%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET630+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:03 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET630+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 05:32:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(disjoint_type, type, (
% 0.12/0.38 disjoint: ( $i * $i ) > $o)).
% 0.12/0.38 tff(difference_type, type, (
% 0.12/0.38 difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_3_type, type, (
% 0.12/0.38 tptp_fun_B_3: $i)).
% 0.12/0.38 tff(tptp_fun_C_2_type, type, (
% 0.12/0.38 tptp_fun_C_2: $i)).
% 0.12/0.38 tff(intersection_type, type, (
% 0.12/0.38 intersection: ( $i * $i ) > $i)).
% 0.12/0.38 tff(intersect_type, type, (
% 0.12/0.38 intersect: ( $i * $i ) > $o)).
% 0.12/0.38 tff(union_type, type, (
% 0.12/0.38 union: ( $i * $i ) > $i)).
% 0.12/0.38 tff(symmetric_difference_type, type, (
% 0.12/0.38 symmetric_difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!2, B!3) = intersection(B!3, C!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.12/0.38 inference(symmetry,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (disjoint(intersection(B!3, C!2), difference(C!2, B!3)) <=> disjoint(intersection(C!2, B!3), difference(C!2, B!3))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (disjoint(intersection(C!2, B!3), difference(C!2, B!3)) <=> disjoint(intersection(B!3, C!2), difference(C!2, B!3))),
% 0.12/0.38 inference(symmetry,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl(disjoint(intersection(B, C), difference(B, C)) <=> disjoint(intersection(B, C), difference(B, C)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C)) <=> ![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C)) <=> ![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,axiom,(![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_and_union_disjoint')).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.38 tff(18,plain,(
% 0.12/0.38 ![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.12/0.38 inference(skolemize,[status(sab)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))) | disjoint(intersection(C!2, B!3), difference(C!2, B!3))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (disjoint(intersection(C!2, B!3), difference(C!2, B!3))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (disjoint(intersection(B!3, C!2), difference(C!2, B!3))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl((~(intersect(B, C) <=> disjoint(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (^[B: $i, C: $i] : trans(rewrite((disjoint(B, C) <=> (~intersect(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))), rewrite((~(intersect(B, C) <=> disjoint(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))), ((disjoint(B, C) <=> (~intersect(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.38 tff(28,axiom,(![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','disjoint_defn')).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.38 tff(31,plain,(
% 0.12/0.38 ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))) | (~(intersect(intersection(B!3, C!2), difference(C!2, B!3)) <=> disjoint(intersection(B!3, C!2), difference(C!2, B!3))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~(intersect(intersection(B!3, C!2), difference(C!2, B!3)) <=> disjoint(intersection(B!3, C!2), difference(C!2, B!3)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))) | (~(intersect(intersection(B!3, C!2), difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), difference(B!3, C!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (~(intersect(intersection(B!3, C!2), difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), difference(B!3, C!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))) | disjoint(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (disjoint(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 19])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((intersect(intersection(B!3, C!2), difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), difference(B!3, C!2))) | (~intersect(intersection(B!3, C!2), difference(B!3, C!2))) | (~disjoint(intersection(B!3, C!2), difference(B!3, C!2)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((intersect(intersection(B!3, C!2), difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), difference(B!3, C!2))) | (~intersect(intersection(B!3, C!2), difference(B!3, C!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (~intersect(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[40, 36])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (^[B: $i, C: $i, D: $i] : refl((intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C))) <=> (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C))) <=> ![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C))) <=> ![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (^[B: $i, C: $i, D: $i] : rewrite((intersect(B, union(C, D)) <=> (intersect(B, C) | intersect(B, D))) <=> (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, C) | intersect(B, D))) <=> ![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.39 tff(47,axiom,(![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, C) | intersect(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_with_union')).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.39 tff(50,plain,(
% 0.20/0.39 ![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[49])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) | (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3))))) <=> ((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) | (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(C!2, B!3)) | intersect(intersection(B!3, C!2), difference(B!3, C!2)))) <=> (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) | (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(C!2, B!3)) | intersect(intersection(B!3, C!2), difference(B!3, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) | (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) | (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(C!2, B!3)) | intersect(intersection(B!3, C!2), difference(B!3, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) | (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) | (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(C!2, B!3)) | intersect(intersection(B!3, C!2), difference(B!3, C!2))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) | (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[57, 51])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetric_difference_defn')).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,(
% 0.20/0.39 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[63])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(B!3, C!2) = union(difference(B!3, C!2), difference(C!2, B!3)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (symmetric_difference(B!3, C!2) = union(difference(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (union(difference(B!3, C!2), difference(C!2, B!3)) = symmetric_difference(B!3, C!2)),
% 0.20/0.39 inference(symmetry,[status(thm)],[67])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) <=> intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3)))),
% 0.20/0.39 inference(symmetry,[status(thm)],[69])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 ((~![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))) | (~(intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), symmetric_difference(B!3, C!2))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (~(intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), symmetric_difference(B!3, C!2)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 32])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 ((~![B: $i, C: $i] : disjoint(intersection(B, C), symmetric_difference(B, C))) <=> (~![B: $i, C: $i] : disjoint(intersection(B, C), symmetric_difference(B, C)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(74,axiom,(~![B: $i, C: $i] : disjoint(intersection(B, C), symmetric_difference(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_intersection_and_symmetric_difference_disjoint')).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), symmetric_difference(B, C))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), symmetric_difference(B, C))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[75, 73])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), symmetric_difference(B, C))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), symmetric_difference(B, C))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.39 tff(79,plain,(
% 0.20/0.39 ~disjoint(intersection(B!3, C!2), symmetric_difference(B!3, C!2))),
% 0.20/0.39 inference(skolemize,[status(sab)],[78])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 ((intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), symmetric_difference(B!3, C!2))) | intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) | disjoint(intersection(B!3, C!2), symmetric_difference(B!3, C!2))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 ((intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), symmetric_difference(B!3, C!2))) | intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (intersect(intersection(B!3, C!2), symmetric_difference(B!3, C!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[81, 72])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[82, 70])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 ((~(intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3))) <=> (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3))))) | (~intersect(intersection(B!3, C!2), union(difference(B!3, C!2), difference(C!2, B!3)))) | (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 (intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[84, 83, 58])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((~(intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3)))) | intersect(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (intersect(intersection(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[86, 85, 41])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 ((intersect(intersection(B!3, C!2), difference(C!2, B!3)) <=> disjoint(intersection(B!3, C!2), difference(C!2, B!3))) | (~intersect(intersection(B!3, C!2), difference(C!2, B!3))) | (~disjoint(intersection(B!3, C!2), difference(C!2, B!3)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (~disjoint(intersection(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[88, 87, 34])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[89, 22])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------