%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET611+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:00 AM UTC 2025
% Result : Theorem 2.66s 2.87s
% Output : Proof 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET611+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:31:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.66/2.87 % SZS status Theorem
% 2.66/2.87 % SZS output start Proof
% 2.66/2.87 tff(empty_set_type, type, (
% 2.66/2.87 empty_set: $i)).
% 2.66/2.87 tff(intersection_type, type, (
% 2.66/2.87 intersection: ( $i * $i ) > $i)).
% 2.66/2.87 tff(tptp_fun_C_3_type, type, (
% 2.66/2.87 tptp_fun_C_3: $i)).
% 2.66/2.87 tff(tptp_fun_B_4_type, type, (
% 2.66/2.87 tptp_fun_B_4: $i)).
% 2.66/2.87 tff(difference_type, type, (
% 2.66/2.87 difference: ( $i * $i ) > $i)).
% 2.66/2.87 tff(member_type, type, (
% 2.66/2.87 member: ( $i * $i ) > $o)).
% 2.66/2.87 tff(tptp_fun_D_0_type, type, (
% 2.66/2.87 tptp_fun_D_0: ( $i * $i ) > $i)).
% 2.66/2.87 tff(tptp_fun_D_1_type, type, (
% 2.66/2.87 tptp_fun_D_1: ( $i * $i ) > $i)).
% 2.66/2.87 tff(empty_type, type, (
% 2.66/2.87 empty: $i > $o)).
% 2.66/2.87 tff(tptp_fun_C_2_type, type, (
% 2.66/2.87 tptp_fun_C_2: $i > $i)).
% 2.66/2.87 tff(1,assumption,(~(member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3)))), introduced(assumption)).
% 2.66/2.87 tff(2,plain,
% 2.66/2.87 (^[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)))))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(3,plain,
% 2.66/2.87 (![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))))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[2])).
% 2.66/2.87 tff(4,plain,
% 2.66/2.87 (^[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))))))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(5,plain,
% 2.66/2.87 (![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))))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[4])).
% 2.66/2.87 tff(6,plain,
% 2.66/2.87 (![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))))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(7,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')).
% 2.66/2.87 tff(8,plain,
% 2.66/2.87 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.66/2.87 tff(9,plain,(
% 2.66/2.87 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 2.66/2.87 inference(skolemize,[status(sab)],[8])).
% 2.66/2.87 tff(10,plain,
% 2.66/2.87 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[9, 5])).
% 2.66/2.87 tff(11,plain,
% 2.66/2.87 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[10, 3])).
% 2.66/2.87 tff(12,plain,
% 2.66/2.87 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(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_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(13,plain,
% 2.66/2.87 ((~(((~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), C!3)) | member(tptp_fun_D_0(difference(C!3, C!3), empty_set), C!3)) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3)))) <=> (~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3)))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(14,plain,
% 2.66/2.87 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), C!3)) | member(tptp_fun_D_0(difference(C!3, C!3), empty_set), C!3)) <=> member(tptp_fun_D_0(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_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 2.66/2.87 inference(monotonicity,[status(thm)],[13])).
% 2.66/2.87 tff(15,plain,
% 2.66/2.87 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), C!3)) | member(tptp_fun_D_0(difference(C!3, C!3), empty_set), C!3)) <=> member(tptp_fun_D_0(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_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 2.66/2.87 inference(transitivity,[status(thm)],[14, 12])).
% 2.66/2.87 tff(16,plain,
% 2.66/2.87 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), C!3)) | member(tptp_fun_D_0(difference(C!3, C!3), empty_set), C!3)) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 2.66/2.87 inference(quant_inst,[status(thm)],[])).
% 2.66/2.87 tff(17,plain,
% 2.66/2.87 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3)))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[16, 15])).
% 2.66/2.87 tff(18,plain,
% 2.66/2.87 (~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[17, 11])).
% 2.66/2.87 tff(19,plain,
% 2.66/2.87 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(20,plain,
% 2.66/2.87 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[19])).
% 2.66/2.87 tff(21,plain,
% 2.66/2.87 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(22,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 2.66/2.87 tff(23,plain,
% 2.66/2.87 (![B: $i] : (~member(B, empty_set))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[22, 21])).
% 2.66/2.87 tff(24,plain,(
% 2.66/2.87 ![B: $i] : (~member(B, empty_set))),
% 2.66/2.87 inference(skolemize,[status(sab)],[23])).
% 2.66/2.87 tff(25,plain,
% 2.66/2.87 (![B: $i] : (~member(B, empty_set))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[24, 20])).
% 2.66/2.87 tff(26,plain,
% 2.66/2.87 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set))),
% 2.66/2.87 inference(quant_inst,[status(thm)],[])).
% 2.66/2.87 tff(27,plain,
% 2.66/2.87 (~member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set)),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[26, 25])).
% 2.66/2.87 tff(28,plain,
% 2.66/2.87 ((member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) | member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(29,plain,
% 2.66/2.87 ($false),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[28, 27, 18, 1])).
% 2.66/2.87 tff(30,plain,(member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.87 tff(31,plain,
% 2.66/2.87 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(32,plain,
% 2.66/2.87 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[31])).
% 2.66/2.87 tff(33,plain,
% 2.66/2.87 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.87 inference(pull_quant,[status(thm)],[])).
% 2.66/2.87 tff(34,plain,
% 2.66/2.87 (^[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_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(35,plain,
% 2.66/2.87 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[34])).
% 2.66/2.87 tff(36,plain,
% 2.66/2.87 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.88 inference(transitivity,[status(thm)],[35, 33])).
% 2.66/2.88 tff(37,plain,
% 2.66/2.88 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.88 inference(transitivity,[status(thm)],[36, 32])).
% 2.66/2.88 tff(38,plain,
% 2.66/2.88 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 2.66/2.88 inference(bind,[status(th)],[])).
% 2.66/2.88 tff(39,plain,
% 2.66/2.88 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.88 inference(quant_intro,[status(thm)],[38])).
% 2.66/2.88 tff(40,plain,
% 2.66/2.88 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.88 inference(transitivity,[status(thm)],[39, 37])).
% 2.66/2.88 tff(41,plain,
% 2.66/2.88 (^[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_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) <=> (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))))),
% 2.66/2.88 inference(bind,[status(th)],[])).
% 2.66/2.88 tff(42,plain,
% 2.66/2.88 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.88 inference(quant_intro,[status(thm)],[41])).
% 2.66/2.88 tff(43,plain,
% 2.66/2.88 (![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)))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(44,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')).
% 2.66/2.88 tff(45,plain,
% 2.66/2.88 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.66/2.88 tff(46,plain,(
% 2.66/2.88 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))),
% 2.66/2.88 inference(skolemize,[status(sab)],[45])).
% 2.66/2.88 tff(47,plain,
% 2.66/2.88 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[46, 42])).
% 2.66/2.88 tff(48,plain,
% 2.66/2.88 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[47, 40])).
% 2.66/2.88 tff(49,plain,
% 2.66/2.88 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(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_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))))))),
% 2.66/2.88 inference(quant_inst,[status(thm)],[])).
% 2.66/2.88 tff(50,plain,
% 2.66/2.88 (~((~((~(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_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3)))))))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[49, 48])).
% 2.66/2.88 tff(51,plain,
% 2.66/2.88 (((~((~(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_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))))) | ((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3)))))),
% 2.66/2.88 inference(tautology,[status(thm)],[])).
% 2.66/2.88 tff(52,plain,
% 2.66/2.88 ((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[51, 50])).
% 2.66/2.88 tff(53,plain,
% 2.66/2.88 ((~((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3)))))) | (empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 2.66/2.88 inference(tautology,[status(thm)],[])).
% 2.66/2.88 tff(54,plain,
% 2.66/2.88 ((empty_set = difference(C!3, C!3)) | (~(member(tptp_fun_D_0(difference(C!3, C!3), empty_set), empty_set) <=> member(tptp_fun_D_0(difference(C!3, C!3), empty_set), difference(C!3, C!3))))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[53, 52])).
% 2.66/2.88 tff(55,plain,
% 2.66/2.88 (empty_set = difference(C!3, C!3)),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[54, 30])).
% 2.66/2.88 tff(56,plain,
% 2.66/2.88 (difference(C!3, C!3) = empty_set),
% 2.66/2.88 inference(symmetry,[status(thm)],[55])).
% 2.66/2.88 tff(57,assumption,(~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))), introduced(assumption)).
% 2.66/2.88 tff(58,plain,
% 2.66/2.88 (^[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)))))),
% 2.66/2.88 inference(bind,[status(th)],[])).
% 2.66/2.88 tff(59,plain,
% 2.66/2.88 (![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))))),
% 2.66/2.88 inference(quant_intro,[status(thm)],[58])).
% 2.66/2.88 tff(60,plain,
% 2.66/2.88 (^[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))))))),
% 2.66/2.88 inference(bind,[status(th)],[])).
% 2.66/2.88 tff(61,plain,
% 2.66/2.88 (![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))))),
% 2.66/2.88 inference(quant_intro,[status(thm)],[60])).
% 2.66/2.88 tff(62,plain,
% 2.66/2.88 (![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)))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(63,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')).
% 2.66/2.88 tff(64,plain,
% 2.66/2.88 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.66/2.88 tff(65,plain,(
% 2.66/2.88 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 2.66/2.88 inference(skolemize,[status(sab)],[64])).
% 2.66/2.88 tff(66,plain,
% 2.66/2.88 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[65, 61])).
% 2.66/2.88 tff(67,plain,
% 2.66/2.88 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[66, 59])).
% 2.66/2.88 tff(68,plain,
% 2.66/2.88 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), tptp_fun_D_1(C!3, difference(C!3, C!3))))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)))))),
% 2.66/2.88 inference(quant_inst,[status(thm)],[])).
% 2.66/2.88 tff(69,plain,
% 2.66/2.88 (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), tptp_fun_D_1(C!3, difference(C!3, C!3))))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[68, 67])).
% 2.66/2.88 tff(70,assumption,(member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3))), introduced(assumption)).
% 2.66/2.88 tff(71,plain,
% 2.66/2.88 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_C_2(difference(C!3, C!3)), 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_C_2(difference(C!3, C!3)), difference(C!3, C!3))))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(72,plain,
% 2.66/2.88 ((~(((~member(tptp_fun_C_2(difference(C!3, C!3)), C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), C!3)) <=> member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))) <=> (~member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(73,plain,
% 2.66/2.88 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_C_2(difference(C!3, C!3)), C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), C!3)) <=> member(tptp_fun_C_2(difference(C!3, C!3)), 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_C_2(difference(C!3, C!3)), difference(C!3, C!3))))),
% 2.66/2.88 inference(monotonicity,[status(thm)],[72])).
% 2.66/2.88 tff(74,plain,
% 2.66/2.88 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_C_2(difference(C!3, C!3)), C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), C!3)) <=> member(tptp_fun_C_2(difference(C!3, C!3)), 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_C_2(difference(C!3, C!3)), difference(C!3, C!3))))),
% 2.66/2.88 inference(transitivity,[status(thm)],[73, 71])).
% 2.66/2.88 tff(75,plain,
% 2.66/2.88 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_C_2(difference(C!3, C!3)), C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), C!3)) <=> member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3))))),
% 2.66/2.88 inference(quant_inst,[status(thm)],[])).
% 2.66/2.88 tff(76,plain,
% 2.66/2.88 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.66/2.88 tff(77,plain,
% 2.66/2.88 ($false),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[76, 11, 70])).
% 2.66/2.88 tff(78,plain,(~member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.88 tff(79,plain,
% 2.66/2.88 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B)))))))),
% 2.66/2.88 inference(bind,[status(th)],[])).
% 2.66/2.88 tff(80,plain,
% 2.66/2.88 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 2.66/2.88 inference(quant_intro,[status(thm)],[79])).
% 2.66/2.88 tff(81,plain,
% 2.66/2.88 (^[B: $i] : refl((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))))),
% 2.66/2.88 inference(bind,[status(th)],[])).
% 2.66/2.88 tff(82,plain,
% 2.66/2.88 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 2.66/2.88 inference(quant_intro,[status(thm)],[81])).
% 2.66/2.88 tff(83,plain,
% 2.66/2.88 (^[B: $i] : rewrite((~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))))),
% 2.66/2.88 inference(bind,[status(th)],[])).
% 2.66/2.88 tff(84,plain,
% 2.66/2.88 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 2.66/2.88 inference(quant_intro,[status(thm)],[83])).
% 2.66/2.88 tff(85,plain,
% 2.66/2.88 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B))))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 2.66/2.88 inference(transitivity,[status(thm)],[84, 82])).
% 2.66/2.88 tff(86,plain,
% 2.66/2.88 (^[B: $i] : trans(monotonicity(rewrite(((~empty(B)) | ![C: $i] : (~member(C, B))) <=> ((~empty(B)) | ![C: $i] : (~member(C, B)))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))))), rewrite((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))), ((((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))))),
% 2.66/2.88 inference(bind,[status(th)],[])).
% 2.66/2.88 tff(87,plain,
% 2.66/2.88 (![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B))) <=> ![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 2.66/2.88 inference(quant_intro,[status(thm)],[86])).
% 2.66/2.88 tff(88,plain,
% 2.66/2.88 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B))) <=> ![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(89,axiom,(![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_defn')).
% 2.66/2.88 tff(90,plain,
% 2.66/2.88 (![B: $i] : (empty(B) <=> ![C: $i] : (~member(C, B)))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[89, 88])).
% 2.66/2.88 tff(91,plain,(
% 2.66/2.88 ![B: $i] : (((~empty(B)) | ![C: $i] : (~member(C, B))) & (empty(B) | member(tptp_fun_C_2(B), B)))),
% 2.66/2.88 inference(skolemize,[status(sab)],[90])).
% 2.66/2.88 tff(92,plain,
% 2.66/2.88 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[91, 87])).
% 2.66/2.88 tff(93,plain,
% 2.66/2.88 (![B: $i] : (~((~((~empty(B)) | ![C: $i] : (~member(C, B)))) | (~(empty(B) | member(tptp_fun_C_2(B), B)))))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[92, 85])).
% 2.66/2.88 tff(94,plain,
% 2.66/2.88 (![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))),
% 2.66/2.88 inference(modus_ponens,[status(thm)],[93, 80])).
% 2.66/2.88 tff(95,plain,
% 2.66/2.88 ((~![B: $i] : (~((~(empty(B) | member(tptp_fun_C_2(B), B))) | (~((~empty(B)) | ![C: $i] : (~member(C, B))))))) | (~((~(empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))) | (~((~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3)))))))),
% 2.66/2.88 inference(quant_inst,[status(thm)],[])).
% 2.66/2.88 tff(96,plain,
% 2.66/2.88 (~((~(empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))) | (~((~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3))))))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[95, 94])).
% 2.66/2.88 tff(97,plain,
% 2.66/2.88 (((~(empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))) | (~((~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3)))))) | (empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))),
% 2.66/2.88 inference(tautology,[status(thm)],[])).
% 2.66/2.88 tff(98,plain,
% 2.66/2.88 (empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[97, 96])).
% 2.66/2.88 tff(99,plain,
% 2.66/2.88 ((~(empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))) | empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3))),
% 2.66/2.88 inference(tautology,[status(thm)],[])).
% 2.66/2.88 tff(100,plain,
% 2.66/2.88 (empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[99, 98])).
% 2.66/2.88 tff(101,plain,
% 2.66/2.88 (empty(difference(C!3, C!3))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[100, 78])).
% 2.66/2.88 tff(102,plain,
% 2.66/2.88 (((~(empty(difference(C!3, C!3)) | member(tptp_fun_C_2(difference(C!3, C!3)), difference(C!3, C!3)))) | (~((~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3)))))) | ((~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3))))),
% 2.66/2.88 inference(tautology,[status(thm)],[])).
% 2.66/2.88 tff(103,plain,
% 2.66/2.88 ((~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3)))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[102, 96])).
% 2.66/2.88 tff(104,plain,
% 2.66/2.88 ((~((~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3))))) | (~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3)))),
% 2.66/2.88 inference(tautology,[status(thm)],[])).
% 2.66/2.88 tff(105,plain,
% 2.66/2.88 ((~empty(difference(C!3, C!3))) | ![C: $i] : (~member(C, difference(C!3, C!3)))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[104, 103])).
% 2.66/2.88 tff(106,plain,
% 2.66/2.88 (![C: $i] : (~member(C, difference(C!3, C!3)))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[105, 101])).
% 2.66/2.88 tff(107,plain,
% 2.66/2.88 ((~![C: $i] : (~member(C, difference(C!3, C!3)))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))),
% 2.66/2.88 inference(quant_inst,[status(thm)],[])).
% 2.66/2.88 tff(108,plain,
% 2.66/2.88 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[107, 106])).
% 2.66/2.88 tff(109,plain,
% 2.66/2.88 (((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))),
% 2.66/2.88 inference(tautology,[status(thm)],[])).
% 2.66/2.88 tff(110,plain,
% 2.66/2.88 ((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.66/2.88 inference(unit_resolution,[status(thm)],[109, 108])).
% 2.66/2.88 tff(111,assumption,(~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))), introduced(assumption)).
% 2.66/2.88 tff(112,plain,
% 2.66/2.88 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(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_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(113,plain,
% 2.66/2.88 ((~(~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) <=> (member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(114,plain,
% 2.66/2.88 ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) <=> (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(115,plain,
% 2.66/2.88 (((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))) <=> (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(116,plain,
% 2.66/2.88 (((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))),
% 2.66/2.88 inference(rewrite,[status(thm)],[])).
% 2.66/2.88 tff(117,plain,
% 2.66/2.88 ((((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))) <=> ((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))),
% 2.66/2.88 inference(monotonicity,[status(thm)],[116])).
% 2.66/2.88 tff(118,plain,
% 2.66/2.88 ((((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))) <=> (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))),
% 2.66/2.88 inference(transitivity,[status(thm)],[117, 115])).
% 2.66/2.88 tff(119,plain,
% 2.66/2.88 ((((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))) <=> (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))),
% 2.66/2.88 inference(transitivity,[status(thm)],[118, 114])).
% 2.66/2.88 tff(120,plain,
% 2.66/2.88 ((~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) <=> (~(~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))))),
% 2.66/2.89 inference(monotonicity,[status(thm)],[119])).
% 2.66/2.89 tff(121,plain,
% 2.66/2.89 ((~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) <=> (member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))),
% 2.66/2.89 inference(transitivity,[status(thm)],[120, 113])).
% 2.66/2.89 tff(122,plain,
% 2.66/2.89 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(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_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))),
% 2.66/2.89 inference(monotonicity,[status(thm)],[121])).
% 2.66/2.89 tff(123,plain,
% 2.66/2.89 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(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_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))),
% 2.66/2.89 inference(transitivity,[status(thm)],[122, 112])).
% 2.66/2.89 tff(124,plain,
% 2.66/2.89 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))),
% 2.66/2.89 inference(quant_inst,[status(thm)],[])).
% 2.66/2.89 tff(125,plain,
% 2.66/2.89 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))),
% 2.66/2.89 inference(modus_ponens,[status(thm)],[124, 123])).
% 2.66/2.89 tff(126,plain,
% 2.66/2.89 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.66/2.89 inference(unit_resolution,[status(thm)],[125, 67])).
% 2.66/2.89 tff(127,plain,
% 2.66/2.89 ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3)) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))),
% 2.66/2.89 inference(tautology,[status(thm)],[])).
% 2.66/2.89 tff(128,plain,
% 2.66/2.89 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.66/2.89 inference(unit_resolution,[status(thm)],[127, 108, 126])).
% 2.66/2.89 tff(129,plain,
% 2.66/2.89 ((member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.66/2.89 inference(tautology,[status(thm)],[])).
% 2.66/2.89 tff(130,plain,
% 2.66/2.89 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)))),
% 2.66/2.89 inference(unit_resolution,[status(thm)],[129, 128, 111])).
% 2.66/2.89 tff(131,plain,
% 2.66/2.89 ((((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), tptp_fun_D_1(C!3, difference(C!3, C!3))))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)))) | (~((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))))),
% 2.66/2.89 inference(tautology,[status(thm)],[])).
% 2.66/2.89 tff(132,plain,
% 2.66/2.89 ($false),
% 2.66/2.89 inference(unit_resolution,[status(thm)],[131, 130, 110, 69])).
% 2.66/2.89 tff(133,plain,(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.89 tff(134,plain,
% 2.66/2.89 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))))))))),
% 2.74/2.89 inference(rewrite,[status(thm)],[])).
% 2.74/2.89 tff(135,plain,
% 2.74/2.89 ((~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))))))) <=> (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))))))),
% 2.74/2.89 inference(rewrite,[status(thm)],[])).
% 2.74/2.89 tff(136,plain,
% 2.74/2.89 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))))))))),
% 2.74/2.89 inference(monotonicity,[status(thm)],[135])).
% 2.74/2.89 tff(137,plain,
% 2.74/2.89 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))))))))),
% 2.74/2.89 inference(transitivity,[status(thm)],[136, 134])).
% 2.74/2.89 tff(138,plain,
% 2.74/2.89 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3)))))))))),
% 2.74/2.89 inference(quant_inst,[status(thm)],[])).
% 2.74/2.89 tff(139,plain,
% 2.74/2.89 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))))))),
% 2.74/2.89 inference(modus_ponens,[status(thm)],[138, 137])).
% 2.74/2.89 tff(140,plain,
% 2.74/2.89 (~((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))))))),
% 2.74/2.89 inference(unit_resolution,[status(thm)],[139, 48])).
% 2.74/2.89 tff(141,plain,
% 2.74/2.89 (((~((~(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))))),
% 2.74/2.90 inference(tautology,[status(thm)],[])).
% 2.74/2.90 tff(142,plain,
% 2.74/2.90 ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[141, 140])).
% 2.74/2.90 tff(143,plain,
% 2.74/2.90 ((~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(tautology,[status(thm)],[])).
% 2.74/2.90 tff(144,plain,
% 2.74/2.90 ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[143, 142])).
% 2.74/2.90 tff(145,plain,
% 2.74/2.90 (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), difference(C!3, C!3))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[144, 133])).
% 2.74/2.90 tff(146,plain,
% 2.74/2.90 (intersection(difference(C!3, C!3), difference(C!3, C!3)) = intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))),
% 2.74/2.90 inference(symmetry,[status(thm)],[145])).
% 2.74/2.90 tff(147,plain,
% 2.74/2.90 (tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)) = tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[146])).
% 2.74/2.90 tff(148,plain,
% 2.74/2.90 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[147])).
% 2.74/2.90 tff(149,plain,
% 2.74/2.90 (member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))),
% 2.74/2.90 inference(symmetry,[status(thm)],[148])).
% 2.74/2.90 tff(150,plain,
% 2.74/2.90 ((~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))) <=> (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[149])).
% 2.74/2.90 tff(151,plain,
% 2.74/2.90 ((~![C: $i] : (~member(C, difference(C!3, C!3)))) | (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(152,plain,
% 2.74/2.90 (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[151, 106])).
% 2.74/2.90 tff(153,plain,
% 2.74/2.90 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[152, 150])).
% 2.74/2.90 tff(154,plain,
% 2.74/2.90 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[147, 146])).
% 2.74/2.90 tff(155,plain,
% 2.74/2.90 (member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(symmetry,[status(thm)],[154])).
% 2.74/2.90 tff(156,plain,
% 2.74/2.90 ((~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)))) <=> (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[155])).
% 2.74/2.90 tff(157,plain,
% 2.74/2.90 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), tptp_fun_D_1(C!3, difference(C!3, C!3))))) <=> member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(158,plain,
% 2.74/2.90 (~(((~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), tptp_fun_D_1(C!3, difference(C!3, C!3))))) <=> member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[157, 67])).
% 2.74/2.90 tff(159,plain,
% 2.74/2.90 (((~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))),
% 2.74/2.90 inference(tautology,[status(thm)],[])).
% 2.74/2.90 tff(160,plain,
% 2.74/2.90 ((~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[159, 152])).
% 2.74/2.90 tff(161,plain,
% 2.74/2.90 ((((~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), tptp_fun_D_1(C!3, difference(C!3, C!3))))) <=> member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)))) | (~((~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3))) | (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))))),
% 2.74/2.90 inference(tautology,[status(thm)],[])).
% 2.74/2.90 tff(162,plain,
% 2.74/2.90 (~member(tptp_fun_D_0(intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)), intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[161, 160, 158])).
% 2.74/2.90 tff(163,plain,
% 2.74/2.90 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[162, 156])).
% 2.74/2.90 tff(164,plain,
% 2.74/2.90 ((member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(tautology,[status(thm)],[])).
% 2.74/2.90 tff(165,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[164, 163, 153, 57])).
% 2.74/2.90 tff(166,plain,(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(167,plain,
% 2.74/2.90 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(168,plain,
% 2.74/2.90 ((~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))))))) <=> (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(169,plain,
% 2.74/2.90 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[168])).
% 2.74/2.90 tff(170,plain,
% 2.74/2.90 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[169, 167])).
% 2.74/2.90 tff(171,plain,
% 2.74/2.90 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(172,plain,
% 2.74/2.90 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[171, 170])).
% 2.74/2.90 tff(173,plain,
% 2.74/2.90 (~((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[172, 48])).
% 2.74/2.90 tff(174,plain,
% 2.74/2.90 (((~((~(difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))) | (member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(tptp_fun_C_2(B!4), difference(B!4, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))))) | ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))))),
% 2.74/2.90 inference(tautology,[status(thm)],[])).
% 2.74/2.90 tff(175,plain,
% 2.74/2.90 ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[174, 173])).
% 2.74/2.90 tff(176,plain,
% 2.74/2.90 ((~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(tautology,[status(thm)],[])).
% 2.74/2.90 tff(177,plain,
% 2.74/2.90 ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), difference(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), difference(C!3, C!3)), difference(C!3, C!3)), intersection(difference(C!3, C!3), difference(C!3, C!3))))) | (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[176, 175])).
% 2.74/2.90 tff(178,plain,
% 2.74/2.90 (difference(C!3, C!3) = intersection(difference(C!3, C!3), difference(C!3, C!3))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[177, 166])).
% 2.74/2.90 tff(179,plain,
% 2.74/2.90 (intersection(difference(C!3, C!3), difference(C!3, C!3)) = difference(C!3, C!3)),
% 2.74/2.90 inference(symmetry,[status(thm)],[178])).
% 2.74/2.90 tff(180,plain,
% 2.74/2.90 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 2.74/2.90 inference(bind,[status(th)],[])).
% 2.74/2.90 tff(181,plain,
% 2.74/2.90 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.74/2.90 inference(quant_intro,[status(thm)],[180])).
% 2.74/2.91 tff(182,plain,
% 2.74/2.91 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(183,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 2.74/2.91 tff(184,plain,
% 2.74/2.91 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[183, 182])).
% 2.74/2.91 tff(185,plain,(
% 2.74/2.91 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.74/2.91 inference(skolemize,[status(sab)],[184])).
% 2.74/2.91 tff(186,plain,
% 2.74/2.91 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[185, 181])).
% 2.74/2.91 tff(187,plain,
% 2.74/2.91 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(188,plain,
% 2.74/2.91 (intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3)) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[187, 186])).
% 2.74/2.91 tff(189,plain,
% 2.74/2.91 (intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))) = intersection(tptp_fun_D_1(C!3, difference(C!3, C!3)), difference(C!3, C!3))),
% 2.74/2.91 inference(symmetry,[status(thm)],[188])).
% 2.74/2.91 tff(190,plain,
% 2.74/2.91 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(191,plain,
% 2.74/2.91 ((~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))))))) <=> (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(192,plain,
% 2.74/2.91 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[191])).
% 2.74/2.91 tff(193,plain,
% 2.74/2.91 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[192, 190])).
% 2.74/2.91 tff(194,plain,
% 2.74/2.91 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(195,plain,
% 2.74/2.91 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[194, 193])).
% 2.74/2.91 tff(196,plain,
% 2.74/2.91 (~((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[195, 48])).
% 2.74/2.91 tff(197,plain,
% 2.74/2.91 (((~((~(intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | (~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))))) | ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))),
% 2.74/2.91 inference(tautology,[status(thm)],[])).
% 2.74/2.91 tff(198,plain,
% 2.74/2.91 ((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[197, 196])).
% 2.74/2.91 tff(199,assumption,(~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))), introduced(assumption)).
% 2.74/2.91 tff(200,assumption,(~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))), introduced(assumption)).
% 2.74/2.91 tff(201,plain,
% 2.74/2.91 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(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_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(202,plain,
% 2.74/2.91 ((~(~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) <=> (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(203,plain,
% 2.74/2.91 ((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(204,plain,
% 2.74/2.91 (((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(205,plain,
% 2.74/2.91 (((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(206,plain,
% 2.74/2.91 ((((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[205])).
% 2.74/2.91 tff(207,plain,
% 2.74/2.91 ((((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[206, 204])).
% 2.74/2.91 tff(208,plain,
% 2.74/2.91 ((((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) <=> (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[207, 203])).
% 2.74/2.91 tff(209,plain,
% 2.74/2.91 ((~(((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (~(~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[208])).
% 2.74/2.91 tff(210,plain,
% 2.74/2.91 ((~(((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) <=> (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 2.74/2.91 inference(transitivity,[status(thm)],[209, 202])).
% 2.74/2.91 tff(211,plain,
% 2.74/2.91 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_0(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_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[210])).
% 2.74/2.91 tff(212,plain,
% 2.74/2.91 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_0(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_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[211, 201])).
% 2.74/2.91 tff(213,plain,
% 2.74/2.91 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(214,plain,
% 2.74/2.91 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[213, 212])).
% 2.74/2.91 tff(215,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[214, 67, 200])).
% 2.74/2.91 tff(216,plain,(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(217,plain,
% 2.74/2.91 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3)))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(218,plain,
% 2.74/2.91 ((~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))))) <=> (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(219,plain,
% 2.74/2.91 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3)))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[218])).
% 2.74/2.92 tff(220,plain,
% 2.74/2.92 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3)))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[219, 217])).
% 2.74/2.92 tff(221,plain,
% 2.74/2.92 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(222,plain,
% 2.74/2.92 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[221, 220])).
% 2.74/2.92 tff(223,plain,
% 2.74/2.92 (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[222, 48])).
% 2.74/2.92 tff(224,plain,
% 2.74/2.92 (((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_1(difference(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_1(difference(C!3, C!3), C!3), intersection(C!3, C!3))))) | (~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3))))) | ((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3)))),
% 2.74/2.92 inference(tautology,[status(thm)],[])).
% 2.74/2.92 tff(225,plain,
% 2.74/2.92 ((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[224, 223])).
% 2.74/2.92 tff(226,plain,
% 2.74/2.92 ((~((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3)))) | (~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3))),
% 2.74/2.92 inference(tautology,[status(thm)],[])).
% 2.74/2.92 tff(227,plain,
% 2.74/2.92 ((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (C!3 = intersection(C!3, C!3))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[226, 225])).
% 2.74/2.92 tff(228,plain,
% 2.74/2.92 (C!3 = intersection(C!3, C!3)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[227, 216])).
% 2.74/2.92 tff(229,plain,
% 2.74/2.92 (intersection(C!3, C!3) = C!3),
% 2.74/2.92 inference(symmetry,[status(thm)],[228])).
% 2.74/2.92 tff(230,plain,
% 2.74/2.92 (difference(intersection(C!3, C!3), intersection(C!3, C!3)) = difference(C!3, C!3)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[229, 229])).
% 2.74/2.92 tff(231,plain,
% 2.74/2.92 (difference(intersection(C!3, C!3), intersection(C!3, C!3)) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[230, 178, 146, 188])).
% 2.74/2.92 tff(232,plain,
% 2.74/2.92 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[231])).
% 2.74/2.92 tff(233,plain,
% 2.74/2.92 ((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))) <=> (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[232])).
% 2.74/2.92 tff(234,plain,
% 2.74/2.92 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(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_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(235,plain,
% 2.74/2.92 ((~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3))))) <=> (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(236,plain,
% 2.74/2.92 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(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_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[235])).
% 2.74/2.92 tff(237,plain,
% 2.74/2.92 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(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_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[236, 234])).
% 2.74/2.92 tff(238,plain,
% 2.74/2.92 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(239,plain,
% 2.74/2.92 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[238, 237])).
% 2.74/2.92 tff(240,plain,
% 2.74/2.92 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[239, 11])).
% 2.74/2.92 tff(241,plain,
% 2.74/2.92 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[240, 233])).
% 2.74/2.92 tff(242,assumption,(~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))), introduced(assumption)).
% 2.74/2.92 tff(243,plain,
% 2.74/2.92 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(244,plain,
% 2.74/2.92 ((~(~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))) <=> (member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(245,plain,
% 2.74/2.92 ((~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) <=> (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(246,plain,
% 2.74/2.92 (((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) <=> (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(247,plain,
% 2.74/2.92 (((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(248,plain,
% 2.74/2.92 ((((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) <=> ((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[247])).
% 2.74/2.92 tff(249,plain,
% 2.74/2.92 ((((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) <=> (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[248, 246])).
% 2.74/2.92 tff(250,plain,
% 2.74/2.92 ((((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) <=> (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[249, 245])).
% 2.74/2.92 tff(251,plain,
% 2.74/2.92 ((~(((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) <=> (~(~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[250])).
% 2.74/2.92 tff(252,plain,
% 2.74/2.92 ((~(((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) <=> (member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[251, 244])).
% 2.74/2.92 tff(253,plain,
% 2.74/2.92 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[252])).
% 2.74/2.92 tff(254,plain,
% 2.74/2.92 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[253, 243])).
% 2.74/2.92 tff(255,plain,
% 2.74/2.92 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4))) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(256,plain,
% 2.74/2.92 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[255, 254])).
% 2.74/2.92 tff(257,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[256, 67, 242])).
% 2.74/2.92 tff(258,plain,(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(259,plain,
% 2.74/2.92 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_C_2(B!4), B!4) <=> member(tptp_fun_C_2(B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(260,plain,
% 2.74/2.92 (~((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_C_2(B!4), B!4) <=> member(tptp_fun_C_2(B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[259, 48])).
% 2.74/2.92 tff(261,plain,
% 2.74/2.92 (((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_C_2(B!4), B!4) <=> member(tptp_fun_C_2(B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))))) | ((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))),
% 2.74/2.92 inference(tautology,[status(thm)],[])).
% 2.74/2.92 tff(262,plain,
% 2.74/2.92 ((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[261, 260])).
% 2.74/2.92 tff(263,plain,
% 2.74/2.92 ((~((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))) | (B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(tautology,[status(thm)],[])).
% 2.74/2.92 tff(264,plain,
% 2.74/2.92 ((B!4 = intersection(B!4, B!4)) | (~(member(tptp_fun_D_0(intersection(B!4, B!4), B!4), B!4) <=> member(tptp_fun_D_0(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[263, 262])).
% 2.74/2.92 tff(265,plain,
% 2.74/2.92 (B!4 = intersection(B!4, B!4)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[264, 258])).
% 2.74/2.92 tff(266,plain,
% 2.74/2.92 (intersection(B!4, B!4) = B!4),
% 2.74/2.92 inference(symmetry,[status(thm)],[265])).
% 2.74/2.92 tff(267,plain,
% 2.74/2.92 ((difference(B!4, C!3) = intersection(B!4, B!4)) <=> (difference(B!4, C!3) = B!4)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[266])).
% 2.74/2.92 tff(268,plain,
% 2.74/2.92 ((~(difference(B!4, C!3) = intersection(B!4, B!4))) <=> (~(difference(B!4, C!3) = B!4))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[267])).
% 2.74/2.92 tff(269,assumption,(~(difference(B!4, C!3) = intersection(B!4, B!4))), introduced(assumption)).
% 2.74/2.92 tff(270,plain,
% 2.74/2.92 (~(difference(B!4, C!3) = B!4)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[269, 268])).
% 2.74/2.92 tff(271,plain,
% 2.74/2.92 ((~((intersection(B!4, C!3) = empty_set) <=> (difference(B!4, C!3) = B!4))) <=> (~((intersection(B!4, C!3) = empty_set) <=> (difference(B!4, C!3) = B!4)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(272,plain,
% 2.74/2.92 ((~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))) <=> (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(273,axiom,(~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th84')).
% 2.74/2.92 tff(274,plain,
% 2.74/2.92 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[273, 272])).
% 2.74/2.92 tff(275,plain,
% 2.74/2.92 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[274, 272])).
% 2.74/2.92 tff(276,plain,
% 2.74/2.92 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[275, 272])).
% 2.74/2.92 tff(277,plain,
% 2.74/2.92 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[276, 272])).
% 2.74/2.92 tff(278,plain,(
% 2.74/2.92 ~((intersection(B!4, C!3) = empty_set) <=> (difference(B!4, C!3) = B!4))),
% 2.74/2.92 inference(skolemize,[status(sab)],[277])).
% 2.74/2.92 tff(279,plain,
% 2.74/2.92 (~((intersection(B!4, C!3) = empty_set) <=> (difference(B!4, C!3) = B!4))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[278, 271])).
% 2.74/2.92 tff(280,plain,
% 2.74/2.92 (((intersection(B!4, C!3) = empty_set) <=> (difference(B!4, C!3) = B!4)) | (intersection(B!4, C!3) = empty_set) | (difference(B!4, C!3) = B!4)),
% 2.74/2.92 inference(tautology,[status(thm)],[])).
% 2.74/2.92 tff(281,plain,
% 2.74/2.92 ((intersection(B!4, C!3) = empty_set) | (difference(B!4, C!3) = B!4)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[280, 279])).
% 2.74/2.92 tff(282,plain,
% 2.74/2.92 (intersection(B!4, C!3) = empty_set),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[281, 270])).
% 2.74/2.92 tff(283,plain,
% 2.74/2.92 ((B!4 = difference(B!4, C!3)) <=> (difference(B!4, C!3) = B!4)),
% 2.74/2.92 inference(commutativity,[status(thm)],[])).
% 2.74/2.92 tff(284,plain,
% 2.74/2.92 ((intersection(B!4, B!4) = difference(B!4, C!3)) <=> (B!4 = difference(B!4, C!3))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[266])).
% 2.74/2.92 tff(285,plain,
% 2.74/2.92 ((intersection(B!4, B!4) = difference(B!4, C!3)) <=> (difference(B!4, C!3) = B!4)),
% 2.74/2.92 inference(transitivity,[status(thm)],[284, 283])).
% 2.74/2.92 tff(286,plain,
% 2.74/2.92 ((difference(B!4, C!3) = B!4) <=> (intersection(B!4, B!4) = difference(B!4, C!3))),
% 2.74/2.92 inference(symmetry,[status(thm)],[285])).
% 2.74/2.92 tff(287,plain,
% 2.74/2.92 ((difference(B!4, C!3) = intersection(B!4, B!4)) <=> (intersection(B!4, B!4) = difference(B!4, C!3))),
% 2.74/2.92 inference(transitivity,[status(thm)],[267, 286])).
% 2.74/2.92 tff(288,plain,
% 2.74/2.92 ((~(difference(B!4, C!3) = intersection(B!4, B!4))) <=> (~(intersection(B!4, B!4) = difference(B!4, C!3)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[287])).
% 2.74/2.92 tff(289,plain,
% 2.74/2.92 (~(intersection(B!4, B!4) = difference(B!4, C!3))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[269, 288])).
% 2.74/2.92 tff(290,plain,
% 2.74/2.92 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(B!4, B!4) = difference(B!4, C!3))) | (member(tptp_fun_C_2(B!4), intersection(B!4, B!4)) <=> member(tptp_fun_C_2(B!4), difference(B!4, C!3))))) | (~((intersection(B!4, B!4) = difference(B!4, C!3)) | (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(291,plain,
% 2.74/2.93 (~((~((~(intersection(B!4, B!4) = difference(B!4, C!3))) | (member(tptp_fun_C_2(B!4), intersection(B!4, B!4)) <=> member(tptp_fun_C_2(B!4), difference(B!4, C!3))))) | (~((intersection(B!4, B!4) = difference(B!4, C!3)) | (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[290, 48])).
% 2.74/2.93 tff(292,plain,
% 2.74/2.93 (((~((~(intersection(B!4, B!4) = difference(B!4, C!3))) | (member(tptp_fun_C_2(B!4), intersection(B!4, B!4)) <=> member(tptp_fun_C_2(B!4), difference(B!4, C!3))))) | (~((intersection(B!4, B!4) = difference(B!4, C!3)) | (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))))))) | ((intersection(B!4, B!4) = difference(B!4, C!3)) | (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))))),
% 2.74/2.93 inference(tautology,[status(thm)],[])).
% 2.74/2.93 tff(293,plain,
% 2.74/2.93 ((intersection(B!4, B!4) = difference(B!4, C!3)) | (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[292, 291])).
% 2.74/2.93 tff(294,plain,
% 2.74/2.93 ((~((intersection(B!4, B!4) = difference(B!4, C!3)) | (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))))) | (intersection(B!4, B!4) = difference(B!4, C!3)) | (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))))),
% 2.74/2.93 inference(tautology,[status(thm)],[])).
% 2.74/2.93 tff(295,plain,
% 2.74/2.93 ((intersection(B!4, B!4) = difference(B!4, C!3)) | (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[294, 293])).
% 2.74/2.93 tff(296,plain,
% 2.74/2.93 (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[295, 289])).
% 2.74/2.93 tff(297,plain,
% 2.74/2.93 (difference(intersection(B!4, B!4), intersection(C!3, C!3)) = difference(B!4, C!3)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[266, 229])).
% 2.74/2.93 tff(298,plain,
% 2.74/2.93 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[297])).
% 2.74/2.93 tff(299,plain,
% 2.74/2.93 ((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))) <=> (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[298])).
% 2.74/2.93 tff(300,plain,
% 2.74/2.93 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(301,plain,
% 2.74/2.93 (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[300, 11])).
% 2.74/2.93 tff(302,assumption,(~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))), introduced(assumption)).
% 2.74/2.93 tff(303,plain,
% 2.74/2.93 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(304,plain,
% 2.74/2.93 ((~(~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) <=> (member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(305,plain,
% 2.74/2.93 ((~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) <=> (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(306,plain,
% 2.74/2.93 (((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))) <=> (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(307,plain,
% 2.74/2.93 (((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(308,plain,
% 2.74/2.93 ((((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))) <=> ((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[307])).
% 2.74/2.93 tff(309,plain,
% 2.74/2.93 ((((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))) <=> (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[308, 306])).
% 2.74/2.93 tff(310,plain,
% 2.74/2.93 ((((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))) <=> (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[309, 305])).
% 2.74/2.93 tff(311,plain,
% 2.74/2.93 ((~(((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) <=> (~(~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[310])).
% 2.74/2.93 tff(312,plain,
% 2.74/2.93 ((~(((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) <=> (member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[311, 304])).
% 2.74/2.93 tff(313,plain,
% 2.74/2.93 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[312])).
% 2.74/2.93 tff(314,plain,
% 2.74/2.93 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[313, 303])).
% 2.74/2.93 tff(315,plain,
% 2.74/2.93 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(316,plain,
% 2.74/2.93 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[315, 314])).
% 2.74/2.93 tff(317,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[316, 67, 302])).
% 2.74/2.93 tff(318,plain,(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(319,plain,
% 2.74/2.93 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3)))) | (member(tptp_fun_D_0(difference(B!4, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) | (~((difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(320,plain,
% 2.74/2.93 (~((~((~(difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3)))) | (member(tptp_fun_D_0(difference(B!4, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) | (~((difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[319, 48])).
% 2.74/2.93 tff(321,plain,
% 2.74/2.93 (((~((~(difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3)))) | (member(tptp_fun_D_0(difference(B!4, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) | (~((difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))))) | ((difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))))),
% 2.74/2.93 inference(tautology,[status(thm)],[])).
% 2.74/2.93 tff(322,plain,
% 2.74/2.93 ((difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[321, 320])).
% 2.74/2.93 tff(323,plain,
% 2.74/2.93 ((~((difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3))))))) | (difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(tautology,[status(thm)],[])).
% 2.74/2.93 tff(324,plain,
% 2.74/2.93 ((difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))) | (~(member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(difference(B!4, C!3), difference(B!4, C!3)), difference(B!4, C!3)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[323, 322])).
% 2.74/2.93 tff(325,plain,
% 2.74/2.93 (difference(B!4, C!3) = intersection(difference(B!4, C!3), difference(B!4, C!3))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[324, 318])).
% 2.74/2.93 tff(326,plain,
% 2.74/2.93 (intersection(difference(B!4, C!3), difference(B!4, C!3)) = difference(B!4, C!3)),
% 2.74/2.93 inference(symmetry,[status(thm)],[325])).
% 2.74/2.93 tff(327,plain,
% 2.74/2.93 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[326])).
% 2.74/2.93 tff(328,plain,
% 2.74/2.93 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))),
% 2.74/2.93 inference(symmetry,[status(thm)],[327])).
% 2.74/2.93 tff(329,plain,
% 2.74/2.93 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[298, 328])).
% 2.74/2.93 tff(330,assumption,(~((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))), introduced(assumption)).
% 2.74/2.93 tff(331,plain,
% 2.74/2.93 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))) | ((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.93 inference(tautology,[status(thm)],[])).
% 2.74/2.93 tff(332,plain,
% 2.74/2.93 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[331, 330, 301])).
% 2.74/2.93 tff(333,plain,
% 2.74/2.93 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[332, 329])).
% 2.74/2.93 tff(334,plain,
% 2.74/2.93 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(335,plain,
% 2.74/2.93 ((~(~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) <=> (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(336,plain,
% 2.74/2.93 ((~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) <=> (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(337,plain,
% 2.74/2.94 (((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))) <=> (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(338,plain,
% 2.74/2.94 (((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(339,plain,
% 2.74/2.94 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))) <=> ((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[338])).
% 2.74/2.94 tff(340,plain,
% 2.74/2.94 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))) <=> (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[339, 337])).
% 2.74/2.94 tff(341,plain,
% 2.74/2.94 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))) <=> (~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[340, 336])).
% 2.74/2.94 tff(342,plain,
% 2.74/2.94 ((~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) <=> (~(~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[341])).
% 2.74/2.94 tff(343,plain,
% 2.74/2.94 ((~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) <=> (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[342, 335])).
% 2.74/2.94 tff(344,plain,
% 2.74/2.94 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[343])).
% 2.74/2.94 tff(345,plain,
% 2.74/2.94 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[344, 334])).
% 2.74/2.94 tff(346,plain,
% 2.74/2.94 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(347,plain,
% 2.74/2.94 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[346, 345])).
% 2.74/2.94 tff(348,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[347, 67])).
% 2.74/2.94 tff(349,assumption,(~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))), introduced(assumption)).
% 2.74/2.94 tff(350,plain,
% 2.74/2.94 (((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 2.74/2.94 inference(tautology,[status(thm)],[])).
% 2.74/2.94 tff(351,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[350, 330])).
% 2.74/2.94 tff(352,plain,
% 2.74/2.94 ((member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))),
% 2.74/2.94 inference(tautology,[status(thm)],[])).
% 2.74/2.94 tff(353,plain,
% 2.74/2.94 (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[352, 351, 349])).
% 2.74/2.94 tff(354,plain,
% 2.74/2.94 ((~(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3))))),
% 2.74/2.94 inference(tautology,[status(thm)],[])).
% 2.74/2.94 tff(355,plain,
% 2.74/2.94 (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(B!4, C!3), difference(B!4, C!3)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[354, 353, 348])).
% 2.74/2.94 tff(356,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[355, 333])).
% 2.74/2.94 tff(357,plain,(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(358,plain,
% 2.74/2.94 ((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[357, 296])).
% 2.74/2.94 tff(359,plain,
% 2.74/2.94 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))) | (~((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.94 inference(tautology,[status(thm)],[])).
% 2.74/2.94 tff(360,plain,
% 2.74/2.94 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[359, 358])).
% 2.74/2.94 tff(361,plain,
% 2.74/2.94 (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[360, 301])).
% 2.74/2.94 tff(362,plain,
% 2.74/2.94 (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[361, 299])).
% 2.74/2.94 tff(363,plain,
% 2.74/2.94 ((member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(B!4, C!3))),
% 2.74/2.94 inference(tautology,[status(thm)],[])).
% 2.74/2.94 tff(364,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[363, 362, 296])).
% 2.74/2.94 tff(365,plain,
% 2.74/2.94 ((~((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))),
% 2.74/2.94 inference(tautology,[status(thm)],[])).
% 2.74/2.94 tff(366,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[365, 364, 358])).
% 2.74/2.94 tff(367,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[231])).
% 2.74/2.94 tff(368,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))),
% 2.74/2.94 inference(symmetry,[status(thm)],[367])).
% 2.74/2.94 tff(369,assumption,(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))), introduced(assumption)).
% 2.74/2.94 tff(370,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[369, 368])).
% 2.74/2.94 tff(371,plain,
% 2.74/2.94 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(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_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(372,plain,
% 2.74/2.94 ((~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3))))) <=> (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(373,plain,
% 2.74/2.94 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(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_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[372])).
% 2.74/2.94 tff(374,plain,
% 2.74/2.94 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(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_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[373, 371])).
% 2.74/2.94 tff(375,plain,
% 2.74/2.94 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(376,plain,
% 2.74/2.94 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[375, 374])).
% 2.74/2.94 tff(377,plain,
% 2.74/2.94 (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), difference(intersection(C!3, C!3), intersection(C!3, C!3)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[376, 11])).
% 2.74/2.94 tff(378,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[377, 370])).
% 2.74/2.94 tff(379,plain,(~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(380,assumption,(intersection(B!4, C!3) = empty_set), introduced(assumption)).
% 2.74/2.94 tff(381,plain,
% 2.74/2.94 (intersection(intersection(B!4, B!4), intersection(C!3, C!3)) = intersection(B!4, C!3)),
% 2.74/2.94 inference(monotonicity,[status(thm)],[266, 229])).
% 2.74/2.94 tff(382,plain,
% 2.74/2.94 (intersection(intersection(B!4, B!4), intersection(C!3, C!3)) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))),
% 2.74/2.94 inference(transitivity,[status(thm)],[381, 380, 55, 178, 146, 188])).
% 2.74/2.94 tff(383,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[382])).
% 2.74/2.94 tff(384,plain,
% 2.74/2.94 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.94 inference(symmetry,[status(thm)],[383])).
% 2.74/2.94 tff(385,plain,
% 2.74/2.94 ((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) <=> (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[384])).
% 2.74/2.94 tff(386,assumption,(~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))), introduced(assumption)).
% 2.74/2.94 tff(387,plain,
% 2.74/2.94 (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[386, 385])).
% 2.74/2.94 tff(388,plain,
% 2.74/2.94 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), 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_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(389,plain,
% 2.74/2.94 ((~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))) <=> (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(390,plain,
% 2.74/2.94 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))) <=> (((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(391,plain,
% 2.74/2.94 ((~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))) <=> (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[390])).
% 2.74/2.94 tff(392,plain,
% 2.74/2.94 ((~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))) <=> (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[391, 389])).
% 2.74/2.94 tff(393,plain,
% 2.74/2.94 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), 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_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[392])).
% 2.74/2.94 tff(394,plain,
% 2.74/2.94 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), 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_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[393, 388])).
% 2.74/2.95 tff(395,plain,
% 2.74/2.95 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(396,plain,
% 2.74/2.95 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[395, 394])).
% 2.74/2.95 tff(397,plain,
% 2.74/2.95 (~(((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[396, 67])).
% 2.74/2.95 tff(398,assumption,(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))), introduced(assumption)).
% 2.74/2.95 tff(399,assumption,(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))), introduced(assumption)).
% 2.74/2.95 tff(400,plain,
% 2.74/2.95 ((~((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(401,plain,
% 2.74/2.95 (~((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[400, 399, 398])).
% 2.74/2.95 tff(402,plain,
% 2.74/2.95 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))) | ((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(403,plain,
% 2.74/2.95 ((((~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))) | member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[402, 401])).
% 2.74/2.95 tff(404,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[403, 397])).
% 2.74/2.95 tff(405,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[404, 387])).
% 2.74/2.95 tff(406,plain,(member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))) | (~(intersection(B!4, C!3) = empty_set)) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(407,plain,
% 2.74/2.95 ((~(intersection(B!4, C!3) = empty_set)) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(B!4, B!4))) | (~member(tptp_fun_D_0(difference(B!4, C!3), intersection(B!4, B!4)), intersection(C!3, C!3)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[406, 379])).
% 2.74/2.95 tff(408,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[407, 366, 364, 282])).
% 2.74/2.95 tff(409,plain,(difference(B!4, C!3) = intersection(B!4, B!4)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(410,plain,
% 2.74/2.95 (difference(B!4, C!3) = B!4),
% 2.74/2.95 inference(transitivity,[status(thm)],[409, 266])).
% 2.74/2.95 tff(411,plain,
% 2.74/2.95 (intersection(intersection(C!3, C!3), difference(B!4, C!3)) = intersection(C!3, B!4)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[229, 410])).
% 2.74/2.95 tff(412,plain,
% 2.74/2.95 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[411])).
% 2.74/2.95 tff(413,plain,
% 2.74/2.95 ((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3)))) <=> (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[412])).
% 2.74/2.95 tff(414,plain,
% 2.74/2.95 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(415,plain,
% 2.74/2.95 (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[414, 67])).
% 2.74/2.95 tff(416,plain,
% 2.74/2.95 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3)))) | (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))))) | (~((intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(417,plain,
% 2.74/2.95 (~((~((~(intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3)))) | (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))))) | (~((intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3))))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[416, 48])).
% 2.74/2.95 tff(418,plain,
% 2.74/2.95 (((~((~(intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3)))) | (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))))) | (~((intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))))))) | ((intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3))))))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(419,plain,
% 2.74/2.95 ((intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[418, 417])).
% 2.74/2.95 tff(420,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[297])).
% 2.74/2.95 tff(421,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.95 inference(symmetry,[status(thm)],[420])).
% 2.74/2.95 tff(422,assumption,(~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3))))), introduced(assumption)).
% 2.74/2.95 tff(423,plain,
% 2.74/2.95 (difference(intersection(C!3, C!3), difference(B!4, C!3)) = difference(C!3, difference(B!4, C!3))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[229])).
% 2.74/2.95 tff(424,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[423])).
% 2.74/2.95 tff(425,plain,
% 2.74/2.95 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(426,plain,
% 2.74/2.95 (~(((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[425, 11])).
% 2.74/2.95 tff(427,assumption,(~((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3)))), introduced(assumption)).
% 2.74/2.95 tff(428,plain,
% 2.74/2.95 ((((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3)))) | ((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3)))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(429,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[428, 427, 426])).
% 2.74/2.95 tff(430,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[429, 424])).
% 2.74/2.95 tff(431,plain,
% 2.74/2.95 (((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(432,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[431, 427])).
% 2.74/2.95 tff(433,plain,
% 2.74/2.95 ((member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))) | (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3))))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(434,plain,
% 2.74/2.95 (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[433, 432, 422])).
% 2.74/2.95 tff(435,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[434, 430])).
% 2.74/2.95 tff(436,plain,(((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))) | (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(437,plain,
% 2.74/2.95 ((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[436, 422])).
% 2.74/2.95 tff(438,plain,
% 2.74/2.95 ((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3)))) <=> (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[424])).
% 2.74/2.95 tff(439,plain,
% 2.74/2.95 ((((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3)))) | (~((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3)))) | (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3))))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(440,plain,
% 2.74/2.95 (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(C!3, C!3), difference(B!4, C!3)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[439, 437, 426])).
% 2.74/2.95 tff(441,plain,
% 2.74/2.95 (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[440, 438])).
% 2.74/2.95 tff(442,plain,
% 2.74/2.95 ((member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(443,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[442, 441, 422])).
% 2.74/2.95 tff(444,plain,
% 2.74/2.95 ((~((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3)))) | (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(445,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(B!4, C!3))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[444, 443, 437])).
% 2.74/2.95 tff(446,plain,
% 2.74/2.95 (member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[445, 421])).
% 2.74/2.95 tff(447,plain,
% 2.74/2.95 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(448,plain,
% 2.74/2.95 (~(((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[447, 11])).
% 2.74/2.95 tff(449,plain,
% 2.74/2.95 (((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) | (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(450,plain,
% 2.74/2.95 ((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[449, 443])).
% 2.74/2.95 tff(451,plain,
% 2.74/2.95 ((((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))) | (~((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)))) | (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(452,plain,
% 2.74/2.95 ((((~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(B!4, B!4))) | member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3))) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))) | (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[451, 450])).
% 2.74/2.95 tff(453,plain,
% 2.74/2.95 (~member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(intersection(B!4, B!4), intersection(C!3, C!3)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[452, 448])).
% 2.74/2.95 tff(454,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[453, 446])).
% 2.74/2.95 tff(455,plain,(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(456,plain,
% 2.74/2.95 ((~((intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3))))))) | (intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3)))))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(457,plain,
% 2.74/2.95 ((~((intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))) | (~(member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(difference(C!3, difference(B!4, C!3)), intersection(C!3, C!3)), difference(C!3, difference(B!4, C!3))))))) | (intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[456, 455])).
% 2.74/2.95 tff(458,plain,
% 2.74/2.95 (intersection(C!3, C!3) = difference(C!3, difference(B!4, C!3))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[457, 419])).
% 2.74/2.95 tff(459,plain,
% 2.74/2.95 (difference(C!3, difference(B!4, C!3)) = intersection(C!3, C!3)),
% 2.74/2.95 inference(symmetry,[status(thm)],[458])).
% 2.74/2.95 tff(460,plain,
% 2.74/2.95 (difference(intersection(C!3, C!3), difference(B!4, C!3)) = intersection(C!3, C!3)),
% 2.74/2.95 inference(transitivity,[status(thm)],[423, 459])).
% 2.74/2.95 tff(461,plain,
% 2.74/2.95 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[460])).
% 2.74/2.95 tff(462,plain,
% 2.74/2.95 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3)))),
% 2.74/2.95 inference(symmetry,[status(thm)],[461])).
% 2.74/2.95 tff(463,assumption,(~((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))))), introduced(assumption)).
% 2.74/2.95 tff(464,plain,
% 2.74/2.95 (((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))),
% 2.74/2.95 inference(tautology,[status(thm)],[])).
% 2.74/2.95 tff(465,plain,
% 2.74/2.95 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[464, 463])).
% 2.74/2.95 tff(466,plain,
% 2.74/2.95 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3)))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[465, 462])).
% 2.74/2.95 tff(467,plain,
% 2.74/2.95 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(468,plain,
% 2.74/2.95 (~(((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[467, 11])).
% 2.74/2.96 tff(469,plain,
% 2.74/2.96 (((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3)))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))),
% 2.74/2.96 inference(tautology,[status(thm)],[])).
% 2.74/2.96 tff(470,plain,
% 2.74/2.96 (member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[469, 463])).
% 2.74/2.96 tff(471,plain,
% 2.74/2.96 (((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3)))),
% 2.74/2.96 inference(tautology,[status(thm)],[])).
% 2.74/2.96 tff(472,plain,
% 2.74/2.96 ((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[471, 470])).
% 2.74/2.96 tff(473,plain,
% 2.74/2.96 ((((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3)))) | (~((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3)))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3))))),
% 2.74/2.96 inference(tautology,[status(thm)],[])).
% 2.74/2.96 tff(474,plain,
% 2.74/2.96 ((((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3)))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[473, 472])).
% 2.74/2.96 tff(475,plain,
% 2.74/2.96 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(intersection(C!3, C!3), difference(B!4, C!3)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[474, 468])).
% 2.74/2.96 tff(476,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[475, 466])).
% 2.74/2.96 tff(477,plain,((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(478,plain,
% 2.74/2.96 ((((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3)))) | (~((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3))))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3))))),
% 2.74/2.96 inference(tautology,[status(thm)],[])).
% 2.74/2.96 tff(479,plain,
% 2.74/2.96 ((((~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, C!3)))) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3)))) | (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[478, 477])).
% 2.74/2.96 tff(480,plain,
% 2.74/2.96 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(intersection(C!3, C!3), difference(B!4, C!3)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[479, 415])).
% 2.74/2.96 tff(481,plain,
% 2.74/2.96 (~member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[480, 413])).
% 2.74/2.96 tff(482,plain,
% 2.74/2.96 ((member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) | member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.96 inference(tautology,[status(thm)],[])).
% 2.74/2.96 tff(483,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[482, 481, 241, 199])).
% 2.74/2.96 tff(484,plain,(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(485,plain,
% 2.74/2.96 ((~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.96 inference(tautology,[status(thm)],[])).
% 2.74/2.96 tff(486,plain,
% 2.74/2.96 ((~((~(member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))), intersection(C!3, B!4)), intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))))) | (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[485, 484])).
% 2.74/2.96 tff(487,plain,
% 2.74/2.96 (intersection(C!3, B!4) = intersection(difference(C!3, C!3), tptp_fun_D_1(C!3, difference(C!3, C!3)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[486, 198])).
% 2.74/2.96 tff(488,plain,
% 2.74/2.96 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, C!3) = intersection(C!3, B!4))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(489,plain,
% 2.74/2.96 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[488, 186])).
% 2.74/2.96 tff(490,plain,
% 2.74/2.96 (intersection(B!4, C!3) = empty_set),
% 2.74/2.96 inference(transitivity,[status(thm)],[489, 487, 189, 145, 179, 56])).
% 2.74/2.96 tff(491,plain,
% 2.74/2.96 (difference(B!4, C!3) = B!4),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[409, 267])).
% 2.74/2.96 tff(492,plain,
% 2.74/2.96 (((intersection(B!4, C!3) = empty_set) <=> (difference(B!4, C!3) = B!4)) | (~(intersection(B!4, C!3) = empty_set)) | (~(difference(B!4, C!3) = B!4))),
% 2.74/2.96 inference(tautology,[status(thm)],[])).
% 2.74/2.96 tff(493,plain,
% 2.74/2.96 ((~(intersection(B!4, C!3) = empty_set)) | (~(difference(B!4, C!3) = B!4))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[492, 279])).
% 2.74/2.96 tff(494,plain,
% 2.74/2.96 (~(intersection(B!4, C!3) = empty_set)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[493, 491])).
% 2.74/2.96 tff(495,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[494, 490])).
% 2.74/2.96 % SZS output end Proof
% 2.74/2.96 % E exiting
%------------------------------------------------------------------------------