%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET008+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:24:44 AM UTC 2025
% Result : Theorem 0.64s 0.83s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET008+3 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 04:01:11 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.64/0.83 % SZS status Theorem
% 0.64/0.83 % SZS output start Proof
% 0.64/0.83 tff(member_type, type, (
% 0.64/0.83 member: ( $i * $i ) > $o)).
% 0.64/0.83 tff(difference_type, type, (
% 0.64/0.83 difference: ( $i * $i ) > $i)).
% 0.64/0.83 tff(intersection_type, type, (
% 0.64/0.83 intersection: ( $i * $i ) > $i)).
% 0.64/0.83 tff(tptp_fun_C_3_type, type, (
% 0.64/0.83 tptp_fun_C_3: $i)).
% 0.64/0.83 tff(tptp_fun_B_4_type, type, (
% 0.64/0.83 tptp_fun_B_4: $i)).
% 0.64/0.83 tff(tptp_fun_D_2_type, type, (
% 0.64/0.83 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.64/0.83 tff(empty_set_type, type, (
% 0.64/0.83 empty_set: $i)).
% 0.64/0.83 tff(tptp_fun_D_0_type, type, (
% 0.64/0.83 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.64/0.83 tff(empty_type, type, (
% 0.64/0.83 empty: $i > $o)).
% 0.64/0.83 tff(tptp_fun_C_1_type, type, (
% 0.64/0.83 tptp_fun_C_1: $i > $i)).
% 0.64/0.83 tff(1,plain,
% 0.64/0.83 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(2,plain,
% 0.64/0.83 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[1])).
% 0.64/0.83 tff(3,plain,
% 0.64/0.83 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(pull_quant,[status(thm)],[])).
% 0.64/0.83 tff(4,plain,
% 0.64/0.83 (^[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_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(5,plain,
% 0.64/0.83 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[4])).
% 0.64/0.83 tff(6,plain,
% 0.64/0.83 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[5, 3])).
% 0.64/0.83 tff(7,plain,
% 0.64/0.83 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[6, 2])).
% 0.64/0.83 tff(8,plain,
% 0.64/0.83 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(9,plain,
% 0.64/0.83 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[8])).
% 0.64/0.83 tff(10,plain,
% 0.64/0.83 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[9, 7])).
% 0.64/0.83 tff(11,plain,
% 0.64/0.83 (^[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_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))) <=> (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(12,plain,
% 0.64/0.83 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[11])).
% 0.64/0.83 tff(13,plain,
% 0.64/0.83 (![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)))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(14,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')).
% 0.64/0.83 tff(15,plain,
% 0.64/0.83 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.64/0.83 tff(16,plain,(
% 0.64/0.83 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))),
% 0.64/0.83 inference(skolemize,[status(sab)],[15])).
% 0.64/0.83 tff(17,plain,
% 0.64/0.83 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.64/0.83 tff(18,plain,
% 0.64/0.83 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.64/0.83 tff(19,plain,
% 0.64/0.83 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4))) | (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))))) | (~((difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)) | (~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(20,plain,
% 0.64/0.83 (~((~((~(difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4))) | (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))))) | (~((difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)) | (~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.64/0.83 tff(21,plain,
% 0.64/0.83 (((~((~(difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4))) | (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))))) | (~((difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)) | (~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))))))) | ((difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)) | (~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))))),
% 0.64/0.83 inference(tautology,[status(thm)],[])).
% 0.64/0.83 tff(22,plain,
% 0.64/0.83 ((difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)) | (~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.64/0.83 tff(23,assumption,(~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))), introduced(assumption)).
% 0.64/0.83 tff(24,plain,
% 0.64/0.83 (^[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)))))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(25,plain,
% 0.64/0.83 (![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))))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[24])).
% 0.64/0.83 tff(26,plain,
% 0.64/0.83 (^[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))))))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(27,plain,
% 0.64/0.83 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[26])).
% 0.64/0.83 tff(28,plain,
% 0.64/0.83 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(29,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')).
% 0.64/0.83 tff(30,plain,
% 0.64/0.83 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.64/0.83 tff(31,plain,(
% 0.64/0.83 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.64/0.83 inference(skolemize,[status(sab)],[30])).
% 0.64/0.83 tff(32,plain,
% 0.64/0.83 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.64/0.83 tff(33,plain,
% 0.64/0.83 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.64/0.83 tff(34,plain,
% 0.64/0.83 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(35,plain,
% 0.64/0.83 ((~(~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> (member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(36,plain,
% 0.64/0.83 ((~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(37,plain,
% 0.64/0.83 (((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(38,plain,
% 0.64/0.83 (((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(39,plain,
% 0.64/0.83 ((((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> ((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[38])).
% 0.64/0.83 tff(40,plain,
% 0.64/0.83 ((((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[39, 37])).
% 0.64/0.83 tff(41,plain,
% 0.64/0.83 ((((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[40, 36])).
% 0.64/0.83 tff(42,plain,
% 0.64/0.83 ((~(((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (~(~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[41])).
% 0.64/0.83 tff(43,plain,
% 0.64/0.83 ((~(((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.64/0.83 inference(transitivity,[status(thm)],[42, 35])).
% 0.64/0.83 tff(44,plain,
% 0.64/0.83 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[43])).
% 0.64/0.84 tff(45,plain,
% 0.64/0.84 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[44, 34])).
% 0.64/0.84 tff(46,plain,
% 0.64/0.84 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(47,plain,
% 0.64/0.84 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.64/0.84 tff(48,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[47, 33, 23])).
% 0.64/0.84 tff(49,plain,(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(50,plain,
% 0.64/0.84 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_0(difference(B!4, C!3), C!3), C!3) <=> member(tptp_fun_D_0(difference(B!4, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(51,plain,
% 0.64/0.84 (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_0(difference(B!4, C!3), C!3), C!3) <=> member(tptp_fun_D_0(difference(B!4, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[50, 18])).
% 0.64/0.84 tff(52,plain,
% 0.64/0.84 (((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_0(difference(B!4, C!3), C!3), C!3) <=> member(tptp_fun_D_0(difference(B!4, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))) | ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(53,plain,
% 0.64/0.84 ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.64/0.84 tff(54,plain,
% 0.64/0.84 ((~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))) | (C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(55,plain,
% 0.64/0.84 ((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_2(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_2(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.64/0.84 tff(56,plain,
% 0.64/0.84 (C!3 = intersection(C!3, C!3)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[55, 49])).
% 0.64/0.84 tff(57,plain,
% 0.64/0.84 (intersection(C!3, C!3) = C!3),
% 0.64/0.84 inference(symmetry,[status(thm)],[56])).
% 0.64/0.84 tff(58,plain,
% 0.64/0.84 (difference(B!4, intersection(C!3, C!3)) = difference(B!4, C!3)),
% 0.64/0.84 inference(monotonicity,[status(thm)],[57])).
% 0.64/0.84 tff(59,plain,
% 0.64/0.84 (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[58])).
% 0.64/0.84 tff(60,plain,
% 0.64/0.84 (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, intersection(C!3, C!3)))),
% 0.64/0.84 inference(symmetry,[status(thm)],[59])).
% 0.64/0.84 tff(61,assumption,(~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))), introduced(assumption)).
% 0.64/0.84 tff(62,plain,
% 0.64/0.84 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(63,plain,
% 0.64/0.84 (~(((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[62, 33])).
% 0.64/0.84 tff(64,assumption,(~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3))), introduced(assumption)).
% 0.64/0.84 tff(65,plain,
% 0.64/0.84 ((member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(66,plain,
% 0.64/0.84 (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[65, 64, 61])).
% 0.64/0.84 tff(67,plain,
% 0.64/0.84 (((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(68,plain,
% 0.64/0.84 ((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.64/0.84 tff(69,plain,
% 0.64/0.84 ((((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))) | (~((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3))))) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(70,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[69, 68, 66, 63])).
% 0.64/0.84 tff(71,plain,(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) | (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(72,plain,
% 0.64/0.84 (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[71, 61])).
% 0.64/0.84 tff(73,plain,
% 0.64/0.84 (member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, intersection(C!3, C!3)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[72, 60])).
% 0.64/0.84 tff(74,plain,
% 0.64/0.84 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(75,plain,
% 0.64/0.84 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[74])).
% 0.64/0.84 tff(76,plain,
% 0.64/0.84 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(77,plain,
% 0.64/0.84 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[76])).
% 0.64/0.84 tff(78,plain,
% 0.64/0.84 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(79,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.64/0.84 tff(80,plain,
% 0.64/0.84 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.64/0.84 tff(81,plain,(
% 0.64/0.84 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.64/0.84 inference(skolemize,[status(sab)],[80])).
% 0.64/0.84 tff(82,plain,
% 0.64/0.84 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.64/0.84 tff(83,plain,
% 0.64/0.84 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.64/0.84 tff(84,plain,
% 0.64/0.84 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, intersection(C!3, C!3)))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(85,plain,
% 0.64/0.84 (~(((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, intersection(C!3, C!3))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.64/0.84 tff(86,plain,
% 0.64/0.84 ((member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(87,plain,
% 0.64/0.84 (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[86, 72, 61])).
% 0.64/0.84 tff(88,plain,
% 0.64/0.84 ((((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))) | ((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(89,plain,
% 0.64/0.84 ((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[88, 87, 63])).
% 0.64/0.84 tff(90,plain,
% 0.64/0.84 ((~((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3))))) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(91,plain,
% 0.64/0.84 (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[90, 89, 72])).
% 0.64/0.84 tff(92,plain,
% 0.64/0.84 (((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(93,plain,
% 0.64/0.84 ((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(C!3, C!3))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.64/0.84 tff(94,plain,
% 0.64/0.84 ((((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, intersection(C!3, C!3)))) | (~((~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), B!4)) | member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(C!3, C!3)))) | (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, intersection(C!3, C!3))))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(95,plain,
% 0.64/0.84 (~member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, intersection(C!3, C!3)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[94, 93, 85])).
% 0.64/0.84 tff(96,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[95, 73])).
% 0.64/0.84 tff(97,plain,(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(98,plain,
% 0.64/0.84 ((~((difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)) | (~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))))) | (difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)) | (~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4))))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(99,plain,
% 0.64/0.84 ((~((difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)) | (~(member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_2(intersection(difference(B!4, C!3), B!4), difference(B!4, C!3)), intersection(difference(B!4, C!3), B!4)))))) | (difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.64/0.84 tff(100,plain,
% 0.64/0.84 (difference(B!4, C!3) = intersection(difference(B!4, C!3), B!4)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[99, 22])).
% 0.64/0.84 tff(101,plain,
% 0.64/0.84 (difference(B!4, intersection(C!3, C!3)) = intersection(difference(B!4, C!3), B!4)),
% 0.64/0.84 inference(transitivity,[status(thm)],[58, 100])).
% 0.64/0.84 tff(102,plain,
% 0.64/0.84 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[101])).
% 0.64/0.84 tff(103,plain,
% 0.64/0.84 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3)))),
% 0.64/0.84 inference(symmetry,[status(thm)],[102])).
% 0.64/0.84 tff(104,plain,
% 0.64/0.84 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(105,plain,
% 0.64/0.84 ((~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))) <=> (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(106,plain,
% 0.64/0.84 ((((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))) <=> (((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(107,plain,
% 0.64/0.84 ((~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))) <=> (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[106])).
% 0.64/0.84 tff(108,plain,
% 0.64/0.84 ((~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))) <=> (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[107, 105])).
% 0.64/0.85 tff(109,plain,
% 0.64/0.85 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[108])).
% 0.64/0.85 tff(110,plain,
% 0.64/0.85 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[109, 104])).
% 0.64/0.85 tff(111,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(112,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.64/0.85 tff(113,plain,
% 0.64/0.85 (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[112, 33])).
% 0.64/0.85 tff(114,plain,
% 0.64/0.85 (intersection(difference(B!4, C!3), B!4) = difference(B!4, C!3)),
% 0.64/0.85 inference(symmetry,[status(thm)],[100])).
% 0.64/0.85 tff(115,plain,
% 0.64/0.85 (intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)) = intersection(C!3, difference(B!4, C!3))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[57, 114])).
% 0.64/0.85 tff(116,plain,
% 0.64/0.85 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3)))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[115])).
% 0.64/0.85 tff(117,plain,
% 0.64/0.85 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))),
% 0.64/0.85 inference(symmetry,[status(thm)],[116])).
% 0.64/0.85 tff(118,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3)))) | (member(tptp_fun_D_2(C!3, intersection(difference(B!4, C!3), B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(C!3, intersection(difference(B!4, C!3), B!4)), intersection(C!3, difference(B!4, C!3)))))) | (~((intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3)))))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(119,plain,
% 0.64/0.85 (~((~((~(intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3)))) | (member(tptp_fun_D_2(C!3, intersection(difference(B!4, C!3), B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(C!3, intersection(difference(B!4, C!3), B!4)), intersection(C!3, difference(B!4, C!3)))))) | (~((intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3))))))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[118, 18])).
% 0.64/0.85 tff(120,plain,
% 0.64/0.85 (((~((~(intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3)))) | (member(tptp_fun_D_2(C!3, intersection(difference(B!4, C!3), B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(C!3, intersection(difference(B!4, C!3), B!4)), intersection(C!3, difference(B!4, C!3)))))) | (~((intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3)))))))) | ((intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3))))))),
% 0.64/0.85 inference(tautology,[status(thm)],[])).
% 0.64/0.85 tff(121,plain,
% 0.64/0.85 ((intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3)))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.64/0.85 tff(122,plain,
% 0.64/0.85 ((empty_set = intersection(difference(B!4, C!3), C!3)) <=> (intersection(difference(B!4, C!3), C!3) = empty_set)),
% 0.64/0.85 inference(commutativity,[status(thm)],[])).
% 0.64/0.85 tff(123,plain,
% 0.64/0.85 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(124,plain,
% 0.64/0.85 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[123])).
% 0.64/0.85 tff(125,plain,
% 0.64/0.85 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(126,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.64/0.85 tff(127,plain,
% 0.64/0.85 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.64/0.85 tff(128,plain,(
% 0.64/0.85 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.64/0.85 inference(skolemize,[status(sab)],[127])).
% 0.64/0.85 tff(129,plain,
% 0.64/0.85 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.64/0.85 tff(130,plain,
% 0.64/0.85 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(difference(B!4, C!3), C!3) = intersection(C!3, difference(B!4, C!3)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(131,plain,
% 0.64/0.85 (intersection(difference(B!4, C!3), C!3) = intersection(C!3, difference(B!4, C!3))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.64/0.85 tff(132,plain,
% 0.64/0.85 (intersection(C!3, difference(B!4, C!3)) = intersection(difference(B!4, C!3), C!3)),
% 0.64/0.85 inference(symmetry,[status(thm)],[131])).
% 0.64/0.85 tff(133,assumption,(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))), introduced(assumption)).
% 0.64/0.85 tff(134,plain,
% 0.64/0.85 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(135,plain,
% 0.64/0.85 ((~(((~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), C!3)) | member(tptp_fun_D_2(difference(C!3, C!3), empty_set), C!3)) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3)))) <=> (~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(136,plain,
% 0.64/0.85 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), C!3)) | member(tptp_fun_D_2(difference(C!3, C!3), empty_set), C!3)) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[135])).
% 0.64/0.85 tff(137,plain,
% 0.64/0.85 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), C!3)) | member(tptp_fun_D_2(difference(C!3, C!3), empty_set), C!3)) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[136, 134])).
% 0.64/0.85 tff(138,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), C!3)) | member(tptp_fun_D_2(difference(C!3, C!3), empty_set), C!3)) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(139,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.64/0.85 tff(140,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[139, 83, 133])).
% 0.64/0.85 tff(141,plain,(~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(142,assumption,(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set)), introduced(assumption)).
% 0.64/0.85 tff(143,plain,
% 0.64/0.85 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(144,plain,
% 0.64/0.85 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[143])).
% 0.64/0.85 tff(145,plain,
% 0.64/0.85 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(146,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.64/0.85 tff(147,plain,
% 0.64/0.85 (![B: $i] : (~member(B, empty_set))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.64/0.85 tff(148,plain,(
% 0.64/0.85 ![B: $i] : (~member(B, empty_set))),
% 0.64/0.85 inference(skolemize,[status(sab)],[147])).
% 0.64/0.85 tff(149,plain,
% 0.64/0.85 (![B: $i] : (~member(B, empty_set))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.64/0.85 tff(150,plain,
% 0.64/0.85 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(151,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[150, 149, 142])).
% 0.64/0.85 tff(152,plain,(~member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(153,plain,
% 0.64/0.85 ((member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))) | member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) | member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))),
% 0.64/0.85 inference(tautology,[status(thm)],[])).
% 0.64/0.85 tff(154,plain,
% 0.64/0.85 ((member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))) | member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.64/0.85 tff(155,plain,
% 0.64/0.85 (member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[154, 141])).
% 0.64/0.85 tff(156,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(empty_set = difference(C!3, C!3))) | (member(C!3, empty_set) <=> member(C!3, difference(C!3, C!3))))) | (~((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(157,plain,
% 0.64/0.85 (~((~((~(empty_set = difference(C!3, C!3))) | (member(C!3, empty_set) <=> member(C!3, difference(C!3, C!3))))) | (~((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3)))))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[156, 18])).
% 0.64/0.85 tff(158,plain,
% 0.64/0.85 (((~((~(empty_set = difference(C!3, C!3))) | (member(C!3, empty_set) <=> member(C!3, difference(C!3, C!3))))) | (~((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))))) | ((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3)))))),
% 0.64/0.85 inference(tautology,[status(thm)],[])).
% 0.64/0.85 tff(159,plain,
% 0.64/0.85 ((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.64/0.85 tff(160,plain,
% 0.64/0.85 ((~((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3)))))) | (empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(tautology,[status(thm)],[])).
% 0.64/0.85 tff(161,plain,
% 0.64/0.85 ((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_2(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_2(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.64/0.85 tff(162,plain,
% 0.64/0.85 (empty_set = difference(C!3, C!3)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[161, 155])).
% 0.64/0.85 tff(163,plain,
% 0.64/0.85 (difference(C!3, C!3) = empty_set),
% 0.64/0.85 inference(symmetry,[status(thm)],[162])).
% 0.64/0.85 tff(164,plain,
% 0.64/0.85 (intersection(B!4, difference(C!3, C!3)) = intersection(B!4, empty_set)),
% 0.64/0.85 inference(monotonicity,[status(thm)],[163])).
% 0.64/0.85 tff(165,plain,
% 0.64/0.85 (member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, difference(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[164])).
% 0.64/0.85 tff(166,plain,
% 0.64/0.85 (member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set)) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, difference(C!3, C!3)))),
% 0.64/0.85 inference(symmetry,[status(thm)],[165])).
% 0.64/0.85 tff(167,assumption,(~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set)))), introduced(assumption)).
% 0.64/0.85 tff(168,plain,
% 0.64/0.85 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(169,plain,
% 0.64/0.85 (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[168, 149])).
% 0.64/0.85 tff(170,plain,
% 0.64/0.85 ((member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))) | member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) | member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))),
% 0.64/0.85 inference(tautology,[status(thm)],[])).
% 0.64/0.85 tff(171,plain,
% 0.64/0.85 (member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[170, 169, 167])).
% 0.64/0.85 tff(172,plain,
% 0.64/0.85 (member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, difference(C!3, C!3)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[171, 166])).
% 0.64/0.85 tff(173,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), B!4))) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, difference(C!3, C!3)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(174,plain,
% 0.64/0.85 (~(((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), B!4))) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, difference(C!3, C!3))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[173, 33])).
% 0.64/0.85 tff(175,plain,
% 0.64/0.85 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(176,plain,
% 0.64/0.85 ((~(((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), C!3)) | member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), C!3)) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3)))) <=> (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(177,plain,
% 0.64/0.85 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), C!3)) | member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), C!3)) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[176])).
% 0.64/0.85 tff(178,plain,
% 0.64/0.85 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), C!3)) | member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), C!3)) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[177, 175])).
% 0.64/0.85 tff(179,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), C!3)) | member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), C!3)) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(180,plain,
% 0.64/0.85 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.64/0.85 tff(181,plain,
% 0.64/0.85 (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[180, 83])).
% 0.64/0.85 tff(182,plain,
% 0.64/0.85 (((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), B!4))) | member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))),
% 0.64/0.85 inference(tautology,[status(thm)],[])).
% 0.64/0.85 tff(183,plain,
% 0.64/0.85 ((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), B!4))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.64/0.85 tff(184,plain,
% 0.64/0.85 ((((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), B!4))) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, difference(C!3, C!3)))) | (~((~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), difference(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), B!4)))) | (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, difference(C!3, C!3))))),
% 0.64/0.86 inference(tautology,[status(thm)],[])).
% 0.64/0.86 tff(185,plain,
% 0.64/0.86 (~member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, difference(C!3, C!3)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[184, 183, 174])).
% 0.64/0.86 tff(186,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[185, 172])).
% 0.64/0.86 tff(187,plain,(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(188,plain,
% 0.64/0.86 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(empty_set = intersection(B!4, empty_set))) | (member(tptp_fun_D_2(C!3, B!4), empty_set) <=> member(tptp_fun_D_2(C!3, B!4), intersection(B!4, empty_set))))) | (~((empty_set = intersection(B!4, empty_set)) | (~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(189,plain,
% 0.64/0.86 (~((~((~(empty_set = intersection(B!4, empty_set))) | (member(tptp_fun_D_2(C!3, B!4), empty_set) <=> member(tptp_fun_D_2(C!3, B!4), intersection(B!4, empty_set))))) | (~((empty_set = intersection(B!4, empty_set)) | (~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set)))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[188, 18])).
% 0.64/0.86 tff(190,plain,
% 0.64/0.86 (((~((~(empty_set = intersection(B!4, empty_set))) | (member(tptp_fun_D_2(C!3, B!4), empty_set) <=> member(tptp_fun_D_2(C!3, B!4), intersection(B!4, empty_set))))) | (~((empty_set = intersection(B!4, empty_set)) | (~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))))))) | ((empty_set = intersection(B!4, empty_set)) | (~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set)))))),
% 0.64/0.86 inference(tautology,[status(thm)],[])).
% 0.64/0.86 tff(191,plain,
% 0.64/0.86 ((empty_set = intersection(B!4, empty_set)) | (~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.64/0.86 tff(192,plain,
% 0.64/0.86 ((~((empty_set = intersection(B!4, empty_set)) | (~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set)))))) | (empty_set = intersection(B!4, empty_set)) | (~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))))),
% 0.64/0.86 inference(tautology,[status(thm)],[])).
% 0.64/0.86 tff(193,plain,
% 0.64/0.86 ((empty_set = intersection(B!4, empty_set)) | (~(member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), empty_set) <=> member(tptp_fun_D_2(intersection(B!4, empty_set), empty_set), intersection(B!4, empty_set))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.64/0.86 tff(194,plain,
% 0.64/0.86 (empty_set = intersection(B!4, empty_set)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[193, 187])).
% 0.64/0.86 tff(195,plain,
% 0.64/0.86 (intersection(B!4, empty_set) = empty_set),
% 0.64/0.86 inference(symmetry,[status(thm)],[194])).
% 0.64/0.86 tff(196,plain,
% 0.64/0.86 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, empty_set) = intersection(empty_set, B!4))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(197,plain,
% 0.64/0.86 (intersection(B!4, empty_set) = intersection(empty_set, B!4)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[196, 129])).
% 0.64/0.86 tff(198,plain,
% 0.64/0.86 (intersection(empty_set, B!4) = intersection(B!4, empty_set)),
% 0.64/0.86 inference(symmetry,[status(thm)],[197])).
% 0.64/0.86 tff(199,plain,
% 0.64/0.86 (intersection(empty_set, B!4) = empty_set),
% 0.64/0.86 inference(transitivity,[status(thm)],[198, 195])).
% 0.64/0.86 tff(200,plain,
% 0.64/0.86 ((intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) <=> (empty_set = intersection(difference(B!4, C!3), C!3))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[199, 132])).
% 0.64/0.86 tff(201,plain,
% 0.64/0.86 ((intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) <=> (intersection(difference(B!4, C!3), C!3) = empty_set)),
% 0.64/0.86 inference(transitivity,[status(thm)],[200, 122])).
% 0.64/0.86 tff(202,plain,
% 0.64/0.86 ((intersection(difference(B!4, C!3), C!3) = empty_set) <=> (intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3)))),
% 0.64/0.86 inference(symmetry,[status(thm)],[201])).
% 0.64/0.86 tff(203,plain,
% 0.64/0.86 ((~(intersection(difference(B!4, C!3), C!3) = empty_set)) <=> (~(intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[202])).
% 0.64/0.86 tff(204,plain,
% 0.64/0.86 ((~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)) <=> (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(205,axiom,(~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_intersection_difference_empty_set')).
% 0.64/0.86 tff(206,plain,
% 0.64/0.86 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.64/0.86 tff(207,plain,
% 0.64/0.86 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[206, 204])).
% 0.64/0.86 tff(208,plain,
% 0.64/0.86 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[207, 204])).
% 0.64/0.86 tff(209,plain,
% 0.64/0.86 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.64/0.86 tff(210,plain,(
% 0.64/0.86 ~(intersection(difference(B!4, C!3), C!3) = empty_set)),
% 0.64/0.86 inference(skolemize,[status(sab)],[209])).
% 0.64/0.86 tff(211,plain,
% 0.64/0.86 (~(intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.64/0.86 tff(212,plain,
% 0.64/0.86 ((~((intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3))))))) | (intersection(empty_set, B!4) = intersection(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3)))))),
% 0.64/0.86 inference(tautology,[status(thm)],[])).
% 0.64/0.86 tff(213,plain,
% 0.64/0.86 (~(member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[212, 211, 121])).
% 0.64/0.86 tff(214,plain,
% 0.64/0.86 (empty_set = intersection(empty_set, B!4)),
% 0.64/0.86 inference(transitivity,[status(thm)],[194, 197])).
% 0.64/0.86 tff(215,plain,
% 0.64/0.86 (member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), empty_set) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[214])).
% 0.71/0.86 tff(216,plain,
% 0.71/0.86 (member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), empty_set)),
% 0.71/0.86 inference(symmetry,[status(thm)],[215])).
% 0.71/0.86 tff(217,assumption,(~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4)))), introduced(assumption)).
% 0.71/0.86 tff(218,plain,
% 0.71/0.86 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(219,plain,
% 0.71/0.86 ((~(((~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), B!4)) | member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)))) <=> (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(220,plain,
% 0.71/0.86 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), B!4)) | member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[219])).
% 0.71/0.86 tff(221,plain,
% 0.71/0.86 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), B!4)) | member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4))))),
% 0.71/0.86 inference(transitivity,[status(thm)],[220, 218])).
% 0.71/0.86 tff(222,plain,
% 0.71/0.86 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), B!4)) | member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(223,plain,
% 0.71/0.86 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.71/0.86 tff(224,plain,
% 0.71/0.86 (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[223, 83])).
% 0.71/0.86 tff(225,plain,
% 0.71/0.86 ((member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))) | member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) | member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(226,plain,
% 0.71/0.86 (member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[225, 224, 217])).
% 0.71/0.86 tff(227,plain,
% 0.71/0.86 (member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), empty_set)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[226, 216])).
% 0.71/0.86 tff(228,plain,
% 0.71/0.86 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), empty_set))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(229,plain,
% 0.71/0.86 (~member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), empty_set)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[228, 149])).
% 0.71/0.86 tff(230,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[229, 227])).
% 0.71/0.86 tff(231,plain,(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(232,plain,
% 0.71/0.86 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))))) | (~((~((~(difference(B!4, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_2(B!4, intersection(empty_set, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(B!4, intersection(empty_set, B!4)), intersection(empty_set, B!4))))) | (~((difference(B!4, B!4) = intersection(empty_set, B!4)) | (~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))))))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(233,plain,
% 0.71/0.86 (~((~((~(difference(B!4, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_2(B!4, intersection(empty_set, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(B!4, intersection(empty_set, B!4)), intersection(empty_set, B!4))))) | (~((difference(B!4, B!4) = intersection(empty_set, B!4)) | (~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4)))))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[232, 18])).
% 0.71/0.86 tff(234,plain,
% 0.71/0.86 (((~((~(difference(B!4, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_2(B!4, intersection(empty_set, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(B!4, intersection(empty_set, B!4)), intersection(empty_set, B!4))))) | (~((difference(B!4, B!4) = intersection(empty_set, B!4)) | (~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))))))) | ((difference(B!4, B!4) = intersection(empty_set, B!4)) | (~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4)))))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(235,plain,
% 0.71/0.86 ((difference(B!4, B!4) = intersection(empty_set, B!4)) | (~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.71/0.86 tff(236,plain,
% 0.71/0.86 ((~((difference(B!4, B!4) = intersection(empty_set, B!4)) | (~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4)))))) | (difference(B!4, B!4) = intersection(empty_set, B!4)) | (~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(237,plain,
% 0.71/0.86 ((difference(B!4, B!4) = intersection(empty_set, B!4)) | (~(member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), difference(B!4, B!4)) <=> member(tptp_fun_D_2(intersection(empty_set, B!4), difference(B!4, B!4)), intersection(empty_set, B!4))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.71/0.86 tff(238,plain,
% 0.71/0.86 (difference(B!4, B!4) = intersection(empty_set, B!4)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[237, 231])).
% 0.71/0.86 tff(239,plain,
% 0.71/0.86 (intersection(empty_set, B!4) = difference(B!4, B!4)),
% 0.71/0.86 inference(symmetry,[status(thm)],[238])).
% 0.71/0.86 tff(240,plain,
% 0.71/0.86 (empty(intersection(empty_set, B!4)) <=> empty(difference(B!4, B!4))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[239])).
% 0.71/0.86 tff(241,plain,
% 0.71/0.86 (empty(difference(B!4, B!4)) <=> empty(intersection(empty_set, B!4))),
% 0.71/0.86 inference(symmetry,[status(thm)],[240])).
% 0.71/0.86 tff(242,assumption,(member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))), introduced(assumption)).
% 0.71/0.86 tff(243,plain,
% 0.71/0.86 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(244,plain,
% 0.71/0.86 ((~(((~member(tptp_fun_C_1(difference(B!4, B!4)), B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), B!4)) <=> member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))) <=> (~member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(245,plain,
% 0.71/0.86 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_C_1(difference(B!4, B!4)), B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), B!4)) <=> member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[244])).
% 0.71/0.86 tff(246,plain,
% 0.71/0.86 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_C_1(difference(B!4, B!4)), B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), B!4)) <=> member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))))),
% 0.71/0.86 inference(transitivity,[status(thm)],[245, 243])).
% 0.71/0.86 tff(247,plain,
% 0.71/0.86 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_C_1(difference(B!4, B!4)), B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), B!4)) <=> member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(248,plain,
% 0.71/0.86 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.71/0.86 tff(249,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[248, 83, 242])).
% 0.71/0.86 tff(250,plain,(~member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(251,plain,
% 0.71/0.86 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B)))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(252,plain,
% 0.71/0.86 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> ![B: $i] : (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[251])).
% 0.71/0.86 tff(253,plain,
% 0.71/0.86 (^[B: $i] : refl((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(254,plain,
% 0.71/0.86 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[253])).
% 0.71/0.86 tff(255,plain,
% 0.71/0.86 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(256,plain,
% 0.71/0.86 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[255])).
% 0.71/0.86 tff(257,plain,
% 0.71/0.86 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.71/0.86 inference(transitivity,[status(thm)],[256, 254])).
% 0.71/0.86 tff(258,plain,
% 0.71/0.86 (^[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_1(B), B))) <=> (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))))), rewrite((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(259,plain,
% 0.71/0.86 (![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[258])).
% 0.71/0.86 tff(260,plain,
% 0.71/0.86 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B))) <=> ![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(261,axiom,(![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_defn')).
% 0.71/0.86 tff(262,plain,
% 0.71/0.86 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.71/0.86 tff(263,plain,(
% 0.71/0.86 ![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_1(B), B)))),
% 0.71/0.86 inference(skolemize,[status(sab)],[262])).
% 0.71/0.86 tff(264,plain,
% 0.71/0.86 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.71/0.86 tff(265,plain,
% 0.71/0.86 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_1(B), B)))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[264, 257])).
% 0.71/0.86 tff(266,plain,
% 0.71/0.86 (![B: $i] : (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[265, 252])).
% 0.71/0.86 tff(267,plain,
% 0.71/0.86 ((~![B: $i] : (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))) | (~((~(empty(difference(B!4, B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))) | (~((~empty(difference(B!4, B!4))) | ![C: $i] : (~member(C, difference(B!4, B!4)))))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(268,plain,
% 0.71/0.86 (~((~(empty(difference(B!4, B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))) | (~((~empty(difference(B!4, B!4))) | ![C: $i] : (~member(C, difference(B!4, B!4))))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.71/0.86 tff(269,plain,
% 0.71/0.86 (((~(empty(difference(B!4, B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))) | (~((~empty(difference(B!4, B!4))) | ![C: $i] : (~member(C, difference(B!4, B!4)))))) | (empty(difference(B!4, B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(270,plain,
% 0.71/0.86 (empty(difference(B!4, B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[269, 268])).
% 0.71/0.86 tff(271,plain,
% 0.71/0.86 ((~(empty(difference(B!4, B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4)))) | empty(difference(B!4, B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(272,plain,
% 0.71/0.86 (empty(difference(B!4, B!4)) | member(tptp_fun_C_1(difference(B!4, B!4)), difference(B!4, B!4))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.71/0.86 tff(273,plain,
% 0.71/0.86 (empty(difference(B!4, B!4))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[272, 250])).
% 0.71/0.86 tff(274,plain,
% 0.71/0.86 (empty(intersection(empty_set, B!4))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[273, 241])).
% 0.71/0.86 tff(275,plain,
% 0.71/0.86 ((~![B: $i] : (~((~(empty(B) | member(tptp_fun_C_1(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))) | (~((~(empty(intersection(empty_set, B!4)) | member(tptp_fun_C_1(intersection(empty_set, B!4)), intersection(empty_set, B!4)))) | (~((~empty(intersection(empty_set, B!4))) | ![C: $i] : (~member(C, intersection(empty_set, B!4)))))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(276,plain,
% 0.71/0.86 (~((~(empty(intersection(empty_set, B!4)) | member(tptp_fun_C_1(intersection(empty_set, B!4)), intersection(empty_set, B!4)))) | (~((~empty(intersection(empty_set, B!4))) | ![C: $i] : (~member(C, intersection(empty_set, B!4))))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[275, 266])).
% 0.71/0.86 tff(277,plain,
% 0.71/0.86 (((~(empty(intersection(empty_set, B!4)) | member(tptp_fun_C_1(intersection(empty_set, B!4)), intersection(empty_set, B!4)))) | (~((~empty(intersection(empty_set, B!4))) | ![C: $i] : (~member(C, intersection(empty_set, B!4)))))) | ((~empty(intersection(empty_set, B!4))) | ![C: $i] : (~member(C, intersection(empty_set, B!4))))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(278,plain,
% 0.71/0.86 ((~empty(intersection(empty_set, B!4))) | ![C: $i] : (~member(C, intersection(empty_set, B!4)))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[277, 276])).
% 0.71/0.86 tff(279,plain,
% 0.71/0.86 ((~((~empty(intersection(empty_set, B!4))) | ![C: $i] : (~member(C, intersection(empty_set, B!4))))) | (~empty(intersection(empty_set, B!4))) | ![C: $i] : (~member(C, intersection(empty_set, B!4)))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(280,plain,
% 0.71/0.86 ((~empty(intersection(empty_set, B!4))) | ![C: $i] : (~member(C, intersection(empty_set, B!4)))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[279, 278])).
% 0.71/0.86 tff(281,plain,
% 0.71/0.86 (![C: $i] : (~member(C, intersection(empty_set, B!4)))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[280, 274])).
% 0.71/0.86 tff(282,plain,
% 0.71/0.86 ((~![C: $i] : (~member(C, intersection(empty_set, B!4)))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(283,plain,
% 0.71/0.86 (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.71/0.86 tff(284,plain,
% 0.71/0.86 ((member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(empty_set, B!4)) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3)))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(285,plain,
% 0.71/0.86 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, difference(B!4, C!3)))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[284, 283, 213])).
% 0.71/0.86 tff(286,plain,
% 0.71/0.86 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[285, 117])).
% 0.71/0.86 tff(287,plain,
% 0.71/0.86 ((((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4)))) | (~((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(intersection(C!3, C!3), intersection(difference(B!4, C!3), B!4))))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(288,plain,
% 0.71/0.86 (~((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[287, 286, 113])).
% 0.71/0.86 tff(289,plain,
% 0.71/0.86 (((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(290,plain,
% 0.71/0.86 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.71/0.86 tff(291,plain,
% 0.71/0.86 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[290, 103])).
% 0.71/0.86 tff(292,plain,
% 0.71/0.86 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), B!4)) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3)))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(293,plain,
% 0.71/0.86 (~(((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), B!4)) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[292, 83])).
% 0.71/0.86 tff(294,plain,
% 0.71/0.86 (((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(difference(B!4, C!3), B!4)))) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(295,plain,
% 0.71/0.87 (member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[294, 288])).
% 0.71/0.87 tff(296,plain,
% 0.71/0.87 (((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), B!4)) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3)))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(297,plain,
% 0.71/0.87 ((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), B!4)) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.71/0.87 tff(298,plain,
% 0.71/0.87 ((((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), B!4)) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3)))) | (~((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), B!4)) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3)))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3))))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(299,plain,
% 0.71/0.87 ((((~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), B!4)) | member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3)))) | (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[298, 297])).
% 0.71/0.87 tff(300,plain,
% 0.71/0.87 (~member(tptp_fun_D_2(intersection(C!3, difference(B!4, C!3)), intersection(empty_set, B!4)), difference(B!4, intersection(C!3, C!3)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[299, 293])).
% 0.71/0.87 tff(301,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[300, 291])).
% 0.71/0.87 % SZS output end Proof
% 0.71/0.87 % E exiting
%------------------------------------------------------------------------------