%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET143+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:25:20 AM UTC 2025
% Result : Theorem 0.62s 0.82s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET143+3 : TPTP v9.0.0. Released v2.2.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 04:24:38 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.62/0.82 % SZS status Theorem
% 0.62/0.82 % SZS output start Proof
% 0.62/0.82 tff(intersection_type, type, (
% 0.62/0.82 intersection: ( $i * $i ) > $i)).
% 0.62/0.82 tff(tptp_fun_D_2_type, type, (
% 0.62/0.82 tptp_fun_D_2: $i)).
% 0.62/0.82 tff(tptp_fun_C_3_type, type, (
% 0.62/0.82 tptp_fun_C_3: $i)).
% 0.62/0.82 tff(tptp_fun_B_4_type, type, (
% 0.62/0.82 tptp_fun_B_4: $i)).
% 0.62/0.82 tff(member_type, type, (
% 0.62/0.82 member: ( $i * $i ) > $o)).
% 0.62/0.82 tff(tptp_fun_D_1_type, type, (
% 0.62/0.82 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.62/0.82 tff(subset_type, type, (
% 0.62/0.82 subset: ( $i * $i ) > $o)).
% 0.62/0.82 tff(tptp_fun_D_0_type, type, (
% 0.62/0.82 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.62/0.82 tff(1,plain,
% 0.62/0.82 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(2,plain,
% 0.62/0.82 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[1])).
% 0.62/0.82 tff(3,plain,
% 0.62/0.82 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(4,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.62/0.82 tff(5,plain,
% 0.62/0.82 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.62/0.82 tff(6,plain,(
% 0.62/0.82 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.62/0.82 inference(skolemize,[status(sab)],[5])).
% 0.62/0.82 tff(7,plain,
% 0.62/0.82 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.62/0.82 tff(8,plain,
% 0.62/0.82 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, intersection(C!3, D!2)) = intersection(intersection(C!3, D!2), B!4))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(9,plain,
% 0.62/0.82 (intersection(B!4, intersection(C!3, D!2)) = intersection(intersection(C!3, D!2), B!4)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.62/0.82 tff(10,plain,
% 0.62/0.82 (intersection(intersection(C!3, D!2), B!4) = intersection(B!4, intersection(C!3, D!2))),
% 0.62/0.82 inference(symmetry,[status(thm)],[9])).
% 0.62/0.82 tff(11,plain,
% 0.62/0.82 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(12,plain,
% 0.62/0.82 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[11])).
% 0.62/0.82 tff(13,plain,
% 0.62/0.82 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(pull_quant,[status(thm)],[])).
% 0.62/0.82 tff(14,plain,
% 0.62/0.82 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(15,plain,
% 0.62/0.82 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[14])).
% 0.62/0.82 tff(16,plain,
% 0.62/0.82 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(transitivity,[status(thm)],[15, 13])).
% 0.62/0.82 tff(17,plain,
% 0.62/0.82 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(transitivity,[status(thm)],[16, 12])).
% 0.62/0.82 tff(18,plain,
% 0.62/0.82 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(19,plain,
% 0.62/0.82 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[18])).
% 0.62/0.82 tff(20,plain,
% 0.62/0.82 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(transitivity,[status(thm)],[19, 17])).
% 0.62/0.82 tff(21,plain,
% 0.62/0.82 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), trans(monotonicity(rewrite((~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))) <=> (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(22,plain,
% 0.62/0.82 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[21])).
% 0.62/0.82 tff(23,plain,
% 0.62/0.82 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(24,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 0.62/0.82 tff(25,plain,
% 0.62/0.82 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.62/0.82 tff(26,plain,(
% 0.62/0.82 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.62/0.82 inference(skolemize,[status(sab)],[25])).
% 0.62/0.82 tff(27,plain,
% 0.62/0.82 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.62/0.82 tff(28,plain,
% 0.62/0.82 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.62/0.82 tff(29,plain,
% 0.62/0.82 ((~![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(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))) | (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))) | (~((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))))))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(30,plain,
% 0.62/0.82 (~((~((~(intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))) | (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))) | (~((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))))))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.62/0.82 tff(31,plain,
% 0.62/0.82 (((~((~(intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))) | (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))) | (~((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))))) | ((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(32,plain,
% 0.62/0.82 ((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.62/0.82 tff(33,plain,
% 0.62/0.82 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, D!2) = intersection(D!2, C!3))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(34,plain,
% 0.62/0.82 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[33, 7])).
% 0.62/0.82 tff(35,plain,
% 0.62/0.82 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 0.62/0.82 inference(symmetry,[status(thm)],[34])).
% 0.62/0.82 tff(36,plain,
% 0.62/0.82 (intersection(intersection(D!2, C!3), B!4) = intersection(intersection(C!3, D!2), B!4)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[35])).
% 0.62/0.82 tff(37,plain,
% 0.62/0.82 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[36])).
% 0.62/0.83 tff(38,plain,
% 0.62/0.83 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4))),
% 0.62/0.83 inference(symmetry,[status(thm)],[37])).
% 0.62/0.83 tff(39,plain,
% 0.62/0.83 ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4))) <=> (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4)))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[38])).
% 0.62/0.83 tff(40,assumption,(~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4))), introduced(assumption)).
% 0.62/0.83 tff(41,plain,
% 0.62/0.83 (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.62/0.83 tff(42,plain,
% 0.62/0.83 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(43,plain,
% 0.62/0.83 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[42])).
% 0.62/0.83 tff(44,plain,
% 0.62/0.83 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, B)) | (~member(D, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(45,plain,
% 0.62/0.83 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[44])).
% 0.62/0.83 tff(46,plain,
% 0.62/0.83 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(47,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.62/0.83 tff(48,plain,
% 0.62/0.83 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.62/0.83 tff(49,plain,(
% 0.62/0.83 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[48])).
% 0.62/0.83 tff(50,plain,
% 0.62/0.83 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.62/0.83 tff(51,plain,
% 0.62/0.83 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.62/0.83 tff(52,plain,
% 0.62/0.83 ((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4))))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(53,plain,
% 0.62/0.83 (~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4)))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.62/0.83 tff(54,assumption,(~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))), introduced(assumption)).
% 0.62/0.83 tff(55,plain,
% 0.62/0.83 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(56,plain,
% 0.62/0.83 ((~(~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(57,plain,
% 0.62/0.83 ((~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(58,plain,
% 0.62/0.83 (((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(59,plain,
% 0.62/0.83 (((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(60,plain,
% 0.62/0.83 ((((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> ((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[59])).
% 0.62/0.83 tff(61,plain,
% 0.62/0.83 ((((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(transitivity,[status(thm)],[60, 58])).
% 0.62/0.83 tff(62,plain,
% 0.62/0.83 ((((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(transitivity,[status(thm)],[61, 57])).
% 0.62/0.83 tff(63,plain,
% 0.62/0.83 ((~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (~(~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[62])).
% 0.62/0.83 tff(64,plain,
% 0.62/0.83 ((~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[63, 56])).
% 0.62/0.83 tff(65,plain,
% 0.62/0.83 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[64])).
% 0.62/0.83 tff(66,plain,
% 0.62/0.83 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(transitivity,[status(thm)],[65, 55])).
% 0.62/0.83 tff(67,plain,
% 0.62/0.83 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(68,plain,
% 0.62/0.83 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.62/0.83 tff(69,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[68, 51, 54])).
% 0.62/0.83 tff(70,plain,(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(71,plain,
% 0.62/0.83 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(D!2, C!3), C!3) <=> member(tptp_fun_D_1(D!2, C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(72,plain,
% 0.62/0.83 (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(D!2, C!3), C!3) <=> member(tptp_fun_D_1(D!2, C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[71, 28])).
% 0.62/0.83 tff(73,plain,
% 0.62/0.83 (((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(D!2, C!3), C!3) <=> member(tptp_fun_D_1(D!2, C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))) | ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))),
% 0.62/0.83 inference(tautology,[status(thm)],[])).
% 0.62/0.83 tff(74,plain,
% 0.62/0.83 ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.62/0.83 tff(75,plain,
% 0.62/0.83 ((~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))) | (C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(tautology,[status(thm)],[])).
% 0.62/0.83 tff(76,plain,
% 0.62/0.83 ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_1(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.62/0.83 tff(77,plain,
% 0.62/0.83 (C!3 = intersection(C!3, C!3)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[76, 70])).
% 0.62/0.83 tff(78,plain,
% 0.62/0.83 (intersection(C!3, C!3) = C!3),
% 0.62/0.83 inference(symmetry,[status(thm)],[77])).
% 0.62/0.83 tff(79,plain,
% 0.62/0.83 (intersection(D!2, intersection(C!3, C!3)) = intersection(D!2, C!3)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[78])).
% 0.62/0.83 tff(80,plain,
% 0.62/0.83 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[79])).
% 0.62/0.83 tff(81,plain,
% 0.62/0.83 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.83 inference(symmetry,[status(thm)],[80])).
% 0.62/0.83 tff(82,plain,
% 0.62/0.83 ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) <=> (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[81])).
% 0.62/0.83 tff(83,assumption,(~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))), introduced(assumption)).
% 0.62/0.83 tff(84,plain,
% 0.62/0.83 (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.62/0.83 tff(85,plain,
% 0.62/0.83 ((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(86,plain,
% 0.62/0.83 (~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3))))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[85, 51])).
% 0.62/0.83 tff(87,plain,
% 0.62/0.83 (((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, 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(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(88,plain,
% 0.62/0.83 ((~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(89,plain,
% 0.62/0.83 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))) <=> (((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(90,plain,
% 0.62/0.83 ((~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[89])).
% 0.62/0.83 tff(91,plain,
% 0.62/0.83 ((~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))) <=> (~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))))),
% 0.62/0.83 inference(transitivity,[status(thm)],[90, 88])).
% 0.62/0.83 tff(92,plain,
% 0.62/0.83 (((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, 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(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[91])).
% 0.62/0.83 tff(93,plain,
% 0.62/0.83 (((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, 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(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))))),
% 0.62/0.83 inference(transitivity,[status(thm)],[92, 87])).
% 0.62/0.83 tff(94,plain,
% 0.62/0.83 ((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(95,plain,
% 0.62/0.83 ((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.62/0.83 tff(96,plain,
% 0.62/0.83 (~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[95, 51])).
% 0.62/0.83 tff(97,plain,
% 0.62/0.83 (intersection(intersection(C!3, C!3), B!4) = intersection(C!3, B!4)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[78])).
% 0.62/0.83 tff(98,plain,
% 0.62/0.83 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[97])).
% 0.62/0.83 tff(99,plain,
% 0.62/0.83 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))),
% 0.62/0.83 inference(symmetry,[status(thm)],[98])).
% 0.62/0.83 tff(100,plain,
% 0.62/0.83 ((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(101,plain,
% 0.62/0.83 (~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4))))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[100, 51])).
% 0.62/0.83 tff(102,plain,
% 0.62/0.83 ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4))) <=> (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[99])).
% 0.62/0.83 tff(103,assumption,(~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))), introduced(assumption)).
% 0.62/0.83 tff(104,plain,
% 0.62/0.83 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))) | ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))),
% 0.62/0.83 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(105,plain,
% 0.62/0.84 ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[104, 103, 101])).
% 0.62/0.84 tff(106,plain,
% 0.62/0.84 ((~![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, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(B!4, intersection(D!2, C!3)))))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(107,plain,
% 0.62/0.84 (~(((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(B!4, intersection(D!2, C!3))))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[106, 51])).
% 0.62/0.84 tff(108,plain,
% 0.62/0.84 (intersection(B!4, intersection(D!2, C!3)) = intersection(B!4, intersection(C!3, D!2))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[35])).
% 0.62/0.84 tff(109,plain,
% 0.62/0.84 (intersection(B!4, intersection(D!2, C!3)) = intersection(intersection(C!3, D!2), B!4)),
% 0.62/0.84 inference(transitivity,[status(thm)],[108, 9])).
% 0.62/0.84 tff(110,plain,
% 0.62/0.84 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(B!4, intersection(D!2, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[109])).
% 0.62/0.84 tff(111,plain,
% 0.62/0.84 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(B!4, intersection(D!2, C!3)))),
% 0.62/0.84 inference(symmetry,[status(thm)],[110])).
% 0.62/0.84 tff(112,plain,
% 0.62/0.84 ((~![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(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))) | (member(tptp_fun_D_1(intersection(C!3, B!4), intersection(intersection(C!3, B!4), intersection(intersection(C!3, D!2), B!4))), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(C!3, B!4), intersection(intersection(C!3, B!4), intersection(intersection(C!3, D!2), B!4))), intersection(D!2, intersection(B!4, C!3)))))) | (~((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))))))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(113,plain,
% 0.62/0.84 (~((~((~(intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))) | (member(tptp_fun_D_1(intersection(C!3, B!4), intersection(intersection(C!3, B!4), intersection(intersection(C!3, D!2), B!4))), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(C!3, B!4), intersection(intersection(C!3, B!4), intersection(intersection(C!3, D!2), B!4))), intersection(D!2, intersection(B!4, C!3)))))) | (~((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))))))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[112, 28])).
% 0.62/0.84 tff(114,plain,
% 0.62/0.84 (((~((~(intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))) | (member(tptp_fun_D_1(intersection(C!3, B!4), intersection(intersection(C!3, B!4), intersection(intersection(C!3, D!2), B!4))), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(C!3, B!4), intersection(intersection(C!3, B!4), intersection(intersection(C!3, D!2), B!4))), intersection(D!2, intersection(B!4, C!3)))))) | (~((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))))) | ((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(115,plain,
% 0.62/0.84 ((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.62/0.84 tff(116,plain,
% 0.62/0.84 ((intersection(B!4, intersection(C!3, D!2)) = intersection(intersection(B!4, C!3), D!2)) <=> (intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2)))),
% 0.62/0.84 inference(commutativity,[status(thm)],[])).
% 0.62/0.84 tff(117,plain,
% 0.62/0.84 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(intersection(B!4, C!3), D!2) = intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(118,plain,
% 0.62/0.84 (intersection(intersection(B!4, C!3), D!2) = intersection(D!2, intersection(B!4, C!3))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[117, 7])).
% 0.62/0.84 tff(119,plain,
% 0.62/0.84 (intersection(D!2, intersection(B!4, C!3)) = intersection(intersection(B!4, C!3), D!2)),
% 0.62/0.84 inference(symmetry,[status(thm)],[118])).
% 0.62/0.84 tff(120,plain,
% 0.62/0.84 ((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) <=> (intersection(B!4, intersection(C!3, D!2)) = intersection(intersection(B!4, C!3), D!2))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[10, 119])).
% 0.62/0.84 tff(121,plain,
% 0.62/0.84 ((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) <=> (intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[120, 116])).
% 0.62/0.84 tff(122,plain,
% 0.62/0.84 ((intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2))) <=> (intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.84 inference(symmetry,[status(thm)],[121])).
% 0.62/0.84 tff(123,plain,
% 0.62/0.84 ((~(intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2)))) <=> (~(intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[122])).
% 0.62/0.84 tff(124,plain,
% 0.62/0.84 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) <=> (~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D))))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(125,axiom,(~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_associativity_of_intersection')).
% 0.62/0.84 tff(126,plain,
% 0.62/0.84 (~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.62/0.84 tff(127,plain,
% 0.62/0.84 (~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[126, 124])).
% 0.62/0.84 tff(128,plain,
% 0.62/0.84 (~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[127, 124])).
% 0.62/0.84 tff(129,plain,
% 0.62/0.84 (~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.62/0.84 tff(130,plain,(
% 0.62/0.84 ~(intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2)))),
% 0.62/0.84 inference(skolemize,[status(sab)],[129])).
% 0.62/0.84 tff(131,plain,
% 0.62/0.84 (~(intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.62/0.84 tff(132,plain,
% 0.62/0.84 ((~((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))))) | (intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(133,plain,
% 0.62/0.84 (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[132, 131, 115])).
% 0.62/0.84 tff(134,plain,
% 0.62/0.84 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, C!3) = intersection(C!3, B!4))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(135,plain,
% 0.62/0.84 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[134, 7])).
% 0.62/0.84 tff(136,plain,
% 0.62/0.84 (intersection(C!3, B!4) = intersection(B!4, C!3)),
% 0.62/0.84 inference(symmetry,[status(thm)],[135])).
% 0.62/0.84 tff(137,plain,
% 0.62/0.84 (intersection(D!2, intersection(C!3, B!4)) = intersection(D!2, intersection(B!4, C!3))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[136])).
% 0.62/0.84 tff(138,plain,
% 0.62/0.84 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[137])).
% 0.62/0.84 tff(139,plain,
% 0.62/0.84 ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))) <=> (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[138])).
% 0.62/0.84 tff(140,plain,
% 0.62/0.84 (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[103, 139])).
% 0.62/0.84 tff(141,plain,
% 0.62/0.84 ((member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(142,plain,
% 0.62/0.84 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[141, 140, 133])).
% 0.62/0.84 tff(143,plain,
% 0.62/0.84 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(B!4, intersection(D!2, C!3)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[142, 111])).
% 0.62/0.84 tff(144,plain,
% 0.62/0.84 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(B!4, intersection(D!2, C!3)))) | (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(B!4, intersection(D!2, C!3))))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(145,plain,
% 0.62/0.84 (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[144, 143, 107])).
% 0.62/0.84 tff(146,plain,
% 0.62/0.84 (((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(147,plain,
% 0.62/0.84 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.62/0.84 tff(148,plain,
% 0.62/0.84 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[147, 81])).
% 0.62/0.84 tff(149,plain,
% 0.62/0.84 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))) | (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3))))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(150,plain,
% 0.62/0.84 (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[149, 148, 86])).
% 0.62/0.84 tff(151,plain,
% 0.62/0.84 (((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(152,plain,
% 0.62/0.84 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.62/0.84 tff(153,plain,
% 0.62/0.84 ((~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4))))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(154,plain,
% 0.62/0.84 (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[153, 152, 105])).
% 0.62/0.84 tff(155,plain,
% 0.62/0.84 (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[154, 102])).
% 0.62/0.84 tff(156,plain,
% 0.62/0.84 (member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[79])).
% 0.62/0.84 tff(157,plain,
% 0.62/0.84 (member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.84 inference(symmetry,[status(thm)],[156])).
% 0.62/0.84 tff(158,assumption,(~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))), introduced(assumption)).
% 0.62/0.84 tff(159,plain,
% 0.62/0.84 (((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(160,plain,
% 0.62/0.84 (member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.62/0.84 tff(161,plain,
% 0.62/0.84 (member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[160, 157])).
% 0.62/0.84 tff(162,plain,
% 0.62/0.84 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3)))))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(163,plain,
% 0.62/0.84 (~(((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3))))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[162, 51])).
% 0.62/0.84 tff(164,plain,
% 0.62/0.84 (((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(165,plain,
% 0.62/0.84 (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[164, 158])).
% 0.62/0.84 tff(166,plain,
% 0.62/0.84 (((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(167,plain,
% 0.62/0.84 ((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.62/0.84 tff(168,plain,
% 0.62/0.84 ((((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3)))) | (~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))))) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3))))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(169,plain,
% 0.62/0.84 ((((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), D!2)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3)))) | (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3))))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.62/0.84 tff(170,plain,
% 0.62/0.84 (~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[169, 163])).
% 0.62/0.84 tff(171,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[170, 161])).
% 0.62/0.84 tff(172,plain,((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(173,plain,
% 0.62/0.84 (^[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))))))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(174,plain,
% 0.62/0.84 (![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)))))))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[173])).
% 0.62/0.84 tff(175,plain,
% 0.62/0.84 (^[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))))))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(176,plain,
% 0.62/0.84 (![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)))))))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[175])).
% 0.62/0.84 tff(177,plain,
% 0.62/0.84 (![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)))))))),
% 0.62/0.84 inference(transitivity,[status(thm)],[176, 174])).
% 0.62/0.84 tff(178,plain,
% 0.62/0.84 (^[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)))))))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(179,plain,
% 0.62/0.84 (![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)))))))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[178])).
% 0.62/0.84 tff(180,plain,
% 0.62/0.84 (![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)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(181,plain,
% 0.62/0.84 (^[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))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(182,plain,
% 0.62/0.84 (![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)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[181])).
% 0.62/0.84 tff(183,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')).
% 0.62/0.84 tff(184,plain,
% 0.62/0.84 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.62/0.84 tff(185,plain,
% 0.62/0.84 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.62/0.84 tff(186,plain,(
% 0.62/0.84 ![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)))))),
% 0.62/0.84 inference(skolemize,[status(sab)],[185])).
% 0.62/0.84 tff(187,plain,
% 0.62/0.84 (![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)))))))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.62/0.84 tff(188,plain,
% 0.62/0.84 (![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)))))))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[187, 177])).
% 0.62/0.84 tff(189,plain,
% 0.62/0.84 (((~![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(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3))))))) <=> ((~![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(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3)))))))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(190,plain,
% 0.62/0.84 ((~((~((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~(subset(intersection(D!2, C!3), intersection(C!3, C!3)) | (~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))))))) <=> (~((~((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3))))))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(191,plain,
% 0.62/0.84 (((~![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(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~(subset(intersection(D!2, C!3), intersection(C!3, C!3)) | (~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))))))))) <=> ((~![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(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3)))))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[190])).
% 0.62/0.85 tff(192,plain,
% 0.62/0.85 (((~![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(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~(subset(intersection(D!2, C!3), intersection(C!3, C!3)) | (~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))))))))) <=> ((~![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(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3)))))))),
% 0.62/0.85 inference(transitivity,[status(thm)],[191, 189])).
% 0.62/0.85 tff(193,plain,
% 0.62/0.85 ((~![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(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~(subset(intersection(D!2, C!3), intersection(C!3, C!3)) | (~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3))))))))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(194,plain,
% 0.62/0.85 ((~![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(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3))))))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.62/0.85 tff(195,plain,
% 0.62/0.85 (~((~((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3)))))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[194, 188])).
% 0.62/0.85 tff(196,plain,
% 0.62/0.85 (((~((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3))))) | ((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3)))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(197,plain,
% 0.62/0.85 ((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.62/0.85 tff(198,plain,
% 0.62/0.85 ((~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3)))) | (~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(199,plain,
% 0.62/0.85 ((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.62/0.85 tff(200,plain,
% 0.62/0.85 (subset(intersection(D!2, C!3), intersection(C!3, C!3))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[199, 172])).
% 0.62/0.85 tff(201,plain,
% 0.62/0.85 (((~((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~((~((~member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), intersection(D!2, C!3)), intersection(C!3, C!3)))) | subset(intersection(D!2, C!3), intersection(C!3, C!3))))) | ((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(202,plain,
% 0.62/0.85 ((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3)))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[201, 195])).
% 0.62/0.85 tff(203,plain,
% 0.62/0.85 ((~((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3))))) | (~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3)))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(204,plain,
% 0.62/0.85 ((~subset(intersection(D!2, C!3), intersection(C!3, C!3))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3)))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.62/0.85 tff(205,plain,
% 0.62/0.85 (![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3)))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[204, 200])).
% 0.62/0.85 tff(206,plain,
% 0.62/0.85 (((~![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3)))) | ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> ((~![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3)))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(207,plain,
% 0.62/0.85 ((~![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3)))) | ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(208,plain,
% 0.62/0.85 ((~![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, intersection(C!3, C!3)))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.62/0.85 tff(209,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[208, 205, 147])).
% 0.62/0.85 tff(210,plain,
% 0.62/0.85 (((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(211,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[210, 145])).
% 0.62/0.85 tff(212,plain,
% 0.62/0.85 ((~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(213,plain,
% 0.62/0.85 (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[212, 211, 209])).
% 0.62/0.85 tff(214,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))) | ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(215,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.62/0.85 tff(216,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[215, 96])).
% 0.62/0.85 tff(217,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[216, 155])).
% 0.62/0.85 tff(218,plain,(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(219,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))) | (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4))))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4))))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(220,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))) | (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.62/0.85 tff(221,plain,
% 0.62/0.85 (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4))))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[220, 101])).
% 0.62/0.85 tff(222,plain,
% 0.62/0.85 (((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(223,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.62/0.85 tff(224,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[223, 99])).
% 0.62/0.85 tff(225,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4))) | (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, C!3), B!4)))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(226,plain,
% 0.62/0.85 (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[225, 224, 96])).
% 0.62/0.85 tff(227,plain,
% 0.62/0.85 (((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(228,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.62/0.85 tff(229,plain,
% 0.62/0.85 (((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, B!4)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(230,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[229, 221])).
% 0.62/0.85 tff(231,plain,
% 0.62/0.85 ((~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(232,plain,
% 0.62/0.85 (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3))))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[231, 230, 228])).
% 0.62/0.85 tff(233,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))) | ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(234,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), D!2)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.62/0.85 tff(235,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, C!3)))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[234, 86])).
% 0.62/0.85 tff(236,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[235, 84])).
% 0.62/0.85 tff(237,plain,(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(238,plain,
% 0.62/0.85 (((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(239,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[238, 226])).
% 0.62/0.85 tff(240,plain,
% 0.62/0.85 ((~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(241,plain,
% 0.62/0.85 (~((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4)))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[240, 239, 237])).
% 0.62/0.85 tff(242,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4))) | ((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4))),
% 0.62/0.85 inference(tautology,[status(thm)],[])).
% 0.62/0.85 tff(243,plain,
% 0.62/0.85 ((((~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4))) | member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.62/0.85 tff(244,plain,
% 0.62/0.85 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(D!2, C!3), B!4))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[243, 53])).
% 0.62/0.85 tff(245,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[244, 41])).
% 0.62/0.85 tff(246,plain,(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.86 tff(247,plain,
% 0.62/0.86 (intersection(D!2, intersection(B!4, C!3)) = intersection(D!2, intersection(C!3, B!4))),
% 0.62/0.86 inference(symmetry,[status(thm)],[137])).
% 0.62/0.86 tff(248,plain,
% 0.62/0.86 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4)))),
% 0.62/0.86 inference(monotonicity,[status(thm)],[247])).
% 0.62/0.86 tff(249,plain,
% 0.62/0.86 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.86 inference(symmetry,[status(thm)],[248])).
% 0.62/0.86 tff(250,plain,
% 0.62/0.86 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.86 inference(modus_ponens,[status(thm)],[218, 249])).
% 0.62/0.86 tff(251,plain,
% 0.62/0.86 ((member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))),
% 0.62/0.86 inference(tautology,[status(thm)],[])).
% 0.62/0.86 tff(252,plain,
% 0.62/0.86 (member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[251, 250, 246])).
% 0.62/0.86 tff(253,plain,
% 0.62/0.86 ((~((intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))) | (~(member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(intersection(D!2, intersection(B!4, C!3)), intersection(intersection(C!3, D!2), B!4)), intersection(D!2, intersection(B!4, C!3))))))) | (intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3)))),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[132, 252])).
% 0.62/0.86 tff(254,plain,
% 0.62/0.86 (intersection(intersection(C!3, D!2), B!4) = intersection(D!2, intersection(B!4, C!3))),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[253, 32])).
% 0.62/0.86 tff(255,plain,
% 0.62/0.86 (intersection(D!2, intersection(B!4, C!3)) = intersection(intersection(C!3, D!2), B!4)),
% 0.62/0.86 inference(symmetry,[status(thm)],[254])).
% 0.62/0.86 tff(256,plain,
% 0.62/0.86 (intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2))),
% 0.62/0.86 inference(transitivity,[status(thm)],[118, 255, 10])).
% 0.62/0.86 tff(257,plain,
% 0.62/0.86 ($false),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[130, 256])).
% 0.62/0.86 % SZS output end Proof
% 0.62/0.86 % E exiting
%------------------------------------------------------------------------------