%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET619+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:26:01 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET619+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:33:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(union_type, type, (
% 0.12/0.37 union: ( $i * $i ) > $i)).
% 0.12/0.37 tff(intersection_type, type, (
% 0.12/0.37 intersection: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_C_2_type, type, (
% 0.12/0.37 tptp_fun_C_2: $i)).
% 0.12/0.37 tff(tptp_fun_B_3_type, type, (
% 0.12/0.37 tptp_fun_B_3: $i)).
% 0.12/0.37 tff(symmetric_difference_type, type, (
% 0.12/0.37 symmetric_difference: ( $i * $i ) > $i)).
% 0.12/0.37 tff(difference_type, type, (
% 0.12/0.37 difference: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) = union(symmetric_difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (union(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) = union(symmetric_difference(B!3, C!2), intersection(B!3, C!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,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')).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.37 tff(15,plain,(
% 0.12/0.37 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[14])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(C!2, B!3) = union(difference(C!2, B!3), difference(B!3, C!2)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (symmetric_difference(C!2, B!3) = union(difference(C!2, B!3), difference(B!3, C!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = symmetric_difference(C, B)) <=> (symmetric_difference(B, C) = symmetric_difference(C, B)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(22,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_symmetric_difference')).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.37 tff(24,plain,(
% 0.12/0.37 ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.37 inference(skolemize,[status(sab)],[23])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))) | (symmetric_difference(C!2, B!3) = symmetric_difference(B!3, C!2))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (symmetric_difference(C!2, B!3) = symmetric_difference(B!3, C!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (symmetric_difference(B!3, C!2) = symmetric_difference(C!2, B!3)),
% 0.12/0.37 inference(symmetry,[status(thm)],[27])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (symmetric_difference(B!3, C!2) = union(difference(C!2, B!3), difference(B!3, C!2))),
% 0.12/0.37 inference(transitivity,[status(thm)],[28, 18])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (union(intersection(B!3, C!2), symmetric_difference(B!3, C!2)) = union(intersection(B!3, C!2), union(difference(C!2, B!3), difference(B!3, C!2)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (union(intersection(B!3, C!2), union(difference(C!2, B!3), difference(B!3, C!2))) = union(intersection(B!3, C!2), symmetric_difference(B!3, C!2))),
% 0.12/0.37 inference(symmetry,[status(thm)],[30])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (^[B: $i, C: $i, D: $i] : refl((union(union(B, C), D) = union(B, union(C, D))) <=> (union(union(B, C), D) = union(B, union(C, D))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D))) <=> ![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D))) <=> ![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(35,axiom,(![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','associativity_of_union')).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.37 tff(37,plain,(
% 0.12/0.37 ![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[36])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(intersection(B!3, C!2), difference(C!2, B!3)), difference(B!3, C!2)) = union(intersection(B!3, C!2), union(difference(C!2, B!3), difference(B!3, C!2))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (union(union(intersection(B!3, C!2), difference(C!2, B!3)), difference(B!3, C!2)) = union(intersection(B!3, C!2), union(difference(C!2, B!3), difference(B!3, C!2)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(44,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.37 tff(46,plain,(
% 0.12/0.37 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.37 inference(skolemize,[status(sab)],[45])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!2, B!3) = intersection(B!3, C!2))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.12/0.37 inference(symmetry,[status(thm)],[49])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (union(C!2, intersection(B!3, C!2)) = union(C!2, intersection(C!2, B!3))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[50])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (union(C!2, intersection(C!2, B!3)) = union(C!2, intersection(B!3, C!2))),
% 0.12/0.37 inference(symmetry,[status(thm)],[51])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (^[B: $i, C: $i] : refl((union(B, intersection(B, C)) = B) <=> (union(B, intersection(B, C)) = B))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B) <=> ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B) <=> ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(56,axiom,(![B: $i, C: $i] : (union(B, intersection(B, C)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_intersection')).
% 0.12/0.37 tff(57,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.37 tff(58,plain,(
% 0.12/0.37 ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.12/0.37 inference(skolemize,[status(sab)],[57])).
% 0.12/0.37 tff(59,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.12/0.37 tff(60,plain,
% 0.12/0.37 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(C!2, intersection(C!2, B!3)) = C!2)),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 (union(C!2, intersection(C!2, B!3)) = C!2),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.12/0.37 tff(62,plain,
% 0.12/0.37 (C!2 = union(C!2, intersection(C!2, B!3))),
% 0.12/0.37 inference(symmetry,[status(thm)],[61])).
% 0.12/0.37 tff(63,plain,
% 0.12/0.37 (^[B: $i, C: $i] : refl((union(intersection(B, C), difference(B, C)) = B) <=> (union(intersection(B, C), difference(B, C)) = B))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(64,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B) <=> ![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[63])).
% 0.12/0.37 tff(65,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B) <=> ![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(66,axiom,(![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_intersection_difference')).
% 0.12/0.37 tff(67,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.37 tff(68,plain,(
% 0.12/0.37 ![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.12/0.37 inference(skolemize,[status(sab)],[67])).
% 0.12/0.37 tff(69,plain,
% 0.12/0.37 (![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.12/0.37 tff(70,plain,
% 0.12/0.37 ((~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)) | (union(intersection(C!2, B!3), difference(C!2, B!3)) = C!2)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 (union(intersection(C!2, B!3), difference(C!2, B!3)) = C!2),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 (union(intersection(B!3, C!2), difference(C!2, B!3)) = union(intersection(C!2, B!3), difference(C!2, B!3))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[50])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 (union(intersection(B!3, C!2), difference(C!2, B!3)) = union(C!2, intersection(B!3, C!2))),
% 0.12/0.38 inference(transitivity,[status(thm)],[72, 71, 62, 52])).
% 0.12/0.38 tff(74,plain,
% 0.12/0.38 (union(union(intersection(B!3, C!2), difference(C!2, B!3)), difference(B!3, C!2)) = union(union(C!2, intersection(B!3, C!2)), difference(B!3, C!2))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[73])).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 (union(union(C!2, intersection(B!3, C!2)), difference(B!3, C!2)) = union(union(intersection(B!3, C!2), difference(C!2, B!3)), difference(B!3, C!2))),
% 0.12/0.38 inference(symmetry,[status(thm)],[74])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(C!2, intersection(B!3, C!2)), difference(B!3, C!2)) = union(C!2, union(intersection(B!3, C!2), difference(B!3, C!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(77,plain,
% 0.12/0.38 (union(union(C!2, intersection(B!3, C!2)), difference(B!3, C!2)) = union(C!2, union(intersection(B!3, C!2), difference(B!3, C!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[76, 38])).
% 0.12/0.38 tff(78,plain,
% 0.12/0.38 (union(C!2, union(intersection(B!3, C!2), difference(B!3, C!2))) = union(union(C!2, intersection(B!3, C!2)), difference(B!3, C!2))),
% 0.12/0.38 inference(symmetry,[status(thm)],[77])).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)) | (union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(80,plain,
% 0.12/0.38 (union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[79, 69])).
% 0.12/0.38 tff(81,plain,
% 0.12/0.38 (union(C!2, union(intersection(B!3, C!2), difference(B!3, C!2))) = union(C!2, B!3)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[80])).
% 0.12/0.38 tff(82,plain,
% 0.12/0.38 (union(C!2, B!3) = union(C!2, union(intersection(B!3, C!2), difference(B!3, C!2)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[81])).
% 0.12/0.38 tff(83,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(C!2, B!3) = union(B!3, C!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(84,plain,
% 0.12/0.38 (union(C!2, B!3) = union(B!3, C!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[83, 7])).
% 0.12/0.38 tff(85,plain,
% 0.12/0.38 (union(B!3, C!2) = union(C!2, B!3)),
% 0.12/0.38 inference(symmetry,[status(thm)],[84])).
% 0.12/0.38 tff(86,plain,
% 0.12/0.38 (union(B!3, C!2) = union(symmetric_difference(B!3, C!2), intersection(B!3, C!2))),
% 0.12/0.38 inference(transitivity,[status(thm)],[85, 82, 78, 75, 40, 31, 9])).
% 0.12/0.38 tff(87,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (union(B, C) = union(symmetric_difference(B, C), intersection(B, C)))) <=> (~![B: $i, C: $i] : (union(B, C) = union(symmetric_difference(B, C), intersection(B, C))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(88,axiom,(~![B: $i, C: $i] : (union(B, C) = union(symmetric_difference(B, C), intersection(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th95')).
% 0.12/0.38 tff(89,plain,
% 0.12/0.38 (~![B: $i, C: $i] : (union(B, C) = union(symmetric_difference(B, C), intersection(B, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.12/0.38 tff(90,plain,
% 0.12/0.38 (~![B: $i, C: $i] : (union(B, C) = union(symmetric_difference(B, C), intersection(B, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[89, 87])).
% 0.12/0.38 tff(91,plain,
% 0.12/0.38 (~![B: $i, C: $i] : (union(B, C) = union(symmetric_difference(B, C), intersection(B, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.12/0.38 tff(92,plain,
% 0.12/0.38 (~![B: $i, C: $i] : (union(B, C) = union(symmetric_difference(B, C), intersection(B, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.12/0.38 tff(93,plain,(
% 0.12/0.38 ~(union(B!3, C!2) = union(symmetric_difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[92])).
% 0.12/0.38 tff(94,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[93, 86])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------