%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET608+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET608+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:30:10 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 tff(member_type, type, (
% 0.19/0.51 member: ( $i * $i ) > $o)).
% 0.19/0.51 tff(difference_type, type, (
% 0.19/0.51 difference: ( $i * $i ) > $i)).
% 0.19/0.51 tff(tptp_fun_C_2_type, type, (
% 0.19/0.51 tptp_fun_C_2: $i)).
% 0.19/0.51 tff(tptp_fun_B_3_type, type, (
% 0.19/0.51 tptp_fun_B_3: $i)).
% 0.19/0.51 tff(tptp_fun_D_1_type, type, (
% 0.19/0.51 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.19/0.51 tff(union_type, type, (
% 0.19/0.51 union: ( $i * $i ) > $i)).
% 0.19/0.51 tff(intersection_type, type, (
% 0.19/0.51 intersection: ( $i * $i ) > $i)).
% 0.19/0.51 tff(1,plain,
% 0.19/0.51 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(2,plain,
% 0.19/0.51 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.51 tff(3,plain,
% 0.19/0.51 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(4,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.19/0.51 tff(5,plain,
% 0.19/0.51 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.51 tff(6,plain,(
% 0.19/0.51 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.51 inference(skolemize,[status(sab)],[5])).
% 0.19/0.51 tff(7,plain,
% 0.19/0.51 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.51 tff(8,plain,
% 0.19/0.51 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, C!2) = intersection(C!2, B!3))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(9,plain,
% 0.19/0.51 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.51 tff(10,plain,
% 0.19/0.51 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.19/0.51 inference(symmetry,[status(thm)],[9])).
% 0.19/0.51 tff(11,plain,
% 0.19/0.51 (union(difference(B!3, C!2), intersection(C!2, B!3)) = union(difference(B!3, C!2), intersection(B!3, C!2))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.51 tff(12,plain,
% 0.19/0.51 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[11])).
% 0.19/0.51 tff(13,plain,
% 0.19/0.51 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[12])).
% 0.19/0.51 tff(14,plain,
% 0.19/0.51 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[13])).
% 0.19/0.51 tff(15,assumption,(~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)), introduced(assumption)).
% 0.19/0.51 tff(16,assumption,(~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))), introduced(assumption)).
% 0.19/0.51 tff(17,plain,
% 0.19/0.51 (^[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)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(18,plain,
% 0.19/0.51 (![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))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.51 tff(19,plain,
% 0.19/0.51 (^[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))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(20,plain,
% 0.19/0.51 (![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))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.51 tff(21,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(22,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_defn')).
% 0.19/0.51 tff(23,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.51 tff(24,plain,(
% 0.19/0.51 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[23])).
% 0.19/0.51 tff(25,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.51 tff(26,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.51 tff(27,plain,
% 0.19/0.51 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(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_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(28,plain,
% 0.19/0.51 ((~(~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))) <=> (member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(29,plain,
% 0.19/0.51 ((~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))) <=> (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(30,plain,
% 0.19/0.51 (((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))) <=> (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(31,plain,
% 0.19/0.51 (((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(32,plain,
% 0.19/0.51 ((((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))) <=> ((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.51 tff(33,plain,
% 0.19/0.51 ((((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))) <=> (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[32, 30])).
% 0.19/0.51 tff(34,plain,
% 0.19/0.51 ((((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))) <=> (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[33, 29])).
% 0.19/0.51 tff(35,plain,
% 0.19/0.51 ((~(((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))) <=> (~(~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.51 tff(36,plain,
% 0.19/0.51 ((~(((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))) <=> (member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[35, 28])).
% 0.19/0.51 tff(37,plain,
% 0.19/0.51 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_1(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_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.51 tff(38,plain,
% 0.19/0.51 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_1(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_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[37, 27])).
% 0.19/0.51 tff(39,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2)) | (~member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2))) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(40,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.51 tff(41,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[40, 26, 16])).
% 0.19/0.51 tff(42,plain,(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(43,plain,
% 0.19/0.51 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(44,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.51 tff(45,plain,
% 0.19/0.51 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.51 inference(pull_quant,[status(thm)],[])).
% 0.19/0.51 tff(46,plain,
% 0.19/0.51 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(47,plain,
% 0.19/0.51 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.51 tff(48,plain,
% 0.19/0.51 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.51 tff(49,plain,
% 0.19/0.51 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[48, 44])).
% 0.19/0.51 tff(50,plain,
% 0.19/0.51 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(51,plain,
% 0.19/0.51 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.51 tff(52,plain,
% 0.19/0.51 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.51 tff(53,plain,
% 0.19/0.51 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), trans(monotonicity(rewrite((~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))) <=> (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(54,plain,
% 0.19/0.52 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.52 tff(55,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(56,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_member_defn')).
% 0.19/0.52 tff(57,plain,
% 0.19/0.52 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.52 tff(58,plain,(
% 0.19/0.52 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[57])).
% 0.19/0.52 tff(59,plain,
% 0.19/0.52 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.52 tff(60,plain,
% 0.19/0.52 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.52 tff(61,plain,
% 0.19/0.52 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(C!2 = intersection(C!2, C!2))) | (member(tptp_fun_D_1(difference(B!3, C!2), C!2), C!2) <=> member(tptp_fun_D_1(difference(B!3, C!2), C!2), intersection(C!2, C!2))))) | (~((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(62,plain,
% 0.19/0.52 (~((~((~(C!2 = intersection(C!2, C!2))) | (member(tptp_fun_D_1(difference(B!3, C!2), C!2), C!2) <=> member(tptp_fun_D_1(difference(B!3, C!2), C!2), intersection(C!2, C!2))))) | (~((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.52 tff(63,plain,
% 0.19/0.52 (((~((~(C!2 = intersection(C!2, C!2))) | (member(tptp_fun_D_1(difference(B!3, C!2), C!2), C!2) <=> member(tptp_fun_D_1(difference(B!3, C!2), C!2), intersection(C!2, C!2))))) | (~((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))))) | ((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(64,plain,
% 0.19/0.52 ((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.52 tff(65,plain,
% 0.19/0.52 ((~((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2)))))) | (C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(66,plain,
% 0.19/0.52 ((C!2 = intersection(C!2, C!2)) | (~(member(tptp_fun_D_1(intersection(C!2, C!2), C!2), C!2) <=> member(tptp_fun_D_1(intersection(C!2, C!2), C!2), intersection(C!2, C!2))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.52 tff(67,plain,
% 0.19/0.52 (C!2 = intersection(C!2, C!2)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[66, 42])).
% 0.19/0.52 tff(68,assumption,(C!2 = intersection(C!2, C!2)), introduced(assumption)).
% 0.19/0.52 tff(69,plain,
% 0.19/0.52 (intersection(C!2, C!2) = C!2),
% 0.19/0.52 inference(symmetry,[status(thm)],[68])).
% 0.19/0.52 tff(70,plain,
% 0.19/0.52 (intersection(intersection(C!2, C!2), B!3) = intersection(C!2, B!3)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.52 tff(71,plain,
% 0.19/0.52 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3)) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.52 tff(72,plain,
% 0.19/0.52 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))),
% 0.19/0.52 inference(symmetry,[status(thm)],[71])).
% 0.19/0.52 tff(73,assumption,(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))), introduced(assumption)).
% 0.19/0.52 tff(74,plain,
% 0.19/0.52 (difference(B!3, intersection(C!2, C!2)) = difference(B!3, C!2)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.52 tff(75,plain,
% 0.19/0.52 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.52 tff(76,plain,
% 0.19/0.52 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))),
% 0.19/0.52 inference(symmetry,[status(thm)],[75])).
% 0.19/0.52 tff(77,assumption,(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))), introduced(assumption)).
% 0.19/0.52 tff(78,plain,
% 0.19/0.52 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.52 tff(79,plain,
% 0.19/0.52 (^[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)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(80,plain,
% 0.19/0.52 (![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))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.52 tff(81,plain,
% 0.19/0.52 (^[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))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(82,plain,
% 0.19/0.52 (![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))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.52 tff(83,plain,
% 0.19/0.52 (![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))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(84,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_defn')).
% 0.19/0.52 tff(85,plain,
% 0.19/0.52 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.52 tff(86,plain,(
% 0.19/0.52 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[85])).
% 0.19/0.52 tff(87,plain,
% 0.19/0.52 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.52 tff(88,plain,
% 0.19/0.52 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.19/0.52 tff(89,plain,
% 0.19/0.52 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(90,plain,
% 0.19/0.52 (~(((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.52 tff(91,plain,
% 0.19/0.52 (((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(92,plain,
% 0.19/0.52 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[91, 15])).
% 0.19/0.52 tff(93,plain,
% 0.19/0.52 ((((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))) | (~((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(94,plain,
% 0.19/0.52 ((((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.52 tff(95,plain,
% 0.19/0.52 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[94, 90])).
% 0.19/0.52 tff(96,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[95, 78])).
% 0.19/0.52 tff(97,plain,((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))) | (~(C!2 = intersection(C!2, C!2))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(98,plain,
% 0.19/0.52 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[97, 68, 15])).
% 0.19/0.52 tff(99,plain,
% 0.19/0.52 ((~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(100,plain,
% 0.19/0.52 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[99, 98, 73])).
% 0.19/0.52 tff(101,plain,
% 0.19/0.52 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[100, 72])).
% 0.19/0.52 tff(102,plain,
% 0.19/0.52 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(103,plain,
% 0.19/0.52 (~(((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[102, 26])).
% 0.19/0.52 tff(104,plain,
% 0.19/0.52 (((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(105,plain,
% 0.19/0.52 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[104, 15])).
% 0.19/0.52 tff(106,plain,
% 0.19/0.52 ((((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))) | (~((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(107,plain,
% 0.19/0.52 ((((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.52 tff(108,plain,
% 0.19/0.52 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[107, 103])).
% 0.19/0.52 tff(109,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[108, 101])).
% 0.19/0.52 tff(110,plain,((~(C!2 = intersection(C!2, C!2))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(111,plain,
% 0.19/0.52 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[110, 67])).
% 0.19/0.52 tff(112,plain,
% 0.19/0.52 (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[111, 15])).
% 0.19/0.52 tff(113,assumption,((~((~(B!3 = union(difference(B!3, C!2), intersection(B!3, C!2)))) | (member(tptp_fun_D_1(intersection(C!2, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(C!2, B!3), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))) | (~((B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))))), introduced(assumption)).
% 0.19/0.52 tff(114,plain,
% 0.19/0.52 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~(B!3 = union(difference(B!3, C!2), intersection(B!3, C!2)))) | (member(tptp_fun_D_1(intersection(C!2, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(C!2, B!3), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))) | (~((B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(115,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[114, 60, 113])).
% 0.19/0.52 tff(116,plain,(~((~((~(B!3 = union(difference(B!3, C!2), intersection(B!3, C!2)))) | (member(tptp_fun_D_1(intersection(C!2, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(C!2, B!3), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))) | (~((B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(117,plain,
% 0.19/0.52 (((~((~(B!3 = union(difference(B!3, C!2), intersection(B!3, C!2)))) | (member(tptp_fun_D_1(intersection(C!2, B!3), B!3), B!3) <=> member(tptp_fun_D_1(intersection(C!2, B!3), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))) | (~((B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))))) | ((B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2))))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(118,plain,
% 0.19/0.53 ((B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.53 tff(119,assumption,(B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))), introduced(assumption)).
% 0.19/0.53 tff(120,plain,
% 0.19/0.53 (union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3),
% 0.19/0.53 inference(symmetry,[status(thm)],[119])).
% 0.19/0.53 tff(121,plain,
% 0.19/0.53 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(122,plain,
% 0.19/0.53 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.53 tff(123,plain,
% 0.19/0.53 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(124,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.19/0.53 tff(125,plain,
% 0.19/0.53 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.53 tff(126,plain,(
% 0.19/0.53 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.53 inference(skolemize,[status(sab)],[125])).
% 0.19/0.53 tff(127,plain,
% 0.19/0.53 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.19/0.53 tff(128,plain,
% 0.19/0.53 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(B!3, C!2), difference(B!3, C!2)) = union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(129,plain,
% 0.19/0.53 (union(intersection(B!3, C!2), difference(B!3, C!2)) = union(difference(B!3, C!2), intersection(B!3, C!2))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.53 tff(130,plain,
% 0.19/0.53 (union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3),
% 0.19/0.53 inference(transitivity,[status(thm)],[129, 120])).
% 0.19/0.53 tff(131,plain,
% 0.19/0.53 ((~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)) <=> (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(132,axiom,(~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_union_intersection_difference')).
% 0.19/0.53 tff(133,plain,
% 0.19/0.53 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.53 tff(134,plain,
% 0.19/0.53 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[133, 131])).
% 0.19/0.53 tff(135,plain,
% 0.19/0.53 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[134, 131])).
% 0.19/0.53 tff(136,plain,
% 0.19/0.53 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.19/0.53 tff(137,plain,(
% 0.19/0.53 ~(union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3)),
% 0.19/0.53 inference(skolemize,[status(sab)],[136])).
% 0.19/0.53 tff(138,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[137, 130])).
% 0.19/0.53 tff(139,plain,(~(B!3 = union(difference(B!3, C!2), intersection(B!3, C!2)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(140,plain,
% 0.19/0.53 ((~((B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2))))))) | (B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(141,plain,
% 0.19/0.53 ((~((B!3 = union(difference(B!3, C!2), intersection(B!3, C!2))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2))))))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.53 tff(142,plain,
% 0.19/0.53 (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[141, 118])).
% 0.19/0.53 tff(143,plain,
% 0.19/0.53 ((member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(144,plain,
% 0.19/0.53 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.53 tff(145,plain,
% 0.19/0.53 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[144, 15])).
% 0.19/0.53 tff(146,assumption,(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))), introduced(assumption)).
% 0.19/0.53 tff(147,plain,
% 0.19/0.53 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[146, 13])).
% 0.19/0.53 tff(148,plain,
% 0.19/0.53 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(149,plain,
% 0.19/0.53 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.53 tff(150,plain,
% 0.19/0.53 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(151,plain,
% 0.19/0.53 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(152,plain,
% 0.19/0.53 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.53 tff(153,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_defn')).
% 0.19/0.53 tff(154,plain,
% 0.19/0.53 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.53 tff(155,plain,
% 0.19/0.53 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.19/0.53 tff(156,plain,(
% 0.19/0.53 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.53 inference(skolemize,[status(sab)],[155])).
% 0.19/0.53 tff(157,plain,
% 0.19/0.53 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.19/0.53 tff(158,plain,
% 0.19/0.53 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(159,plain,
% 0.19/0.53 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.53 tff(160,assumption,(~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)))), introduced(assumption)).
% 0.19/0.53 tff(161,plain,
% 0.19/0.53 ((~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3)))) | (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(162,plain,
% 0.19/0.53 ((~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.19/0.53 tff(163,plain,
% 0.19/0.53 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.19/0.53 tff(164,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[163, 147])).
% 0.19/0.53 tff(165,plain,((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))) | (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(166,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[165, 145, 112])).
% 0.19/0.53 tff(167,plain,(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(168,plain,
% 0.19/0.53 ((member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(169,plain,
% 0.19/0.53 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[168, 142])).
% 0.19/0.53 tff(170,plain,
% 0.19/0.53 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[169, 167])).
% 0.19/0.53 tff(171,plain,
% 0.19/0.53 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[170, 14])).
% 0.19/0.53 tff(172,assumption,(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3)))), introduced(assumption)).
% 0.19/0.53 tff(173,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.19/0.53 tff(174,plain,(~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(175,plain,
% 0.19/0.53 ((member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(176,plain,
% 0.19/0.53 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[175, 160])).
% 0.19/0.53 tff(177,plain,
% 0.19/0.53 ((member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(178,plain,
% 0.19/0.53 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[177, 160])).
% 0.19/0.53 tff(179,assumption,(((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))), introduced(assumption)).
% 0.19/0.53 tff(180,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[89, 88, 179])).
% 0.19/0.53 tff(181,plain,(~(((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(182,plain,
% 0.19/0.53 (intersection(C!2, C!2) = C!2),
% 0.19/0.53 inference(symmetry,[status(thm)],[67])).
% 0.19/0.53 tff(183,plain,
% 0.19/0.53 (intersection(intersection(C!2, C!2), B!3) = intersection(C!2, B!3)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[182])).
% 0.19/0.53 tff(184,plain,
% 0.19/0.53 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3)) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[183])).
% 0.19/0.53 tff(185,plain,
% 0.19/0.53 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))),
% 0.19/0.53 inference(symmetry,[status(thm)],[184])).
% 0.19/0.53 tff(186,plain,
% 0.19/0.53 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3))) <=> (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3)))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[185])).
% 0.19/0.53 tff(187,assumption,(~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3))), introduced(assumption)).
% 0.19/0.53 tff(188,plain,
% 0.19/0.53 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.53 tff(189,plain,
% 0.19/0.53 ((((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))) | ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(intersection(C!2, C!2), B!3))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(190,plain,
% 0.19/0.53 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[189, 188, 103])).
% 0.19/0.53 tff(191,assumption,(~(((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2))))), introduced(assumption)).
% 0.19/0.53 tff(192,plain,
% 0.19/0.53 (difference(B!3, intersection(C!2, C!2)) = difference(B!3, C!2)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[182])).
% 0.19/0.53 tff(193,plain,
% 0.19/0.53 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[192])).
% 0.19/0.53 tff(194,plain,
% 0.19/0.53 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2)) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))),
% 0.19/0.53 inference(symmetry,[status(thm)],[193])).
% 0.19/0.53 tff(195,plain,
% 0.19/0.53 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))) <=> (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[194])).
% 0.19/0.53 tff(196,assumption,(~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))), introduced(assumption)).
% 0.19/0.53 tff(197,plain,
% 0.19/0.53 (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.53 tff(198,plain,
% 0.19/0.53 ((((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))) | ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(199,plain,
% 0.19/0.54 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[198, 197, 191])).
% 0.19/0.54 tff(200,assumption,(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)), introduced(assumption)).
% 0.19/0.54 tff(201,plain,
% 0.19/0.54 ((~((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(202,plain,
% 0.19/0.54 ((~((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.19/0.54 tff(203,plain,
% 0.19/0.54 (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[202, 199])).
% 0.19/0.54 tff(204,plain,
% 0.19/0.54 ((~((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(205,plain,
% 0.19/0.54 ((~((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[204, 200])).
% 0.19/0.54 tff(206,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[205, 203, 190])).
% 0.19/0.54 tff(207,plain,((((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, intersection(C!2, C!2)))) | (~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(208,plain,
% 0.19/0.54 ((~member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[207, 181])).
% 0.19/0.54 tff(209,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[208, 178, 176, 167])).
% 0.19/0.54 tff(210,plain,(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(211,plain,
% 0.19/0.54 ((~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))))) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))) | (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(212,plain,
% 0.19/0.54 (~(member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), intersection(C!2, B!3)) | member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), B!3), difference(B!3, C!2))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[211, 210, 174])).
% 0.19/0.54 tff(213,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[158, 157, 212])).
% 0.19/0.54 % SZS output end Proof
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------