%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET623+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:26:02 AM UTC 2025
% Result : Theorem 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET623+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 05:31:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(symmetric_difference_type, type, (
% 0.19/0.50 symmetric_difference: ( $i * $i ) > $i)).
% 0.19/0.50 tff(tptp_fun_D_2_type, type, (
% 0.19/0.50 tptp_fun_D_2: $i)).
% 0.19/0.50 tff(tptp_fun_C_3_type, type, (
% 0.19/0.50 tptp_fun_C_3: $i)).
% 0.19/0.50 tff(tptp_fun_B_4_type, type, (
% 0.19/0.50 tptp_fun_B_4: $i)).
% 0.19/0.50 tff(union_type, type, (
% 0.19/0.50 union: ( $i * $i ) > $i)).
% 0.19/0.50 tff(difference_type, type, (
% 0.19/0.50 difference: ( $i * $i ) > $i)).
% 0.19/0.50 tff(intersection_type, type, (
% 0.19/0.50 intersection: ( $i * $i ) > $i)).
% 0.19/0.50 tff(1,plain,
% 0.19/0.50 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = symmetric_difference(C, B)) <=> (symmetric_difference(B, C) = symmetric_difference(C, B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(4,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_symmetric_difference')).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.50 tff(6,plain,(
% 0.19/0.50 ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.50 inference(skolemize,[status(sab)],[5])).
% 0.19/0.50 tff(7,plain,
% 0.19/0.50 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))) | (symmetric_difference(symmetric_difference(C!3, D!2), B!4) = symmetric_difference(B!4, symmetric_difference(C!3, D!2)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 (symmetric_difference(symmetric_difference(C!3, D!2), B!4) = symmetric_difference(B!4, symmetric_difference(C!3, D!2))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 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')).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.50 tff(15,plain,(
% 0.19/0.50 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[14])).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(symmetric_difference(C!3, D!2), B!4) = union(difference(symmetric_difference(C!3, D!2), B!4), difference(B!4, symmetric_difference(C!3, D!2))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (symmetric_difference(symmetric_difference(C!3, D!2), B!4) = union(difference(symmetric_difference(C!3, D!2), B!4), difference(B!4, symmetric_difference(C!3, D!2)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 (union(difference(symmetric_difference(C!3, D!2), B!4), difference(B!4, symmetric_difference(C!3, D!2))) = symmetric_difference(symmetric_difference(C!3, D!2), B!4)),
% 0.19/0.50 inference(symmetry,[status(thm)],[18])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (^[B: $i, C: $i, D: $i] : refl((difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D))) <=> (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D))) <=> ![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D))) <=> ![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(23,axiom,(![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_difference_union1')).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.50 tff(25,plain,(
% 0.19/0.50 ![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[24])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 ((~![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))) | (difference(B!4, difference(union(C!3, D!2), intersection(D!2, C!3))) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(D!2, C!3))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 (difference(B!4, difference(union(C!3, D!2), intersection(D!2, C!3))) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(D!2, C!3)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))) | (symmetric_difference(D!2, C!3) = symmetric_difference(C!3, D!2))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (symmetric_difference(D!2, C!3) = symmetric_difference(C!3, D!2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[29, 7])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(D!2, C!3) = union(difference(D!2, C!3), difference(C!3, D!2)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (symmetric_difference(D!2, C!3) = union(difference(D!2, C!3), difference(C!3, D!2))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[31, 16])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (union(difference(D!2, C!3), difference(C!3, D!2)) = symmetric_difference(D!2, C!3)),
% 0.19/0.50 inference(symmetry,[status(thm)],[32])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 (^[B: $i, C: $i] : refl((difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B))) <=> (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(37,axiom,(![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_union_intersection')).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.50 tff(39,plain,(
% 0.19/0.50 ![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[38])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 (![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))) | (difference(union(D!2, C!3), intersection(D!2, C!3)) = union(difference(D!2, C!3), difference(C!3, D!2)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 (difference(union(D!2, C!3), intersection(D!2, C!3)) = union(difference(D!2, C!3), difference(C!3, D!2))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(46,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.50 tff(48,plain,(
% 0.19/0.50 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.50 inference(skolemize,[status(sab)],[47])).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, C!3) = union(C!3, D!2))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 (union(D!2, C!3) = union(C!3, D!2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (union(C!3, D!2) = union(D!2, C!3)),
% 0.19/0.50 inference(symmetry,[status(thm)],[51])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 (difference(union(C!3, D!2), intersection(D!2, C!3)) = difference(union(D!2, C!3), intersection(D!2, C!3))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 (difference(union(C!3, D!2), intersection(D!2, C!3)) = symmetric_difference(C!3, D!2)),
% 0.19/0.50 inference(transitivity,[status(thm)],[53, 42, 33, 30])).
% 0.19/0.50 tff(55,plain,
% 0.19/0.50 (difference(B!4, difference(union(C!3, D!2), intersection(D!2, C!3))) = difference(B!4, symmetric_difference(C!3, D!2))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 (difference(B!4, symmetric_difference(C!3, D!2)) = difference(B!4, difference(union(C!3, D!2), intersection(D!2, C!3)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[55])).
% 0.19/0.50 tff(57,plain,
% 0.19/0.50 (difference(B!4, symmetric_difference(C!3, D!2)) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(D!2, C!3)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[56, 28])).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 (^[B: $i, C: $i, D: $i] : refl((difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> (difference(union(B, C), D) = union(difference(B, D), difference(C, D))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(59,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.50 tff(60,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(61,axiom,(![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_distributes_over_union')).
% 0.19/0.50 tff(62,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.50 tff(63,plain,(
% 0.19/0.50 ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[62])).
% 0.19/0.50 tff(64,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 ((~![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))) | (difference(union(difference(C!3, D!2), difference(D!2, C!3)), B!4) = union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 (difference(union(difference(C!3, D!2), difference(D!2, C!3)), B!4) = union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(C!3, D!2) = union(difference(C!3, D!2), difference(D!2, C!3)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 (symmetric_difference(C!3, D!2) = union(difference(C!3, D!2), difference(D!2, C!3))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[67, 16])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 (difference(symmetric_difference(C!3, D!2), B!4) = difference(union(difference(C!3, D!2), difference(D!2, C!3)), B!4)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 (difference(symmetric_difference(C!3, D!2), B!4) = union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4))),
% 0.19/0.50 inference(transitivity,[status(thm)],[69, 66])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (union(difference(symmetric_difference(C!3, D!2), B!4), difference(B!4, symmetric_difference(C!3, D!2))) = union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(D!2, C!3))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[70, 57])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 (union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(D!2, C!3)))) = union(difference(symmetric_difference(C!3, D!2), B!4), difference(B!4, symmetric_difference(C!3, D!2)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[71])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(76,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')).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.50 tff(78,plain,(
% 0.19/0.50 ![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[77])).
% 0.19/0.50 tff(79,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.50 tff(80,plain,
% 0.19/0.50 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(C!3, D!2))), intersection(B!4, intersection(D!2, C!3))) = union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(D!2, C!3)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(81,plain,
% 0.19/0.50 (union(union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(C!3, D!2))), intersection(B!4, intersection(D!2, C!3))) = union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(D!2, C!3))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(83,plain,
% 0.19/0.50 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.50 tff(84,plain,
% 0.19/0.50 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(85,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.19/0.50 tff(86,plain,
% 0.19/0.50 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.50 tff(87,plain,(
% 0.19/0.50 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.50 inference(skolemize,[status(sab)],[86])).
% 0.19/0.50 tff(88,plain,
% 0.19/0.50 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.50 tff(89,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, intersection(D!2, C!3)) = intersection(intersection(D!2, C!3), B!4))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(90,plain,
% 0.19/0.50 (intersection(B!4, intersection(D!2, C!3)) = intersection(intersection(D!2, C!3), B!4)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.50 tff(91,plain,
% 0.19/0.50 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, C!3) = union(C!3, B!4))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(92,plain,
% 0.19/0.50 (union(B!4, C!3) = union(C!3, B!4)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[91, 49])).
% 0.19/0.50 tff(93,plain,
% 0.19/0.50 (difference(D!2, union(B!4, C!3)) = difference(D!2, union(C!3, B!4))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.50 tff(94,plain,
% 0.19/0.50 (^[B: $i, C: $i, D: $i] : refl((difference(difference(B, C), D) = difference(B, union(C, D))) <=> (difference(difference(B, C), D) = difference(B, union(C, D))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(95,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.50 tff(96,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D))) <=> ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(97,axiom,(![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_difference_union2')).
% 0.19/0.50 tff(98,plain,
% 0.19/0.50 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.50 tff(99,plain,(
% 0.19/0.50 ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[98])).
% 0.19/0.51 tff(100,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.19/0.51 tff(101,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(D!2, B!4), C!3) = difference(D!2, union(B!4, C!3)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(102,plain,
% 0.19/0.51 (difference(difference(D!2, B!4), C!3) = difference(D!2, union(B!4, C!3))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.51 tff(103,plain,
% 0.19/0.51 (difference(difference(D!2, B!4), C!3) = difference(D!2, union(C!3, B!4))),
% 0.19/0.51 inference(transitivity,[status(thm)],[102, 93])).
% 0.19/0.51 tff(104,plain,
% 0.19/0.51 (union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(difference(D!2, B!4), C!3)) = union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(D!2, union(C!3, B!4)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.51 tff(105,plain,
% 0.19/0.51 (difference(D!2, union(B!4, C!3)) = difference(difference(D!2, B!4), C!3)),
% 0.19/0.51 inference(symmetry,[status(thm)],[102])).
% 0.19/0.51 tff(106,plain,
% 0.19/0.51 (difference(D!2, union(C!3, B!4)) = difference(D!2, union(B!4, C!3))),
% 0.19/0.51 inference(symmetry,[status(thm)],[93])).
% 0.19/0.51 tff(107,plain,
% 0.19/0.51 (difference(D!2, union(C!3, B!4)) = difference(difference(D!2, B!4), C!3)),
% 0.19/0.51 inference(transitivity,[status(thm)],[106, 105])).
% 0.19/0.51 tff(108,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(C!3, B!4), D!2) = difference(C!3, union(B!4, D!2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(109,plain,
% 0.19/0.51 (difference(difference(C!3, B!4), D!2) = difference(C!3, union(B!4, D!2))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[108, 100])).
% 0.19/0.51 tff(110,plain,
% 0.19/0.51 (difference(C!3, union(B!4, D!2)) = difference(difference(C!3, B!4), D!2)),
% 0.19/0.51 inference(symmetry,[status(thm)],[109])).
% 0.19/0.51 tff(111,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(B!4, C!3), D!2) = difference(B!4, union(C!3, D!2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(112,plain,
% 0.19/0.51 (difference(difference(B!4, C!3), D!2) = difference(B!4, union(C!3, D!2))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[111, 100])).
% 0.19/0.51 tff(113,plain,
% 0.19/0.51 (difference(B!4, union(C!3, D!2)) = difference(difference(B!4, C!3), D!2)),
% 0.19/0.51 inference(symmetry,[status(thm)],[112])).
% 0.19/0.51 tff(114,plain,
% 0.19/0.51 (union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2))) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[113, 110])).
% 0.19/0.51 tff(115,plain,
% 0.19/0.51 (union(union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2))), difference(D!2, union(C!3, B!4))) = union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(difference(D!2, B!4), C!3))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[114, 107])).
% 0.19/0.51 tff(116,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2))), difference(D!2, union(C!3, B!4))) = union(difference(B!4, union(C!3, D!2)), union(difference(C!3, union(B!4, D!2)), difference(D!2, union(C!3, B!4)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(117,plain,
% 0.19/0.51 (union(union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2))), difference(D!2, union(C!3, B!4))) = union(difference(B!4, union(C!3, D!2)), union(difference(C!3, union(B!4, D!2)), difference(D!2, union(C!3, B!4))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[116, 79])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 (union(difference(B!4, union(C!3, D!2)), union(difference(C!3, union(B!4, D!2)), difference(D!2, union(C!3, B!4)))) = union(union(difference(B!4, union(C!3, D!2)), difference(C!3, union(B!4, D!2))), difference(D!2, union(C!3, B!4)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[117])).
% 0.19/0.51 tff(119,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(D!2, C!3), B!4) = difference(D!2, union(C!3, B!4)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 (difference(difference(D!2, C!3), B!4) = difference(D!2, union(C!3, B!4))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[119, 100])).
% 0.19/0.51 tff(121,plain,
% 0.19/0.51 (difference(D!2, union(C!3, B!4)) = difference(difference(D!2, C!3), B!4)),
% 0.19/0.51 inference(symmetry,[status(thm)],[120])).
% 0.19/0.51 tff(122,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))) | (difference(difference(C!3, D!2), B!4) = difference(C!3, union(D!2, B!4)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(123,plain,
% 0.19/0.51 (difference(difference(C!3, D!2), B!4) = difference(C!3, union(D!2, B!4))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[122, 100])).
% 0.19/0.51 tff(124,plain,
% 0.19/0.51 (difference(C!3, union(D!2, B!4)) = difference(difference(C!3, D!2), B!4)),
% 0.19/0.51 inference(symmetry,[status(thm)],[123])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, B!4) = union(B!4, D!2))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 (union(D!2, B!4) = union(B!4, D!2)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[125, 49])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 (difference(C!3, union(D!2, B!4)) = difference(C!3, union(B!4, D!2))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[126])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 (difference(C!3, union(B!4, D!2)) = difference(C!3, union(D!2, B!4))),
% 0.19/0.51 inference(symmetry,[status(thm)],[127])).
% 0.19/0.51 tff(129,plain,
% 0.19/0.51 (difference(C!3, union(B!4, D!2)) = difference(difference(C!3, D!2), B!4)),
% 0.19/0.51 inference(transitivity,[status(thm)],[128, 124])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 (union(difference(C!3, union(B!4, D!2)), difference(D!2, union(C!3, B!4))) = union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[129, 121])).
% 0.19/0.51 tff(131,plain,
% 0.19/0.51 (union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)) = union(difference(C!3, union(B!4, D!2)), difference(D!2, union(C!3, B!4)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[130])).
% 0.19/0.51 tff(132,plain,
% 0.19/0.51 (union(difference(B!4, union(C!3, D!2)), union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4))) = union(difference(B!4, union(C!3, D!2)), union(difference(C!3, union(B!4, D!2)), difference(D!2, union(C!3, B!4))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[131])).
% 0.19/0.51 tff(133,plain,
% 0.19/0.51 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(difference(B!4, union(C!3, D!2)), union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4))) = union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(C!3, D!2))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(134,plain,
% 0.19/0.51 (union(difference(B!4, union(C!3, D!2)), union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4))) = union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(C!3, D!2)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[133, 49])).
% 0.19/0.51 tff(135,plain,
% 0.19/0.51 (union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[134])).
% 0.19/0.51 tff(136,plain,
% 0.19/0.51 (union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(C!3, D!2))) = union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(D!2, union(C!3, B!4)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[135, 132, 118, 115, 104])).
% 0.19/0.51 tff(137,plain,
% 0.19/0.51 (union(union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(C!3, D!2))), intersection(B!4, intersection(D!2, C!3))) = union(union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(D!2, union(C!3, B!4))), intersection(intersection(D!2, C!3), B!4))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[136, 90])).
% 0.19/0.51 tff(138,plain,
% 0.19/0.51 (union(union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(D!2, union(C!3, B!4))), intersection(intersection(D!2, C!3), B!4)) = union(union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(C!3, D!2))), intersection(B!4, intersection(D!2, C!3)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[137])).
% 0.19/0.51 tff(139,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(D!2, union(C!3, B!4))), intersection(intersection(D!2, C!3), B!4)) = union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(140,plain,
% 0.19/0.51 (union(union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(D!2, union(C!3, B!4))), intersection(intersection(D!2, C!3), B!4)) = union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[139, 79])).
% 0.19/0.51 tff(141,plain,
% 0.19/0.51 (union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4))) = union(union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), difference(D!2, union(C!3, B!4))), intersection(intersection(D!2, C!3), B!4))),
% 0.19/0.51 inference(symmetry,[status(thm)],[140])).
% 0.19/0.51 tff(142,plain,
% 0.19/0.51 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4)) = union(intersection(intersection(D!2, C!3), B!4), difference(D!2, union(C!3, B!4))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(143,plain,
% 0.19/0.51 (union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4)) = union(intersection(intersection(D!2, C!3), B!4), difference(D!2, union(C!3, B!4)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[142, 49])).
% 0.19/0.51 tff(144,plain,
% 0.19/0.51 (union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4))) = union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(intersection(intersection(D!2, C!3), B!4), difference(D!2, union(C!3, B!4))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[143])).
% 0.19/0.51 tff(145,plain,
% 0.19/0.51 (union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(intersection(intersection(D!2, C!3), B!4), difference(D!2, union(C!3, B!4)))) = union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[144])).
% 0.19/0.51 tff(146,plain,
% 0.19/0.51 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(B!4, C!3) = union(difference(B!4, C!3), difference(C!3, B!4)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(147,plain,
% 0.19/0.51 (symmetric_difference(B!4, C!3) = union(difference(B!4, C!3), difference(C!3, B!4))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[146, 16])).
% 0.19/0.51 tff(148,plain,
% 0.19/0.51 (union(difference(B!4, C!3), difference(C!3, B!4)) = symmetric_difference(B!4, C!3)),
% 0.19/0.51 inference(symmetry,[status(thm)],[147])).
% 0.19/0.51 tff(149,plain,
% 0.19/0.51 ((~![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))) | (difference(union(B!4, C!3), intersection(B!4, C!3)) = union(difference(B!4, C!3), difference(C!3, B!4)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(150,plain,
% 0.19/0.51 (difference(union(B!4, C!3), intersection(B!4, C!3)) = union(difference(B!4, C!3), difference(C!3, B!4))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[149, 40])).
% 0.19/0.51 tff(151,plain,
% 0.19/0.51 (union(C!3, B!4) = union(B!4, C!3)),
% 0.19/0.51 inference(symmetry,[status(thm)],[92])).
% 0.19/0.51 tff(152,plain,
% 0.19/0.51 (difference(union(C!3, B!4), intersection(B!4, C!3)) = difference(union(B!4, C!3), intersection(B!4, C!3))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.51 tff(153,plain,
% 0.19/0.51 (difference(union(C!3, B!4), intersection(B!4, C!3)) = symmetric_difference(B!4, C!3)),
% 0.19/0.51 inference(transitivity,[status(thm)],[152, 150, 148])).
% 0.19/0.51 tff(154,plain,
% 0.19/0.51 (difference(D!2, difference(union(C!3, B!4), intersection(B!4, C!3))) = difference(D!2, symmetric_difference(B!4, C!3))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.51 tff(155,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))) | (difference(D!2, difference(union(C!3, B!4), intersection(B!4, C!3))) = union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(156,plain,
% 0.19/0.51 (difference(D!2, difference(union(C!3, B!4), intersection(B!4, C!3))) = union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[155, 26])).
% 0.19/0.51 tff(157,plain,
% 0.19/0.51 (union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3))) = difference(D!2, difference(union(C!3, B!4), intersection(B!4, C!3)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[156])).
% 0.19/0.51 tff(158,plain,
% 0.19/0.51 (^[B: $i, C: $i, D: $i] : refl((intersection(intersection(B, C), D) = intersection(B, intersection(C, D))) <=> (intersection(intersection(B, C), D) = intersection(B, intersection(C, D))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(159,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[158])).
% 0.19/0.51 tff(160,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(161,axiom,(![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','associativity_of_intersection')).
% 0.19/0.51 tff(162,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.51 tff(163,plain,(
% 0.19/0.51 ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[162])).
% 0.19/0.51 tff(164,plain,
% 0.19/0.51 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.19/0.51 tff(165,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(D!2, B!4), C!3) = intersection(D!2, intersection(B!4, C!3)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(166,plain,
% 0.19/0.51 (intersection(intersection(D!2, B!4), C!3) = intersection(D!2, intersection(B!4, C!3))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.51 tff(167,plain,
% 0.19/0.51 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(D!2, B!4) = intersection(B!4, D!2))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(168,plain,
% 0.19/0.51 (intersection(D!2, B!4) = intersection(B!4, D!2)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[167, 88])).
% 0.19/0.51 tff(169,plain,
% 0.19/0.51 (intersection(intersection(D!2, B!4), C!3) = intersection(intersection(B!4, D!2), C!3)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.51 tff(170,plain,
% 0.19/0.51 (intersection(intersection(B!4, D!2), C!3) = intersection(intersection(D!2, B!4), C!3)),
% 0.19/0.51 inference(symmetry,[status(thm)],[169])).
% 0.19/0.51 tff(171,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(B!4, D!2), C!3) = intersection(B!4, intersection(D!2, C!3)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(172,plain,
% 0.19/0.51 (intersection(intersection(B!4, D!2), C!3) = intersection(B!4, intersection(D!2, C!3))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[171, 164])).
% 0.19/0.51 tff(173,plain,
% 0.19/0.51 (intersection(B!4, intersection(D!2, C!3)) = intersection(intersection(B!4, D!2), C!3)),
% 0.19/0.51 inference(symmetry,[status(thm)],[172])).
% 0.19/0.51 tff(174,plain,
% 0.19/0.51 (intersection(intersection(D!2, C!3), B!4) = intersection(B!4, intersection(D!2, C!3))),
% 0.19/0.51 inference(symmetry,[status(thm)],[90])).
% 0.19/0.51 tff(175,plain,
% 0.19/0.51 (intersection(intersection(D!2, C!3), B!4) = intersection(D!2, intersection(B!4, C!3))),
% 0.19/0.51 inference(transitivity,[status(thm)],[174, 173, 170, 166])).
% 0.19/0.51 tff(176,plain,
% 0.19/0.51 (union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4)) = union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[175])).
% 0.19/0.51 tff(177,plain,
% 0.19/0.51 (union(intersection(intersection(D!2, C!3), B!4), difference(D!2, union(C!3, B!4))) = union(difference(D!2, union(C!3, B!4)), intersection(intersection(D!2, C!3), B!4))),
% 0.19/0.51 inference(symmetry,[status(thm)],[143])).
% 0.19/0.51 tff(178,plain,
% 0.19/0.51 (union(intersection(intersection(D!2, C!3), B!4), difference(D!2, union(C!3, B!4))) = difference(D!2, symmetric_difference(B!4, C!3))),
% 0.19/0.51 inference(transitivity,[status(thm)],[177, 176, 157, 154])).
% 0.19/0.51 tff(179,plain,
% 0.19/0.51 (difference(symmetric_difference(B!4, C!3), D!2) = difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[147])).
% 0.19/0.51 tff(180,plain,
% 0.19/0.51 (difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2) = difference(symmetric_difference(B!4, C!3), D!2)),
% 0.19/0.51 inference(symmetry,[status(thm)],[179])).
% 0.19/0.51 tff(181,plain,
% 0.19/0.51 ((~![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))) | (difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(182,plain,
% 0.19/0.51 (difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[181, 64])).
% 0.19/0.51 tff(183,plain,
% 0.19/0.51 (union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)) = difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2)),
% 0.19/0.51 inference(symmetry,[status(thm)],[182])).
% 0.19/0.51 tff(184,plain,
% 0.19/0.51 (union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)) = difference(symmetric_difference(B!4, C!3), D!2)),
% 0.19/0.51 inference(transitivity,[status(thm)],[183, 180])).
% 0.19/0.51 tff(185,plain,
% 0.19/0.51 (union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(intersection(intersection(D!2, C!3), B!4), difference(D!2, union(C!3, B!4)))) = union(difference(symmetric_difference(B!4, C!3), D!2), difference(D!2, symmetric_difference(B!4, C!3)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[184, 178])).
% 0.19/0.51 tff(186,plain,
% 0.19/0.51 (union(difference(symmetric_difference(B!4, C!3), D!2), difference(D!2, symmetric_difference(B!4, C!3))) = union(union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)), union(intersection(intersection(D!2, C!3), B!4), difference(D!2, union(C!3, B!4))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[185])).
% 0.19/0.51 tff(187,plain,
% 0.19/0.51 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(symmetric_difference(B!4, C!3), D!2) = union(difference(symmetric_difference(B!4, C!3), D!2), difference(D!2, symmetric_difference(B!4, C!3))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(188,plain,
% 0.19/0.52 (symmetric_difference(symmetric_difference(B!4, C!3), D!2) = union(difference(symmetric_difference(B!4, C!3), D!2), difference(D!2, symmetric_difference(B!4, C!3)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[187, 16])).
% 0.19/0.52 tff(189,plain,
% 0.19/0.52 (symmetric_difference(symmetric_difference(B!4, C!3), D!2) = symmetric_difference(B!4, symmetric_difference(C!3, D!2))),
% 0.19/0.52 inference(transitivity,[status(thm)],[188, 186, 145, 141, 138, 81, 72, 19, 9])).
% 0.19/0.52 tff(190,plain,
% 0.19/0.52 ((~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))) <=> (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(191,axiom,(~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th99')).
% 0.19/0.52 tff(192,plain,
% 0.19/0.52 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.52 tff(193,plain,
% 0.19/0.52 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[192, 190])).
% 0.19/0.52 tff(194,plain,
% 0.19/0.52 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[193, 190])).
% 0.19/0.52 tff(195,plain,
% 0.19/0.52 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.19/0.52 tff(196,plain,(
% 0.19/0.52 ~(symmetric_difference(symmetric_difference(B!4, C!3), D!2) = symmetric_difference(B!4, symmetric_difference(C!3, D!2)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[195])).
% 0.19/0.52 tff(197,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[196, 189])).
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------