%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET601+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:58 AM UTC 2025
% Result : Theorem 1.50s 1.67s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET601+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 05:30:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.50/1.67 % SZS status Theorem
% 1.50/1.67 % SZS output start Proof
% 1.50/1.67 tff(intersection_type, type, (
% 1.50/1.67 intersection: ( $i * $i ) > $i)).
% 1.50/1.67 tff(union_type, type, (
% 1.50/1.67 union: ( $i * $i ) > $i)).
% 1.50/1.67 tff(tptp_fun_B_4_type, type, (
% 1.50/1.67 tptp_fun_B_4: $i)).
% 1.50/1.67 tff(tptp_fun_D_2_type, type, (
% 1.50/1.67 tptp_fun_D_2: $i)).
% 1.50/1.67 tff(tptp_fun_C_3_type, type, (
% 1.50/1.67 tptp_fun_C_3: $i)).
% 1.50/1.67 tff(1,plain,
% 1.50/1.67 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(2,plain,
% 1.50/1.67 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[1])).
% 1.50/1.67 tff(3,plain,
% 1.50/1.67 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(4,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 1.50/1.67 tff(5,plain,
% 1.50/1.67 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.50/1.67 tff(6,plain,(
% 1.50/1.67 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 1.50/1.67 inference(skolemize,[status(sab)],[5])).
% 1.50/1.67 tff(7,plain,
% 1.50/1.67 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.50/1.67 tff(8,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2))) = intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(9,plain,
% 1.50/1.67 (intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2))) = intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.50/1.67 tff(10,plain,
% 1.50/1.67 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(11,plain,
% 1.50/1.67 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[10])).
% 1.50/1.67 tff(12,plain,
% 1.50/1.67 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(13,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 1.50/1.67 tff(14,plain,
% 1.50/1.67 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.50/1.67 tff(15,plain,(
% 1.50/1.67 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.50/1.67 inference(skolemize,[status(sab)],[14])).
% 1.50/1.67 tff(16,plain,
% 1.50/1.67 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[15, 11])).
% 1.50/1.67 tff(17,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, D!2) = union(D!2, B!4))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(18,plain,
% 1.50/1.67 (union(B!4, D!2) = union(D!2, B!4)),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.50/1.67 tff(19,plain,
% 1.50/1.67 (^[B: $i, C: $i] : refl((union(B, intersection(B, C)) = B) <=> (union(B, intersection(B, C)) = B))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(20,plain,
% 1.50/1.67 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B) <=> ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 1.50/1.67 inference(quant_intro,[status(thm)],[19])).
% 1.50/1.67 tff(21,plain,
% 1.50/1.67 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B) <=> ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(22,axiom,(![B: $i, C: $i] : (union(B, intersection(B, C)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_intersection')).
% 1.50/1.67 tff(23,plain,
% 1.50/1.67 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.50/1.67 tff(24,plain,(
% 1.50/1.67 ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 1.50/1.67 inference(skolemize,[status(sab)],[23])).
% 1.50/1.67 tff(25,plain,
% 1.50/1.67 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[24, 20])).
% 1.50/1.67 tff(26,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(D!2, intersection(D!2, B!4)) = D!2)),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(27,plain,
% 1.50/1.67 (union(D!2, intersection(D!2, B!4)) = D!2),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[26, 25])).
% 1.50/1.67 tff(28,plain,
% 1.50/1.67 (union(B!4, union(D!2, intersection(D!2, B!4))) = union(B!4, D!2)),
% 1.50/1.67 inference(monotonicity,[status(thm)],[27])).
% 1.50/1.67 tff(29,plain,
% 1.50/1.67 (^[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))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(30,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[29])).
% 1.50/1.67 tff(31,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(32,axiom,(![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','associativity_of_union')).
% 1.50/1.67 tff(33,plain,
% 1.50/1.67 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.50/1.67 tff(34,plain,(
% 1.50/1.67 ![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.50/1.67 inference(skolemize,[status(sab)],[33])).
% 1.50/1.67 tff(35,plain,
% 1.50/1.67 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.50/1.67 tff(36,plain,
% 1.50/1.67 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(B!4, D!2), intersection(D!2, B!4)) = union(B!4, union(D!2, intersection(D!2, B!4))))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(37,plain,
% 1.50/1.67 (union(union(B!4, D!2), intersection(D!2, B!4)) = union(B!4, union(D!2, intersection(D!2, B!4)))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[36, 35])).
% 1.50/1.67 tff(38,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, D!2) = intersection(D!2, B!4))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(39,plain,
% 1.50/1.67 (intersection(B!4, D!2) = intersection(D!2, B!4)),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[38, 7])).
% 1.50/1.67 tff(40,plain,
% 1.50/1.67 (union(D!2, B!4) = union(B!4, D!2)),
% 1.50/1.67 inference(symmetry,[status(thm)],[18])).
% 1.50/1.67 tff(41,plain,
% 1.50/1.67 (union(union(D!2, B!4), intersection(B!4, D!2)) = union(union(B!4, D!2), intersection(D!2, B!4))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[40, 39])).
% 1.50/1.67 tff(42,plain,
% 1.50/1.67 (^[B: $i, C: $i, D: $i] : refl((union(B, intersection(C, D)) = intersection(union(B, C), union(B, D))) <=> (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(43,plain,
% 1.50/1.67 (![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D))) <=> ![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[42])).
% 1.50/1.67 tff(44,plain,
% 1.50/1.67 (![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D))) <=> ![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(45,axiom,(![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_distributes_over_intersection')).
% 1.50/1.67 tff(46,plain,
% 1.50/1.67 (![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.50/1.67 tff(47,plain,(
% 1.50/1.67 ![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 1.50/1.67 inference(skolemize,[status(sab)],[46])).
% 1.50/1.67 tff(48,plain,
% 1.50/1.67 (![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[47, 43])).
% 1.50/1.67 tff(49,plain,
% 1.50/1.67 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(union(D!2, B!4), intersection(B!4, D!2)) = intersection(union(union(D!2, B!4), B!4), union(union(D!2, B!4), D!2)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(50,plain,
% 1.50/1.67 (union(union(D!2, B!4), intersection(B!4, D!2)) = intersection(union(union(D!2, B!4), B!4), union(union(D!2, B!4), D!2))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[49, 48])).
% 1.50/1.67 tff(51,plain,
% 1.50/1.67 (intersection(union(union(D!2, B!4), B!4), union(union(D!2, B!4), D!2)) = union(union(D!2, B!4), intersection(B!4, D!2))),
% 1.50/1.67 inference(symmetry,[status(thm)],[50])).
% 1.50/1.67 tff(52,plain,
% 1.50/1.67 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(D!2, intersection(B!4, D!2)) = intersection(union(D!2, B!4), union(D!2, D!2)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(53,plain,
% 1.50/1.67 (union(D!2, intersection(B!4, D!2)) = intersection(union(D!2, B!4), union(D!2, D!2))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[52, 48])).
% 1.50/1.67 tff(54,plain,
% 1.50/1.67 (union(D!2, intersection(B!4, D!2)) = union(D!2, intersection(D!2, B!4))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[39])).
% 1.50/1.67 tff(55,plain,
% 1.50/1.67 (union(D!2, intersection(D!2, B!4)) = union(D!2, intersection(B!4, D!2))),
% 1.50/1.67 inference(symmetry,[status(thm)],[54])).
% 1.50/1.67 tff(56,plain,
% 1.50/1.67 (D!2 = union(D!2, intersection(D!2, B!4))),
% 1.50/1.67 inference(symmetry,[status(thm)],[27])).
% 1.50/1.67 tff(57,plain,
% 1.50/1.67 (D!2 = intersection(union(D!2, B!4), union(D!2, D!2))),
% 1.50/1.67 inference(transitivity,[status(thm)],[56, 55, 53])).
% 1.50/1.67 tff(58,plain,
% 1.50/1.67 (union(union(D!2, B!4), D!2) = union(union(D!2, B!4), intersection(union(D!2, B!4), union(D!2, D!2)))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[57])).
% 1.50/1.67 tff(59,plain,
% 1.50/1.67 (union(union(D!2, B!4), intersection(union(D!2, B!4), union(D!2, D!2))) = union(union(D!2, B!4), D!2)),
% 1.50/1.67 inference(symmetry,[status(thm)],[58])).
% 1.50/1.67 tff(60,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(union(D!2, B!4), intersection(union(D!2, B!4), union(D!2, D!2))) = union(D!2, B!4))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(61,plain,
% 1.50/1.67 (union(union(D!2, B!4), intersection(union(D!2, B!4), union(D!2, D!2))) = union(D!2, B!4)),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[60, 25])).
% 1.50/1.67 tff(62,plain,
% 1.50/1.67 (union(D!2, B!4) = union(union(D!2, B!4), intersection(union(D!2, B!4), union(D!2, D!2)))),
% 1.50/1.67 inference(symmetry,[status(thm)],[61])).
% 1.50/1.67 tff(63,plain,
% 1.50/1.67 (union(D!2, B!4) = union(union(D!2, B!4), D!2)),
% 1.50/1.67 inference(transitivity,[status(thm)],[62, 59])).
% 1.50/1.67 tff(64,plain,
% 1.50/1.67 (intersection(union(union(D!2, B!4), B!4), union(D!2, B!4)) = intersection(union(union(D!2, B!4), B!4), union(union(D!2, B!4), D!2))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[63])).
% 1.50/1.67 tff(65,plain,
% 1.50/1.67 (intersection(union(union(D!2, B!4), B!4), union(D!2, B!4)) = union(D!2, B!4)),
% 1.50/1.67 inference(transitivity,[status(thm)],[64, 51, 41, 37, 28, 18])).
% 1.50/1.67 tff(66,plain,
% 1.50/1.67 (intersection(intersection(union(union(D!2, B!4), B!4), union(D!2, B!4)), intersection(union(B!4, C!3), union(C!3, D!2))) = intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2)))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[65])).
% 1.50/1.67 tff(67,plain,
% 1.50/1.67 (^[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))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(68,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[67])).
% 1.50/1.67 tff(69,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(70,axiom,(![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','associativity_of_intersection')).
% 1.50/1.67 tff(71,plain,
% 1.50/1.67 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.50/1.67 tff(72,plain,(
% 1.50/1.67 ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 1.50/1.67 inference(skolemize,[status(sab)],[71])).
% 1.50/1.67 tff(73,plain,
% 1.50/1.67 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.50/1.67 tff(74,plain,
% 1.50/1.67 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(union(union(D!2, B!4), B!4), union(D!2, B!4)), intersection(union(B!4, C!3), union(C!3, D!2))) = intersection(union(union(D!2, B!4), B!4), intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2)))))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(75,plain,
% 1.50/1.67 (intersection(intersection(union(union(D!2, B!4), B!4), union(D!2, B!4)), intersection(union(B!4, C!3), union(C!3, D!2))) = intersection(union(union(D!2, B!4), B!4), intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2))))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[74, 73])).
% 1.50/1.67 tff(76,plain,
% 1.50/1.67 (intersection(union(union(D!2, B!4), B!4), intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2)))) = intersection(intersection(union(union(D!2, B!4), B!4), union(D!2, B!4)), intersection(union(B!4, C!3), union(C!3, D!2)))),
% 1.50/1.67 inference(symmetry,[status(thm)],[75])).
% 1.50/1.67 tff(77,plain,
% 1.50/1.67 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(union(D!2, B!4), union(B!4, C!3)), union(C!3, D!2)) = intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2))))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(78,plain,
% 1.50/1.67 (intersection(intersection(union(D!2, B!4), union(B!4, C!3)), union(C!3, D!2)) = intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2)))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[77, 73])).
% 1.50/1.67 tff(79,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3))) = intersection(intersection(union(D!2, B!4), union(B!4, C!3)), union(C!3, D!2)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(80,plain,
% 1.50/1.67 (intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3))) = intersection(intersection(union(D!2, B!4), union(B!4, C!3)), union(C!3, D!2))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[79, 7])).
% 1.50/1.67 tff(81,plain,
% 1.50/1.67 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(B!4, intersection(B!4, C!3)), D!2) = union(B!4, union(intersection(B!4, C!3), D!2)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(82,plain,
% 1.50/1.67 (union(union(B!4, intersection(B!4, C!3)), D!2) = union(B!4, union(intersection(B!4, C!3), D!2))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[81, 35])).
% 1.50/1.67 tff(83,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(B!4, intersection(B!4, C!3)) = B!4)),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(84,plain,
% 1.50/1.67 (union(B!4, intersection(B!4, C!3)) = B!4),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[83, 25])).
% 1.50/1.67 tff(85,plain,
% 1.50/1.67 (union(union(B!4, intersection(B!4, C!3)), D!2) = union(B!4, D!2)),
% 1.50/1.67 inference(monotonicity,[status(thm)],[84])).
% 1.50/1.67 tff(86,plain,
% 1.50/1.67 (union(B!4, D!2) = union(union(B!4, intersection(B!4, C!3)), D!2)),
% 1.50/1.67 inference(symmetry,[status(thm)],[85])).
% 1.50/1.67 tff(87,plain,
% 1.50/1.67 (union(D!2, B!4) = union(B!4, union(intersection(B!4, C!3), D!2))),
% 1.50/1.67 inference(transitivity,[status(thm)],[40, 86, 82])).
% 1.50/1.67 tff(88,plain,
% 1.50/1.67 (intersection(union(D!2, B!4), union(B!4, C!3)) = intersection(union(B!4, union(intersection(B!4, C!3), D!2)), union(B!4, C!3))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[87])).
% 1.50/1.67 tff(89,plain,
% 1.50/1.67 (intersection(union(B!4, union(intersection(B!4, C!3), D!2)), union(B!4, C!3)) = intersection(union(D!2, B!4), union(B!4, C!3))),
% 1.50/1.67 inference(symmetry,[status(thm)],[88])).
% 1.50/1.67 tff(90,plain,
% 1.50/1.67 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(B!4, intersection(union(intersection(B!4, C!3), D!2), C!3)) = intersection(union(B!4, union(intersection(B!4, C!3), D!2)), union(B!4, C!3)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(91,plain,
% 1.50/1.67 (union(B!4, intersection(union(intersection(B!4, C!3), D!2), C!3)) = intersection(union(B!4, union(intersection(B!4, C!3), D!2)), union(B!4, C!3))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[90, 48])).
% 1.50/1.67 tff(92,plain,
% 1.50/1.67 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(intersection(B!4, C!3), intersection(C!3, D!2)) = intersection(union(intersection(B!4, C!3), C!3), union(intersection(B!4, C!3), D!2)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(93,plain,
% 1.50/1.67 (union(intersection(B!4, C!3), intersection(C!3, D!2)) = intersection(union(intersection(B!4, C!3), C!3), union(intersection(B!4, C!3), D!2))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[92, 48])).
% 1.50/1.67 tff(94,plain,
% 1.50/1.67 (intersection(union(intersection(B!4, C!3), C!3), union(intersection(B!4, C!3), D!2)) = union(intersection(B!4, C!3), intersection(C!3, D!2))),
% 1.50/1.67 inference(symmetry,[status(thm)],[93])).
% 1.50/1.67 tff(95,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(union(intersection(B!4, C!3), D!2), union(intersection(B!4, C!3), C!3)) = intersection(union(intersection(B!4, C!3), C!3), union(intersection(B!4, C!3), D!2)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(96,plain,
% 1.50/1.67 (intersection(union(intersection(B!4, C!3), D!2), union(intersection(B!4, C!3), C!3)) = intersection(union(intersection(B!4, C!3), C!3), union(intersection(B!4, C!3), D!2))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[95, 7])).
% 1.50/1.67 tff(97,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(C!3, intersection(B!4, C!3)) = union(intersection(B!4, C!3), C!3))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(98,plain,
% 1.50/1.67 (union(C!3, intersection(B!4, C!3)) = union(intersection(B!4, C!3), C!3)),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[97, 16])).
% 1.50/1.67 tff(99,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, B!4) = intersection(B!4, C!3))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(100,plain,
% 1.50/1.67 (intersection(C!3, B!4) = intersection(B!4, C!3)),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[99, 7])).
% 1.50/1.67 tff(101,plain,
% 1.50/1.67 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 1.50/1.67 inference(symmetry,[status(thm)],[100])).
% 1.50/1.67 tff(102,plain,
% 1.50/1.67 (union(C!3, intersection(B!4, C!3)) = union(C!3, intersection(C!3, B!4))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[101])).
% 1.50/1.67 tff(103,plain,
% 1.50/1.67 (union(C!3, intersection(C!3, B!4)) = union(C!3, intersection(B!4, C!3))),
% 1.50/1.67 inference(symmetry,[status(thm)],[102])).
% 1.50/1.67 tff(104,plain,
% 1.50/1.67 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(C!3, intersection(C!3, B!4)) = C!3)),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(105,plain,
% 1.50/1.67 (union(C!3, intersection(C!3, B!4)) = C!3),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[104, 25])).
% 1.50/1.67 tff(106,plain,
% 1.50/1.67 (C!3 = union(C!3, intersection(C!3, B!4))),
% 1.50/1.67 inference(symmetry,[status(thm)],[105])).
% 1.50/1.67 tff(107,plain,
% 1.50/1.67 (C!3 = union(intersection(B!4, C!3), C!3)),
% 1.50/1.67 inference(transitivity,[status(thm)],[106, 103, 98])).
% 1.50/1.67 tff(108,plain,
% 1.50/1.67 (intersection(union(intersection(B!4, C!3), D!2), C!3) = intersection(union(intersection(B!4, C!3), D!2), union(intersection(B!4, C!3), C!3))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[107])).
% 1.50/1.67 tff(109,plain,
% 1.50/1.67 (intersection(union(intersection(B!4, C!3), D!2), C!3) = union(intersection(B!4, C!3), intersection(C!3, D!2))),
% 1.50/1.67 inference(transitivity,[status(thm)],[108, 96, 94])).
% 1.50/1.68 tff(110,plain,
% 1.50/1.68 (union(B!4, intersection(union(intersection(B!4, C!3), D!2), C!3)) = union(B!4, union(intersection(B!4, C!3), intersection(C!3, D!2)))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[109])).
% 1.50/1.68 tff(111,plain,
% 1.50/1.68 (union(B!4, union(intersection(B!4, C!3), intersection(C!3, D!2))) = union(B!4, intersection(union(intersection(B!4, C!3), D!2), C!3))),
% 1.50/1.68 inference(symmetry,[status(thm)],[110])).
% 1.50/1.68 tff(112,plain,
% 1.50/1.68 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, union(intersection(B!4, C!3), intersection(C!3, D!2))) = union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(113,plain,
% 1.50/1.68 (union(B!4, union(intersection(B!4, C!3), intersection(C!3, D!2))) = union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[112, 16])).
% 1.50/1.68 tff(114,plain,
% 1.50/1.68 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4) = union(B!4, union(intersection(B!4, C!3), intersection(C!3, D!2)))),
% 1.50/1.68 inference(symmetry,[status(thm)],[113])).
% 1.50/1.68 tff(115,plain,
% 1.50/1.68 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4) = intersection(union(D!2, B!4), union(B!4, C!3))),
% 1.50/1.68 inference(transitivity,[status(thm)],[114, 111, 91, 89])).
% 1.50/1.68 tff(116,plain,
% 1.50/1.68 (intersection(union(C!3, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3)))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[115])).
% 1.50/1.68 tff(117,plain,
% 1.50/1.68 (intersection(union(C!3, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2)))),
% 1.50/1.68 inference(transitivity,[status(thm)],[116, 80, 78])).
% 1.50/1.68 tff(118,plain,
% 1.50/1.68 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, union(D!2, B!4)) = union(union(D!2, B!4), B!4))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(119,plain,
% 1.50/1.68 (union(B!4, union(D!2, B!4)) = union(union(D!2, B!4), B!4)),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[118, 16])).
% 1.50/1.68 tff(120,plain,
% 1.50/1.68 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(B!4, C!3), B!4) = union(B!4, intersection(B!4, C!3)))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(121,plain,
% 1.50/1.68 (union(intersection(B!4, C!3), B!4) = union(B!4, intersection(B!4, C!3))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[120, 16])).
% 1.50/1.68 tff(122,plain,
% 1.50/1.68 (union(B!4, intersection(B!4, C!3)) = union(intersection(B!4, C!3), B!4)),
% 1.50/1.68 inference(symmetry,[status(thm)],[121])).
% 1.50/1.68 tff(123,plain,
% 1.50/1.68 (B!4 = union(B!4, intersection(B!4, C!3))),
% 1.50/1.68 inference(symmetry,[status(thm)],[84])).
% 1.50/1.68 tff(124,plain,
% 1.50/1.68 (B!4 = union(intersection(B!4, C!3), B!4)),
% 1.50/1.68 inference(transitivity,[status(thm)],[123, 122])).
% 1.50/1.68 tff(125,plain,
% 1.50/1.68 (union(intersection(C!3, D!2), B!4) = union(intersection(C!3, D!2), union(intersection(B!4, C!3), B!4))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[124])).
% 1.50/1.68 tff(126,plain,
% 1.50/1.68 (union(intersection(C!3, D!2), union(intersection(B!4, C!3), B!4)) = union(intersection(C!3, D!2), B!4)),
% 1.50/1.68 inference(symmetry,[status(thm)],[125])).
% 1.50/1.68 tff(127,plain,
% 1.50/1.68 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(intersection(C!3, D!2), intersection(B!4, C!3)), B!4) = union(intersection(C!3, D!2), union(intersection(B!4, C!3), B!4)))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(128,plain,
% 1.50/1.68 (union(union(intersection(C!3, D!2), intersection(B!4, C!3)), B!4) = union(intersection(C!3, D!2), union(intersection(B!4, C!3), B!4))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[127, 35])).
% 1.50/1.68 tff(129,plain,
% 1.50/1.68 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(C!3, D!2), intersection(B!4, C!3)) = union(intersection(B!4, C!3), intersection(C!3, D!2)))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(130,plain,
% 1.50/1.68 (union(intersection(C!3, D!2), intersection(B!4, C!3)) = union(intersection(B!4, C!3), intersection(C!3, D!2))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[129, 16])).
% 1.50/1.68 tff(131,plain,
% 1.50/1.68 (union(union(intersection(C!3, D!2), intersection(B!4, C!3)), B!4) = union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)),
% 1.50/1.68 inference(monotonicity,[status(thm)],[130])).
% 1.50/1.68 tff(132,plain,
% 1.50/1.68 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4) = union(union(intersection(C!3, D!2), intersection(B!4, C!3)), B!4)),
% 1.50/1.68 inference(symmetry,[status(thm)],[131])).
% 1.50/1.68 tff(133,plain,
% 1.50/1.68 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4) = union(intersection(C!3, D!2), B!4)),
% 1.50/1.68 inference(transitivity,[status(thm)],[132, 128, 126])).
% 1.50/1.68 tff(134,plain,
% 1.50/1.68 (union(D!2, union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = union(D!2, union(intersection(C!3, D!2), B!4))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[133])).
% 1.50/1.68 tff(135,plain,
% 1.50/1.68 (union(D!2, union(intersection(C!3, D!2), B!4)) = union(D!2, union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))),
% 1.50/1.68 inference(symmetry,[status(thm)],[134])).
% 1.50/1.68 tff(136,plain,
% 1.50/1.68 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(D!2, intersection(C!3, D!2)), B!4) = union(D!2, union(intersection(C!3, D!2), B!4)))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(137,plain,
% 1.50/1.68 (union(union(D!2, intersection(C!3, D!2)), B!4) = union(D!2, union(intersection(C!3, D!2), B!4))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[136, 35])).
% 1.50/1.68 tff(138,plain,
% 1.50/1.68 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(D!2, intersection(D!2, C!3)) = D!2)),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(139,plain,
% 1.50/1.68 (union(D!2, intersection(D!2, C!3)) = D!2),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[138, 25])).
% 1.50/1.68 tff(140,plain,
% 1.50/1.68 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(D!2, C!3) = intersection(C!3, D!2))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(141,plain,
% 1.50/1.68 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[140, 7])).
% 1.50/1.68 tff(142,plain,
% 1.50/1.68 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 1.50/1.68 inference(symmetry,[status(thm)],[141])).
% 1.50/1.68 tff(143,plain,
% 1.50/1.68 (union(D!2, intersection(C!3, D!2)) = union(D!2, intersection(D!2, C!3))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[142])).
% 1.50/1.68 tff(144,plain,
% 1.50/1.68 (union(D!2, intersection(C!3, D!2)) = D!2),
% 1.50/1.68 inference(transitivity,[status(thm)],[143, 139])).
% 1.50/1.68 tff(145,plain,
% 1.50/1.68 (union(union(D!2, intersection(C!3, D!2)), B!4) = union(D!2, B!4)),
% 1.50/1.68 inference(monotonicity,[status(thm)],[144])).
% 1.50/1.68 tff(146,plain,
% 1.50/1.68 (union(D!2, B!4) = union(union(D!2, intersection(C!3, D!2)), B!4)),
% 1.50/1.68 inference(symmetry,[status(thm)],[145])).
% 1.50/1.68 tff(147,plain,
% 1.50/1.68 (union(D!2, B!4) = union(D!2, union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))),
% 1.50/1.68 inference(transitivity,[status(thm)],[146, 137, 135])).
% 1.50/1.68 tff(148,plain,
% 1.50/1.68 (union(B!4, union(D!2, B!4)) = union(B!4, union(D!2, union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[147])).
% 1.50/1.68 tff(149,plain,
% 1.50/1.68 (union(B!4, union(D!2, union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))) = union(B!4, union(D!2, B!4))),
% 1.50/1.68 inference(symmetry,[status(thm)],[148])).
% 1.50/1.68 tff(150,plain,
% 1.50/1.68 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(B!4, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = union(B!4, union(D!2, union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(151,plain,
% 1.50/1.68 (union(union(B!4, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = union(B!4, union(D!2, union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[150, 35])).
% 1.50/1.68 tff(152,plain,
% 1.50/1.68 (union(union(B!4, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = union(union(D!2, B!4), intersection(union(D!2, B!4), union(B!4, C!3)))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[18, 115])).
% 1.50/1.68 tff(153,plain,
% 1.50/1.68 (union(union(D!2, B!4), intersection(union(D!2, B!4), union(B!4, C!3))) = union(union(B!4, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))),
% 1.53/1.68 inference(symmetry,[status(thm)],[152])).
% 1.53/1.68 tff(154,plain,
% 1.53/1.68 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(union(D!2, B!4), intersection(union(D!2, B!4), union(B!4, C!3))) = union(D!2, B!4))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(155,plain,
% 1.53/1.68 (union(union(D!2, B!4), intersection(union(D!2, B!4), union(B!4, C!3))) = union(D!2, B!4)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[154, 25])).
% 1.53/1.68 tff(156,plain,
% 1.53/1.68 (union(D!2, B!4) = union(union(D!2, B!4), intersection(union(D!2, B!4), union(B!4, C!3)))),
% 1.53/1.68 inference(symmetry,[status(thm)],[155])).
% 1.53/1.68 tff(157,plain,
% 1.53/1.68 (union(D!2, B!4) = union(union(D!2, B!4), B!4)),
% 1.53/1.68 inference(transitivity,[status(thm)],[156, 153, 151, 149, 119])).
% 1.53/1.68 tff(158,plain,
% 1.53/1.68 (intersection(union(D!2, B!4), intersection(union(C!3, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))) = intersection(union(union(D!2, B!4), B!4), intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2))))),
% 1.53/1.68 inference(monotonicity,[status(thm)],[157, 117])).
% 1.53/1.68 tff(159,plain,
% 1.53/1.68 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(union(D!2, B!4), union(C!3, D!2)), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = intersection(union(D!2, B!4), intersection(union(C!3, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(160,plain,
% 1.53/1.68 (intersection(intersection(union(D!2, B!4), union(C!3, D!2)), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = intersection(union(D!2, B!4), intersection(union(C!3, D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)))),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[159, 73])).
% 1.53/1.68 tff(161,plain,
% 1.53/1.68 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, C!3) = union(C!3, D!2))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(162,plain,
% 1.53/1.68 (union(D!2, C!3) = union(C!3, D!2)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[161, 16])).
% 1.53/1.68 tff(163,plain,
% 1.53/1.68 (union(C!3, D!2) = union(D!2, C!3)),
% 1.53/1.68 inference(symmetry,[status(thm)],[162])).
% 1.53/1.68 tff(164,plain,
% 1.53/1.68 (intersection(union(D!2, B!4), union(C!3, D!2)) = intersection(union(D!2, B!4), union(D!2, C!3))),
% 1.53/1.68 inference(monotonicity,[status(thm)],[163])).
% 1.53/1.68 tff(165,plain,
% 1.53/1.68 (intersection(union(D!2, B!4), union(D!2, C!3)) = intersection(union(D!2, B!4), union(C!3, D!2))),
% 1.53/1.68 inference(symmetry,[status(thm)],[164])).
% 1.53/1.68 tff(166,plain,
% 1.53/1.68 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(D!2, intersection(B!4, C!3)) = intersection(union(D!2, B!4), union(D!2, C!3)))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(167,plain,
% 1.53/1.68 (union(D!2, intersection(B!4, C!3)) = intersection(union(D!2, B!4), union(D!2, C!3))),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[166, 48])).
% 1.53/1.68 tff(168,plain,
% 1.53/1.68 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, intersection(B!4, C!3)) = union(intersection(B!4, C!3), D!2))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(169,plain,
% 1.53/1.68 (union(D!2, intersection(B!4, C!3)) = union(intersection(B!4, C!3), D!2)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[168, 16])).
% 1.53/1.68 tff(170,plain,
% 1.53/1.68 (union(intersection(B!4, C!3), D!2) = union(D!2, intersection(B!4, C!3))),
% 1.53/1.68 inference(symmetry,[status(thm)],[169])).
% 1.53/1.68 tff(171,plain,
% 1.53/1.68 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, intersection(C!3, D!2)) = union(intersection(C!3, D!2), D!2))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(172,plain,
% 1.53/1.68 (union(D!2, intersection(C!3, D!2)) = union(intersection(C!3, D!2), D!2)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[171, 16])).
% 1.53/1.68 tff(173,plain,
% 1.53/1.68 (union(D!2, intersection(D!2, C!3)) = union(D!2, intersection(C!3, D!2))),
% 1.53/1.68 inference(symmetry,[status(thm)],[143])).
% 1.53/1.68 tff(174,plain,
% 1.53/1.68 (D!2 = union(D!2, intersection(D!2, C!3))),
% 1.53/1.68 inference(symmetry,[status(thm)],[139])).
% 1.53/1.68 tff(175,plain,
% 1.53/1.68 (D!2 = union(intersection(C!3, D!2), D!2)),
% 1.53/1.68 inference(transitivity,[status(thm)],[174, 173, 172])).
% 1.53/1.68 tff(176,plain,
% 1.53/1.68 (union(intersection(B!4, C!3), D!2) = union(intersection(B!4, C!3), union(intersection(C!3, D!2), D!2))),
% 1.53/1.68 inference(monotonicity,[status(thm)],[175])).
% 1.53/1.68 tff(177,plain,
% 1.53/1.68 (union(intersection(B!4, C!3), union(intersection(C!3, D!2), D!2)) = union(intersection(B!4, C!3), D!2)),
% 1.53/1.68 inference(symmetry,[status(thm)],[176])).
% 1.53/1.68 tff(178,plain,
% 1.53/1.68 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), D!2) = union(intersection(B!4, C!3), union(intersection(C!3, D!2), D!2)))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(179,plain,
% 1.53/1.68 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), D!2) = union(intersection(B!4, C!3), union(intersection(C!3, D!2), D!2))),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[178, 35])).
% 1.53/1.68 tff(180,plain,
% 1.53/1.68 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), D!2) = intersection(union(D!2, B!4), union(C!3, D!2))),
% 1.53/1.68 inference(transitivity,[status(thm)],[179, 177, 170, 167, 165])).
% 1.53/1.68 tff(181,plain,
% 1.53/1.68 (intersection(union(union(intersection(B!4, C!3), intersection(C!3, D!2)), D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)) = intersection(intersection(union(D!2, B!4), union(C!3, D!2)), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))),
% 1.53/1.68 inference(monotonicity,[status(thm)],[180])).
% 1.53/1.68 tff(182,plain,
% 1.53/1.68 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), intersection(D!2, B!4)) = intersection(union(union(intersection(B!4, C!3), intersection(C!3, D!2)), D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4)))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(183,plain,
% 1.53/1.68 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), intersection(D!2, B!4)) = intersection(union(union(intersection(B!4, C!3), intersection(C!3, D!2)), D!2), union(union(intersection(B!4, C!3), intersection(C!3, D!2)), B!4))),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[182, 48])).
% 1.53/1.68 tff(184,plain,
% 1.53/1.68 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), intersection(D!2, B!4)) = intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4))),
% 1.53/1.68 inference(transitivity,[status(thm)],[183, 181, 160, 158, 76, 66, 9])).
% 1.53/1.68 tff(185,plain,
% 1.53/1.68 ((~![B: $i, C: $i, D: $i] : (union(union(intersection(B, C), intersection(C, D)), intersection(D, B)) = intersection(intersection(union(B, C), union(C, D)), union(D, B)))) <=> (~![B: $i, C: $i, D: $i] : (union(union(intersection(B, C), intersection(C, D)), intersection(D, B)) = intersection(intersection(union(B, C), union(C, D)), union(D, B))))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(186,axiom,(~![B: $i, C: $i, D: $i] : (union(union(intersection(B, C), intersection(C, D)), intersection(D, B)) = intersection(intersection(union(B, C), union(C, D)), union(D, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th72')).
% 1.53/1.68 tff(187,plain,
% 1.53/1.68 (~![B: $i, C: $i, D: $i] : (union(union(intersection(B, C), intersection(C, D)), intersection(D, B)) = intersection(intersection(union(B, C), union(C, D)), union(D, B)))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.53/1.68 tff(188,plain,
% 1.53/1.68 (~![B: $i, C: $i, D: $i] : (union(union(intersection(B, C), intersection(C, D)), intersection(D, B)) = intersection(intersection(union(B, C), union(C, D)), union(D, B)))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[187, 185])).
% 1.53/1.68 tff(189,plain,
% 1.53/1.68 (~![B: $i, C: $i, D: $i] : (union(union(intersection(B, C), intersection(C, D)), intersection(D, B)) = intersection(intersection(union(B, C), union(C, D)), union(D, B)))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[188, 185])).
% 1.53/1.68 tff(190,plain,
% 1.53/1.68 (~![B: $i, C: $i, D: $i] : (union(union(intersection(B, C), intersection(C, D)), intersection(D, B)) = intersection(intersection(union(B, C), union(C, D)), union(D, B)))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[189, 185])).
% 1.53/1.68 tff(191,plain,(
% 1.53/1.68 ~(union(union(intersection(B!4, C!3), intersection(C!3, D!2)), intersection(D!2, B!4)) = intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4)))),
% 1.53/1.68 inference(skolemize,[status(sab)],[190])).
% 1.53/1.68 tff(192,plain,
% 1.53/1.68 ($false),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[191, 184])).
% 1.53/1.68 % SZS output end Proof
% 1.53/1.68 % E exiting
%------------------------------------------------------------------------------