TSTP Solution File: SET601+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET601+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Tue Sep 20 05:07:14 EDT 2022
% Result : Theorem 3.31s 2.37s
% Output : Proof 3.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET601+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 07:03:15 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 3.31/2.37 % SZS status Theorem
% 3.31/2.37 % SZS output start Proof
% 3.31/2.37 tff(intersection_type, type, (
% 3.31/2.37 intersection: ( $i * $i ) > $i)).
% 3.31/2.37 tff(union_type, type, (
% 3.31/2.37 union: ( $i * $i ) > $i)).
% 3.31/2.37 tff(tptp_fun_B_4_type, type, (
% 3.31/2.37 tptp_fun_B_4: $i)).
% 3.31/2.37 tff(tptp_fun_D_2_type, type, (
% 3.31/2.37 tptp_fun_D_2: $i)).
% 3.31/2.37 tff(tptp_fun_C_3_type, type, (
% 3.31/2.37 tptp_fun_C_3: $i)).
% 3.31/2.37 tff(1,plain,
% 3.31/2.37 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 3.31/2.37 inference(bind,[status(th)],[])).
% 3.31/2.37 tff(2,plain,
% 3.31/2.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 3.31/2.37 inference(quant_intro,[status(thm)],[1])).
% 3.31/2.37 tff(3,plain,
% 3.31/2.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 3.31/2.37 inference(rewrite,[status(thm)],[])).
% 3.31/2.37 tff(4,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 3.31/2.37 tff(5,plain,
% 3.31/2.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 3.31/2.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.31/2.37 tff(6,plain,(
% 3.31/2.37 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 3.31/2.37 inference(skolemize,[status(sab)],[5])).
% 3.31/2.37 tff(7,plain,
% 3.31/2.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 3.31/2.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.31/2.37 tff(8,plain,
% 3.31/2.37 ((~![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)))),
% 3.31/2.37 inference(quant_inst,[status(thm)],[])).
% 3.31/2.37 tff(9,plain,
% 3.31/2.37 (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))),
% 3.31/2.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.31/2.37 tff(10,plain,
% 3.31/2.37 (^[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))))),
% 3.31/2.37 inference(bind,[status(th)],[])).
% 3.31/2.37 tff(11,plain,
% 3.31/2.37 (![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)))),
% 3.31/2.37 inference(quant_intro,[status(thm)],[10])).
% 3.31/2.37 tff(12,plain,
% 3.31/2.37 (![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)))),
% 3.31/2.37 inference(rewrite,[status(thm)],[])).
% 3.31/2.37 tff(13,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')).
% 3.31/2.37 tff(14,plain,
% 3.31/2.37 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 3.31/2.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 3.31/2.37 tff(15,plain,(
% 3.31/2.37 ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 3.31/2.37 inference(skolemize,[status(sab)],[14])).
% 3.31/2.37 tff(16,plain,
% 3.31/2.37 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 3.31/2.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 3.31/2.37 tff(17,plain,
% 3.31/2.37 ((~![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))))),
% 3.31/2.37 inference(quant_inst,[status(thm)],[])).
% 3.31/2.37 tff(18,plain,
% 3.31/2.37 (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)))),
% 3.31/2.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 3.31/2.37 tff(19,plain,
% 3.31/2.37 ((~![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)))),
% 3.31/2.37 inference(quant_inst,[status(thm)],[])).
% 3.31/2.37 tff(20,plain,
% 3.31/2.37 (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))),
% 3.31/2.37 inference(unit_resolution,[status(thm)],[19, 7])).
% 3.31/2.37 tff(21,plain,
% 3.31/2.37 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 3.31/2.37 inference(bind,[status(th)],[])).
% 3.31/2.37 tff(22,plain,
% 3.31/2.37 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 3.31/2.37 inference(quant_intro,[status(thm)],[21])).
% 3.31/2.37 tff(23,plain,
% 3.31/2.37 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 3.31/2.37 inference(rewrite,[status(thm)],[])).
% 3.31/2.37 tff(24,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 3.31/2.37 tff(25,plain,
% 3.31/2.37 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 3.31/2.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 3.31/2.37 tff(26,plain,(
% 3.31/2.37 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 3.31/2.37 inference(skolemize,[status(sab)],[25])).
% 3.31/2.37 tff(27,plain,
% 3.31/2.37 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 3.31/2.37 inference(modus_ponens,[status(thm)],[26, 22])).
% 3.31/2.37 tff(28,plain,
% 3.31/2.37 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, C!3) = union(C!3, D!2))),
% 3.31/2.37 inference(quant_inst,[status(thm)],[])).
% 3.31/2.37 tff(29,plain,
% 3.31/2.37 (union(D!2, C!3) = union(C!3, D!2)),
% 3.31/2.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 3.31/2.37 tff(30,plain,
% 3.31/2.37 (^[B: $i, C: $i] : refl((union(B, intersection(B, C)) = B) <=> (union(B, intersection(B, C)) = B))),
% 3.31/2.37 inference(bind,[status(th)],[])).
% 3.31/2.37 tff(31,plain,
% 3.31/2.37 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B) <=> ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 3.31/2.37 inference(quant_intro,[status(thm)],[30])).
% 3.31/2.37 tff(32,plain,
% 3.31/2.37 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B) <=> ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 3.31/2.37 inference(rewrite,[status(thm)],[])).
% 3.31/2.37 tff(33,axiom,(![B: $i, C: $i] : (union(B, intersection(B, C)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_intersection')).
% 3.31/2.37 tff(34,plain,
% 3.31/2.37 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 3.31/2.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 3.31/2.37 tff(35,plain,(
% 3.31/2.37 ![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 3.31/2.37 inference(skolemize,[status(sab)],[34])).
% 3.31/2.37 tff(36,plain,
% 3.31/2.37 (![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 3.31/2.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 3.31/2.37 tff(37,plain,
% 3.31/2.37 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(C!3, intersection(C!3, D!2)) = C!3)),
% 3.31/2.37 inference(quant_inst,[status(thm)],[])).
% 3.31/2.37 tff(38,plain,
% 3.31/2.37 (union(C!3, intersection(C!3, D!2)) = C!3),
% 3.31/2.37 inference(unit_resolution,[status(thm)],[37, 36])).
% 3.31/2.37 tff(39,plain,
% 3.31/2.37 (^[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))))),
% 3.31/2.37 inference(bind,[status(th)],[])).
% 3.31/2.37 tff(40,plain,
% 3.31/2.37 (![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)))),
% 3.31/2.37 inference(quant_intro,[status(thm)],[39])).
% 3.31/2.37 tff(41,plain,
% 3.31/2.37 (![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)))),
% 3.31/2.37 inference(rewrite,[status(thm)],[])).
% 3.31/2.37 tff(42,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')).
% 3.31/2.37 tff(43,plain,
% 3.31/2.37 (![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 3.31/2.38 tff(44,plain,(
% 3.31/2.38 ![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 3.31/2.38 inference(skolemize,[status(sab)],[43])).
% 3.31/2.38 tff(45,plain,
% 3.31/2.38 (![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[44, 40])).
% 3.31/2.38 tff(46,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(C!3, intersection(C!3, D!2)) = intersection(union(C!3, C!3), union(C!3, D!2)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(47,plain,
% 3.31/2.38 (union(C!3, intersection(C!3, D!2)) = intersection(union(C!3, C!3), union(C!3, D!2))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 3.31/2.38 tff(48,plain,
% 3.31/2.38 (intersection(union(C!3, C!3), union(C!3, D!2)) = union(C!3, intersection(C!3, D!2))),
% 3.31/2.38 inference(symmetry,[status(thm)],[47])).
% 3.31/2.38 tff(49,plain,
% 3.31/2.38 (intersection(union(C!3, C!3), union(C!3, D!2)) = C!3),
% 3.31/2.38 inference(transitivity,[status(thm)],[48, 38])).
% 3.31/2.38 tff(50,plain,
% 3.31/2.38 (union(D!2, intersection(union(C!3, C!3), union(C!3, D!2))) = union(D!2, C!3)),
% 3.31/2.38 inference(monotonicity,[status(thm)],[49])).
% 3.31/2.38 tff(51,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(D!2, intersection(union(C!3, C!3), union(C!3, D!2))) = intersection(union(D!2, union(C!3, C!3)), union(D!2, union(C!3, D!2))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(52,plain,
% 3.31/2.38 (union(D!2, intersection(union(C!3, C!3), union(C!3, D!2))) = intersection(union(D!2, union(C!3, C!3)), union(D!2, union(C!3, D!2)))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[51, 45])).
% 3.31/2.38 tff(53,plain,
% 3.31/2.38 (intersection(union(D!2, union(C!3, C!3)), union(D!2, union(C!3, D!2))) = union(D!2, intersection(union(C!3, C!3), union(C!3, D!2)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[52])).
% 3.31/2.38 tff(54,plain,
% 3.31/2.38 (^[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))))),
% 3.31/2.38 inference(bind,[status(th)],[])).
% 3.31/2.38 tff(55,plain,
% 3.31/2.38 (![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)))),
% 3.31/2.38 inference(quant_intro,[status(thm)],[54])).
% 3.31/2.38 tff(56,plain,
% 3.31/2.38 (![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)))),
% 3.31/2.38 inference(rewrite,[status(thm)],[])).
% 3.31/2.38 tff(57,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')).
% 3.31/2.38 tff(58,plain,
% 3.31/2.38 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 3.31/2.38 tff(59,plain,(
% 3.31/2.38 ![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 3.31/2.38 inference(skolemize,[status(sab)],[58])).
% 3.31/2.38 tff(60,plain,
% 3.31/2.38 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[59, 55])).
% 3.31/2.38 tff(61,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(C!3, intersection(B!4, C!3)), D!2) = union(C!3, union(intersection(B!4, C!3), D!2)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(62,plain,
% 3.31/2.38 (union(union(C!3, intersection(B!4, C!3)), D!2) = union(C!3, union(intersection(B!4, C!3), D!2))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[61, 60])).
% 3.31/2.38 tff(63,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(C!3, intersection(C!3, B!4)) = C!3)),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(64,plain,
% 3.31/2.38 (union(C!3, intersection(C!3, B!4)) = C!3),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[63, 36])).
% 3.31/2.38 tff(65,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, B!4) = intersection(B!4, C!3))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(66,plain,
% 3.31/2.38 (intersection(C!3, B!4) = intersection(B!4, C!3)),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[65, 7])).
% 3.31/2.38 tff(67,plain,
% 3.31/2.38 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 3.31/2.38 inference(symmetry,[status(thm)],[66])).
% 3.31/2.38 tff(68,plain,
% 3.31/2.38 (union(C!3, intersection(B!4, C!3)) = union(C!3, intersection(C!3, B!4))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[67])).
% 3.31/2.38 tff(69,plain,
% 3.31/2.38 (union(C!3, intersection(B!4, C!3)) = C!3),
% 3.31/2.38 inference(transitivity,[status(thm)],[68, 64])).
% 3.31/2.38 tff(70,plain,
% 3.31/2.38 (union(union(C!3, intersection(B!4, C!3)), D!2) = union(C!3, D!2)),
% 3.31/2.38 inference(monotonicity,[status(thm)],[69])).
% 3.31/2.38 tff(71,plain,
% 3.31/2.38 (union(C!3, D!2) = union(union(C!3, intersection(B!4, C!3)), D!2)),
% 3.31/2.38 inference(symmetry,[status(thm)],[70])).
% 3.31/2.38 tff(72,plain,
% 3.31/2.38 (union(C!3, D!2) = union(C!3, union(intersection(B!4, C!3), D!2))),
% 3.31/2.38 inference(transitivity,[status(thm)],[71, 62])).
% 3.31/2.38 tff(73,plain,
% 3.31/2.38 (union(D!2, union(C!3, D!2)) = union(D!2, union(C!3, union(intersection(B!4, C!3), D!2)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[72])).
% 3.31/2.38 tff(74,plain,
% 3.31/2.38 (union(D!2, union(C!3, union(intersection(B!4, C!3), D!2))) = union(D!2, union(C!3, D!2))),
% 3.31/2.38 inference(symmetry,[status(thm)],[73])).
% 3.31/2.38 tff(75,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(D!2, C!3), union(intersection(B!4, C!3), D!2)) = union(D!2, union(C!3, union(intersection(B!4, C!3), D!2))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(76,plain,
% 3.31/2.38 (union(union(D!2, C!3), union(intersection(B!4, C!3), D!2)) = union(D!2, union(C!3, union(intersection(B!4, C!3), D!2)))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[75, 60])).
% 3.31/2.38 tff(77,plain,
% 3.31/2.38 (union(C!3, D!2) = union(D!2, C!3)),
% 3.31/2.38 inference(symmetry,[status(thm)],[29])).
% 3.31/2.38 tff(78,plain,
% 3.31/2.38 (intersection(union(C!3, D!2), union(D!2, B!4)) = intersection(union(D!2, C!3), union(D!2, B!4))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[77])).
% 3.31/2.38 tff(79,plain,
% 3.31/2.38 (intersection(union(D!2, C!3), union(D!2, B!4)) = intersection(union(C!3, D!2), union(D!2, B!4))),
% 3.31/2.38 inference(symmetry,[status(thm)],[78])).
% 3.31/2.38 tff(80,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(D!2, intersection(C!3, B!4)) = intersection(union(D!2, C!3), union(D!2, B!4)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(81,plain,
% 3.31/2.38 (union(D!2, intersection(C!3, B!4)) = intersection(union(D!2, C!3), union(D!2, B!4))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[80, 45])).
% 3.31/2.38 tff(82,plain,
% 3.31/2.38 (union(D!2, intersection(C!3, B!4)) = union(D!2, intersection(B!4, C!3))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[66])).
% 3.31/2.38 tff(83,plain,
% 3.31/2.38 (union(D!2, intersection(B!4, C!3)) = union(D!2, intersection(C!3, B!4))),
% 3.31/2.38 inference(symmetry,[status(thm)],[82])).
% 3.31/2.38 tff(84,plain,
% 3.31/2.38 ((~![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))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(85,plain,
% 3.31/2.38 (union(D!2, intersection(B!4, C!3)) = union(intersection(B!4, C!3), D!2)),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[84, 27])).
% 3.31/2.38 tff(86,plain,
% 3.31/2.38 (union(intersection(B!4, C!3), D!2) = union(D!2, intersection(B!4, C!3))),
% 3.31/2.38 inference(symmetry,[status(thm)],[85])).
% 3.31/2.38 tff(87,plain,
% 3.31/2.38 (union(intersection(B!4, C!3), D!2) = intersection(union(C!3, D!2), union(D!2, B!4))),
% 3.31/2.38 inference(transitivity,[status(thm)],[86, 83, 81, 79])).
% 3.31/2.38 tff(88,plain,
% 3.31/2.38 (union(union(D!2, C!3), union(intersection(B!4, C!3), D!2)) = union(union(C!3, D!2), intersection(union(C!3, D!2), union(D!2, B!4)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[29, 87])).
% 3.31/2.38 tff(89,plain,
% 3.31/2.38 (union(union(C!3, D!2), intersection(union(C!3, D!2), union(D!2, B!4))) = union(union(D!2, C!3), union(intersection(B!4, C!3), D!2))),
% 3.31/2.38 inference(symmetry,[status(thm)],[88])).
% 3.31/2.38 tff(90,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(union(C!3, D!2), intersection(union(C!3, D!2), union(D!2, B!4))) = union(C!3, D!2))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(91,plain,
% 3.31/2.38 (union(union(C!3, D!2), intersection(union(C!3, D!2), union(D!2, B!4))) = union(C!3, D!2)),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[90, 36])).
% 3.31/2.38 tff(92,plain,
% 3.31/2.38 (union(C!3, D!2) = union(union(C!3, D!2), intersection(union(C!3, D!2), union(D!2, B!4)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[91])).
% 3.31/2.38 tff(93,plain,
% 3.31/2.38 (union(C!3, D!2) = union(D!2, union(C!3, D!2))),
% 3.31/2.38 inference(transitivity,[status(thm)],[92, 89, 76, 74])).
% 3.31/2.38 tff(94,plain,
% 3.31/2.38 (intersection(union(D!2, union(C!3, C!3)), union(C!3, D!2)) = intersection(union(D!2, union(C!3, C!3)), union(D!2, union(C!3, D!2)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[93])).
% 3.31/2.38 tff(95,plain,
% 3.31/2.38 (intersection(union(D!2, union(C!3, C!3)), union(C!3, D!2)) = union(C!3, D!2)),
% 3.31/2.38 inference(transitivity,[status(thm)],[94, 53, 50, 29])).
% 3.31/2.38 tff(96,plain,
% 3.31/2.38 (intersection(intersection(union(D!2, union(C!3, C!3)), union(C!3, D!2)), intersection(union(D!2, B!4), union(B!4, C!3))) = intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[95])).
% 3.31/2.38 tff(97,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(union(D!2, union(C!3, C!3)), union(C!3, D!2)), intersection(union(D!2, B!4), union(B!4, C!3))) = intersection(union(D!2, union(C!3, C!3)), intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3)))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(98,plain,
% 3.31/2.38 (intersection(intersection(union(D!2, union(C!3, C!3)), union(C!3, D!2)), intersection(union(D!2, B!4), union(B!4, C!3))) = intersection(union(D!2, union(C!3, C!3)), intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3))))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[97, 16])).
% 3.31/2.38 tff(99,plain,
% 3.31/2.38 (intersection(union(D!2, union(C!3, C!3)), intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3)))) = intersection(intersection(union(D!2, union(C!3, C!3)), union(C!3, D!2)), intersection(union(D!2, B!4), union(B!4, C!3)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[98])).
% 3.31/2.38 tff(100,plain,
% 3.31/2.38 (intersection(intersection(union(D!2, B!4), union(B!4, C!3)), union(C!3, D!2)) = intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[20])).
% 3.31/2.38 tff(101,plain,
% 3.31/2.38 (intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2))) = intersection(intersection(union(D!2, B!4), union(B!4, C!3)), union(C!3, D!2))),
% 3.31/2.38 inference(symmetry,[status(thm)],[18])).
% 3.31/2.38 tff(102,plain,
% 3.31/2.38 (intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4)) = intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[9])).
% 3.31/2.38 tff(103,plain,
% 3.31/2.38 (intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4)) = intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3)))),
% 3.31/2.38 inference(transitivity,[status(thm)],[102, 101, 100])).
% 3.31/2.38 tff(104,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(union(C!3, C!3), D!2) = union(D!2, union(C!3, C!3)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(105,plain,
% 3.31/2.38 (union(union(C!3, C!3), D!2) = union(D!2, union(C!3, C!3))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[104, 27])).
% 3.31/2.38 tff(106,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(C!3, C!3), D!2) = union(C!3, union(C!3, D!2)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(107,plain,
% 3.31/2.38 (union(union(C!3, C!3), D!2) = union(C!3, union(C!3, D!2))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[106, 60])).
% 3.31/2.38 tff(108,plain,
% 3.31/2.38 (union(C!3, union(C!3, D!2)) = union(union(C!3, C!3), D!2)),
% 3.31/2.38 inference(symmetry,[status(thm)],[107])).
% 3.31/2.38 tff(109,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(C!3, intersection(D!2, B!4)) = intersection(union(C!3, D!2), union(C!3, B!4)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(110,plain,
% 3.31/2.38 (union(C!3, intersection(D!2, B!4)) = intersection(union(C!3, D!2), union(C!3, B!4))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[109, 45])).
% 3.31/2.38 tff(111,plain,
% 3.31/2.38 (intersection(union(C!3, D!2), union(C!3, B!4)) = union(C!3, intersection(D!2, B!4))),
% 3.31/2.38 inference(symmetry,[status(thm)],[110])).
% 3.31/2.38 tff(112,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(C!3, B!4) = union(B!4, C!3))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(113,plain,
% 3.31/2.38 (union(C!3, B!4) = union(B!4, C!3)),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[112, 27])).
% 3.31/2.38 tff(114,plain,
% 3.31/2.38 (intersection(union(C!3, D!2), union(C!3, B!4)) = intersection(union(C!3, D!2), union(B!4, C!3))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[113])).
% 3.31/2.38 tff(115,plain,
% 3.31/2.38 (intersection(union(C!3, D!2), union(B!4, C!3)) = intersection(union(C!3, D!2), union(C!3, B!4))),
% 3.31/2.38 inference(symmetry,[status(thm)],[114])).
% 3.31/2.38 tff(116,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(union(C!3, D!2), union(B!4, C!3)) = intersection(union(B!4, C!3), union(C!3, D!2)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(117,plain,
% 3.31/2.38 (intersection(union(C!3, D!2), union(B!4, C!3)) = intersection(union(B!4, C!3), union(C!3, D!2))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[116, 7])).
% 3.31/2.38 tff(118,plain,
% 3.31/2.38 (intersection(union(B!4, C!3), union(C!3, D!2)) = intersection(union(C!3, D!2), union(B!4, C!3))),
% 3.31/2.38 inference(symmetry,[status(thm)],[117])).
% 3.31/2.38 tff(119,plain,
% 3.31/2.38 (intersection(union(B!4, C!3), union(C!3, D!2)) = union(C!3, intersection(D!2, B!4))),
% 3.31/2.38 inference(transitivity,[status(thm)],[118, 115, 111])).
% 3.31/2.38 tff(120,plain,
% 3.31/2.38 (union(D!2, intersection(union(B!4, C!3), union(C!3, D!2))) = union(D!2, union(C!3, intersection(D!2, B!4)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[119])).
% 3.31/2.38 tff(121,plain,
% 3.31/2.38 (union(D!2, union(C!3, intersection(D!2, B!4))) = union(D!2, intersection(union(B!4, C!3), union(C!3, D!2)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[120])).
% 3.31/2.38 tff(122,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(D!2, C!3), intersection(D!2, B!4)) = union(D!2, union(C!3, intersection(D!2, B!4))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(123,plain,
% 3.31/2.38 (union(union(D!2, C!3), intersection(D!2, B!4)) = union(D!2, union(C!3, intersection(D!2, B!4)))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[122, 60])).
% 3.31/2.38 tff(124,plain,
% 3.31/2.38 (union(union(D!2, C!3), intersection(D!2, B!4)) = union(union(C!3, D!2), intersection(D!2, B!4))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[29])).
% 3.31/2.38 tff(125,plain,
% 3.31/2.38 (union(union(C!3, D!2), intersection(D!2, B!4)) = union(union(D!2, C!3), intersection(D!2, B!4))),
% 3.31/2.38 inference(symmetry,[status(thm)],[124])).
% 3.31/2.38 tff(126,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(C!3, D!2), intersection(D!2, B!4)) = union(C!3, union(D!2, intersection(D!2, B!4))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(127,plain,
% 3.31/2.38 (union(union(C!3, D!2), intersection(D!2, B!4)) = union(C!3, union(D!2, intersection(D!2, B!4)))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[126, 60])).
% 3.31/2.38 tff(128,plain,
% 3.31/2.38 (union(C!3, union(D!2, intersection(D!2, B!4))) = union(union(C!3, D!2), intersection(D!2, B!4))),
% 3.31/2.38 inference(symmetry,[status(thm)],[127])).
% 3.31/2.38 tff(129,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(D!2, intersection(D!2, B!4)) = D!2)),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(130,plain,
% 3.31/2.38 (union(D!2, intersection(D!2, B!4)) = D!2),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[129, 36])).
% 3.31/2.38 tff(131,plain,
% 3.31/2.38 (union(C!3, union(D!2, intersection(D!2, B!4))) = union(C!3, D!2)),
% 3.31/2.38 inference(monotonicity,[status(thm)],[130])).
% 3.31/2.38 tff(132,plain,
% 3.31/2.38 (union(C!3, D!2) = union(C!3, union(D!2, intersection(D!2, B!4)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[131])).
% 3.31/2.38 tff(133,plain,
% 3.31/2.38 (union(C!3, D!2) = union(D!2, intersection(union(B!4, C!3), union(C!3, D!2)))),
% 3.31/2.38 inference(transitivity,[status(thm)],[132, 128, 125, 123, 121])).
% 3.31/2.38 tff(134,plain,
% 3.31/2.38 (union(C!3, union(C!3, D!2)) = union(C!3, union(D!2, intersection(union(B!4, C!3), union(C!3, D!2))))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[133])).
% 3.31/2.38 tff(135,plain,
% 3.31/2.38 (union(C!3, union(D!2, intersection(union(B!4, C!3), union(C!3, D!2)))) = union(C!3, union(C!3, D!2))),
% 3.31/2.38 inference(symmetry,[status(thm)],[134])).
% 3.31/2.38 tff(136,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(C!3, D!2), intersection(union(B!4, C!3), union(C!3, D!2))) = union(C!3, union(D!2, intersection(union(B!4, C!3), union(C!3, D!2)))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(137,plain,
% 3.31/2.38 (union(union(C!3, D!2), intersection(union(B!4, C!3), union(C!3, D!2))) = union(C!3, union(D!2, intersection(union(B!4, C!3), union(C!3, D!2))))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[136, 60])).
% 3.31/2.38 tff(138,plain,
% 3.31/2.38 (union(union(C!3, D!2), intersection(union(B!4, C!3), union(C!3, D!2))) = union(union(C!3, D!2), intersection(union(C!3, D!2), union(B!4, C!3)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[118])).
% 3.31/2.38 tff(139,plain,
% 3.31/2.38 (union(union(C!3, D!2), intersection(union(C!3, D!2), union(B!4, C!3))) = union(union(C!3, D!2), intersection(union(B!4, C!3), union(C!3, D!2)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[138])).
% 3.31/2.38 tff(140,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) | (union(union(C!3, D!2), intersection(union(C!3, D!2), union(B!4, C!3))) = union(C!3, D!2))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(141,plain,
% 3.31/2.38 (union(union(C!3, D!2), intersection(union(C!3, D!2), union(B!4, C!3))) = union(C!3, D!2)),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[140, 36])).
% 3.31/2.38 tff(142,plain,
% 3.31/2.38 (union(C!3, D!2) = union(union(C!3, D!2), intersection(union(C!3, D!2), union(B!4, C!3)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[141])).
% 3.31/2.38 tff(143,plain,
% 3.31/2.38 (union(C!3, D!2) = union(D!2, union(C!3, C!3))),
% 3.31/2.38 inference(transitivity,[status(thm)],[142, 139, 137, 135, 108, 105])).
% 3.31/2.38 tff(144,plain,
% 3.31/2.38 (intersection(union(C!3, D!2), intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4))) = intersection(union(D!2, union(C!3, C!3)), intersection(union(C!3, D!2), intersection(union(D!2, B!4), union(B!4, C!3))))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[143, 103])).
% 3.31/2.38 tff(145,plain,
% 3.31/2.38 (intersection(union(C!3, D!2), intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2)))) = intersection(union(C!3, D!2), intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[9])).
% 3.31/2.38 tff(146,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(union(C!3, D!2), union(D!2, B!4)), intersection(union(B!4, C!3), union(C!3, D!2))) = intersection(union(C!3, D!2), intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2)))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(147,plain,
% 3.31/2.38 (intersection(intersection(union(C!3, D!2), union(D!2, B!4)), intersection(union(B!4, C!3), union(C!3, D!2))) = intersection(union(C!3, D!2), intersection(union(D!2, B!4), intersection(union(B!4, C!3), union(C!3, D!2))))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[146, 16])).
% 3.31/2.38 tff(148,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(C!3, intersection(D!2, B!4)) = union(intersection(D!2, B!4), C!3))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(149,plain,
% 3.31/2.38 (union(C!3, intersection(D!2, B!4)) = union(intersection(D!2, B!4), C!3)),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[148, 27])).
% 3.31/2.38 tff(150,plain,
% 3.31/2.38 (union(intersection(D!2, B!4), C!3) = union(C!3, intersection(D!2, B!4))),
% 3.31/2.38 inference(symmetry,[status(thm)],[149])).
% 3.31/2.38 tff(151,plain,
% 3.31/2.38 (union(intersection(D!2, B!4), C!3) = intersection(union(B!4, C!3), union(C!3, D!2))),
% 3.31/2.38 inference(transitivity,[status(thm)],[150, 110, 114, 117])).
% 3.31/2.38 tff(152,plain,
% 3.31/2.38 (union(intersection(B!4, C!3), union(D!2, intersection(D!2, B!4))) = union(intersection(B!4, C!3), D!2)),
% 3.31/2.38 inference(monotonicity,[status(thm)],[130])).
% 3.31/2.38 tff(153,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(intersection(B!4, C!3), D!2), intersection(D!2, B!4)) = union(intersection(B!4, C!3), union(D!2, intersection(D!2, B!4))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(154,plain,
% 3.31/2.38 (union(union(intersection(B!4, C!3), D!2), intersection(D!2, B!4)) = union(intersection(B!4, C!3), union(D!2, intersection(D!2, B!4)))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[153, 60])).
% 3.31/2.38 tff(155,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)) = union(union(intersection(B!4, C!3), D!2), intersection(D!2, B!4)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(156,plain,
% 3.31/2.38 (union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)) = union(union(intersection(B!4, C!3), D!2), intersection(D!2, B!4))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[155, 27])).
% 3.31/2.38 tff(157,plain,
% 3.31/2.38 (union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)) = intersection(union(C!3, D!2), union(D!2, B!4))),
% 3.31/2.38 inference(transitivity,[status(thm)],[156, 154, 152, 86, 83, 81, 79])).
% 3.31/2.38 tff(158,plain,
% 3.31/2.38 (intersection(union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)), union(intersection(D!2, B!4), C!3)) = intersection(intersection(union(C!3, D!2), union(D!2, B!4)), intersection(union(B!4, C!3), union(C!3, D!2)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[157, 151])).
% 3.31/2.38 tff(159,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)), union(intersection(D!2, B!4), C!3)) = intersection(union(intersection(D!2, B!4), C!3), union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(160,plain,
% 3.31/2.38 (intersection(union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)), union(intersection(D!2, B!4), C!3)) = intersection(union(intersection(D!2, B!4), C!3), union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[159, 7])).
% 3.31/2.38 tff(161,plain,
% 3.31/2.38 (intersection(union(intersection(D!2, B!4), C!3), union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2))) = intersection(union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)), union(intersection(D!2, B!4), C!3))),
% 3.31/2.38 inference(symmetry,[status(thm)],[160])).
% 3.31/2.38 tff(162,plain,
% 3.31/2.38 ((~![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))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(163,plain,
% 3.31/2.38 (union(C!3, intersection(B!4, C!3)) = union(intersection(B!4, C!3), C!3)),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[162, 27])).
% 3.31/2.38 tff(164,plain,
% 3.31/2.38 (union(intersection(B!4, C!3), C!3) = union(C!3, intersection(B!4, C!3))),
% 3.31/2.38 inference(symmetry,[status(thm)],[163])).
% 3.31/2.38 tff(165,plain,
% 3.31/2.38 (union(intersection(B!4, C!3), C!3) = C!3),
% 3.31/2.38 inference(transitivity,[status(thm)],[164, 68, 64])).
% 3.31/2.38 tff(166,plain,
% 3.31/2.38 (union(intersection(D!2, B!4), union(intersection(B!4, C!3), C!3)) = union(intersection(D!2, B!4), C!3)),
% 3.31/2.38 inference(monotonicity,[status(thm)],[165])).
% 3.31/2.38 tff(167,plain,
% 3.31/2.38 (intersection(union(intersection(D!2, B!4), union(intersection(B!4, C!3), C!3)), union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2))) = intersection(union(intersection(D!2, B!4), C!3), union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[166])).
% 3.31/2.38 tff(168,plain,
% 3.31/2.38 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) | (union(intersection(D!2, B!4), intersection(union(intersection(B!4, C!3), C!3), union(intersection(B!4, C!3), D!2))) = intersection(union(intersection(D!2, B!4), union(intersection(B!4, C!3), C!3)), union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2))))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(169,plain,
% 3.31/2.38 (union(intersection(D!2, B!4), intersection(union(intersection(B!4, C!3), C!3), union(intersection(B!4, C!3), D!2))) = intersection(union(intersection(D!2, B!4), union(intersection(B!4, C!3), C!3)), union(intersection(D!2, B!4), union(intersection(B!4, C!3), D!2)))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[168, 45])).
% 3.31/2.38 tff(170,plain,
% 3.31/2.38 ((~![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)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(171,plain,
% 3.31/2.38 (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))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[170, 45])).
% 3.31/2.38 tff(172,plain,
% 3.31/2.38 (union(intersection(D!2, B!4), union(intersection(B!4, C!3), intersection(C!3, D!2))) = union(intersection(D!2, B!4), intersection(union(intersection(B!4, C!3), C!3), union(intersection(B!4, C!3), D!2)))),
% 3.31/2.38 inference(monotonicity,[status(thm)],[171])).
% 3.31/2.38 tff(173,plain,
% 3.31/2.38 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(D!2, 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)), intersection(D!2, B!4)))),
% 3.31/2.38 inference(quant_inst,[status(thm)],[])).
% 3.31/2.38 tff(174,plain,
% 3.31/2.38 (union(intersection(D!2, 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)), intersection(D!2, B!4))),
% 3.31/2.38 inference(unit_resolution,[status(thm)],[173, 27])).
% 3.31/2.38 tff(175,plain,
% 3.31/2.38 (union(union(intersection(B!4, C!3), intersection(C!3, D!2)), intersection(D!2, B!4)) = union(intersection(D!2, B!4), union(intersection(B!4, C!3), intersection(C!3, D!2)))),
% 3.31/2.38 inference(symmetry,[status(thm)],[174])).
% 3.31/2.38 tff(176,plain,
% 3.31/2.38 (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))),
% 3.31/2.38 inference(transitivity,[status(thm)],[175, 172, 169, 167, 161, 158, 147, 145, 144, 99, 96, 20, 18, 9])).
% 3.31/2.38 tff(177,plain,
% 3.31/2.38 ((~![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))))),
% 3.31/2.38 inference(rewrite,[status(thm)],[])).
% 3.31/2.38 tff(178,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')).
% 3.31/2.38 tff(179,plain,
% 3.31/2.38 (~![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)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[178, 177])).
% 3.31/2.38 tff(180,plain,
% 3.31/2.38 (~![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)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[179, 177])).
% 3.31/2.38 tff(181,plain,
% 3.31/2.38 (~![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)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[180, 177])).
% 3.31/2.38 tff(182,plain,
% 3.31/2.38 (~![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)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[181, 177])).
% 3.31/2.38 tff(183,plain,
% 3.31/2.38 (~![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)))),
% 3.31/2.38 inference(modus_ponens,[status(thm)],[182, 177])).
% 3.31/2.38 tff(184,plain,
% 3.31/2.38 (~![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)))),
% 3.31/2.39 inference(modus_ponens,[status(thm)],[183, 177])).
% 3.31/2.39 tff(185,plain,
% 3.31/2.39 (~![B: $i, C: $i, D: $i] : (union(union(intersection(B, C), intersection(C, D)), intersection(D, B)) = intersection(intersection(union(B, C), union(C, D)), union(D, B)))),
% 3.31/2.39 inference(modus_ponens,[status(thm)],[184, 177])).
% 3.31/2.39 tff(186,plain,(
% 3.31/2.39 ~(union(union(intersection(B!4, C!3), intersection(C!3, D!2)), intersection(D!2, B!4)) = intersection(intersection(union(B!4, C!3), union(C!3, D!2)), union(D!2, B!4)))),
% 3.31/2.39 inference(skolemize,[status(sab)],[185])).
% 3.31/2.39 tff(187,plain,
% 3.31/2.39 ($false),
% 3.31/2.39 inference(unit_resolution,[status(thm)],[186, 176])).
% 3.31/2.39 % SZS output end Proof
%------------------------------------------------------------------------------