 80.80/80.97 tff(207,assumption,(((~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))), introduced(assumption)).
% 80.80/80.97 tff(208,plain,
% 80.80/80.97 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.97 inference(quant_inst,[status(thm)],[])).
% 80.80/80.97 tff(209,plain,
% 80.80/80.97 ($false),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[208, 104, 207])).
% 80.80/80.97 tff(210,plain,(~(((~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.97 tff(211,plain,
% 80.80/80.97 ((((~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3))) | (~((~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), C!3)))) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(212,plain,
% 80.80/80.97 ((~((~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), C!3)))) | (~member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), intersection(D!2, C!3)))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[211, 210])).
% 80.80/80.97 tff(213,plain,
% 80.80/80.97 ($false),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[212, 206, 199])).
% 80.80/80.97 tff(214,plain,(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2)), inference(lemma,lemma(discharge,[]))).
% 80.80/80.97 tff(215,plain,
% 80.80/80.97 ((~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2))) | (~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2)),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(216,plain,
% 80.80/80.97 ((~((~(member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(D!2, union(D!2, intersection(D!2, C!3))), D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2))) | (union(D!2, intersection(D!2, C!3)) = D!2)),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[215, 214])).
% 80.80/80.97 tff(217,plain,
% 80.80/80.97 (union(D!2, intersection(D!2, C!3)) = D!2),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[216, 178])).
% 80.80/80.97 tff(218,plain,
% 80.80/80.97 (subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) <=> subset(D!2, union(D!2, B!4))),
% 80.80/80.97 inference(monotonicity,[status(thm)],[217])).
% 80.80/80.97 tff(219,plain,
% 80.80/80.97 (subset(D!2, union(D!2, B!4)) <=> subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4))),
% 80.80/80.97 inference(symmetry,[status(thm)],[218])).
% 80.80/80.97 tff(220,plain,
% 80.80/80.97 ((~subset(D!2, union(D!2, B!4))) <=> (~subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)))),
% 80.80/80.97 inference(monotonicity,[status(thm)],[219])).
% 80.80/80.97 tff(221,assumption,(~subset(D!2, union(D!2, B!4))), introduced(assumption)).
% 80.80/80.97 tff(222,plain,
% 80.80/80.97 (~subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4))),
% 80.80/80.97 inference(modus_ponens,[status(thm)],[221, 220])).
% 80.80/80.97 tff(223,plain,
% 80.80/80.97 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4))) | ![D: $i] : ((~member(D, union(D!2, intersection(D!2, C!3)))) | member(D, union(D!2, B!4))))) | (~(subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))))))))),
% 80.80/80.97 inference(quant_inst,[status(thm)],[])).
% 80.80/80.97 tff(224,plain,
% 80.80/80.97 (~((~((~subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4))) | ![D: $i] : ((~member(D, union(D!2, intersection(D!2, C!3)))) | member(D, union(D!2, B!4))))) | (~(subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4)))))))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[223, 163])).
% 80.80/80.97 tff(225,plain,
% 80.80/80.97 (((~((~subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4))) | ![D: $i] : ((~member(D, union(D!2, intersection(D!2, C!3)))) | member(D, union(D!2, B!4))))) | (~(subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))))))) | (subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4)))))),
% 80.80/80.97 inference(tautology,[status(thm)],[])).
% 80.80/80.97 tff(226,plain,
% 80.80/80.97 (subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[225, 224])).
% 80.80/80.97 tff(227,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)).
% 80.80/80.97 tff(228,plain,
% 80.80/80.97 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> 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, B)) | (~member(D, C))) <=> 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))))),
% 80.80/80.97 inference(rewrite,[status(thm)],[])).
% 80.80/80.97 tff(229,plain,
% 80.80/80.97 ((~(~(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)))),
% 80.80/80.97 inference(rewrite,[status(thm)],[])).
% 80.80/80.97 tff(230,plain,
% 80.80/80.97 ((~(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))))),
% 80.80/80.97 inference(rewrite,[status(thm)],[])).
% 80.80/80.97 tff(231,plain,
% 80.80/80.97 (((~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))))),
% 80.80/80.97 inference(rewrite,[status(thm)],[])).
% 80.80/80.97 tff(232,plain,
% 80.80/80.97 (((~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))),
% 80.80/80.97 inference(rewrite,[status(thm)],[])).
% 80.80/80.97 tff(233,plain,
% 80.80/80.97 ((((~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)))),
% 80.80/80.97 inference(monotonicity,[status(thm)],[232])).
% 80.80/80.97 tff(234,plain,
% 80.80/80.97 ((((~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))))),
% 80.80/80.97 inference(transitivity,[status(thm)],[233, 231])).
% 80.80/80.97 tff(235,plain,
% 80.80/80.97 ((((~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))))),
% 80.80/80.97 inference(transitivity,[status(thm)],[234, 230])).
% 80.80/80.97 tff(236,plain,
% 80.80/80.97 ((~(((~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)))))),
% 80.80/80.97 inference(monotonicity,[status(thm)],[235])).
% 80.80/80.97 tff(237,plain,
% 80.80/80.97 ((~(((~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)))),
% 80.80/80.97 inference(transitivity,[status(thm)],[236, 229])).
% 80.80/80.97 tff(238,plain,
% 80.80/80.97 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> 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, B)) | (~member(D, C))) <=> 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))))),
% 80.80/80.97 inference(monotonicity,[status(thm)],[237])).
% 80.80/80.97 tff(239,plain,
% 80.80/80.97 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> 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, B)) | (~member(D, C))) <=> 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))))),
% 80.80/80.97 inference(transitivity,[status(thm)],[238, 228])).
% 80.80/80.97 tff(240,plain,
% 80.80/80.97 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> 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))))),
% 80.80/80.97 inference(quant_inst,[status(thm)],[])).
% 80.80/80.97 tff(241,plain,
% 80.80/80.97 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 80.80/80.97 inference(modus_ponens,[status(thm)],[240, 239])).
% 80.80/80.97 tff(242,plain,
% 80.80/80.97 ($false),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[241, 104, 227])).
% 80.80/80.97 tff(243,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,[]))).
% 80.80/80.97 tff(244,plain,
% 80.80/80.97 ((~![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, intersection(D!2, C!3)), B!4) <=> member(tptp_fun_D_1(C!3, intersection(D!2, C!3)), 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))))))))),
% 80.80/80.97 inference(quant_inst,[status(thm)],[])).
% 80.80/80.97 tff(245,plain,
% 80.80/80.97 (~((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_D_1(C!3, intersection(D!2, C!3)), B!4) <=> member(tptp_fun_D_1(C!3, intersection(D!2, C!3)), 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)))))))),
% 80.80/80.97 inference(unit_resolution,[status(thm)],[244, 33])).
% 80.80/80.98 tff(246,plain,
% 80.80/80.98 (((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_D_1(C!3, intersection(D!2, C!3)), B!4) <=> member(tptp_fun_D_1(C!3, intersection(D!2, C!3)), 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)))))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(247,plain,
% 80.80/80.98 ((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))))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[246, 245])).
% 80.80/80.98 tff(248,plain,
% 80.80/80.98 ((~((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))))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(249,plain,
% 80.80/80.98 ((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))))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[248, 247])).
% 80.80/80.98 tff(250,plain,
% 80.80/80.98 (B!4 = intersection(B!4, B!4)),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[249, 243])).
% 80.80/80.98 tff(251,plain,
% 80.80/80.98 (intersection(B!4, B!4) = B!4),
% 80.80/80.98 inference(symmetry,[status(thm)],[250])).
% 80.80/80.98 tff(252,plain,
% 80.80/80.98 (union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4)) = union(D!2, B!4)),
% 80.80/80.98 inference(monotonicity,[status(thm)],[217, 251])).
% 80.80/80.98 tff(253,plain,
% 80.80/80.98 (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4))) <=> member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))),
% 80.80/80.98 inference(monotonicity,[status(thm)],[252])).
% 80.80/80.98 tff(254,plain,
% 80.80/80.98 (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4)) <=> member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4)))),
% 80.80/80.98 inference(symmetry,[status(thm)],[253])).
% 80.80/80.98 tff(255,plain,
% 80.80/80.98 ((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))) <=> (~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4))))),
% 80.80/80.98 inference(monotonicity,[status(thm)],[254])).
% 80.80/80.98 tff(256,assumption,(~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4)))), introduced(assumption)).
% 80.80/80.98 tff(257,plain,
% 80.80/80.98 (((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4)))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(258,plain,
% 80.80/80.98 (~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[257, 256])).
% 80.80/80.98 tff(259,plain,
% 80.80/80.98 (~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4)))),
% 80.80/80.98 inference(modus_ponens,[status(thm)],[258, 255])).
% 80.80/80.98 tff(260,plain,
% 80.80/80.98 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))))),
% 80.80/80.98 inference(quant_inst,[status(thm)],[])).
% 80.80/80.98 tff(261,plain,
% 80.80/80.98 (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[260, 11])).
% 80.80/80.98 tff(262,plain,
% 80.80/80.98 (((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(263,plain,
% 80.80/80.98 (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[262, 256])).
% 80.80/80.98 tff(264,plain,
% 80.80/80.98 ((member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | (~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3))))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(265,plain,
% 80.80/80.98 (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[264, 263])).
% 80.80/80.98 tff(266,plain,
% 80.80/80.98 ((~(member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4))) | (~(member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(267,plain,
% 80.80/80.98 ((~(member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4)))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[266, 265])).
% 80.80/80.98 tff(268,plain,
% 80.80/80.98 (member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(union(D!2, intersection(D!2, C!3)), intersection(B!4, B!4)))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[267, 261])).
% 80.80/80.98 tff(269,plain,
% 80.80/80.98 ($false),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[268, 259])).
% 80.80/80.98 tff(270,plain,((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.98 tff(271,plain,
% 80.80/80.98 ((~(subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4)))))) | subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4))))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(272,plain,
% 80.80/80.98 ((~(subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(D!2, B!4), union(D!2, intersection(D!2, C!3))), union(D!2, B!4)))))) | subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[271, 270])).
% 80.80/80.98 tff(273,plain,
% 80.80/80.98 (subset(union(D!2, intersection(D!2, C!3)), union(D!2, B!4))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[272, 226])).
% 80.80/80.98 tff(274,plain,
% 80.80/80.98 ($false),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[273, 222])).
% 80.80/80.98 tff(275,plain,(subset(D!2, union(D!2, B!4))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.98 tff(276,plain,
% 80.80/80.98 ((~((~subset(D!2, union(D!2, B!4))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4))))) | (~subset(D!2, union(D!2, B!4))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4)))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(277,plain,
% 80.80/80.98 ((~((~subset(D!2, union(D!2, B!4))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4))))) | ![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4)))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[276, 275])).
% 80.80/80.98 tff(278,plain,
% 80.80/80.98 (![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4)))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[277, 167])).
% 80.80/80.98 tff(279,plain,
% 80.80/80.98 (((~![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4)))) | ((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))) <=> ((~![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4)))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))),
% 80.80/80.98 inference(rewrite,[status(thm)],[])).
% 80.80/80.98 tff(280,plain,
% 80.80/80.98 ((~![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4)))) | ((~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4)))),
% 80.80/80.98 inference(quant_inst,[status(thm)],[])).
% 80.80/80.98 tff(281,plain,
% 80.80/80.98 ((~![D: $i] : ((~member(D, D!2)) | member(D, union(D!2, B!4)))) | (~member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), D!2)) | member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), union(D!2, B!4))),
% 80.80/80.98 inference(modus_ponens,[status(thm)],[280, 279])).
% 80.80/80.98 tff(282,plain,
% 80.80/80.98 ($false),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[281, 278, 147, 132])).
% 80.80/80.98 tff(283,plain,(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.98 tff(284,plain,
% 80.80/80.98 ((~((intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)) | (~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))))) | (intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)) | (~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3))))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(285,plain,
% 80.80/80.98 ((~((intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)) | (~(member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(union(D!2, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, C!3), intersection(union(D!2, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)))))) | (intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[284, 283])).
% 80.80/80.98 tff(286,plain,
% 80.80/80.98 (intersection(union(D!2, B!4), intersection(D!2, C!3)) = intersection(D!2, C!3)),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[285, 94])).
% 80.80/80.98 tff(287,plain,
% 80.80/80.98 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(intersection(D!2, C!3), union(D!2, B!4)) = intersection(union(D!2, B!4), intersection(D!2, C!3)))),
% 80.80/80.98 inference(quant_inst,[status(thm)],[])).
% 80.80/80.98 tff(288,plain,
% 80.80/80.98 (intersection(intersection(D!2, C!3), union(D!2, B!4)) = intersection(union(D!2, B!4), intersection(D!2, C!3))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[287, 50])).
% 80.80/80.98 tff(289,plain,
% 80.80/80.98 (intersection(intersection(D!2, C!3), union(D!2, B!4)) = intersection(D!2, C!3)),
% 80.80/80.98 inference(transitivity,[status(thm)],[288, 286])).
% 80.80/80.98 tff(290,plain,
% 80.80/80.98 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 80.80/80.98 inference(monotonicity,[status(thm)],[289])).
% 80.80/80.98 tff(291,plain,
% 80.80/80.98 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4)))),
% 80.80/80.98 inference(symmetry,[status(thm)],[290])).
% 80.80/80.98 tff(292,plain,
% 80.80/80.98 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[12, 11])).
% 80.80/80.98 tff(293,plain,
% 80.80/80.98 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, D!2) = intersection(D!2, C!3))),
% 80.80/80.98 inference(quant_inst,[status(thm)],[])).
% 80.80/80.98 tff(294,plain,
% 80.80/80.98 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[293, 50])).
% 80.80/80.98 tff(295,plain,
% 80.80/80.98 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 80.80/80.98 inference(symmetry,[status(thm)],[294])).
% 80.80/80.98 tff(296,plain,
% 80.80/80.98 (union(intersection(D!2, C!3), intersection(B!4, B!4)) = union(intersection(C!3, D!2), B!4)),
% 80.80/80.98 inference(monotonicity,[status(thm)],[295, 251])).
% 80.80/80.98 tff(297,plain,
% 80.80/80.98 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 80.80/80.98 inference(monotonicity,[status(thm)],[296])).
% 80.80/80.98 tff(298,plain,
% 80.80/80.98 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4)))),
% 80.80/80.98 inference(symmetry,[status(thm)],[297])).
% 80.80/80.98 tff(299,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))), introduced(assumption)).
% 80.80/80.98 tff(300,plain,
% 80.80/80.98 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4)))),
% 80.80/80.98 inference(modus_ponens,[status(thm)],[299, 298])).
% 80.80/80.98 tff(301,plain,
% 80.80/80.98 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))),
% 80.80/80.98 inference(tautology,[status(thm)],[])).
% 80.80/80.98 tff(302,plain,
% 80.80/80.98 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 80.80/80.98 inference(unit_resolution,[status(thm)],[301, 300, 292])).
% 80.80/80.98 tff(303,plain,
% 80.80/80.98 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))))),
% 80.80/80.98 inference(rewrite,[status(thm)],[])).
% 80.80/80.98 tff(304,plain,
% 80.80/80.98 ((~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))) <=> (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))))),
% 80.80/80.98 inference(rewrite,[status(thm)],[])).
% 80.80/80.98 tff(305,plain,
% 80.80/80.98 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))) <=> (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))),
% 80.80/80.98 inference(rewrite,[status(thm)],[])).
% 80.80/80.98 tff(306,plain,
% 80.80/80.98 ((~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))) <=> (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))))),
% 80.80/80.98 inference(monotonicity,[status(thm)],[305])).
% 80.80/80.98 tff(307,plain,
% 80.80/80.98 ((~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))) <=> (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))))),
% 80.80/80.98 inference(transitivity,[status(thm)],[306, 304])).
% 80.80/80.98 tff(308,plain,
% 80.80/80.98 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))))),
% 80.80/80.98 inference(monotonicity,[status(thm)],[307])).
% 80.80/80.98 tff(309,plain,
% 80.80/80.98 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))))),
% 80.80/80.99 inference(transitivity,[status(thm)],[308, 303])).
% 80.80/80.99 tff(310,plain,
% 80.80/80.99 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))))),
% 80.80/80.99 inference(quant_inst,[status(thm)],[])).
% 80.80/80.99 tff(311,plain,
% 80.80/80.99 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))))),
% 80.80/80.99 inference(modus_ponens,[status(thm)],[310, 309])).
% 80.80/80.99 tff(312,plain,
% 80.80/80.99 (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[311, 104])).
% 80.80/80.99 tff(313,plain,
% 80.80/80.99 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, C!3) = union(C!3, B!4))),
% 80.80/80.99 inference(quant_inst,[status(thm)],[])).
% 80.80/80.99 tff(314,plain,
% 80.80/80.99 (union(B!4, C!3) = union(C!3, B!4)),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[313, 62])).
% 80.80/80.99 tff(315,plain,
% 80.80/80.99 (union(C!3, B!4) = union(B!4, C!3)),
% 80.80/80.99 inference(symmetry,[status(thm)],[314])).
% 80.80/80.99 tff(316,plain,
% 80.80/80.99 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, D!2) = union(D!2, B!4))),
% 80.80/80.99 inference(quant_inst,[status(thm)],[])).
% 80.80/80.99 tff(317,plain,
% 80.80/80.99 (union(B!4, D!2) = union(D!2, B!4)),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[316, 62])).
% 80.80/80.99 tff(318,plain,
% 80.80/80.99 (union(D!2, B!4) = union(B!4, D!2)),
% 80.80/80.99 inference(symmetry,[status(thm)],[317])).
% 80.80/80.99 tff(319,plain,
% 80.80/80.99 (intersection(union(D!2, B!4), union(C!3, B!4)) = intersection(union(B!4, D!2), union(B!4, C!3))),
% 80.80/80.99 inference(monotonicity,[status(thm)],[318, 315])).
% 80.80/80.99 tff(320,plain,
% 80.80/80.99 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))),
% 80.80/80.99 inference(monotonicity,[status(thm)],[319])).
% 80.80/80.99 tff(321,plain,
% 80.80/80.99 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 80.80/80.99 inference(symmetry,[status(thm)],[320])).
% 80.80/80.99 tff(322,plain,
% 80.80/80.99 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))),
% 80.80/80.99 inference(monotonicity,[status(thm)],[321])).
% 80.80/80.99 tff(323,plain,
% 80.80/80.99 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 80.80/80.99 inference(modus_ponens,[status(thm)],[88, 322])).
% 80.80/80.99 tff(324,plain,
% 80.80/80.99 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 80.80/80.99 inference(tautology,[status(thm)],[])).
% 80.80/80.99 tff(325,plain,
% 80.80/80.99 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[324, 323, 312])).
% 80.80/80.99 tff(326,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))), introduced(assumption)).
% 80.80/80.99 tff(327,plain,
% 80.80/80.99 ((~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))),
% 80.80/80.99 inference(tautology,[status(thm)],[])).
% 80.80/80.99 tff(328,plain,
% 80.80/80.99 ((~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[327, 326])).
% 80.80/80.99 tff(329,plain,
% 80.80/80.99 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[328, 325])).
% 80.80/80.99 tff(330,plain,
% 80.80/80.99 ((~![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(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4))) | (member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))))) | (~((intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))))))))),
% 80.80/80.99 inference(quant_inst,[status(thm)],[])).
% 80.80/80.99 tff(331,plain,
% 80.80/80.99 (~((~((~(intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4))) | (member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))))) | (~((intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))))))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[330, 33])).
% 80.80/80.99 tff(332,plain,
% 80.80/80.99 (((~((~(intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4))) | (member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))))) | (~((intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))))))) | ((intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))))),
% 80.80/80.99 inference(tautology,[status(thm)],[])).
% 80.80/80.99 tff(333,plain,
% 80.80/80.99 ((intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[332, 331])).
% 80.80/80.99 tff(334,assumption,(~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))), introduced(assumption)).
% 80.80/80.99 tff(335,plain,
% 80.80/80.99 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))))),
% 80.80/80.99 inference(rewrite,[status(thm)],[])).
% 80.80/80.99 tff(336,plain,
% 80.80/80.99 ((~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))) <=> (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))))),
% 80.80/80.99 inference(rewrite,[status(thm)],[])).
% 80.80/80.99 tff(337,plain,
% 80.80/80.99 ((((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))) <=> (((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))),
% 80.80/80.99 inference(rewrite,[status(thm)],[])).
% 80.80/80.99 tff(338,plain,
% 80.80/80.99 ((~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))) <=> (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))))),
% 80.80/80.99 inference(monotonicity,[status(thm)],[337])).
% 80.80/80.99 tff(339,plain,
% 80.80/80.99 ((~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))) <=> (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))))),
% 80.80/80.99 inference(transitivity,[status(thm)],[338, 336])).
% 80.80/80.99 tff(340,plain,
% 80.80/80.99 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))))),
% 80.80/80.99 inference(monotonicity,[status(thm)],[339])).
% 80.80/80.99 tff(341,plain,
% 80.80/80.99 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))))),
% 80.80/80.99 inference(transitivity,[status(thm)],[340, 335])).
% 80.80/80.99 tff(342,plain,
% 80.80/80.99 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))))),
% 80.80/80.99 inference(quant_inst,[status(thm)],[])).
% 80.80/80.99 tff(343,plain,
% 80.80/80.99 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))))),
% 80.80/80.99 inference(modus_ponens,[status(thm)],[342, 341])).
% 80.80/80.99 tff(344,plain,
% 80.80/80.99 (~(((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[343, 104])).
% 80.80/80.99 tff(345,assumption,(~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))), introduced(assumption)).
% 80.80/80.99 tff(346,plain,
% 80.80/80.99 ((member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))),
% 80.80/80.99 inference(tautology,[status(thm)],[])).
% 80.80/80.99 tff(347,plain,
% 80.80/80.99 (member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[346, 345, 334])).
% 80.80/80.99 tff(348,plain,
% 80.80/80.99 (((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))),
% 80.80/80.99 inference(tautology,[status(thm)],[])).
% 80.80/80.99 tff(349,plain,
% 80.80/80.99 ((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[348, 345])).
% 80.80/80.99 tff(350,plain,
% 80.80/80.99 ((((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))) | (~((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))))),
% 80.80/80.99 inference(tautology,[status(thm)],[])).
% 80.80/80.99 tff(351,plain,
% 80.80/80.99 ($false),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[350, 349, 347, 344])).
% 80.80/80.99 tff(352,plain,(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)) | (member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.80/80.99 tff(353,plain,
% 80.80/80.99 (member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))),
% 80.80/80.99 inference(unit_resolution,[status(thm)],[352, 334])).
% 80.80/80.99 tff(354,plain,
% 80.80/80.99 (union(D!2, intersection(B!4, B!4)) = union(D!2, B!4)),
% 80.80/80.99 inference(monotonicity,[status(thm)],[251])).
% 80.80/80.99 tff(355,plain,
% 80.80/80.99 (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4))) <=> member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))),
% 80.80/80.99 inference(monotonicity,[status(thm)],[354])).
% 80.80/80.99 tff(356,plain,
% 80.80/80.99 (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4)) <=> member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4)))),
% 80.80/80.99 inference(symmetry,[status(thm)],[355])).
% 80.80/80.99 tff(357,plain,
% 80.80/80.99 ((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))) <=> (~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4))))),
% 80.80/80.99 inference(monotonicity,[status(thm)],[356])).
% 80.80/80.99 tff(358,assumption,(~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4)))), introduced(assumption)).
% 80.80/80.99 tff(359,plain,
% 80.80/80.99 (((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))) | (~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4)))),
% 80.80/80.99 inference(tautology,[status(thm)],[])).
% 80.80/80.99 tff(360,plain,
% 80.80/81.00 (~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[359, 358])).
% 80.80/81.00 tff(361,plain,
% 80.80/81.00 (~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4)))),
% 80.80/81.00 inference(modus_ponens,[status(thm)],[360, 357])).
% 80.80/81.00 tff(362,plain,
% 80.80/81.00 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), D!2)))),
% 80.80/81.00 inference(quant_inst,[status(thm)],[])).
% 80.80/81.00 tff(363,plain,
% 80.80/81.00 (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), D!2))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[362, 11])).
% 80.80/81.00 tff(364,plain,
% 80.80/81.00 (((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(365,plain,
% 80.80/81.00 (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[364, 358])).
% 80.80/81.00 tff(366,plain,
% 80.80/81.00 ((member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), D!2)) | (~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4)))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(367,plain,
% 80.80/81.00 (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), D!2)),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[366, 365])).
% 80.80/81.00 tff(368,plain,
% 80.80/81.00 ((~(member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), D!2)))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4))) | (~(member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), D!2)))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(369,plain,
% 80.80/81.00 ((~(member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), D!2)))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[368, 367])).
% 80.80/81.00 tff(370,plain,
% 80.80/81.00 (member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, intersection(B!4, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[369, 363])).
% 80.80/81.00 tff(371,plain,
% 80.80/81.00 ($false),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[370, 361])).
% 80.80/81.00 tff(372,plain,((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))), inference(lemma,lemma(discharge,[]))).
% 80.80/81.00 tff(373,plain,
% 80.80/81.00 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4))))) | (~(subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))))))))),
% 80.80/81.00 inference(quant_inst,[status(thm)],[])).
% 80.80/81.00 tff(374,plain,
% 80.80/81.00 (~((~((~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4))))) | (~(subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4)))))))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[373, 163])).
% 80.80/81.00 tff(375,plain,
% 80.80/81.00 (((~((~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4))))) | (~(subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))))))) | (subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4)))))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(376,plain,
% 80.80/81.00 (subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[375, 374])).
% 80.80/81.00 tff(377,plain,
% 80.80/81.00 ((~(subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4)))))) | subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(378,plain,
% 80.80/81.00 (subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[377, 376])).
% 80.80/81.00 tff(379,plain,
% 80.80/81.00 (subset(intersection(B!4, B!4), union(D!2, B!4))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[378, 372])).
% 80.80/81.00 tff(380,plain,
% 80.80/81.00 (((~((~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4))))) | (~(subset(intersection(B!4, B!4), union(D!2, B!4)) | (~((~member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(union(D!2, B!4), intersection(B!4, B!4)), union(D!2, B!4))))))) | ((~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4))))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(381,plain,
% 80.80/81.00 ((~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[380, 374])).
% 80.80/81.00 tff(382,plain,
% 80.80/81.00 ((~((~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4))))) | (~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4)))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(383,plain,
% 80.80/81.00 ((~subset(intersection(B!4, B!4), union(D!2, B!4))) | ![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[382, 381])).
% 80.80/81.00 tff(384,plain,
% 80.80/81.00 (![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[383, 379])).
% 80.80/81.00 tff(385,plain,
% 80.80/81.00 (((~![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4)))) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> ((~![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4)))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))),
% 80.80/81.00 inference(rewrite,[status(thm)],[])).
% 80.80/81.00 tff(386,plain,
% 80.80/81.00 ((~![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4)))) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))),
% 80.80/81.00 inference(quant_inst,[status(thm)],[])).
% 80.80/81.00 tff(387,plain,
% 80.80/81.00 ((~![D: $i] : ((~member(D, intersection(B!4, B!4))) | member(D, union(D!2, B!4)))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))),
% 80.80/81.00 inference(modus_ponens,[status(thm)],[386, 385])).
% 80.80/81.00 tff(388,plain,
% 80.80/81.00 ((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[387, 384])).
% 80.80/81.00 tff(389,plain,
% 80.80/81.00 (member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[388, 353])).
% 80.80/81.00 tff(390,plain,
% 80.80/81.00 ((member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(391,plain,
% 80.80/81.00 (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[390, 353, 334])).
% 80.80/81.00 tff(392,plain,
% 80.80/81.00 ((((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))) | member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4)))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(393,plain,
% 80.80/81.00 ((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[392, 391, 344])).
% 80.80/81.00 tff(394,plain,
% 80.80/81.00 ((~((~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), union(D!2, B!4)))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(395,plain,
% 80.80/81.00 ($false),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[394, 393, 389, 353])).
% 80.80/81.00 tff(396,plain,(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))), inference(lemma,lemma(discharge,[]))).
% 80.80/81.00 tff(397,plain,
% 80.80/81.00 ((~((intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))))) | (intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4))))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(398,plain,
% 80.80/81.00 ((~((intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)) | (~(member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(union(D!2, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(B!4, B!4), intersection(union(D!2, B!4), intersection(B!4, B!4))), intersection(B!4, B!4)))))) | (intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[397, 396])).
% 80.80/81.00 tff(399,plain,
% 80.80/81.00 (intersection(union(D!2, B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[398, 333])).
% 80.80/81.00 tff(400,plain,
% 80.80/81.00 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(intersection(B!4, B!4), union(D!2, B!4)) = intersection(union(D!2, B!4), intersection(B!4, B!4)))),
% 80.80/81.00 inference(quant_inst,[status(thm)],[])).
% 80.80/81.00 tff(401,plain,
% 80.80/81.00 (intersection(intersection(B!4, B!4), union(D!2, B!4)) = intersection(union(D!2, B!4), intersection(B!4, B!4))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[400, 50])).
% 80.80/81.00 tff(402,plain,
% 80.80/81.00 (intersection(intersection(B!4, B!4), union(D!2, B!4)) = intersection(B!4, B!4)),
% 80.80/81.00 inference(transitivity,[status(thm)],[401, 399])).
% 80.80/81.00 tff(403,plain,
% 80.80/81.00 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.80/81.00 inference(monotonicity,[status(thm)],[402])).
% 80.80/81.00 tff(404,plain,
% 80.80/81.00 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4)))),
% 80.80/81.00 inference(symmetry,[status(thm)],[403])).
% 80.80/81.00 tff(405,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))), introduced(assumption)).
% 80.80/81.00 tff(406,plain,
% 80.80/81.00 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4)))),
% 80.80/81.00 inference(modus_ponens,[status(thm)],[405, 404])).
% 80.80/81.00 tff(407,plain,
% 80.80/81.00 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4)))))),
% 80.80/81.00 inference(quant_inst,[status(thm)],[])).
% 80.80/81.00 tff(408,plain,
% 80.80/81.00 (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4))))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[407, 104])).
% 80.80/81.00 tff(409,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))), introduced(assumption)).
% 80.80/81.00 tff(410,plain,
% 80.80/81.00 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(411,plain,
% 80.80/81.00 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[410, 409])).
% 80.80/81.00 tff(412,plain,
% 80.80/81.00 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4)))) | (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4))))),
% 80.80/81.00 inference(tautology,[status(thm)],[])).
% 80.80/81.00 tff(413,plain,
% 80.80/81.00 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4))))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[412, 411])).
% 80.80/81.00 tff(414,plain,
% 80.80/81.00 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(D!2, B!4)))),
% 80.80/81.00 inference(unit_resolution,[status(thm)],[413, 408])).
% 80.80/81.00 tff(415,plain,
% 80.85/81.01 ($false),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[414, 406])).
% 80.85/81.01 tff(416,plain,((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))), inference(lemma,lemma(discharge,[]))).
% 80.85/81.01 tff(417,plain,
% 80.85/81.01 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[416, 329])).
% 80.85/81.01 tff(418,plain,
% 80.85/81.01 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 80.85/81.01 inference(tautology,[status(thm)],[])).
% 80.85/81.01 tff(419,plain,
% 80.85/81.01 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[418, 417, 302])).
% 80.85/81.01 tff(420,plain,
% 80.85/81.01 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4)))),
% 80.85/81.01 inference(modus_ponens,[status(thm)],[419, 291])).
% 80.85/81.01 tff(421,plain,
% 80.85/81.01 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4)))))),
% 80.85/81.01 inference(quant_inst,[status(thm)],[])).
% 80.85/81.01 tff(422,plain,
% 80.85/81.01 (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4))))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[421, 104])).
% 80.85/81.01 tff(423,plain,
% 80.85/81.01 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 80.85/81.01 inference(tautology,[status(thm)],[])).
% 80.85/81.01 tff(424,plain,
% 80.85/81.01 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[423, 329])).
% 80.85/81.01 tff(425,plain,
% 80.85/81.01 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4)))) | (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4))))),
% 80.85/81.01 inference(tautology,[status(thm)],[])).
% 80.85/81.01 tff(426,plain,
% 80.85/81.01 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4))))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[425, 424])).
% 80.85/81.01 tff(427,plain,
% 80.85/81.01 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(D!2, C!3), union(D!2, B!4)))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[426, 422])).
% 80.85/81.01 tff(428,plain,
% 80.85/81.01 ($false),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[427, 420])).
% 80.85/81.01 tff(429,plain,((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.85/81.01 tff(430,plain,
% 80.85/81.01 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[429, 88, 90])).
% 80.85/81.01 tff(431,plain,
% 80.85/81.01 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))))),
% 80.85/81.01 inference(quant_inst,[status(thm)],[])).
% 80.85/81.01 tff(432,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[431, 11])).
% 80.85/81.01 tff(433,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))),
% 80.85/81.01 inference(monotonicity,[status(thm)],[296])).
% 80.85/81.01 tff(434,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4)))),
% 80.85/81.01 inference(symmetry,[status(thm)],[433])).
% 80.85/81.01 tff(435,assumption,(~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))), introduced(assumption)).
% 80.85/81.01 tff(436,plain,
% 80.85/81.01 (((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))),
% 80.85/81.01 inference(tautology,[status(thm)],[])).
% 80.85/81.01 tff(437,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[436, 435])).
% 80.85/81.01 tff(438,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4)))),
% 80.85/81.01 inference(modus_ponens,[status(thm)],[437, 434])).
% 80.85/81.01 tff(439,plain,
% 80.85/81.01 ((~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))),
% 80.85/81.01 inference(tautology,[status(thm)],[])).
% 80.85/81.01 tff(440,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[439, 438, 432])).
% 80.85/81.01 tff(441,plain,
% 80.85/81.01 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)))))),
% 80.85/81.01 inference(rewrite,[status(thm)],[])).
% 80.85/81.01 tff(442,plain,
% 80.85/81.01 ((member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4))))),
% 80.85/81.01 inference(rewrite,[status(thm)],[])).
% 80.85/81.01 tff(443,plain,
% 80.85/81.01 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)))))),
% 80.85/81.01 inference(monotonicity,[status(thm)],[442])).
% 80.85/81.01 tff(444,plain,
% 80.85/81.01 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)))))),
% 80.85/81.01 inference(transitivity,[status(thm)],[443, 441])).
% 80.85/81.01 tff(445,plain,
% 80.85/81.01 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3)))),
% 80.85/81.01 inference(quant_inst,[status(thm)],[])).
% 80.85/81.01 tff(446,plain,
% 80.85/81.01 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4))))),
% 80.85/81.01 inference(modus_ponens,[status(thm)],[445, 444])).
% 80.85/81.01 tff(447,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[446, 11])).
% 80.85/81.01 tff(448,plain,
% 80.85/81.01 (union(C!3, intersection(B!4, B!4)) = union(C!3, B!4)),
% 80.85/81.01 inference(monotonicity,[status(thm)],[251])).
% 80.85/81.01 tff(449,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))),
% 80.85/81.01 inference(monotonicity,[status(thm)],[448])).
% 80.85/81.01 tff(450,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4)))),
% 80.85/81.01 inference(symmetry,[status(thm)],[449])).
% 80.85/81.01 tff(451,plain,
% 80.85/81.01 ((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))) <=> (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))))),
% 80.85/81.01 inference(monotonicity,[status(thm)],[450])).
% 80.85/81.01 tff(452,plain,
% 80.85/81.01 (((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))),
% 80.85/81.01 inference(tautology,[status(thm)],[])).
% 80.85/81.01 tff(453,plain,
% 80.85/81.01 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[452, 435])).
% 80.85/81.01 tff(454,plain,
% 80.85/81.01 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4)))),
% 80.85/81.01 inference(modus_ponens,[status(thm)],[453, 451])).
% 80.85/81.01 tff(455,plain,
% 80.85/81.01 ((~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4))))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, intersection(B!4, B!4))) | (~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4))))),
% 80.85/81.01 inference(tautology,[status(thm)],[])).
% 80.85/81.01 tff(456,plain,
% 80.85/81.01 (~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[455, 454, 447])).
% 80.85/81.01 tff(457,plain,
% 80.85/81.01 ((member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)))),
% 80.85/81.01 inference(tautology,[status(thm)],[])).
% 80.85/81.01 tff(458,plain,
% 80.85/81.01 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[457, 456])).
% 80.85/81.01 tff(459,plain,
% 80.85/81.01 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(C!3, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))))),
% 80.85/81.01 inference(quant_inst,[status(thm)],[])).
% 80.85/81.01 tff(460,plain,
% 80.85/81.01 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(C!3, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[459, 11])).
% 80.85/81.01 tff(461,plain,
% 80.85/81.01 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))))),
% 80.85/81.01 inference(quant_inst,[status(thm)],[])).
% 80.85/81.01 tff(462,plain,
% 80.85/81.01 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))),
% 80.85/81.01 inference(unit_resolution,[status(thm)],[461, 11])).
% 80.85/81.01 tff(463,assumption,(~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))), introduced(assumption)).
% 80.85/81.01 tff(464,assumption,(~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))), introduced(assumption)).
% 80.85/81.01 tff(465,plain,
% 80.85/81.01 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))))),
% 80.85/81.01 inference(quant_inst,[status(thm)],[])).
% 80.85/81.01 tff(466,plain,
% 80.85/81.01 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[465, 11])).
% 80.85/81.02 tff(467,plain,
% 80.85/81.02 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(D!2, C!3), union(C!3, B!4)) = union(union(C!3, B!4), intersection(D!2, C!3)))),
% 80.85/81.02 inference(quant_inst,[status(thm)],[])).
% 80.85/81.02 tff(468,plain,
% 80.85/81.02 (union(intersection(D!2, C!3), union(C!3, B!4)) = union(union(C!3, B!4), intersection(D!2, C!3))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[467, 62])).
% 80.85/81.02 tff(469,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))),
% 80.85/81.02 inference(monotonicity,[status(thm)],[448])).
% 80.85/81.02 tff(470,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4)))),
% 80.85/81.02 inference(symmetry,[status(thm)],[469])).
% 80.85/81.02 tff(471,plain,
% 80.85/81.02 ((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))) <=> (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4))))),
% 80.85/81.02 inference(monotonicity,[status(thm)],[470])).
% 80.85/81.02 tff(472,plain,
% 80.85/81.02 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))),
% 80.85/81.02 inference(quant_inst,[status(thm)],[])).
% 80.85/81.02 tff(473,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[472, 11])).
% 80.85/81.02 tff(474,plain,
% 80.85/81.02 (tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))) = tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4)))),
% 80.85/81.02 inference(monotonicity,[status(thm)],[468])).
% 80.85/81.02 tff(475,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3)))),
% 80.85/81.02 inference(monotonicity,[status(thm)],[474, 468])).
% 80.85/81.02 tff(476,plain,
% 80.85/81.02 ((~member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))) <=> (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3))))),
% 80.85/81.02 inference(monotonicity,[status(thm)],[475])).
% 80.85/81.02 tff(477,assumption,(~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4))))), introduced(assumption)).
% 80.85/81.02 tff(478,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))),
% 80.85/81.02 inference(monotonicity,[status(thm)],[474])).
% 80.85/81.02 tff(479,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))),
% 80.85/81.02 inference(symmetry,[status(thm)],[478])).
% 80.85/81.02 tff(480,plain,
% 80.85/81.02 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)))),
% 80.85/81.02 inference(quant_inst,[status(thm)],[])).
% 80.85/81.02 tff(481,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[480, 11])).
% 80.85/81.02 tff(482,plain,
% 80.85/81.02 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))))),
% 80.85/81.02 inference(rewrite,[status(thm)],[])).
% 80.85/81.02 tff(483,plain,
% 80.85/81.02 ((member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))),
% 80.85/81.02 inference(rewrite,[status(thm)],[])).
% 80.85/81.02 tff(484,plain,
% 80.85/81.02 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))))),
% 80.85/81.02 inference(monotonicity,[status(thm)],[483])).
% 80.85/81.02 tff(485,plain,
% 80.85/81.02 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))))),
% 80.85/81.02 inference(transitivity,[status(thm)],[484, 482])).
% 80.85/81.02 tff(486,plain,
% 80.85/81.02 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4))))),
% 80.85/81.02 inference(quant_inst,[status(thm)],[])).
% 80.85/81.02 tff(487,plain,
% 80.85/81.02 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))),
% 80.85/81.02 inference(modus_ponens,[status(thm)],[486, 485])).
% 80.85/81.02 tff(488,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[487, 11])).
% 80.85/81.02 tff(489,assumption,(~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))), introduced(assumption)).
% 80.85/81.02 tff(490,plain,
% 80.85/81.02 ((~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))),
% 80.85/81.02 inference(tautology,[status(thm)],[])).
% 80.85/81.02 tff(491,plain,
% 80.85/81.02 (~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[490, 489, 488])).
% 80.85/81.02 tff(492,plain,
% 80.85/81.02 ((member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))),
% 80.85/81.02 inference(tautology,[status(thm)],[])).
% 80.85/81.02 tff(493,plain,
% 80.85/81.02 (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[492, 491])).
% 80.85/81.02 tff(494,plain,
% 80.85/81.02 (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4)))),
% 80.85/81.02 inference(modus_ponens,[status(thm)],[493, 471])).
% 80.85/81.02 tff(495,plain,
% 80.85/81.02 ((~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)))) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4))) | (~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)))),
% 80.85/81.02 inference(tautology,[status(thm)],[])).
% 80.85/81.02 tff(496,plain,
% 80.85/81.02 (~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[495, 494, 481])).
% 80.85/81.02 tff(497,plain,
% 80.85/81.02 ((member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))),
% 80.85/81.02 inference(tautology,[status(thm)],[])).
% 80.85/81.02 tff(498,plain,
% 80.85/81.02 (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[497, 496])).
% 80.85/81.02 tff(499,plain,
% 80.85/81.02 ((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))) <=> (~member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))))),
% 80.85/81.02 inference(monotonicity,[status(thm)],[479])).
% 80.85/81.02 tff(500,plain,
% 80.85/81.02 (~member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))),
% 80.85/81.02 inference(modus_ponens,[status(thm)],[489, 499])).
% 80.85/81.02 tff(501,plain,
% 80.85/81.02 ((member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))) | member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) | member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))),
% 80.85/81.02 inference(tautology,[status(thm)],[])).
% 80.85/81.02 tff(502,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[501, 500, 477])).
% 80.85/81.02 tff(503,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3)))),
% 80.85/81.02 inference(modus_ponens,[status(thm)],[502, 475])).
% 80.85/81.02 tff(504,plain,
% 80.85/81.02 ((~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))),
% 80.85/81.02 inference(tautology,[status(thm)],[])).
% 80.85/81.02 tff(505,plain,
% 80.85/81.02 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))),
% 80.85/81.02 inference(unit_resolution,[status(thm)],[504, 503, 473])).
% 80.85/81.02 tff(506,plain,
% 80.85/81.02 ((~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(507,plain,
% 80.85/81.03 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[506, 505, 493])).
% 80.85/81.03 tff(508,assumption,(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))), introduced(assumption)).
% 80.85/81.03 tff(509,plain,
% 80.85/81.03 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(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(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))))),
% 80.85/81.03 inference(rewrite,[status(thm)],[])).
% 80.85/81.03 tff(510,plain,
% 80.85/81.03 ((~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))) <=> (~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))))),
% 80.85/81.03 inference(rewrite,[status(thm)],[])).
% 80.85/81.03 tff(511,plain,
% 80.85/81.03 ((((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))) <=> (((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))),
% 80.85/81.03 inference(rewrite,[status(thm)],[])).
% 80.85/81.03 tff(512,plain,
% 80.85/81.03 ((~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))) <=> (~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))))),
% 80.85/81.03 inference(monotonicity,[status(thm)],[511])).
% 80.85/81.03 tff(513,plain,
% 80.85/81.03 ((~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))) <=> (~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))))),
% 80.85/81.03 inference(transitivity,[status(thm)],[512, 510])).
% 80.85/81.03 tff(514,plain,
% 80.85/81.03 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(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(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))))),
% 80.85/81.03 inference(monotonicity,[status(thm)],[513])).
% 80.85/81.03 tff(515,plain,
% 80.85/81.03 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(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(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))))),
% 80.85/81.03 inference(transitivity,[status(thm)],[514, 509])).
% 80.85/81.03 tff(516,plain,
% 80.85/81.03 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))))),
% 80.85/81.03 inference(quant_inst,[status(thm)],[])).
% 80.85/81.03 tff(517,plain,
% 80.85/81.03 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))))),
% 80.85/81.03 inference(modus_ponens,[status(thm)],[516, 515])).
% 80.85/81.03 tff(518,plain,
% 80.85/81.03 ($false),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[517, 104, 508])).
% 80.85/81.03 tff(519,plain,(~(((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))), inference(lemma,lemma(discharge,[]))).
% 80.85/81.03 tff(520,plain,
% 80.85/81.03 ((((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) <=> member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3))) | (~((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)))) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(521,plain,
% 80.85/81.03 ((~((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)))) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[520, 519])).
% 80.85/81.03 tff(522,plain,
% 80.85/81.03 (~((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2)))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[521, 507])).
% 80.85/81.03 tff(523,plain,
% 80.85/81.03 (((~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), D!2))) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(524,plain,
% 80.85/81.03 ($false),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[523, 522, 498])).
% 80.85/81.03 tff(525,plain,(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) | (member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4))))), inference(lemma,lemma(discharge,[]))).
% 80.85/81.03 tff(526,plain,
% 80.85/81.03 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[525, 477])).
% 80.85/81.03 tff(527,plain,
% 80.85/81.03 (member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))),
% 80.85/81.03 inference(modus_ponens,[status(thm)],[526, 479])).
% 80.85/81.03 tff(528,plain,
% 80.85/81.03 ((member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))) | (~member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))) | (~member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4))))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(529,plain,
% 80.85/81.03 (~member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[528, 527, 477])).
% 80.85/81.03 tff(530,plain,
% 80.85/81.03 (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3)))),
% 80.85/81.03 inference(modus_ponens,[status(thm)],[529, 476])).
% 80.85/81.03 tff(531,plain,
% 80.85/81.03 ((~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(union(C!3, B!4), intersection(D!2, C!3))) | (~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(532,plain,
% 80.85/81.03 (~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[531, 530, 473])).
% 80.85/81.03 tff(533,plain,
% 80.85/81.03 ((member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(534,plain,
% 80.85/81.03 (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[533, 532])).
% 80.85/81.03 tff(535,plain,
% 80.85/81.03 (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4)))),
% 80.85/81.03 inference(modus_ponens,[status(thm)],[534, 471])).
% 80.85/81.03 tff(536,plain,
% 80.85/81.03 ((~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))))) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4)))) | (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(537,plain,
% 80.85/81.03 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[536, 526, 488])).
% 80.85/81.03 tff(538,plain,
% 80.85/81.03 ((~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4)))) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, B!4))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(539,plain,
% 80.85/81.03 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[538, 534, 537])).
% 80.85/81.03 tff(540,plain,
% 80.85/81.03 ((member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)) | (~member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(541,plain,
% 80.85/81.03 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[540, 539])).
% 80.85/81.03 tff(542,plain,
% 80.85/81.03 ((~(member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), C!3)))) | member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4)))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[495, 541])).
% 80.85/81.03 tff(543,plain,
% 80.85/81.03 (member(tptp_fun_D_1(union(union(C!3, B!4), intersection(D!2, C!3)), union(intersection(B!4, B!4), union(C!3, B!4))), union(C!3, intersection(B!4, B!4)))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[542, 481])).
% 80.85/81.03 tff(544,plain,
% 80.85/81.03 ($false),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[543, 535])).
% 80.85/81.03 tff(545,plain,(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.85/81.03 tff(546,plain,
% 80.85/81.03 ((~![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)))))))) | (~((~((~(union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4)))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(intersection(D!2, C!3), union(C!3, B!4)))))) | (~((union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))))))))),
% 80.85/81.03 inference(quant_inst,[status(thm)],[])).
% 80.85/81.03 tff(547,plain,
% 80.85/81.03 (~((~((~(union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4)))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(intersection(D!2, C!3), union(C!3, B!4)))))) | (~((union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4))))))))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[546, 33])).
% 80.85/81.03 tff(548,plain,
% 80.85/81.03 (((~((~(union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4)))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(intersection(D!2, C!3), union(C!3, B!4)))))) | (~((union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))))))) | ((union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4))))))),
% 80.85/81.03 inference(tautology,[status(thm)],[])).
% 80.85/81.03 tff(549,plain,
% 80.85/81.03 ((union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))))),
% 80.85/81.03 inference(unit_resolution,[status(thm)],[548, 547])).
% 80.85/81.03 tff(550,plain,
% 80.85/81.03 ((~((union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4))))))) | (union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(551,plain,
% 80.85/81.04 ((union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(B!4, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(D!2, C!3), union(C!3, B!4)), union(intersection(B!4, B!4), union(C!3, B!4))), union(intersection(D!2, C!3), union(C!3, B!4)))))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[550, 549])).
% 80.85/81.04 tff(552,plain,
% 80.85/81.04 (union(intersection(B!4, B!4), union(C!3, B!4)) = union(intersection(D!2, C!3), union(C!3, B!4))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[551, 545])).
% 80.85/81.04 tff(553,plain,
% 80.85/81.04 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(B!4, B!4), union(C!3, B!4)) = union(union(C!3, B!4), intersection(B!4, B!4)))),
% 80.85/81.04 inference(quant_inst,[status(thm)],[])).
% 80.85/81.04 tff(554,plain,
% 80.85/81.04 (union(intersection(B!4, B!4), union(C!3, B!4)) = union(union(C!3, B!4), intersection(B!4, B!4))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[553, 62])).
% 80.85/81.04 tff(555,plain,
% 80.85/81.04 (union(union(C!3, B!4), intersection(B!4, B!4)) = union(intersection(B!4, B!4), union(C!3, B!4))),
% 80.85/81.04 inference(symmetry,[status(thm)],[554])).
% 80.85/81.04 tff(556,plain,
% 80.85/81.04 (union(union(C!3, B!4), intersection(B!4, B!4)) = union(union(C!3, B!4), intersection(D!2, C!3))),
% 80.85/81.04 inference(transitivity,[status(thm)],[555, 552, 468])).
% 80.85/81.04 tff(557,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3)))),
% 80.85/81.04 inference(monotonicity,[status(thm)],[556])).
% 80.85/81.04 tff(558,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(B!4, B!4)))),
% 80.85/81.04 inference(symmetry,[status(thm)],[557])).
% 80.85/81.04 tff(559,plain,
% 80.85/81.04 ((member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(560,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3)))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[559, 464, 463])).
% 80.85/81.04 tff(561,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(B!4, B!4)))),
% 80.85/81.04 inference(modus_ponens,[status(thm)],[560, 558])).
% 80.85/81.04 tff(562,plain,
% 80.85/81.04 ((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))))) | (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(563,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[562, 561, 466])).
% 80.85/81.04 tff(564,plain,
% 80.85/81.04 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(intersection(B!4, B!4), C!3)) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), C!3) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4))))),
% 80.85/81.04 inference(quant_inst,[status(thm)],[])).
% 80.85/81.04 tff(565,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(intersection(B!4, B!4), C!3)) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), C!3) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[564, 11])).
% 80.85/81.04 tff(566,plain,
% 80.85/81.04 (union(intersection(B!4, B!4), C!3) = union(B!4, C!3)),
% 80.85/81.04 inference(monotonicity,[status(thm)],[251])).
% 80.85/81.04 tff(567,plain,
% 80.85/81.04 (union(intersection(B!4, B!4), C!3) = union(C!3, B!4)),
% 80.85/81.04 inference(transitivity,[status(thm)],[566, 314])).
% 80.85/81.04 tff(568,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(intersection(B!4, B!4), C!3)) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))),
% 80.85/81.04 inference(monotonicity,[status(thm)],[567])).
% 80.85/81.04 tff(569,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(intersection(B!4, B!4), C!3))),
% 80.85/81.04 inference(symmetry,[status(thm)],[568])).
% 80.85/81.04 tff(570,plain,
% 80.85/81.04 ((~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))) <=> (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(intersection(B!4, B!4), C!3)))),
% 80.85/81.04 inference(monotonicity,[status(thm)],[569])).
% 80.85/81.04 tff(571,plain,
% 80.85/81.04 (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(intersection(B!4, B!4), C!3))),
% 80.85/81.04 inference(modus_ponens,[status(thm)],[464, 570])).
% 80.85/81.04 tff(572,plain,
% 80.85/81.04 ((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(intersection(B!4, B!4), C!3)) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), C!3) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4))))) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(intersection(B!4, B!4), C!3)) | (~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), C!3) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4))))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(573,plain,
% 80.85/81.04 (~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), C!3) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[572, 571, 565])).
% 80.85/81.04 tff(574,plain,
% 80.85/81.04 ((member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), C!3) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(575,plain,
% 80.85/81.04 (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[574, 573])).
% 80.85/81.04 tff(576,plain,
% 80.85/81.04 ((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(577,plain,
% 80.85/81.04 ($false),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[576, 575, 563, 464])).
% 80.85/81.04 tff(578,plain,(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)) | (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.85/81.04 tff(579,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[578, 463])).
% 80.85/81.04 tff(580,plain,
% 80.85/81.04 ((member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3)))) | (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(581,plain,
% 80.85/81.04 (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3)))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[580, 579, 463])).
% 80.85/81.04 tff(582,plain,
% 80.85/81.04 ((member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(583,plain,
% 80.85/81.04 (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[582, 579])).
% 80.85/81.04 tff(584,plain,
% 80.85/81.04 ((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> (member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))))) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) | (~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), intersection(D!2, C!3)) | member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))))),
% 80.85/81.04 inference(tautology,[status(thm)],[])).
% 80.85/81.04 tff(585,plain,
% 80.85/81.04 ($false),
% 80.85/81.04 inference(unit_resolution,[status(thm)],[584, 583, 581, 462])).
% 80.85/81.04 tff(586,plain,(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))), inference(lemma,lemma(discharge,[]))).
% 80.85/81.04 tff(587,plain,
% 80.85/81.04 (((~![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)))))))) | (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))))))) <=> ((~![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)))))))) | (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)))))))),
% 80.85/81.04 inference(rewrite,[status(thm)],[])).
% 80.85/81.04 tff(588,plain,
% 80.85/81.04 ((~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)) | (~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))))))) <=> (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))))))),
% 80.85/81.04 inference(rewrite,[status(thm)],[])).
% 80.85/81.04 tff(589,plain,
% 80.85/81.04 (((~![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)))))))) | (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)) | (~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))))))))) <=> ((~![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)))))))) | (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)))))))),
% 80.85/81.04 inference(monotonicity,[status(thm)],[588])).
% 80.85/81.04 tff(590,plain,
% 80.85/81.04 (((~![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)))))))) | (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)) | (~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))))))))) <=> ((~![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)))))))) | (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)))))))),
% 80.85/81.04 inference(transitivity,[status(thm)],[589, 587])).
% 80.85/81.04 tff(591,plain,
% 80.85/81.04 ((~![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)))))))) | (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)) | (~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4))))))))),
% 80.85/81.04 inference(quant_inst,[status(thm)],[])).
% 80.85/81.04 tff(592,plain,
% 80.85/81.04 ((~![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)))))))) | (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))))))),
% 80.85/81.04 inference(modus_ponens,[status(thm)],[591, 590])).
% 80.85/81.04 tff(593,plain,
% 80.85/81.04 (~((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)))))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[592, 33])).
% 80.85/81.05 tff(594,plain,
% 80.85/81.05 (((~((~(union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))) | (member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(D!2, B!4)), union(C!3, B!4))))) | (~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))))) | ((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)))),
% 80.85/81.05 inference(tautology,[status(thm)],[])).
% 80.85/81.05 tff(595,plain,
% 80.85/81.05 ((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[594, 593])).
% 80.85/81.05 tff(596,plain,
% 80.85/81.05 ((~((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)))) | (~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))),
% 80.85/81.05 inference(tautology,[status(thm)],[])).
% 80.85/81.05 tff(597,plain,
% 80.85/81.05 ((~(member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(union(C!3, B!4), intersection(D!2, C!3))) <=> member(tptp_fun_D_1(union(C!3, B!4), union(union(C!3, B!4), intersection(D!2, C!3))), union(C!3, B!4)))) | (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[596, 595])).
% 80.85/81.05 tff(598,plain,
% 80.85/81.05 (union(union(C!3, B!4), intersection(D!2, C!3)) = union(C!3, B!4)),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[597, 586])).
% 80.85/81.05 tff(599,plain,
% 80.85/81.05 (union(intersection(D!2, C!3), union(C!3, B!4)) = union(C!3, B!4)),
% 80.85/81.05 inference(transitivity,[status(thm)],[468, 598])).
% 80.85/81.05 tff(600,plain,
% 80.85/81.05 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(C!3, B!4))) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))),
% 80.85/81.05 inference(monotonicity,[status(thm)],[599])).
% 80.85/81.05 tff(601,plain,
% 80.85/81.05 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(C!3, B!4)))),
% 80.85/81.05 inference(symmetry,[status(thm)],[600])).
% 80.85/81.05 tff(602,plain,
% 80.85/81.05 ((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))) <=> (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(C!3, B!4))))),
% 80.85/81.05 inference(monotonicity,[status(thm)],[601])).
% 80.85/81.05 tff(603,plain,
% 80.85/81.05 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(C!3, B!4)))),
% 80.85/81.05 inference(modus_ponens,[status(thm)],[453, 602])).
% 80.85/81.05 tff(604,plain,
% 80.85/81.05 ((~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(C!3, B!4))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(C!3, B!4))) | (~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))))),
% 80.85/81.05 inference(tautology,[status(thm)],[])).
% 80.85/81.05 tff(605,plain,
% 80.85/81.05 (~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[604, 603, 460])).
% 80.85/81.05 tff(606,plain,
% 80.85/81.05 ((member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))),
% 80.85/81.05 inference(tautology,[status(thm)],[])).
% 80.85/81.05 tff(607,plain,
% 80.85/81.05 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[606, 605])).
% 80.85/81.05 tff(608,plain,
% 80.85/81.05 ((~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))),
% 80.85/81.05 inference(tautology,[status(thm)],[])).
% 80.85/81.05 tff(609,plain,
% 80.85/81.05 ($false),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[608, 607, 458, 440])).
% 80.85/81.05 tff(610,plain,((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))), inference(lemma,lemma(discharge,[]))).
% 80.85/81.05 tff(611,plain,
% 80.85/81.05 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)))))))),
% 80.85/81.05 inference(rewrite,[status(thm)],[])).
% 80.85/81.05 tff(612,plain,
% 80.85/81.05 ((~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))))))) <=> (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))))))),
% 80.85/81.05 inference(rewrite,[status(thm)],[])).
% 80.85/81.05 tff(613,plain,
% 80.85/81.05 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)))))))),
% 80.85/81.05 inference(monotonicity,[status(thm)],[612])).
% 80.85/81.05 tff(614,plain,
% 80.85/81.05 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)))))))),
% 80.85/81.05 inference(transitivity,[status(thm)],[613, 611])).
% 80.85/81.05 tff(615,plain,
% 80.85/81.05 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))))))),
% 80.85/81.05 inference(quant_inst,[status(thm)],[])).
% 80.85/81.05 tff(616,plain,
% 80.85/81.05 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))))))),
% 80.85/81.05 inference(modus_ponens,[status(thm)],[615, 614])).
% 80.85/81.05 tff(617,plain,
% 80.85/81.05 (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)))))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[616, 163])).
% 80.85/81.05 tff(618,plain,
% 80.85/81.05 (((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))))) | ((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)))),
% 80.85/81.05 inference(tautology,[status(thm)],[])).
% 80.85/81.05 tff(619,plain,
% 80.85/81.05 ((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[618, 617])).
% 80.85/81.05 tff(620,plain,
% 80.85/81.05 ((~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)))) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))),
% 80.85/81.05 inference(tautology,[status(thm)],[])).
% 80.85/81.05 tff(621,plain,
% 80.85/81.05 ((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[620, 619])).
% 80.85/81.05 tff(622,plain,
% 80.85/81.05 (subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))),
% 80.85/81.05 inference(unit_resolution,[status(thm)],[621, 610])).
% 80.85/81.05 tff(623,plain,
% 80.85/81.05 (((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))))) | ((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))),
% 80.85/81.05 inference(tautology,[status(thm)],[])).
% 80.85/81.05 tff(624,plain,
% 80.85/81.05 ((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))),
% 80.90/81.05 inference(unit_resolution,[status(thm)],[623, 617])).
% 80.90/81.05 tff(625,plain,
% 80.90/81.05 ((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))),
% 80.90/81.05 inference(tautology,[status(thm)],[])).
% 80.90/81.05 tff(626,plain,
% 80.90/81.05 ((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))),
% 80.90/81.05 inference(unit_resolution,[status(thm)],[625, 624])).
% 80.90/81.05 tff(627,plain,
% 80.90/81.05 (![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))),
% 80.90/81.05 inference(unit_resolution,[status(thm)],[626, 622])).
% 80.90/81.05 tff(628,plain,
% 80.90/81.05 (((~![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))) <=> ((~![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))),
% 80.90/81.05 inference(rewrite,[status(thm)],[])).
% 80.90/81.05 tff(629,plain,
% 80.90/81.05 ((~![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))),
% 80.90/81.05 inference(quant_inst,[status(thm)],[])).
% 80.90/81.05 tff(630,plain,
% 80.90/81.05 ((~![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 80.90/81.05 inference(modus_ponens,[status(thm)],[629, 628])).
% 80.90/81.05 tff(631,plain,
% 80.90/81.05 ($false),
% 80.90/81.05 inference(unit_resolution,[status(thm)],[630, 627, 90, 430])).
% 80.90/81.05 tff(632,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.05 tff(633,plain,
% 80.90/81.05 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 80.90/81.05 inference(tautology,[status(thm)],[])).
% 80.90/81.05 tff(634,plain,
% 80.90/81.05 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 80.90/81.05 inference(unit_resolution,[status(thm)],[633, 632])).
% 80.90/81.05 tff(635,plain,
% 80.90/81.05 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[634, 77])).
% 80.90/81.06 tff(636,plain,
% 80.90/81.06 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(637,plain,
% 80.90/81.06 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[636, 635])).
% 80.90/81.06 tff(638,assumption,(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)))), introduced(assumption)).
% 80.90/81.06 tff(639,plain,
% 80.90/81.06 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)))))),
% 80.90/81.06 inference(quant_inst,[status(thm)],[])).
% 80.90/81.06 tff(640,plain,
% 80.90/81.06 ($false),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[639, 104, 638])).
% 80.90/81.06 tff(641,plain,(~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4))))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.06 tff(642,plain,
% 80.90/81.06 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)))) | (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4))))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(643,plain,
% 80.90/81.06 ((~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4))))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[642, 641])).
% 80.90/81.06 tff(644,plain,
% 80.90/81.06 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[643, 637])).
% 80.90/81.06 tff(645,assumption,(~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))), introduced(assumption)).
% 80.90/81.06 tff(646,assumption,(~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))), introduced(assumption)).
% 80.90/81.06 tff(647,plain,
% 80.90/81.06 (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))),
% 80.90/81.06 inference(monotonicity,[status(thm)],[296])).
% 80.90/81.06 tff(648,plain,
% 80.90/81.06 (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4)))),
% 80.90/81.06 inference(symmetry,[status(thm)],[647])).
% 80.90/81.06 tff(649,plain,
% 80.90/81.06 ((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) <=> (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))))),
% 80.90/81.06 inference(monotonicity,[status(thm)],[648])).
% 80.90/81.06 tff(650,plain,
% 80.90/81.06 (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4)))),
% 80.90/81.06 inference(modus_ponens,[status(thm)],[646, 649])).
% 80.90/81.06 tff(651,assumption,(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4)))), introduced(assumption)).
% 80.90/81.06 tff(652,plain,
% 80.90/81.06 ($false),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[651, 650])).
% 80.90/81.06 tff(653,plain,((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.06 tff(654,plain,
% 80.90/81.06 (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[653, 646])).
% 80.90/81.06 tff(655,assumption,(~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(D!2, C!3))))), introduced(assumption)).
% 80.90/81.06 tff(656,plain,
% 80.90/81.06 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(D!2, C!3))))),
% 80.90/81.06 inference(quant_inst,[status(thm)],[])).
% 80.90/81.06 tff(657,plain,
% 80.90/81.06 ($false),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[656, 11, 655])).
% 80.90/81.06 tff(658,plain,(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(D!2, C!3)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.06 tff(659,plain,
% 80.90/81.06 ((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(D!2, C!3))))) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) | (~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(D!2, C!3))))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(660,plain,
% 80.90/81.06 (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(D!2, C!3), intersection(B!4, B!4))) | (~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(D!2, C!3))))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[659, 658])).
% 80.90/81.06 tff(661,plain,
% 80.90/81.06 (~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(D!2, C!3)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[660, 654])).
% 80.90/81.06 tff(662,plain,
% 80.90/81.06 (((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(663,plain,
% 80.90/81.06 ((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[662, 646])).
% 80.90/81.06 tff(664,assumption,(((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))), introduced(assumption)).
% 80.90/81.06 tff(665,plain,
% 80.90/81.06 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))),
% 80.90/81.06 inference(quant_inst,[status(thm)],[])).
% 80.90/81.06 tff(666,plain,
% 80.90/81.06 ($false),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[665, 104, 664])).
% 80.90/81.06 tff(667,plain,(~(((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.06 tff(668,plain,
% 80.90/81.06 ((((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (~((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(669,plain,
% 80.90/81.06 ((~((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[668, 667])).
% 80.90/81.06 tff(670,plain,
% 80.90/81.06 (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[669, 663])).
% 80.90/81.06 tff(671,plain,
% 80.90/81.06 ((member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(672,plain,
% 80.90/81.06 (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[671, 670, 645])).
% 80.90/81.06 tff(673,plain,
% 80.90/81.06 ((member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(674,plain,
% 80.90/81.06 ($false),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[673, 672, 661])).
% 80.90/81.06 tff(675,plain,(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4)) | (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.06 tff(676,plain,
% 80.90/81.06 (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[675, 645])).
% 80.90/81.06 tff(677,assumption,(~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))), introduced(assumption)).
% 80.90/81.06 tff(678,plain,
% 80.90/81.06 ((((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | ((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(679,plain,
% 80.90/81.06 (((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[678, 667])).
% 80.90/81.06 tff(680,plain,
% 80.90/81.06 ((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[679, 677])).
% 80.90/81.06 tff(681,plain,
% 80.90/81.06 (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[671, 677, 645])).
% 80.90/81.06 tff(682,plain,
% 80.90/81.06 ((~((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(683,plain,
% 80.90/81.06 ($false),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[682, 681, 680, 676])).
% 80.90/81.06 tff(684,plain,(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))) | (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.06 tff(685,plain,
% 80.90/81.06 (member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[684, 645])).
% 80.90/81.06 tff(686,plain,
% 80.90/81.06 (~((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[669, 685])).
% 80.90/81.06 tff(687,plain,
% 80.90/81.06 ((member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(688,plain,
% 80.90/81.06 (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[687, 685, 645])).
% 80.90/81.06 tff(689,plain,
% 80.90/81.06 (((~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 80.90/81.06 inference(tautology,[status(thm)],[])).
% 80.90/81.06 tff(690,plain,
% 80.90/81.06 ($false),
% 80.90/81.06 inference(unit_resolution,[status(thm)],[689, 688, 686])).
% 80.90/81.06 tff(691,plain,(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.07 tff(692,assumption,((~((~(intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))), introduced(assumption)).
% 80.90/81.07 tff(693,plain,
% 80.90/81.07 (((~![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(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))))) <=> ((~![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(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))))))),
% 80.90/81.07 inference(rewrite,[status(thm)],[])).
% 80.90/81.07 tff(694,plain,
% 80.90/81.07 ((~((~((~(intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))) | (~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))))))) <=> (~((~((~(intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))))),
% 80.90/81.07 inference(rewrite,[status(thm)],[])).
% 80.90/81.07 tff(695,plain,
% 80.90/81.07 (((~![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(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))) | (~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))))))) <=> ((~![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(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))))))),
% 80.90/81.07 inference(monotonicity,[status(thm)],[694])).
% 80.90/81.07 tff(696,plain,
% 80.90/81.07 (((~![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(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))) | (~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))))))) <=> ((~![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(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))))))),
% 80.90/81.07 inference(transitivity,[status(thm)],[695, 693])).
% 80.90/81.07 tff(697,plain,
% 80.90/81.07 ((~![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(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))) | (~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))))))),
% 80.90/81.07 inference(quant_inst,[status(thm)],[])).
% 80.90/81.07 tff(698,plain,
% 80.90/81.07 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))))),
% 80.90/81.07 inference(modus_ponens,[status(thm)],[697, 696])).
% 80.90/81.07 tff(699,plain,
% 80.90/81.07 ($false),
% 80.90/81.07 inference(unit_resolution,[status(thm)],[698, 33, 692])).
% 80.90/81.07 tff(700,plain,(~((~((~(intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.07 tff(701,plain,
% 80.90/81.07 (((~((~(intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))) | (member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(tptp_fun_D_1(intersection(B!4, B!4), union(intersection(D!2, C!3), D!2)), intersection(intersection(D!2, C!3), intersection(B!4, B!4))), intersection(tptp_fun_D_1(intersection(B!4, B!4), intersection(D!2, C!3)), tptp_fun_D_0(intersection(D!2, C!3), union(C!3, B!4)))), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | (~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))))) | ((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))),
% 80.90/81.07 inference(tautology,[status(thm)],[])).
% 80.90/81.07 tff(702,plain,
% 80.90/81.07 ((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))),
% 80.90/81.07 inference(unit_resolution,[status(thm)],[701, 700])).
% 80.90/81.07 tff(703,plain,
% 80.90/81.07 ((~((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))),
% 80.90/81.08 inference(tautology,[status(thm)],[])).
% 80.90/81.08 tff(704,plain,
% 80.90/81.08 ((~(member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)), intersection(B!4, B!4)), intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))))) | (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[703, 702])).
% 80.90/81.08 tff(705,plain,
% 80.90/81.08 (intersection(B!4, B!4) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[704, 691])).
% 80.90/81.08 tff(706,plain,
% 80.90/81.08 (intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)) = intersection(B!4, B!4)),
% 80.90/81.08 inference(symmetry,[status(thm)],[705])).
% 80.90/81.08 tff(707,plain,
% 80.90/81.08 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)) = intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)))),
% 80.90/81.08 inference(quant_inst,[status(thm)],[])).
% 80.90/81.08 tff(708,plain,
% 80.90/81.08 (intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4)) = intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[707, 50])).
% 80.90/81.08 tff(709,plain,
% 80.90/81.08 (intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)) = intersection(union(intersection(C!3, D!2), B!4), intersection(B!4, B!4))),
% 80.90/81.08 inference(symmetry,[status(thm)],[708])).
% 80.90/81.08 tff(710,plain,
% 80.90/81.08 (intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)) = intersection(B!4, B!4)),
% 80.90/81.08 inference(transitivity,[status(thm)],[709, 706])).
% 80.90/81.08 tff(711,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.90/81.08 inference(monotonicity,[status(thm)],[710])).
% 80.90/81.08 tff(712,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)))),
% 80.90/81.08 inference(symmetry,[status(thm)],[711])).
% 80.90/81.08 tff(713,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)))),
% 80.90/81.08 inference(modus_ponens,[status(thm)],[405, 712])).
% 80.90/81.08 tff(714,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4)))), introduced(assumption)).
% 80.90/81.08 tff(715,plain,
% 80.90/81.08 ($false),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[714, 713])).
% 80.90/81.08 tff(716,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(intersection(B!4, B!4), union(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.08 tff(717,plain,
% 80.90/81.08 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[716, 644])).
% 80.90/81.08 tff(718,assumption,(~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))), introduced(assumption)).
% 80.90/81.08 tff(719,plain,
% 80.90/81.08 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))))),
% 80.90/81.08 inference(rewrite,[status(thm)],[])).
% 80.90/81.08 tff(720,plain,
% 80.90/81.08 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))),
% 80.90/81.08 inference(rewrite,[status(thm)],[])).
% 80.90/81.08 tff(721,plain,
% 80.90/81.08 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))))),
% 80.90/81.08 inference(monotonicity,[status(thm)],[720])).
% 80.90/81.08 tff(722,plain,
% 80.90/81.08 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))))),
% 80.90/81.08 inference(transitivity,[status(thm)],[721, 719])).
% 80.90/81.08 tff(723,plain,
% 80.90/81.08 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)))),
% 80.90/81.08 inference(quant_inst,[status(thm)],[])).
% 80.90/81.08 tff(724,plain,
% 80.90/81.08 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))),
% 80.90/81.08 inference(modus_ponens,[status(thm)],[723, 722])).
% 80.90/81.08 tff(725,plain,
% 80.90/81.08 ($false),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[724, 11, 718])).
% 80.90/81.08 tff(726,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.08 tff(727,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 80.90/81.08 inference(monotonicity,[status(thm)],[354])).
% 80.90/81.08 tff(728,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4)))),
% 80.90/81.08 inference(symmetry,[status(thm)],[727])).
% 80.90/81.08 tff(729,assumption,(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))), introduced(assumption)).
% 80.90/81.08 tff(730,plain,
% 80.90/81.08 ($false),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[311, 104, 729])).
% 80.90/81.08 tff(731,plain,(~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.08 tff(732,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 80.90/81.08 inference(modus_ponens,[status(thm)],[632, 321])).
% 80.90/81.08 tff(733,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))), introduced(assumption)).
% 80.90/81.08 tff(734,plain,
% 80.90/81.08 ($false),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[733, 732])).
% 80.90/81.08 tff(735,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.08 tff(736,plain,
% 80.90/81.08 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))) | (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))),
% 80.90/81.08 inference(tautology,[status(thm)],[])).
% 80.90/81.08 tff(737,plain,
% 80.90/81.08 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))) | (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[736, 735])).
% 80.90/81.08 tff(738,plain,
% 80.90/81.08 (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[737, 731])).
% 80.90/81.08 tff(739,plain,
% 80.90/81.08 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 80.90/81.08 inference(tautology,[status(thm)],[])).
% 80.90/81.08 tff(740,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[739, 738])).
% 80.90/81.08 tff(741,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4)))),
% 80.90/81.08 inference(modus_ponens,[status(thm)],[740, 728])).
% 80.90/81.08 tff(742,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4)))), introduced(assumption)).
% 80.90/81.08 tff(743,plain,
% 80.90/81.08 ($false),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[742, 741])).
% 80.90/81.08 tff(744,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.08 tff(745,plain,
% 80.90/81.08 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))),
% 80.90/81.08 inference(tautology,[status(thm)],[])).
% 80.90/81.08 tff(746,plain,
% 80.90/81.08 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[745, 744])).
% 80.90/81.08 tff(747,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[746, 726])).
% 80.90/81.08 tff(748,plain,
% 80.90/81.08 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.90/81.08 inference(tautology,[status(thm)],[])).
% 80.90/81.08 tff(749,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[748, 747])).
% 80.90/81.08 tff(750,plain,
% 80.90/81.08 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[749, 717])).
% 80.90/81.08 tff(751,assumption,(~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))), introduced(assumption)).
% 80.90/81.08 tff(752,plain,
% 80.90/81.08 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))))),
% 80.90/81.08 inference(rewrite,[status(thm)],[])).
% 80.90/81.08 tff(753,plain,
% 80.90/81.08 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))),
% 80.90/81.08 inference(rewrite,[status(thm)],[])).
% 80.90/81.08 tff(754,plain,
% 80.90/81.08 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))))),
% 80.90/81.08 inference(monotonicity,[status(thm)],[753])).
% 80.90/81.08 tff(755,plain,
% 80.90/81.08 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))))),
% 80.90/81.08 inference(transitivity,[status(thm)],[754, 752])).
% 80.90/81.08 tff(756,plain,
% 80.90/81.08 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))),
% 80.90/81.08 inference(quant_inst,[status(thm)],[])).
% 80.90/81.08 tff(757,plain,
% 80.90/81.08 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))),
% 80.90/81.08 inference(modus_ponens,[status(thm)],[756, 755])).
% 80.90/81.08 tff(758,plain,
% 80.90/81.08 ($false),
% 80.90/81.08 inference(unit_resolution,[status(thm)],[757, 11, 751])).
% 80.90/81.08 tff(759,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.09 tff(760,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 80.90/81.09 inference(monotonicity,[status(thm)],[448])).
% 80.90/81.09 tff(761,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4)))),
% 80.90/81.09 inference(symmetry,[status(thm)],[760])).
% 80.90/81.09 tff(762,plain,
% 80.90/81.09 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 80.90/81.09 inference(tautology,[status(thm)],[])).
% 80.90/81.09 tff(763,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[762, 738])).
% 80.90/81.09 tff(764,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4)))),
% 80.90/81.09 inference(modus_ponens,[status(thm)],[763, 761])).
% 80.90/81.09 tff(765,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4)))), introduced(assumption)).
% 80.90/81.09 tff(766,plain,
% 80.90/81.09 ($false),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[765, 764])).
% 80.90/81.09 tff(767,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.09 tff(768,plain,
% 80.90/81.09 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))),
% 80.90/81.09 inference(tautology,[status(thm)],[])).
% 80.90/81.09 tff(769,plain,
% 80.90/81.09 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[768, 767])).
% 80.90/81.09 tff(770,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[769, 759])).
% 80.90/81.09 tff(771,plain,
% 80.90/81.09 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.90/81.09 inference(tautology,[status(thm)],[])).
% 80.90/81.09 tff(772,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4))),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[771, 770])).
% 80.90/81.09 tff(773,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[772, 717])).
% 80.90/81.09 tff(774,plain,
% 80.90/81.09 ((~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))),
% 80.90/81.09 inference(tautology,[status(thm)],[])).
% 80.90/81.09 tff(775,plain,
% 80.90/81.09 (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[774, 773, 750])).
% 80.90/81.09 tff(776,assumption,(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))), introduced(assumption)).
% 80.90/81.09 tff(777,plain,
% 80.90/81.09 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))),
% 80.90/81.09 inference(quant_inst,[status(thm)],[])).
% 80.90/81.09 tff(778,plain,
% 80.90/81.09 ($false),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[777, 104, 776])).
% 80.90/81.09 tff(779,plain,(~(((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.09 tff(780,plain,
% 80.90/81.09 ((((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 80.90/81.09 inference(tautology,[status(thm)],[])).
% 80.90/81.09 tff(781,plain,
% 80.90/81.09 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), D!2)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[780, 779])).
% 80.90/81.09 tff(782,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[781, 775])).
% 80.90/81.09 tff(783,plain,
% 80.90/81.09 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))),
% 80.90/81.09 inference(tautology,[status(thm)],[])).
% 80.90/81.09 tff(784,plain,
% 80.90/81.09 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[783, 782])).
% 80.90/81.09 tff(785,plain,
% 80.90/81.09 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) <=> (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))))),
% 80.90/81.09 inference(monotonicity,[status(thm)],[298])).
% 80.90/81.09 tff(786,plain,
% 80.90/81.09 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4)))),
% 80.90/81.09 inference(modus_ponens,[status(thm)],[635, 785])).
% 80.90/81.09 tff(787,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4)))), introduced(assumption)).
% 80.90/81.09 tff(788,plain,
% 80.90/81.09 ($false),
% 80.90/81.09 inference(unit_resolution,[status(thm)],[787, 786])).
% 80.90/81.09 tff(789,plain,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 80.90/81.09 tff(790,plain,
% 80.90/81.09 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))),
% 80.90/81.09 inference(tautology,[status(thm)],[])).
% 80.90/81.09 tff(791,plain,
% 80.90/81.09 (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), intersection(B!4, B!4))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(B!4, B!4)) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))),
% 80.90/81.11 inference(unit_resolution,[status(thm)],[790, 789, 784])).
% 80.90/81.11 tff(792,plain,
% 80.90/81.11 ($false),
% 80.90/81.11 inference(unit_resolution,[status(thm)],[791, 14])).
% 80.90/81.11 % SZS output end Proof
% 80.90/81.11 % E exiting
%------------------------------------------------------------------------------