%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET636+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:04 AM UTC 2025
% Result : Theorem 0.84s 1.04s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET636+3 : TPTP v9.0.0. Released v2.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:32:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.84/1.04 % SZS status Theorem
% 0.84/1.04 % SZS output start Proof
% 0.84/1.04 tff(member_type, type, (
% 0.84/1.04 member: ( $i * $i ) > $o)).
% 0.84/1.04 tff(intersection_type, type, (
% 0.84/1.04 intersection: ( $i * $i ) > $i)).
% 0.84/1.04 tff(tptp_fun_B_5_type, type, (
% 0.84/1.04 tptp_fun_B_5: $i)).
% 0.84/1.04 tff(empty_set_type, type, (
% 0.84/1.04 empty_set: $i)).
% 0.84/1.04 tff(tptp_fun_D_3_type, type, (
% 0.84/1.04 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.84/1.04 tff(tptp_fun_C_4_type, type, (
% 0.84/1.04 tptp_fun_C_4: $i)).
% 0.84/1.04 tff(empty_type, type, (
% 0.84/1.04 empty: $i > $o)).
% 0.84/1.04 tff(tptp_fun_C_2_type, type, (
% 0.84/1.04 tptp_fun_C_2: $i > $i)).
% 0.84/1.04 tff(intersect_type, type, (
% 0.84/1.04 intersect: ( $i * $i ) > $o)).
% 0.84/1.04 tff(disjoint_type, type, (
% 0.84/1.04 disjoint: ( $i * $i ) > $o)).
% 0.84/1.04 tff(tptp_fun_D_0_type, type, (
% 0.84/1.04 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.84/1.04 tff(1,assumption,(empty_set = intersection(empty_set, B!5)), introduced(assumption)).
% 0.84/1.04 tff(2,plain,
% 0.84/1.04 (intersection(empty_set, B!5) = empty_set),
% 0.84/1.04 inference(symmetry,[status(thm)],[1])).
% 0.84/1.04 tff(3,plain,
% 0.84/1.04 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(4,plain,
% 0.84/1.04 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[3])).
% 0.84/1.04 tff(5,plain,
% 0.84/1.04 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(pull_quant,[status(thm)],[])).
% 0.84/1.04 tff(6,plain,
% 0.84/1.04 (^[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_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(7,plain,
% 0.84/1.04 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[6])).
% 0.84/1.04 tff(8,plain,
% 0.84/1.04 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(transitivity,[status(thm)],[7, 5])).
% 0.84/1.04 tff(9,plain,
% 0.84/1.04 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(transitivity,[status(thm)],[8, 4])).
% 0.84/1.04 tff(10,plain,
% 0.84/1.04 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(11,plain,
% 0.84/1.04 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[10])).
% 0.84/1.04 tff(12,plain,
% 0.84/1.04 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(transitivity,[status(thm)],[11, 9])).
% 0.84/1.04 tff(13,plain,
% 0.84/1.04 (^[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_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))) <=> (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(14,plain,
% 0.84/1.04 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[13])).
% 0.84/1.04 tff(15,plain,
% 0.84/1.04 (![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)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(16,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')).
% 0.84/1.04 tff(17,plain,
% 0.84/1.04 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.84/1.04 tff(18,plain,(
% 0.84/1.04 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))),
% 0.84/1.04 inference(skolemize,[status(sab)],[17])).
% 0.84/1.04 tff(19,plain,
% 0.84/1.04 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.84/1.04 tff(20,plain,
% 0.84/1.04 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.84/1.04 tff(21,plain,
% 0.84/1.04 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(intersection(C!4, B!5) = intersection(empty_set, B!5))) | (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))))) | (~((intersection(C!4, B!5) = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))))))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(22,plain,
% 0.84/1.04 (~((~((~(intersection(C!4, B!5) = intersection(empty_set, B!5))) | (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))))) | (~((intersection(C!4, B!5) = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5)))))))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.84/1.04 tff(23,plain,
% 0.84/1.04 (((~((~(intersection(C!4, B!5) = intersection(empty_set, B!5))) | (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))))) | (~((intersection(C!4, B!5) = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))))))) | ((intersection(C!4, B!5) = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5)))))),
% 0.84/1.04 inference(tautology,[status(thm)],[])).
% 0.84/1.04 tff(24,plain,
% 0.84/1.04 ((intersection(C!4, B!5) = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.84/1.04 tff(25,assumption,(~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5)))), introduced(assumption)).
% 0.84/1.04 tff(26,plain,
% 0.84/1.04 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1])).
% 0.84/1.04 tff(27,plain,
% 0.84/1.04 ((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), empty_set)) <=> (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[26])).
% 0.84/1.04 tff(28,assumption,(member(tptp_fun_C_2(empty_set), empty_set)), introduced(assumption)).
% 0.84/1.04 tff(29,plain,
% 0.84/1.04 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(30,plain,
% 0.84/1.04 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[29])).
% 0.84/1.04 tff(31,plain,
% 0.84/1.04 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(32,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.84/1.04 tff(33,plain,
% 0.84/1.04 (![B: $i] : (~member(B, empty_set))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.84/1.04 tff(34,plain,(
% 0.84/1.04 ![B: $i] : (~member(B, empty_set))),
% 0.84/1.04 inference(skolemize,[status(sab)],[33])).
% 0.84/1.04 tff(35,plain,
% 0.84/1.04 (![B: $i] : (~member(B, empty_set))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.84/1.04 tff(36,plain,
% 0.84/1.04 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_C_2(empty_set), empty_set))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(37,plain,
% 0.84/1.04 ($false),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[36, 35, 28])).
% 0.84/1.04 tff(38,plain,(~member(tptp_fun_C_2(empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.04 tff(39,plain,
% 0.84/1.04 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B)))))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(40,plain,
% 0.84/1.04 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[39])).
% 0.84/1.04 tff(41,plain,
% 0.84/1.04 (^[B: $i] : refl((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(42,plain,
% 0.84/1.04 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[41])).
% 0.84/1.04 tff(43,plain,
% 0.84/1.04 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(44,plain,
% 0.84/1.04 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[43])).
% 0.84/1.04 tff(45,plain,
% 0.84/1.04 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.84/1.04 inference(transitivity,[status(thm)],[44, 42])).
% 0.84/1.04 tff(46,plain,
% 0.84/1.04 (^[B: $i] : trans(monotonicity(rewrite(((~empty(B)) | ![C: $i] : (~member(C, B))) <=> ((~empty(B)) | ![C: $i] : (~member(C, B)))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))))), rewrite((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(47,plain,
% 0.84/1.04 (![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[46])).
% 0.84/1.04 tff(48,plain,
% 0.84/1.04 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B))) <=> ![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(49,axiom,(![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_defn')).
% 0.84/1.04 tff(50,plain,
% 0.84/1.04 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.84/1.04 tff(51,plain,(
% 0.84/1.04 ![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B)))),
% 0.84/1.04 inference(skolemize,[status(sab)],[50])).
% 0.84/1.04 tff(52,plain,
% 0.84/1.04 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.84/1.04 tff(53,plain,
% 0.84/1.04 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.84/1.04 tff(54,plain,
% 0.84/1.04 (![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[53, 40])).
% 0.84/1.04 tff(55,plain,
% 0.84/1.04 ((~![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))) | (~((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | (~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(56,plain,
% 0.84/1.04 (~((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | (~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set)))))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.84/1.04 tff(57,plain,
% 0.84/1.04 (((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | (~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))))) | (empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))),
% 0.84/1.04 inference(tautology,[status(thm)],[])).
% 0.84/1.04 tff(58,plain,
% 0.84/1.04 (empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.84/1.04 tff(59,plain,
% 0.84/1.04 ((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set)),
% 0.84/1.05 inference(tautology,[status(thm)],[])).
% 0.84/1.05 tff(60,plain,
% 0.84/1.05 (empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.84/1.05 tff(61,plain,
% 0.84/1.05 (empty(empty_set)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[60, 38])).
% 0.84/1.05 tff(62,plain,
% 0.84/1.05 (((~(empty(empty_set) | member(tptp_fun_C_2(empty_set), empty_set))) | (~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))))) | ((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set)))),
% 0.84/1.05 inference(tautology,[status(thm)],[])).
% 0.84/1.05 tff(63,plain,
% 0.84/1.05 ((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[62, 56])).
% 0.84/1.05 tff(64,plain,
% 0.84/1.05 ((~((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set)))) | (~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))),
% 0.84/1.05 inference(tautology,[status(thm)],[])).
% 0.84/1.05 tff(65,plain,
% 0.84/1.05 ((~empty(empty_set)) | ![C: $i] : (~member(C, empty_set))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.84/1.05 tff(66,plain,
% 0.84/1.05 (![C: $i] : (~member(C, empty_set))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[65, 61])).
% 0.84/1.05 tff(67,plain,
% 0.84/1.05 ((~![C: $i] : (~member(C, empty_set))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), empty_set))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(68,plain,
% 0.84/1.05 (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), empty_set)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.84/1.05 tff(69,plain,
% 0.84/1.05 (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[68, 27])).
% 0.84/1.05 tff(70,assumption,(~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))), introduced(assumption)).
% 0.84/1.05 tff(71,plain,
% 0.84/1.05 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(72,plain,
% 0.84/1.05 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[71])).
% 0.84/1.05 tff(73,plain,
% 0.84/1.05 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, C)) | (~member(D, B))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(74,plain,
% 0.84/1.05 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[73])).
% 0.84/1.05 tff(75,plain,
% 0.84/1.05 (![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)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(76,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')).
% 0.84/1.05 tff(77,plain,
% 0.84/1.05 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.84/1.05 tff(78,plain,(
% 0.84/1.05 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.84/1.05 inference(skolemize,[status(sab)],[77])).
% 0.84/1.05 tff(79,plain,
% 0.84/1.05 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.84/1.05 tff(80,plain,
% 0.84/1.05 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.84/1.05 tff(81,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(82,plain,
% 0.84/1.05 ((~(~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))) <=> (member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(83,plain,
% 0.84/1.05 ((~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))) <=> (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(84,plain,
% 0.84/1.05 (((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))) <=> (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(85,plain,
% 0.84/1.05 (((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(86,plain,
% 0.84/1.05 ((((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))) <=> ((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[85])).
% 0.84/1.05 tff(87,plain,
% 0.84/1.05 ((((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))) <=> (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(transitivity,[status(thm)],[86, 84])).
% 0.84/1.05 tff(88,plain,
% 0.84/1.05 ((((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))) <=> (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(transitivity,[status(thm)],[87, 83])).
% 0.84/1.05 tff(89,plain,
% 0.84/1.05 ((~(((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))) <=> (~(~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[88])).
% 0.84/1.05 tff(90,plain,
% 0.84/1.05 ((~(((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))) <=> (member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[89, 82])).
% 0.84/1.05 tff(91,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[90])).
% 0.84/1.05 tff(92,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(transitivity,[status(thm)],[91, 81])).
% 0.84/1.05 tff(93,plain,
% 0.84/1.05 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5)) | (~member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5))) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(94,plain,
% 0.84/1.05 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.84/1.05 tff(95,plain,
% 0.84/1.05 ($false),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[94, 80, 70])).
% 0.84/1.05 tff(96,plain,(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.05 tff(97,plain,
% 0.84/1.05 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(B!5 = intersection(B!5, B!5))) | (member(tptp_fun_D_3(C!4, B!5), B!5) <=> member(tptp_fun_D_3(C!4, B!5), intersection(B!5, B!5))))) | (~((B!5 = intersection(B!5, B!5)) | (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))))))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(98,plain,
% 0.84/1.05 (~((~((~(B!5 = intersection(B!5, B!5))) | (member(tptp_fun_D_3(C!4, B!5), B!5) <=> member(tptp_fun_D_3(C!4, B!5), intersection(B!5, B!5))))) | (~((B!5 = intersection(B!5, B!5)) | (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))))))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[97, 20])).
% 0.84/1.05 tff(99,plain,
% 0.84/1.05 (((~((~(B!5 = intersection(B!5, B!5))) | (member(tptp_fun_D_3(C!4, B!5), B!5) <=> member(tptp_fun_D_3(C!4, B!5), intersection(B!5, B!5))))) | (~((B!5 = intersection(B!5, B!5)) | (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))))) | ((B!5 = intersection(B!5, B!5)) | (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))))),
% 0.84/1.05 inference(tautology,[status(thm)],[])).
% 0.84/1.05 tff(100,plain,
% 0.84/1.05 ((B!5 = intersection(B!5, B!5)) | (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.84/1.05 tff(101,plain,
% 0.84/1.05 ((~((B!5 = intersection(B!5, B!5)) | (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5)))))) | (B!5 = intersection(B!5, B!5)) | (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(tautology,[status(thm)],[])).
% 0.84/1.05 tff(102,plain,
% 0.84/1.05 ((B!5 = intersection(B!5, B!5)) | (~(member(tptp_fun_D_3(intersection(B!5, B!5), B!5), B!5) <=> member(tptp_fun_D_3(intersection(B!5, B!5), B!5), intersection(B!5, B!5))))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.84/1.05 tff(103,plain,
% 0.84/1.05 (B!5 = intersection(B!5, B!5)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[102, 96])).
% 0.84/1.05 tff(104,plain,
% 0.84/1.05 (intersection(B!5, B!5) = B!5),
% 0.84/1.05 inference(symmetry,[status(thm)],[103])).
% 0.84/1.05 tff(105,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4)))))))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(106,plain,
% 0.84/1.05 ((~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((C!4 = intersection(C!4, C!4)) | (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))))))) <=> (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4))))))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(107,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((C!4 = intersection(C!4, C!4)) | (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4)))))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[106])).
% 0.84/1.05 tff(108,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((C!4 = intersection(C!4, C!4)) | (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4)))))))),
% 0.84/1.05 inference(transitivity,[status(thm)],[107, 105])).
% 0.84/1.05 tff(109,plain,
% 0.84/1.05 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((C!4 = intersection(C!4, C!4)) | (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))))))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(110,plain,
% 0.84/1.05 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4))))))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.84/1.05 tff(111,plain,
% 0.84/1.05 (~((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4)))))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[110, 20])).
% 0.84/1.05 tff(112,plain,
% 0.84/1.05 (((~((~(C!4 = intersection(C!4, C!4))) | (member(tptp_fun_D_3(C!4, empty_set), C!4) <=> member(tptp_fun_D_3(C!4, empty_set), intersection(C!4, C!4))))) | (~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4))))) | ((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4)))),
% 0.84/1.05 inference(tautology,[status(thm)],[])).
% 0.84/1.05 tff(113,plain,
% 0.84/1.05 ((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.84/1.05 tff(114,assumption,(~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))), introduced(assumption)).
% 0.84/1.05 tff(115,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(116,plain,
% 0.84/1.05 ((~(~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))) <=> (member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(117,plain,
% 0.84/1.05 ((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) <=> (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(118,plain,
% 0.84/1.05 (((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))) <=> (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(119,plain,
% 0.84/1.05 (((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(120,plain,
% 0.84/1.05 ((((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))) <=> ((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[119])).
% 0.84/1.05 tff(121,plain,
% 0.84/1.05 ((((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))) <=> (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))),
% 0.84/1.05 inference(transitivity,[status(thm)],[120, 118])).
% 0.84/1.05 tff(122,plain,
% 0.84/1.05 ((((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))) <=> (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))),
% 0.84/1.05 inference(transitivity,[status(thm)],[121, 117])).
% 0.84/1.05 tff(123,plain,
% 0.84/1.05 ((~(((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) <=> (~(~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[122])).
% 0.84/1.05 tff(124,plain,
% 0.84/1.05 ((~(((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) <=> (member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[123, 116])).
% 0.84/1.05 tff(125,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[124])).
% 0.84/1.05 tff(126,plain,
% 0.84/1.05 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))),
% 0.84/1.05 inference(transitivity,[status(thm)],[125, 115])).
% 0.84/1.05 tff(127,plain,
% 0.84/1.05 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4)) | (~member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4))) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(128,plain,
% 0.84/1.05 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.84/1.05 tff(129,plain,
% 0.84/1.05 ($false),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[128, 80, 114])).
% 0.84/1.05 tff(130,plain,(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.05 tff(131,plain,
% 0.84/1.05 ((~((~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4)))) | (~(member(tptp_fun_D_3(intersection(C!4, C!4), C!4), C!4) <=> member(tptp_fun_D_3(intersection(C!4, C!4), C!4), intersection(C!4, C!4)))) | (C!4 = intersection(C!4, C!4))),
% 0.84/1.05 inference(tautology,[status(thm)],[])).
% 0.84/1.05 tff(132,plain,
% 0.84/1.05 (C!4 = intersection(C!4, C!4)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[131, 130, 113])).
% 0.84/1.05 tff(133,plain,
% 0.84/1.05 (intersection(C!4, C!4) = C!4),
% 0.84/1.05 inference(symmetry,[status(thm)],[132])).
% 0.84/1.05 tff(134,plain,
% 0.84/1.05 (intersection(intersection(C!4, C!4), intersection(B!5, B!5)) = intersection(C!4, B!5)),
% 0.84/1.05 inference(monotonicity,[status(thm)],[133, 104])).
% 0.84/1.05 tff(135,plain,
% 0.84/1.05 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[134])).
% 0.84/1.05 tff(136,plain,
% 0.84/1.05 ((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5)))) <=> (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[135])).
% 0.84/1.05 tff(137,plain,
% 0.84/1.05 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5)))))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(138,plain,
% 0.84/1.05 (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5))))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[137, 80])).
% 0.84/1.05 tff(139,plain,
% 0.84/1.05 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[103])).
% 0.84/1.06 tff(140,plain,
% 0.84/1.06 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)),
% 0.84/1.06 inference(symmetry,[status(thm)],[139])).
% 0.84/1.06 tff(141,assumption,(~((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4))))), introduced(assumption)).
% 0.84/1.06 tff(142,plain,
% 0.84/1.06 (((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4)))) | member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(143,plain,
% 0.84/1.06 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.84/1.06 tff(144,plain,
% 0.84/1.06 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[143, 140])).
% 0.84/1.06 tff(145,plain,
% 0.84/1.06 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)),
% 0.84/1.06 inference(monotonicity,[status(thm)],[133])).
% 0.84/1.06 tff(146,plain,
% 0.84/1.06 (((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4)))) | member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(147,plain,
% 0.84/1.06 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[146, 141])).
% 0.84/1.06 tff(148,plain,
% 0.84/1.06 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[147, 145])).
% 0.84/1.06 tff(149,assumption,(~disjoint(B!5, C!4)), introduced(assumption)).
% 0.84/1.06 tff(150,plain,
% 0.84/1.06 ((~(disjoint(B!5, C!4) <=> (intersection(B!5, C!4) = empty_set))) <=> (~(disjoint(B!5, C!4) <=> (intersection(B!5, C!4) = empty_set)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(151,plain,
% 0.84/1.06 ((~![B: $i, C: $i] : (disjoint(B, C) <=> (intersection(B, C) = empty_set))) <=> (~![B: $i, C: $i] : (disjoint(B, C) <=> (intersection(B, C) = empty_set)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(152,axiom,(~![B: $i, C: $i] : (disjoint(B, C) <=> (intersection(B, C) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th118')).
% 0.84/1.06 tff(153,plain,
% 0.84/1.06 (~![B: $i, C: $i] : (disjoint(B, C) <=> (intersection(B, C) = empty_set))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.84/1.06 tff(154,plain,
% 0.84/1.06 (~![B: $i, C: $i] : (disjoint(B, C) <=> (intersection(B, C) = empty_set))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[153, 151])).
% 0.84/1.06 tff(155,plain,
% 0.84/1.06 (~![B: $i, C: $i] : (disjoint(B, C) <=> (intersection(B, C) = empty_set))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[154, 151])).
% 0.84/1.06 tff(156,plain,
% 0.84/1.06 (~![B: $i, C: $i] : (disjoint(B, C) <=> (intersection(B, C) = empty_set))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.84/1.06 tff(157,plain,(
% 0.84/1.06 ~(disjoint(B!5, C!4) <=> (intersection(B!5, C!4) = empty_set))),
% 0.84/1.06 inference(skolemize,[status(sab)],[156])).
% 0.84/1.06 tff(158,plain,
% 0.84/1.06 (~(disjoint(B!5, C!4) <=> (intersection(B!5, C!4) = empty_set))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.84/1.06 tff(159,plain,
% 0.84/1.06 ((disjoint(B!5, C!4) <=> (intersection(B!5, C!4) = empty_set)) | disjoint(B!5, C!4) | (intersection(B!5, C!4) = empty_set)),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(160,plain,
% 0.84/1.06 (disjoint(B!5, C!4) | (intersection(B!5, C!4) = empty_set)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.84/1.06 tff(161,plain,
% 0.84/1.06 (intersection(B!5, C!4) = empty_set),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[160, 149])).
% 0.84/1.06 tff(162,plain,
% 0.84/1.06 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(163,plain,
% 0.84/1.06 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[162])).
% 0.84/1.06 tff(164,plain,
% 0.84/1.06 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(165,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.84/1.06 tff(166,plain,
% 0.84/1.06 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.84/1.06 tff(167,plain,(
% 0.84/1.06 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.84/1.06 inference(skolemize,[status(sab)],[166])).
% 0.84/1.06 tff(168,plain,
% 0.84/1.06 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.84/1.06 tff(169,plain,
% 0.84/1.06 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!5, C!4) = intersection(C!4, B!5))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(170,plain,
% 0.84/1.06 (intersection(B!5, C!4) = intersection(C!4, B!5)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.84/1.06 tff(171,plain,
% 0.84/1.06 (intersection(C!4, B!5) = intersection(B!5, C!4)),
% 0.84/1.06 inference(symmetry,[status(thm)],[170])).
% 0.84/1.06 tff(172,plain,
% 0.84/1.06 (intersection(C!4, B!5) = empty_set),
% 0.84/1.06 inference(transitivity,[status(thm)],[171, 161])).
% 0.84/1.06 tff(173,plain,
% 0.84/1.06 (member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5)) <=> member(tptp_fun_D_0(C!4, B!5), empty_set)),
% 0.84/1.06 inference(monotonicity,[status(thm)],[172])).
% 0.84/1.06 tff(174,plain,
% 0.84/1.06 (member(tptp_fun_D_0(C!4, B!5), empty_set) <=> member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5))),
% 0.84/1.06 inference(symmetry,[status(thm)],[173])).
% 0.84/1.06 tff(175,plain,
% 0.84/1.06 ((~member(tptp_fun_D_0(C!4, B!5), empty_set)) <=> (~member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5)))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[174])).
% 0.84/1.06 tff(176,plain,
% 0.84/1.06 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(C!4, B!5), empty_set))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(177,plain,
% 0.84/1.06 (~member(tptp_fun_D_0(C!4, B!5), empty_set)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[176, 35])).
% 0.84/1.06 tff(178,plain,
% 0.84/1.06 (~member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[177, 175])).
% 0.84/1.06 tff(179,plain,
% 0.84/1.06 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))) <=> member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5))))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(180,plain,
% 0.84/1.06 (~(((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))) <=> member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5)))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[179, 80])).
% 0.84/1.06 tff(181,plain,
% 0.84/1.06 (^[B: $i, C: $i] : refl((~(intersect(B, C) <=> disjoint(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(182,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[181])).
% 0.84/1.06 tff(183,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(184,plain,
% 0.84/1.06 (^[B: $i, C: $i] : trans(rewrite((disjoint(B, C) <=> (~intersect(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))), rewrite((~(intersect(B, C) <=> disjoint(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))), ((disjoint(B, C) <=> (~intersect(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(185,plain,
% 0.84/1.06 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[184])).
% 0.84/1.06 tff(186,axiom,(![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','disjoint_defn')).
% 0.84/1.06 tff(187,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.84/1.06 tff(188,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.84/1.06 tff(189,plain,(
% 0.84/1.06 ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.84/1.06 inference(skolemize,[status(sab)],[188])).
% 0.84/1.06 tff(190,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.84/1.06 tff(191,plain,
% 0.84/1.06 ((~![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))) | (~(intersect(B!5, C!4) <=> disjoint(B!5, C!4)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(192,plain,
% 0.84/1.06 (~(intersect(B!5, C!4) <=> disjoint(B!5, C!4))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.84/1.06 tff(193,plain,
% 0.84/1.06 ((intersect(B!5, C!4) <=> disjoint(B!5, C!4)) | intersect(B!5, C!4) | disjoint(B!5, C!4)),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(194,plain,
% 0.84/1.06 (intersect(B!5, C!4) | disjoint(B!5, C!4)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.84/1.06 tff(195,plain,
% 0.84/1.06 (intersect(B!5, C!4)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[194, 149])).
% 0.84/1.06 tff(196,plain,
% 0.84/1.06 (^[B: $i, C: $i] : refl((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(197,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[196])).
% 0.84/1.06 tff(198,plain,
% 0.84/1.06 (^[B: $i, C: $i] : rewrite((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(199,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[198])).
% 0.84/1.06 tff(200,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.84/1.06 inference(transitivity,[status(thm)],[199, 197])).
% 0.84/1.06 tff(201,plain,
% 0.84/1.06 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) <=> ((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))), rewrite((intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))) <=> (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))), rewrite((((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(202,plain,
% 0.84/1.06 (![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[201])).
% 0.84/1.06 tff(203,plain,
% 0.84/1.06 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C))) <=> ![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(204,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_defn')).
% 0.84/1.06 tff(205,plain,
% 0.84/1.06 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.84/1.06 tff(206,plain,(
% 0.84/1.06 ![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))))),
% 0.84/1.06 inference(skolemize,[status(sab)],[205])).
% 0.84/1.06 tff(207,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.84/1.06 tff(208,plain,
% 0.84/1.06 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.84/1.06 tff(209,plain,
% 0.84/1.06 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))))))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(210,plain,
% 0.84/1.06 ((~((~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))) | (~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))))) <=> (~((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))))))))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(211,plain,
% 0.84/1.06 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))) | (~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[210])).
% 0.84/1.06 tff(212,plain,
% 0.84/1.06 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))) | (~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))))))),
% 0.84/1.06 inference(transitivity,[status(thm)],[211, 209])).
% 0.84/1.06 tff(213,plain,
% 0.84/1.06 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))) | (~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))))))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(214,plain,
% 0.84/1.06 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))))))))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.84/1.06 tff(215,plain,
% 0.84/1.06 (~((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[214, 208])).
% 0.84/1.06 tff(216,plain,
% 0.84/1.06 (((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))))))) | ((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(217,plain,
% 0.84/1.06 ((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.84/1.06 tff(218,plain,
% 0.84/1.06 ((~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))))) | (~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(219,plain,
% 0.84/1.06 ((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.84/1.06 tff(220,plain,
% 0.84/1.06 (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4)))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[219, 195])).
% 0.84/1.06 tff(221,plain,
% 0.84/1.06 ((((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))) <=> member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5))) | ((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))) | member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(222,plain,
% 0.84/1.06 ((((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))) <=> member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5))) | member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.84/1.06 tff(223,plain,
% 0.84/1.06 (member(tptp_fun_D_0(C!4, B!5), intersection(C!4, B!5))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[222, 180])).
% 0.84/1.06 tff(224,plain,
% 0.84/1.06 ($false),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[223, 178])).
% 0.84/1.06 tff(225,plain,(disjoint(B!5, C!4)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.06 tff(226,plain,
% 0.84/1.06 ((intersect(B!5, C!4) <=> disjoint(B!5, C!4)) | (~intersect(B!5, C!4)) | (~disjoint(B!5, C!4))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(227,plain,
% 0.84/1.06 ((~intersect(B!5, C!4)) | (~disjoint(B!5, C!4))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[226, 192])).
% 0.84/1.06 tff(228,plain,
% 0.84/1.06 (~intersect(B!5, C!4)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[227, 225])).
% 0.84/1.06 tff(229,plain,
% 0.84/1.06 (((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | (~((~intersect(B!5, C!4)) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | (~member(tptp_fun_D_0(C!4, B!5), C!4))))))) | (intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(230,plain,
% 0.84/1.06 (intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[229, 215])).
% 0.84/1.06 tff(231,plain,
% 0.84/1.06 ((~(intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5))))) | intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(232,plain,
% 0.84/1.06 (intersect(B!5, C!4) | ![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.84/1.06 tff(233,plain,
% 0.84/1.06 (![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[232, 228])).
% 0.84/1.06 tff(234,plain,
% 0.84/1.06 (((~![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))) | ((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)))) <=> ((~![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(235,plain,
% 0.84/1.06 (((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5))) <=> ((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(236,plain,
% 0.84/1.06 (((~![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))) | ((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)))) <=> ((~![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))) | ((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[235])).
% 0.84/1.06 tff(237,plain,
% 0.84/1.06 (((~![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))) | ((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)))) <=> ((~![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[236, 234])).
% 0.84/1.06 tff(238,plain,
% 0.84/1.06 ((~![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))) | ((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(239,plain,
% 0.84/1.06 ((~![D: $i] : ((~member(D, C!4)) | (~member(D, B!5)))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), C!4))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.84/1.06 tff(240,plain,
% 0.84/1.06 (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), B!5)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[239, 233, 148])).
% 0.84/1.06 tff(241,plain,
% 0.84/1.06 ($false),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[240, 144])).
% 0.84/1.06 tff(242,plain,((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.06 tff(243,plain,
% 0.84/1.06 ((((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5)))) | (~((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4))))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5))))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(244,plain,
% 0.84/1.06 ((((~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, C!4)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5)))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5))))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.84/1.06 tff(245,plain,
% 0.84/1.06 (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(intersection(C!4, C!4), intersection(B!5, B!5)))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[244, 138])).
% 0.84/1.06 tff(246,plain,
% 0.84/1.06 (~member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[245, 136])).
% 0.84/1.06 tff(247,plain,
% 0.84/1.06 ((member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))) | member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) | member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(248,plain,
% 0.84/1.06 ($false),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[247, 246, 69, 25])).
% 0.84/1.06 tff(249,plain,((member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))) | (~(empty_set = intersection(empty_set, B!5)))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.06 tff(250,plain,
% 0.84/1.06 (member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[249, 1])).
% 0.84/1.06 tff(251,plain,
% 0.84/1.06 ((~((intersection(C!4, B!5) = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5)))))) | (intersection(C!4, B!5) = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5))))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(252,plain,
% 0.84/1.06 ((~((intersection(C!4, B!5) = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(C!4, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), intersection(C!4, B!5)), intersection(empty_set, B!5)))))) | (intersection(C!4, B!5) = intersection(empty_set, B!5))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.84/1.06 tff(253,plain,
% 0.84/1.06 (intersection(C!4, B!5) = intersection(empty_set, B!5)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[252, 24])).
% 0.84/1.06 tff(254,plain,
% 0.84/1.06 (intersection(B!5, C!4) = empty_set),
% 0.84/1.06 inference(transitivity,[status(thm)],[170, 253, 2])).
% 0.84/1.06 tff(255,plain,
% 0.84/1.06 ((disjoint(B!5, C!4) <=> (intersection(B!5, C!4) = empty_set)) | (~disjoint(B!5, C!4)) | (~(intersection(B!5, C!4) = empty_set))),
% 0.84/1.06 inference(tautology,[status(thm)],[])).
% 0.84/1.06 tff(256,plain,
% 0.84/1.06 ((~disjoint(B!5, C!4)) | (~(intersection(B!5, C!4) = empty_set))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[255, 158])).
% 0.84/1.06 tff(257,plain,
% 0.84/1.06 (~(intersection(B!5, C!4) = empty_set)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[256, 225])).
% 0.84/1.06 tff(258,plain,
% 0.84/1.06 ($false),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[257, 254])).
% 0.84/1.06 tff(259,plain,(~(empty_set = intersection(empty_set, B!5))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.06 tff(260,plain,
% 0.84/1.06 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_3(C, B), B) <=> member(tptp_fun_D_3(C, B), C)))))))) | (~((~((~(empty_set = intersection(empty_set, B!5))) | (member(tptp_fun_D_3(tptp_fun_D_0(B!5, C!4), tptp_fun_D_3(B!5, C!4)), empty_set) <=> member(tptp_fun_D_3(tptp_fun_D_0(B!5, C!4), tptp_fun_D_3(B!5, C!4)), intersection(empty_set, B!5))))) | (~((empty_set = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))))))))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(261,plain,
% 0.84/1.06 (~((~((~(empty_set = intersection(empty_set, B!5))) | (member(tptp_fun_D_3(tptp_fun_D_0(B!5, C!4), tptp_fun_D_3(B!5, C!4)), empty_set) <=> member(tptp_fun_D_3(tptp_fun_D_0(B!5, C!4), tptp_fun_D_3(B!5, C!4)), intersection(empty_set, B!5))))) | (~((empty_set = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5)))))))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[260, 20])).
% 0.84/1.06 tff(262,plain,
% 0.84/1.06 (((~((~(empty_set = intersection(empty_set, B!5))) | (member(tptp_fun_D_3(tptp_fun_D_0(B!5, C!4), tptp_fun_D_3(B!5, C!4)), empty_set) <=> member(tptp_fun_D_3(tptp_fun_D_0(B!5, C!4), tptp_fun_D_3(B!5, C!4)), intersection(empty_set, B!5))))) | (~((empty_set = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))))))) | ((empty_set = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5)))))),
% 0.84/1.07 inference(tautology,[status(thm)],[])).
% 0.84/1.07 tff(263,plain,
% 0.84/1.07 ((empty_set = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))))),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.84/1.07 tff(264,plain,
% 0.84/1.07 ((~((empty_set = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5)))))) | (empty_set = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))))),
% 0.84/1.07 inference(tautology,[status(thm)],[])).
% 0.84/1.07 tff(265,plain,
% 0.84/1.07 ((empty_set = intersection(empty_set, B!5)) | (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))))),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.84/1.07 tff(266,plain,
% 0.84/1.07 (~(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5)))),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[265, 259])).
% 0.84/1.07 tff(267,plain,
% 0.84/1.07 ((~![C: $i] : (~member(C, empty_set))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(268,plain,
% 0.84/1.07 (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[267, 66])).
% 0.84/1.07 tff(269,plain,
% 0.84/1.07 (intersection(empty_set, intersection(B!5, B!5)) = intersection(empty_set, B!5)),
% 0.84/1.07 inference(monotonicity,[status(thm)],[104])).
% 0.84/1.07 tff(270,plain,
% 0.84/1.07 (member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[269])).
% 0.84/1.07 tff(271,plain,
% 0.84/1.07 (member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5)) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))),
% 0.84/1.07 inference(symmetry,[status(thm)],[270])).
% 0.84/1.07 tff(272,assumption,(member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))), introduced(assumption)).
% 0.84/1.07 tff(273,plain,
% 0.84/1.07 (member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.84/1.07 tff(274,plain,
% 0.84/1.07 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(275,plain,
% 0.84/1.07 ((~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))) <=> (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(276,plain,
% 0.84/1.07 ((((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))) <=> (((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(277,plain,
% 0.84/1.07 ((~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))) <=> (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[276])).
% 0.84/1.07 tff(278,plain,
% 0.84/1.07 ((~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))) <=> (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))))),
% 0.84/1.07 inference(transitivity,[status(thm)],[277, 275])).
% 0.84/1.07 tff(279,plain,
% 0.84/1.07 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[278])).
% 0.84/1.07 tff(280,plain,
% 0.84/1.07 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))))),
% 0.84/1.07 inference(transitivity,[status(thm)],[279, 274])).
% 0.84/1.07 tff(281,plain,
% 0.84/1.07 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(282,plain,
% 0.84/1.07 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.84/1.07 tff(283,plain,
% 0.84/1.07 (~(((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[282, 80])).
% 0.84/1.07 tff(284,assumption,(~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)), introduced(assumption)).
% 0.84/1.07 tff(285,plain,
% 0.84/1.07 (((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) | member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)),
% 0.84/1.07 inference(tautology,[status(thm)],[])).
% 0.84/1.07 tff(286,plain,
% 0.84/1.07 ((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[285, 284])).
% 0.84/1.07 tff(287,plain,
% 0.84/1.07 ((((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))) | (~((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5))))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))),
% 0.84/1.07 inference(tautology,[status(thm)],[])).
% 0.84/1.07 tff(288,plain,
% 0.84/1.07 ((((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(B!5, B!5)))) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))) | (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5))))),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[287, 286])).
% 0.84/1.07 tff(289,plain,
% 0.84/1.07 (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, intersection(B!5, B!5)))),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[288, 283])).
% 0.84/1.07 tff(290,plain,
% 0.84/1.07 ($false),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[289, 273])).
% 0.84/1.07 tff(291,plain,((~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))) | member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.07 tff(292,plain,
% 0.84/1.07 (~member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[291, 268])).
% 0.84/1.07 tff(293,plain,
% 0.84/1.07 ((member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) <=> member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))) | member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), empty_set) | member(tptp_fun_D_3(intersection(empty_set, B!5), empty_set), intersection(empty_set, B!5))),
% 0.84/1.07 inference(tautology,[status(thm)],[])).
% 0.84/1.07 tff(294,plain,
% 0.84/1.07 ($false),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[293, 292, 268, 266])).
% 0.84/1.07 % SZS output end Proof
% 0.84/1.07 % E exiting
%------------------------------------------------------------------------------