%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET606+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:59 AM UTC 2025
% Result : Theorem 0.79s 0.96s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET606+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.12 % 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 05:31:08 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.79/0.96 % SZS status Theorem
% 0.79/0.96 % SZS output start Proof
% 0.79/0.96 tff(member_type, type, (
% 0.79/0.96 member: ( $i * $i ) > $o)).
% 0.79/0.96 tff(intersection_type, type, (
% 0.79/0.96 intersection: ( $i * $i ) > $i)).
% 0.79/0.96 tff(tptp_fun_C_2_type, type, (
% 0.79/0.96 tptp_fun_C_2: $i)).
% 0.79/0.96 tff(tptp_fun_D_0_type, type, (
% 0.79/0.96 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.79/0.96 tff(difference_type, type, (
% 0.79/0.96 difference: ( $i * $i ) > $i)).
% 0.79/0.96 tff(tptp_fun_B_3_type, type, (
% 0.79/0.96 tptp_fun_B_3: $i)).
% 0.79/0.96 tff(1,plain,
% 0.79/0.96 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(2,plain,
% 0.79/0.96 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1])).
% 0.79/0.96 tff(3,plain,
% 0.79/0.96 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, C)) | (~member(D, B))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(4,plain,
% 0.79/0.96 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[3])).
% 0.79/0.96 tff(5,plain,
% 0.79/0.96 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.79/0.96 tff(7,plain,
% 0.79/0.96 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.79/0.96 tff(8,plain,(
% 0.79/0.96 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.79/0.96 inference(skolemize,[status(sab)],[7])).
% 0.79/0.96 tff(9,plain,
% 0.79/0.96 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.79/0.96 tff(10,plain,
% 0.79/0.96 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.79/0.96 tff(11,plain,
% 0.79/0.96 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3)))))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(12,plain,
% 0.79/0.96 (~(((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3))))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.79/0.96 tff(13,assumption,(~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))), introduced(assumption)).
% 0.79/0.96 tff(14,plain,
% 0.79/0.96 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(15,plain,
% 0.79/0.96 ((~(~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> (member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(16,plain,
% 0.79/0.96 ((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(17,plain,
% 0.79/0.96 (((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(18,plain,
% 0.79/0.96 (((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(19,plain,
% 0.79/0.96 ((((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> ((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[18])).
% 0.79/0.96 tff(20,plain,
% 0.79/0.96 ((((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[19, 17])).
% 0.79/0.96 tff(21,plain,
% 0.79/0.96 ((((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))) <=> (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[20, 16])).
% 0.79/0.96 tff(22,plain,
% 0.79/0.96 ((~(((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (~(~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[21])).
% 0.79/0.96 tff(23,plain,
% 0.79/0.96 ((~(((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) <=> (member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[22, 15])).
% 0.79/0.96 tff(24,plain,
% 0.79/0.96 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[23])).
% 0.79/0.96 tff(25,plain,
% 0.79/0.96 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[24, 14])).
% 0.79/0.96 tff(26,plain,
% 0.79/0.96 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3))) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(27,plain,
% 0.79/0.96 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.79/0.96 tff(28,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[27, 10, 13])).
% 0.79/0.96 tff(29,plain,(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(30,plain,
% 0.79/0.96 (^[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))))))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(31,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[30])).
% 0.79/0.96 tff(32,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(pull_quant,[status(thm)],[])).
% 0.79/0.96 tff(33,plain,
% 0.79/0.96 (^[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)))))))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(34,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[33])).
% 0.79/0.96 tff(35,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[34, 32])).
% 0.79/0.96 tff(36,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[35, 31])).
% 0.79/0.96 tff(37,plain,
% 0.79/0.96 (^[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))))))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(38,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[37])).
% 0.79/0.96 tff(39,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[38, 36])).
% 0.79/0.96 tff(40,plain,
% 0.79/0.96 (^[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)))))))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(41,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[40])).
% 0.79/0.96 tff(42,plain,
% 0.79/0.96 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(43,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 0.79/0.96 tff(44,plain,
% 0.79/0.96 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.79/0.96 tff(45,plain,(
% 0.79/0.96 ![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)))))),
% 0.79/0.96 inference(skolemize,[status(sab)],[44])).
% 0.79/0.96 tff(46,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.79/0.96 tff(47,plain,
% 0.79/0.96 (![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)))))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.79/0.96 tff(48,plain,
% 0.79/0.96 (((~![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!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!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)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))))))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(49,plain,
% 0.79/0.96 ((~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))))))) <=> (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))))))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(50,plain,
% 0.79/0.96 (((~![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!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!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)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[49])).
% 0.79/0.96 tff(51,plain,
% 0.79/0.96 (((~![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!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!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)))))))) | (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[50, 48])).
% 0.79/0.96 tff(52,plain,
% 0.79/0.96 ((~![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!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((B!3 = intersection(B!3, B!3)) | (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3))))))))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(53,plain,
% 0.79/0.96 ((~![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!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.79/0.96 tff(54,plain,
% 0.79/0.96 (~((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[53, 47])).
% 0.79/0.96 tff(55,plain,
% 0.79/0.96 (((~((~(B!3 = intersection(B!3, B!3))) | (member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), B!3) <=> member(tptp_fun_D_0(difference(intersection(C!2, B!3), intersection(C!2, B!3)), B!3), intersection(B!3, B!3))))) | (~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))))) | ((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))),
% 0.79/0.96 inference(tautology,[status(thm)],[])).
% 0.79/0.96 tff(56,plain,
% 0.79/0.96 ((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.79/0.96 tff(57,plain,
% 0.79/0.96 ((~((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3)))) | (~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))),
% 0.79/0.96 inference(tautology,[status(thm)],[])).
% 0.79/0.96 tff(58,plain,
% 0.79/0.96 ((~(member(tptp_fun_D_0(intersection(B!3, B!3), B!3), B!3) <=> member(tptp_fun_D_0(intersection(B!3, B!3), B!3), intersection(B!3, B!3)))) | (B!3 = intersection(B!3, B!3))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.79/0.96 tff(59,plain,
% 0.79/0.96 (B!3 = intersection(B!3, B!3)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[58, 29])).
% 0.79/0.96 tff(60,plain,
% 0.79/0.96 (intersection(B!3, B!3) = B!3),
% 0.79/0.96 inference(symmetry,[status(thm)],[59])).
% 0.79/0.96 tff(61,assumption,(~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))), introduced(assumption)).
% 0.79/0.96 tff(62,plain,
% 0.79/0.96 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(63,plain,
% 0.79/0.96 ((~(~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))) <=> (member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(64,plain,
% 0.79/0.96 ((~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))) <=> (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(65,plain,
% 0.79/0.96 (((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))) <=> (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(66,plain,
% 0.79/0.96 (((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(67,plain,
% 0.79/0.96 ((((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))) <=> ((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[66])).
% 0.79/0.96 tff(68,plain,
% 0.79/0.96 ((((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))) <=> (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[67, 65])).
% 0.79/0.96 tff(69,plain,
% 0.79/0.96 ((((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))) <=> (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[68, 64])).
% 0.79/0.96 tff(70,plain,
% 0.79/0.96 ((~(((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))) <=> (~(~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[69])).
% 0.79/0.96 tff(71,plain,
% 0.79/0.96 ((~(((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))) <=> (member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[70, 63])).
% 0.79/0.96 tff(72,plain,
% 0.79/0.96 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[71])).
% 0.79/0.97 tff(73,plain,
% 0.79/0.97 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.97 inference(transitivity,[status(thm)],[72, 62])).
% 0.79/0.97 tff(74,plain,
% 0.79/0.97 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(75,plain,
% 0.79/0.97 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.79/0.97 tff(76,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[75, 10, 61])).
% 0.79/0.97 tff(77,plain,(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(78,plain,
% 0.79/0.97 ((~![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!2 = intersection(C!2, C!2))) | (member(tptp_fun_D_0(B!3, C!2), C!2) <=> member(tptp_fun_D_0(B!3, C!2), intersection(C!2, C!2))))) | (~((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))))))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(79,plain,
% 0.79/0.97 (~((~((~(C!2 = intersection(C!2, C!2))) | (member(tptp_fun_D_0(B!3, C!2), C!2) <=> member(tptp_fun_D_0(B!3, C!2), intersection(C!2, C!2))))) | (~((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[78, 47])).
% 0.79/0.97 tff(80,plain,
% 0.79/0.97 (((~((~(C!2 = intersection(C!2, C!2))) | (member(tptp_fun_D_0(B!3, C!2), C!2) <=> member(tptp_fun_D_0(B!3, C!2), intersection(C!2, C!2))))) | (~((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))))) | ((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(81,plain,
% 0.79/0.97 ((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.79/0.97 tff(82,plain,
% 0.79/0.97 ((~((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))))) | (C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(83,plain,
% 0.79/0.97 ((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_0(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_0(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.79/0.97 tff(84,plain,
% 0.79/0.97 (C!2 = intersection(C!2, C!2)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[83, 77])).
% 0.79/0.97 tff(85,plain,
% 0.79/0.97 (intersection(C!2, C!2) = C!2),
% 0.79/0.97 inference(symmetry,[status(thm)],[84])).
% 0.79/0.97 tff(86,plain,
% 0.79/0.97 (intersection(intersection(C!2, C!2), intersection(B!3, B!3)) = intersection(C!2, B!3)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[85, 60])).
% 0.79/0.97 tff(87,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[86])).
% 0.79/0.97 tff(88,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3)))),
% 0.79/0.97 inference(symmetry,[status(thm)],[87])).
% 0.79/0.97 tff(89,plain,
% 0.79/0.97 ((~![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!3, C!2) = difference(B!3, intersection(B!3, C!2)))) | (member(tptp_fun_D_0(difference(B!3, C!2), difference(B!3, intersection(B!3, C!2))), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, C!2), difference(B!3, intersection(B!3, C!2))), difference(B!3, intersection(B!3, C!2)))))) | (~((difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))) | (~(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))))))))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(90,plain,
% 0.79/0.97 (~((~((~(difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2)))) | (member(tptp_fun_D_0(difference(B!3, C!2), difference(B!3, intersection(B!3, C!2))), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, C!2), difference(B!3, intersection(B!3, C!2))), difference(B!3, intersection(B!3, C!2)))))) | (~((difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))) | (~(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2))))))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[89, 47])).
% 0.79/0.97 tff(91,plain,
% 0.79/0.97 (((~((~(difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2)))) | (member(tptp_fun_D_0(difference(B!3, C!2), difference(B!3, intersection(B!3, C!2))), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, C!2), difference(B!3, intersection(B!3, C!2))), difference(B!3, intersection(B!3, C!2)))))) | (~((difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))) | (~(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))))))) | ((difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))) | (~(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2))))))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(92,plain,
% 0.79/0.97 ((difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))) | (~(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.79/0.97 tff(93,plain,
% 0.79/0.97 ((difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))) <=> (difference(B!3, intersection(B!3, C!2)) = difference(B!3, C!2))),
% 0.79/0.97 inference(commutativity,[status(thm)],[])).
% 0.79/0.97 tff(94,plain,
% 0.79/0.97 ((difference(B!3, intersection(B!3, C!2)) = difference(B!3, C!2)) <=> (difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2)))),
% 0.79/0.97 inference(symmetry,[status(thm)],[93])).
% 0.79/0.97 tff(95,plain,
% 0.79/0.97 ((~(difference(B!3, intersection(B!3, C!2)) = difference(B!3, C!2))) <=> (~(difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[94])).
% 0.79/0.97 tff(96,plain,
% 0.79/0.97 ((~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))) <=> (~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(97,axiom,(~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_difference_into_intersection')).
% 0.79/0.97 tff(98,plain,
% 0.79/0.97 (~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.79/0.97 tff(99,plain,
% 0.79/0.97 (~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[98, 96])).
% 0.79/0.97 tff(100,plain,
% 0.79/0.97 (~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.79/0.97 tff(101,plain,
% 0.79/0.97 (~![B: $i, C: $i] : (difference(B, intersection(B, C)) = difference(B, C))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.79/0.97 tff(102,plain,(
% 0.79/0.97 ~(difference(B!3, intersection(B!3, C!2)) = difference(B!3, C!2))),
% 0.79/0.97 inference(skolemize,[status(sab)],[101])).
% 0.79/0.97 tff(103,plain,
% 0.79/0.97 (~(difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.79/0.97 tff(104,plain,
% 0.79/0.97 ((~((difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))) | (~(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2))))))) | (difference(B!3, C!2) = difference(B!3, intersection(B!3, C!2))) | (~(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(105,plain,
% 0.79/0.97 (~(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[104, 103, 92])).
% 0.79/0.97 tff(106,plain,
% 0.79/0.97 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(107,plain,
% 0.79/0.97 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[106])).
% 0.79/0.97 tff(108,plain,
% 0.79/0.97 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(109,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.79/0.97 tff(110,plain,
% 0.79/0.97 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.79/0.97 tff(111,plain,(
% 0.79/0.97 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.79/0.97 inference(skolemize,[status(sab)],[110])).
% 0.79/0.97 tff(112,plain,
% 0.79/0.97 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.79/0.97 tff(113,plain,
% 0.79/0.97 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, C!2) = intersection(C!2, B!3))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(114,plain,
% 0.79/0.97 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.79/0.97 tff(115,plain,
% 0.79/0.97 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.79/0.97 inference(symmetry,[status(thm)],[114])).
% 0.79/0.97 tff(116,plain,
% 0.79/0.97 (difference(intersection(B!3, B!3), intersection(C!2, B!3)) = difference(B!3, intersection(B!3, C!2))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[60, 115])).
% 0.79/0.97 tff(117,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[116])).
% 0.79/0.97 tff(118,plain,
% 0.79/0.97 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3)))) <=> (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[117])).
% 0.79/0.97 tff(119,plain,
% 0.79/0.97 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(120,plain,
% 0.79/0.97 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[119])).
% 0.79/0.97 tff(121,plain,
% 0.79/0.97 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(122,plain,
% 0.79/0.97 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[121])).
% 0.79/0.97 tff(123,plain,
% 0.79/0.97 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(124,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.79/0.97 tff(125,plain,
% 0.79/0.97 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.79/0.97 tff(126,plain,(
% 0.79/0.97 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.79/0.97 inference(skolemize,[status(sab)],[125])).
% 0.79/0.97 tff(127,plain,
% 0.79/0.97 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.79/0.97 tff(128,plain,
% 0.79/0.97 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.79/0.97 tff(129,plain,
% 0.79/0.97 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3)))))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(130,plain,
% 0.79/0.97 (~(((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.79/0.97 tff(131,assumption,(~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))), introduced(assumption)).
% 0.79/0.97 tff(132,plain,
% 0.79/0.97 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) <=> (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[88])).
% 0.79/0.97 tff(133,plain,
% 0.79/0.97 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[131, 132])).
% 0.79/0.97 tff(134,plain,
% 0.79/0.97 ((((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3)))) | ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3)))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(135,plain,
% 0.79/0.97 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[134, 133, 12])).
% 0.79/0.97 tff(136,assumption,(~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3)))), introduced(assumption)).
% 0.79/0.97 tff(137,plain,
% 0.79/0.97 (((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(138,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.79/0.97 tff(139,plain,
% 0.79/0.97 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(140,plain,
% 0.79/0.97 (~(((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[139, 128])).
% 0.79/0.97 tff(141,plain,
% 0.79/0.97 (difference(intersection(B!3, B!3), intersection(C!2, C!2)) = difference(B!3, C!2)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[60, 85])).
% 0.79/0.97 tff(142,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[141])).
% 0.79/0.97 tff(143,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))),
% 0.79/0.97 inference(symmetry,[status(thm)],[142])).
% 0.79/0.97 tff(144,plain,
% 0.79/0.97 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2))) <=> (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[143])).
% 0.79/0.97 tff(145,plain,
% 0.79/0.97 ((((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3)))) | ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3)))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(146,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3)))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[145, 136, 130])).
% 0.79/0.97 tff(147,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[146, 117])).
% 0.79/0.97 tff(148,plain,
% 0.79/0.97 ((member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2))))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(149,plain,
% 0.79/0.97 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[148, 147, 105])).
% 0.79/0.97 tff(150,plain,
% 0.79/0.97 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[149, 144])).
% 0.79/0.97 tff(151,plain,
% 0.79/0.97 ((((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))) | ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(152,plain,
% 0.79/0.97 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[151, 150, 140])).
% 0.79/0.97 tff(153,plain,
% 0.79/0.97 ((~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(154,plain,
% 0.79/0.97 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[153, 152, 138])).
% 0.79/0.97 tff(155,plain,
% 0.79/0.97 ((~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))),
% 0.79/0.97 inference(tautology,[status(thm)],[])).
% 0.79/0.97 tff(156,plain,
% 0.79/0.97 ((~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[155, 138])).
% 0.79/0.97 tff(157,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[156, 154, 135])).
% 0.79/0.97 tff(158,plain,(((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(159,plain,
% 0.79/0.97 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[158, 131])).
% 0.79/0.97 tff(160,plain,
% 0.79/0.97 ((((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3)))) | (~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3)))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3))))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(161,plain,
% 0.79/0.98 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3)))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[160, 159, 130])).
% 0.79/0.98 tff(162,plain,
% 0.79/0.98 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[161, 118])).
% 0.79/0.98 tff(163,plain,
% 0.79/0.98 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))) <=> (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[142])).
% 0.79/0.98 tff(164,plain,
% 0.79/0.98 ((~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3)))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(165,plain,
% 0.79/0.98 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[164, 159, 131])).
% 0.79/0.98 tff(166,plain,
% 0.79/0.98 (((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(167,plain,
% 0.79/0.98 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.79/0.98 tff(168,plain,
% 0.79/0.98 ((((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))) | (~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2))))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(169,plain,
% 0.79/0.98 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[168, 167, 140])).
% 0.79/0.98 tff(170,plain,
% 0.79/0.98 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[169, 163])).
% 0.79/0.98 tff(171,plain,
% 0.79/0.98 ((member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2)) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(172,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[171, 170, 162, 105])).
% 0.79/0.98 tff(173,plain,(member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(174,plain,
% 0.79/0.98 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[173, 88])).
% 0.79/0.98 tff(175,plain,
% 0.79/0.98 ((((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))) <=> member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3)))) | (~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(intersection(C!2, C!2), intersection(B!3, B!3))))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(176,plain,
% 0.79/0.98 (~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[175, 174, 12])).
% 0.79/0.98 tff(177,plain,
% 0.79/0.98 (((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3)))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(178,plain,
% 0.79/0.98 ((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, B!3))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[177, 173])).
% 0.79/0.98 tff(179,plain,
% 0.79/0.98 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, B!3)))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[160, 178, 130])).
% 0.79/0.98 tff(180,plain,
% 0.79/0.98 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, intersection(B!3, C!2)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[179, 118])).
% 0.79/0.98 tff(181,plain,
% 0.79/0.98 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(B!3, C!2))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[171, 180, 105])).
% 0.79/0.98 tff(182,plain,
% 0.79/0.98 (member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), difference(intersection(B!3, B!3), intersection(C!2, C!2)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[181, 143])).
% 0.79/0.98 tff(183,plain,
% 0.79/0.98 (~((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[168, 182, 140])).
% 0.79/0.98 tff(184,plain,
% 0.79/0.98 (((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(185,plain,
% 0.79/0.98 (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.79/0.98 tff(186,plain,
% 0.79/0.98 (((~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(B!3, B!3))) | (~member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2)))) | member(tptp_fun_D_0(difference(B!3, intersection(B!3, C!2)), difference(B!3, C!2)), intersection(C!2, C!2))),
% 0.79/0.98 inference(tautology,[status(thm)],[])).
% 0.79/0.98 tff(187,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[186, 185, 176])).
% 0.79/0.98 % SZS output end Proof
% 0.79/0.98 % E exiting
%------------------------------------------------------------------------------