TSTP Solution File: SET623+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET623+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 05:07:22 EDT 2022
% Result : Theorem 0.14s 0.32s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET623+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.29 % Computer : n022.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Sat Sep 3 07:01:09 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.30 Usage: tptp [options] [-file:]file
% 0.08/0.30 -h, -? prints this message.
% 0.08/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.30 -m, -model generate model.
% 0.08/0.30 -p, -proof generate proof.
% 0.08/0.30 -c, -core generate unsat core of named formulas.
% 0.08/0.30 -st, -statistics display statistics.
% 0.08/0.30 -t:timeout set timeout (in second).
% 0.08/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.30 -<param>:<value> configuration parameter and value.
% 0.08/0.30 -o:<output-file> file to place output in.
% 0.14/0.32 % SZS status Theorem
% 0.14/0.32 % SZS output start Proof
% 0.14/0.32 tff(symmetric_difference_type, type, (
% 0.14/0.32 symmetric_difference: ( $i * $i ) > $i)).
% 0.14/0.32 tff(tptp_fun_D_2_type, type, (
% 0.14/0.32 tptp_fun_D_2: $i)).
% 0.14/0.32 tff(tptp_fun_C_3_type, type, (
% 0.14/0.32 tptp_fun_C_3: $i)).
% 0.14/0.32 tff(tptp_fun_B_4_type, type, (
% 0.14/0.32 tptp_fun_B_4: $i)).
% 0.14/0.32 tff(union_type, type, (
% 0.14/0.32 union: ( $i * $i ) > $i)).
% 0.14/0.32 tff(difference_type, type, (
% 0.14/0.32 difference: ( $i * $i ) > $i)).
% 0.14/0.32 tff(intersection_type, type, (
% 0.14/0.32 intersection: ( $i * $i ) > $i)).
% 0.14/0.32 tff(1,plain,
% 0.14/0.32 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = symmetric_difference(C, B)) <=> (symmetric_difference(B, C) = symmetric_difference(C, B)))),
% 0.14/0.32 inference(bind,[status(th)],[])).
% 0.14/0.32 tff(2,plain,
% 0.14/0.32 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.14/0.32 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.32 tff(3,plain,
% 0.14/0.32 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.14/0.32 inference(rewrite,[status(thm)],[])).
% 0.14/0.32 tff(4,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_symmetric_difference')).
% 0.14/0.32 tff(5,plain,
% 0.14/0.32 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.14/0.32 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.32 tff(6,plain,(
% 0.14/0.32 ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.14/0.32 inference(skolemize,[status(sab)],[5])).
% 0.14/0.32 tff(7,plain,
% 0.14/0.32 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.14/0.32 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.32 tff(8,plain,
% 0.14/0.32 ((~![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)))),
% 0.14/0.32 inference(quant_inst,[status(thm)],[])).
% 0.14/0.32 tff(9,plain,
% 0.14/0.32 (symmetric_difference(symmetric_difference(C!3, D!2), B!4) = symmetric_difference(B!4, symmetric_difference(C!3, D!2))),
% 0.14/0.32 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.32 tff(10,plain,
% 0.14/0.32 (^[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))))),
% 0.14/0.32 inference(bind,[status(th)],[])).
% 0.14/0.32 tff(11,plain,
% 0.14/0.32 (![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)))),
% 0.14/0.32 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.32 tff(12,plain,
% 0.14/0.32 (![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)))),
% 0.14/0.32 inference(rewrite,[status(thm)],[])).
% 0.14/0.32 tff(13,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetric_difference_defn')).
% 0.14/0.32 tff(14,plain,
% 0.14/0.32 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.14/0.32 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.32 tff(15,plain,(
% 0.14/0.32 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.14/0.32 inference(skolemize,[status(sab)],[14])).
% 0.14/0.32 tff(16,plain,
% 0.14/0.32 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.14/0.32 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.14/0.32 tff(17,plain,
% 0.14/0.32 ((~![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))))),
% 0.14/0.32 inference(quant_inst,[status(thm)],[])).
% 0.14/0.32 tff(18,plain,
% 0.14/0.32 (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)))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.33 tff(19,plain,
% 0.14/0.33 (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)),
% 0.14/0.33 inference(symmetry,[status(thm)],[18])).
% 0.14/0.33 tff(20,plain,
% 0.14/0.33 ((~![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)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(21,plain,
% 0.14/0.33 (symmetric_difference(C!3, D!2) = union(difference(C!3, D!2), difference(D!2, C!3))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[20, 16])).
% 0.14/0.33 tff(22,plain,
% 0.14/0.33 (difference(B!4, symmetric_difference(C!3, D!2)) = difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3)))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[21])).
% 0.14/0.33 tff(23,plain,
% 0.14/0.33 (difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3))) = difference(B!4, symmetric_difference(C!3, D!2))),
% 0.14/0.33 inference(symmetry,[status(thm)],[22])).
% 0.14/0.33 tff(24,plain,
% 0.14/0.33 (difference(symmetric_difference(C!3, D!2), B!4) = difference(union(difference(C!3, D!2), difference(D!2, C!3)), B!4)),
% 0.14/0.33 inference(monotonicity,[status(thm)],[21])).
% 0.14/0.33 tff(25,plain,
% 0.14/0.33 (difference(union(difference(C!3, D!2), difference(D!2, C!3)), B!4) = difference(symmetric_difference(C!3, D!2), B!4)),
% 0.14/0.33 inference(symmetry,[status(thm)],[24])).
% 0.14/0.33 tff(26,plain,
% 0.14/0.33 (^[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))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(27,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[26])).
% 0.14/0.33 tff(28,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(29,axiom,(![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_distributes_over_union')).
% 0.14/0.33 tff(30,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.33 tff(31,plain,(
% 0.14/0.33 ![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.14/0.33 inference(skolemize,[status(sab)],[30])).
% 0.14/0.33 tff(32,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (difference(union(B, C), D) = union(difference(B, D), difference(C, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.14/0.33 tff(33,plain,
% 0.14/0.33 ((~![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)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(34,plain,
% 0.14/0.33 (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))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.14/0.33 tff(35,plain,
% 0.14/0.33 (union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)) = difference(union(difference(C!3, D!2), difference(D!2, C!3)), B!4)),
% 0.14/0.33 inference(symmetry,[status(thm)],[34])).
% 0.14/0.33 tff(36,plain,
% 0.14/0.33 (union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)) = difference(symmetric_difference(C!3, D!2), B!4)),
% 0.14/0.33 inference(transitivity,[status(thm)],[35, 25])).
% 0.14/0.33 tff(37,plain,
% 0.14/0.33 (union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3)))) = union(difference(symmetric_difference(C!3, D!2), B!4), difference(B!4, symmetric_difference(C!3, D!2)))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[36, 23])).
% 0.14/0.33 tff(38,plain,
% 0.14/0.33 (^[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))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(39,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.33 tff(40,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(41,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')).
% 0.14/0.33 tff(42,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.14/0.33 tff(43,plain,(
% 0.14/0.33 ![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.14/0.33 inference(skolemize,[status(sab)],[42])).
% 0.14/0.33 tff(44,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.14/0.33 tff(45,plain,
% 0.14/0.33 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3)))) = union(difference(difference(C!3, D!2), B!4), union(difference(difference(D!2, C!3), B!4), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3))))))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(46,plain,
% 0.14/0.33 (union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3)))) = union(difference(difference(C!3, D!2), B!4), union(difference(difference(D!2, C!3), B!4), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3)))))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.14/0.33 tff(47,plain,
% 0.14/0.33 (union(difference(difference(C!3, D!2), B!4), union(difference(difference(D!2, C!3), B!4), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3))))) = union(union(difference(difference(C!3, D!2), B!4), difference(difference(D!2, C!3), B!4)), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3))))),
% 0.14/0.33 inference(symmetry,[status(thm)],[46])).
% 0.14/0.33 tff(48,plain,
% 0.14/0.33 (union(difference(C!3, D!2), difference(D!2, C!3)) = symmetric_difference(C!3, D!2)),
% 0.14/0.33 inference(symmetry,[status(thm)],[21])).
% 0.14/0.33 tff(49,plain,
% 0.14/0.33 (^[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))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(50,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[49])).
% 0.14/0.33 tff(51,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(52,axiom,(![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_union_intersection')).
% 0.14/0.33 tff(53,plain,
% 0.14/0.33 (![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.14/0.33 tff(54,plain,(
% 0.14/0.33 ![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))),
% 0.14/0.33 inference(skolemize,[status(sab)],[53])).
% 0.14/0.33 tff(55,plain,
% 0.14/0.33 (![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.14/0.33 tff(56,plain,
% 0.14/0.33 ((~![B: $i, C: $i] : (difference(union(B, C), intersection(B, C)) = union(difference(B, C), difference(C, B)))) | (difference(union(C!3, D!2), intersection(C!3, D!2)) = union(difference(C!3, D!2), difference(D!2, C!3)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(57,plain,
% 0.14/0.33 (difference(union(C!3, D!2), intersection(C!3, D!2)) = union(difference(C!3, D!2), difference(D!2, C!3))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.14/0.33 tff(58,plain,
% 0.14/0.33 (difference(union(C!3, D!2), intersection(C!3, D!2)) = symmetric_difference(C!3, D!2)),
% 0.14/0.33 inference(transitivity,[status(thm)],[57, 48])).
% 0.14/0.33 tff(59,plain,
% 0.14/0.33 (difference(B!4, difference(union(C!3, D!2), intersection(C!3, D!2))) = difference(B!4, symmetric_difference(C!3, D!2))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[58])).
% 0.14/0.33 tff(60,plain,
% 0.14/0.33 (^[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))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(61,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[60])).
% 0.14/0.33 tff(62,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(63,axiom,(![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_difference_union1')).
% 0.14/0.33 tff(64,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.14/0.33 tff(65,plain,(
% 0.14/0.33 ![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.14/0.33 inference(skolemize,[status(sab)],[64])).
% 0.14/0.33 tff(66,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.14/0.33 tff(67,plain,
% 0.14/0.33 ((~![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(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2))))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(68,plain,
% 0.14/0.33 (difference(B!4, difference(union(C!3, D!2), intersection(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2)))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.14/0.33 tff(69,plain,
% 0.14/0.33 (union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2))) = difference(B!4, difference(union(C!3, D!2), intersection(C!3, D!2)))),
% 0.14/0.33 inference(symmetry,[status(thm)],[68])).
% 0.14/0.33 tff(70,plain,
% 0.14/0.33 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(71,plain,
% 0.14/0.33 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[70])).
% 0.14/0.33 tff(72,plain,
% 0.14/0.33 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(73,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.14/0.33 tff(74,plain,
% 0.14/0.33 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.14/0.33 tff(75,plain,(
% 0.14/0.33 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.14/0.33 inference(skolemize,[status(sab)],[74])).
% 0.14/0.33 tff(76,plain,
% 0.14/0.33 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.14/0.33 tff(77,plain,
% 0.14/0.33 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(B!4, intersection(C!3, D!2)), difference(B!4, union(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2))))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(78,plain,
% 0.14/0.33 (union(intersection(B!4, intersection(C!3, D!2)), difference(B!4, union(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), intersection(B!4, intersection(C!3, D!2)))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.14/0.33 tff(79,plain,
% 0.14/0.33 (^[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))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(80,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[79])).
% 0.14/0.33 tff(81,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(82,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')).
% 0.14/0.33 tff(83,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.14/0.33 tff(84,plain,(
% 0.14/0.33 ![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.14/0.33 inference(skolemize,[status(sab)],[83])).
% 0.14/0.33 tff(85,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.14/0.33 tff(86,plain,
% 0.14/0.33 ((~![B: $i, C: $i, D: $i] : (intersection(intersection(B, C), D) = intersection(B, intersection(C, D)))) | (intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(87,plain,
% 0.14/0.33 (intersection(intersection(B!4, C!3), D!2) = intersection(B!4, intersection(C!3, D!2))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.14/0.33 tff(88,plain,
% 0.14/0.33 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(89,plain,
% 0.14/0.33 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[88])).
% 0.14/0.33 tff(90,plain,
% 0.14/0.33 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(91,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.14/0.33 tff(92,plain,
% 0.14/0.33 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.14/0.33 tff(93,plain,(
% 0.14/0.33 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.14/0.33 inference(skolemize,[status(sab)],[92])).
% 0.14/0.33 tff(94,plain,
% 0.14/0.33 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.14/0.33 tff(95,plain,
% 0.14/0.33 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(intersection(B!4, C!3), D!2) = intersection(D!2, intersection(B!4, C!3)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(96,plain,
% 0.14/0.33 (intersection(intersection(B!4, C!3), D!2) = intersection(D!2, intersection(B!4, C!3))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.14/0.33 tff(97,plain,
% 0.14/0.33 (intersection(D!2, intersection(B!4, C!3)) = intersection(intersection(B!4, C!3), D!2)),
% 0.14/0.33 inference(symmetry,[status(thm)],[96])).
% 0.14/0.33 tff(98,plain,
% 0.14/0.33 (intersection(D!2, intersection(B!4, C!3)) = intersection(B!4, intersection(C!3, D!2))),
% 0.14/0.33 inference(transitivity,[status(thm)],[97, 87])).
% 0.14/0.33 tff(99,plain,
% 0.14/0.33 (union(intersection(D!2, intersection(B!4, C!3)), difference(B!4, union(C!3, D!2))) = union(intersection(B!4, intersection(C!3, D!2)), difference(B!4, union(C!3, D!2)))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[98])).
% 0.14/0.33 tff(100,plain,
% 0.14/0.33 (union(intersection(D!2, intersection(B!4, C!3)), difference(B!4, union(C!3, D!2))) = difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3)))),
% 0.14/0.33 inference(transitivity,[status(thm)],[99, 78, 69, 59, 22])).
% 0.14/0.33 tff(101,plain,
% 0.14/0.33 (^[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))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(102,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[101])).
% 0.14/0.33 tff(103,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(104,axiom,(![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_difference_union2')).
% 0.14/0.33 tff(105,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.14/0.33 tff(106,plain,(
% 0.14/0.33 ![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.14/0.33 inference(skolemize,[status(sab)],[105])).
% 0.14/0.33 tff(107,plain,
% 0.14/0.33 (![B: $i, C: $i, D: $i] : (difference(difference(B, C), D) = difference(B, union(C, D)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.14/0.33 tff(108,plain,
% 0.14/0.33 ((~![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)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(109,plain,
% 0.14/0.33 (difference(difference(D!2, C!3), B!4) = difference(D!2, union(C!3, B!4))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.14/0.33 tff(110,plain,
% 0.14/0.33 (difference(D!2, union(C!3, B!4)) = difference(difference(D!2, C!3), B!4)),
% 0.14/0.33 inference(symmetry,[status(thm)],[109])).
% 0.14/0.33 tff(111,plain,
% 0.14/0.33 (union(difference(D!2, union(C!3, B!4)), union(intersection(D!2, intersection(B!4, C!3)), difference(B!4, union(C!3, D!2)))) = union(difference(difference(D!2, C!3), B!4), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3))))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[110, 100])).
% 0.14/0.33 tff(112,plain,
% 0.14/0.33 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3))), difference(B!4, union(C!3, D!2))) = union(difference(D!2, union(C!3, B!4)), union(intersection(D!2, intersection(B!4, C!3)), difference(B!4, union(C!3, D!2)))))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(113,plain,
% 0.14/0.33 (union(union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3))), difference(B!4, union(C!3, D!2))) = union(difference(D!2, union(C!3, B!4)), union(intersection(D!2, intersection(B!4, C!3)), difference(B!4, union(C!3, D!2))))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[112, 44])).
% 0.14/0.33 tff(114,plain,
% 0.14/0.33 ((~![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)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(115,plain,
% 0.14/0.33 (difference(difference(B!4, C!3), D!2) = difference(B!4, union(C!3, D!2))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[114, 107])).
% 0.14/0.33 tff(116,plain,
% 0.14/0.33 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(C!3, B!4) = union(B!4, C!3))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(117,plain,
% 0.14/0.33 (union(C!3, B!4) = union(B!4, C!3)),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[116, 76])).
% 0.14/0.33 tff(118,plain,
% 0.14/0.33 (union(B!4, C!3) = union(C!3, B!4)),
% 0.14/0.33 inference(symmetry,[status(thm)],[117])).
% 0.14/0.33 tff(119,plain,
% 0.14/0.33 (difference(D!2, union(B!4, C!3)) = difference(D!2, union(C!3, B!4))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[118])).
% 0.14/0.33 tff(120,plain,
% 0.14/0.33 (difference(D!2, union(C!3, B!4)) = difference(D!2, union(B!4, C!3))),
% 0.14/0.33 inference(symmetry,[status(thm)],[119])).
% 0.14/0.33 tff(121,plain,
% 0.14/0.33 (union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3))) = union(difference(D!2, union(B!4, C!3)), intersection(D!2, intersection(B!4, C!3)))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[120])).
% 0.14/0.33 tff(122,plain,
% 0.14/0.33 (union(difference(D!2, union(B!4, C!3)), intersection(D!2, intersection(B!4, C!3))) = union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.14/0.33 inference(symmetry,[status(thm)],[121])).
% 0.14/0.33 tff(123,plain,
% 0.14/0.33 ((~![B: $i, C: $i, D: $i] : (difference(B, difference(C, D)) = union(difference(B, C), intersection(B, D)))) | (difference(D!2, difference(union(B!4, C!3), intersection(B!4, C!3))) = union(difference(D!2, union(B!4, C!3)), intersection(D!2, intersection(B!4, C!3))))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(124,plain,
% 0.14/0.33 (difference(D!2, difference(union(B!4, C!3), intersection(B!4, C!3))) = union(difference(D!2, union(B!4, C!3)), intersection(D!2, intersection(B!4, C!3)))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[123, 66])).
% 0.14/0.33 tff(125,plain,
% 0.14/0.33 ((~![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)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(126,plain,
% 0.14/0.33 (symmetric_difference(B!4, C!3) = union(difference(B!4, C!3), difference(C!3, B!4))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[125, 16])).
% 0.14/0.33 tff(127,plain,
% 0.14/0.33 (union(difference(B!4, C!3), difference(C!3, B!4)) = symmetric_difference(B!4, C!3)),
% 0.14/0.33 inference(symmetry,[status(thm)],[126])).
% 0.14/0.33 tff(128,plain,
% 0.14/0.33 ((~![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)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(129,plain,
% 0.14/0.33 (difference(union(B!4, C!3), intersection(B!4, C!3)) = union(difference(B!4, C!3), difference(C!3, B!4))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[128, 55])).
% 0.14/0.33 tff(130,plain,
% 0.14/0.33 (difference(union(B!4, C!3), intersection(B!4, C!3)) = symmetric_difference(B!4, C!3)),
% 0.14/0.33 inference(transitivity,[status(thm)],[129, 127])).
% 0.14/0.33 tff(131,plain,
% 0.14/0.33 (difference(D!2, difference(union(B!4, C!3), intersection(B!4, C!3))) = difference(D!2, symmetric_difference(B!4, C!3))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[130])).
% 0.14/0.33 tff(132,plain,
% 0.14/0.33 (difference(D!2, symmetric_difference(B!4, C!3)) = difference(D!2, difference(union(B!4, C!3), intersection(B!4, C!3)))),
% 0.14/0.33 inference(symmetry,[status(thm)],[131])).
% 0.14/0.33 tff(133,plain,
% 0.14/0.33 (difference(D!2, symmetric_difference(B!4, C!3)) = difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4)))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[126])).
% 0.14/0.33 tff(134,plain,
% 0.14/0.33 (difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))) = difference(D!2, symmetric_difference(B!4, C!3))),
% 0.14/0.33 inference(symmetry,[status(thm)],[133])).
% 0.14/0.33 tff(135,plain,
% 0.14/0.33 (difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))) = union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3)))),
% 0.14/0.33 inference(transitivity,[status(thm)],[134, 132, 124, 122])).
% 0.14/0.33 tff(136,plain,
% 0.14/0.33 (union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)) = union(union(difference(D!2, union(C!3, B!4)), intersection(D!2, intersection(B!4, C!3))), difference(B!4, union(C!3, D!2)))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[135, 115])).
% 0.14/0.33 tff(137,plain,
% 0.14/0.33 (difference(B!4, union(C!3, D!2)) = difference(difference(B!4, C!3), D!2)),
% 0.14/0.33 inference(symmetry,[status(thm)],[115])).
% 0.14/0.33 tff(138,plain,
% 0.14/0.33 (union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(B!4, union(C!3, D!2))) = union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[137])).
% 0.14/0.33 tff(139,plain,
% 0.14/0.33 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(difference(B!4, union(C!3, D!2)), difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4)))) = union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(B!4, union(C!3, D!2))))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(140,plain,
% 0.14/0.33 (union(difference(B!4, union(C!3, D!2)), difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4)))) = union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(B!4, union(C!3, D!2)))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[139, 76])).
% 0.14/0.33 tff(141,plain,
% 0.14/0.33 (union(difference(B!4, union(C!3, D!2)), difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4)))) = union(difference(difference(D!2, C!3), B!4), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3))))),
% 0.14/0.33 inference(transitivity,[status(thm)],[140, 138, 136, 113, 111])).
% 0.14/0.33 tff(142,plain,
% 0.14/0.33 ((~![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)))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(143,plain,
% 0.14/0.33 (difference(difference(C!3, D!2), B!4) = difference(C!3, union(D!2, B!4))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[142, 107])).
% 0.14/0.33 tff(144,plain,
% 0.14/0.33 (difference(C!3, union(D!2, B!4)) = difference(difference(C!3, D!2), B!4)),
% 0.14/0.33 inference(symmetry,[status(thm)],[143])).
% 0.14/0.33 tff(145,plain,
% 0.14/0.33 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, B!4) = union(B!4, D!2))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(146,plain,
% 0.14/0.33 (union(D!2, B!4) = union(B!4, D!2)),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[145, 76])).
% 0.14/0.33 tff(147,plain,
% 0.14/0.33 (difference(C!3, union(D!2, B!4)) = difference(C!3, union(B!4, D!2))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[146])).
% 0.14/0.33 tff(148,plain,
% 0.14/0.33 (difference(C!3, union(B!4, D!2)) = difference(C!3, union(D!2, B!4))),
% 0.14/0.33 inference(symmetry,[status(thm)],[147])).
% 0.14/0.33 tff(149,plain,
% 0.14/0.33 (difference(C!3, union(B!4, D!2)) = difference(difference(C!3, D!2), B!4)),
% 0.14/0.33 inference(transitivity,[status(thm)],[148, 144])).
% 0.14/0.33 tff(150,plain,
% 0.14/0.33 (union(difference(C!3, union(B!4, D!2)), union(difference(B!4, union(C!3, D!2)), difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))))) = union(difference(difference(C!3, D!2), B!4), union(difference(difference(D!2, C!3), B!4), difference(B!4, union(difference(C!3, D!2), difference(D!2, C!3)))))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[149, 141])).
% 0.14/0.33 tff(151,plain,
% 0.14/0.33 (union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(B!4, union(C!3, D!2))) = union(difference(B!4, union(C!3, D!2)), difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))))),
% 0.14/0.33 inference(symmetry,[status(thm)],[140])).
% 0.14/0.33 tff(152,plain,
% 0.14/0.33 (union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)) = union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(B!4, union(C!3, D!2)))),
% 0.14/0.33 inference(symmetry,[status(thm)],[138])).
% 0.14/0.33 tff(153,plain,
% 0.14/0.33 (union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)) = union(difference(B!4, union(C!3, D!2)), difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))))),
% 0.14/0.34 inference(transitivity,[status(thm)],[152, 151])).
% 0.14/0.34 tff(154,plain,
% 0.14/0.34 (union(difference(C!3, union(B!4, D!2)), union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2))) = union(difference(C!3, union(B!4, D!2)), union(difference(B!4, union(C!3, D!2)), difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4)))))),
% 0.14/0.34 inference(monotonicity,[status(thm)],[153])).
% 0.14/0.34 tff(155,plain,
% 0.14/0.34 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(difference(C!3, union(B!4, D!2)), union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2))) = union(union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)), difference(C!3, union(B!4, D!2))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(156,plain,
% 0.14/0.34 (union(difference(C!3, union(B!4, D!2)), union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2))) = union(union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)), difference(C!3, union(B!4, D!2)))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[155, 76])).
% 0.14/0.34 tff(157,plain,
% 0.14/0.34 (union(union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)), difference(C!3, union(B!4, D!2))) = union(difference(C!3, union(B!4, D!2)), union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)))),
% 0.14/0.34 inference(symmetry,[status(thm)],[156])).
% 0.14/0.34 tff(158,plain,
% 0.14/0.34 ((~![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)))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(159,plain,
% 0.14/0.34 (difference(difference(C!3, B!4), D!2) = difference(C!3, union(B!4, D!2))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[158, 107])).
% 0.14/0.34 tff(160,plain,
% 0.14/0.34 (union(union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)), difference(difference(C!3, B!4), D!2)) = union(union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)), difference(C!3, union(B!4, D!2)))),
% 0.14/0.34 inference(monotonicity,[status(thm)],[159])).
% 0.14/0.34 tff(161,plain,
% 0.14/0.34 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) | (union(union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)), difference(difference(C!3, B!4), D!2)) = union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(162,plain,
% 0.14/0.34 (union(union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)), difference(difference(C!3, B!4), D!2)) = union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[161, 44])).
% 0.14/0.34 tff(163,plain,
% 0.14/0.34 (union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2))) = union(union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), difference(difference(B!4, C!3), D!2)), difference(difference(C!3, B!4), D!2))),
% 0.14/0.34 inference(symmetry,[status(thm)],[162])).
% 0.14/0.34 tff(164,plain,
% 0.14/0.34 ((~![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)))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(165,plain,
% 0.14/0.34 (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))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[164, 32])).
% 0.14/0.34 tff(166,plain,
% 0.14/0.34 (difference(symmetric_difference(B!4, C!3), D!2) = difference(union(difference(B!4, C!3), difference(C!3, B!4)), D!2)),
% 0.14/0.34 inference(monotonicity,[status(thm)],[126])).
% 0.14/0.34 tff(167,plain,
% 0.14/0.34 (difference(symmetric_difference(B!4, C!3), D!2) = union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2))),
% 0.14/0.34 inference(transitivity,[status(thm)],[166, 165])).
% 0.14/0.34 tff(168,plain,
% 0.14/0.34 (union(difference(D!2, symmetric_difference(B!4, C!3)), difference(symmetric_difference(B!4, C!3), D!2)) = union(difference(D!2, union(difference(B!4, C!3), difference(C!3, B!4))), union(difference(difference(B!4, C!3), D!2), difference(difference(C!3, B!4), D!2)))),
% 0.14/0.34 inference(monotonicity,[status(thm)],[133, 167])).
% 0.14/0.34 tff(169,plain,
% 0.14/0.34 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(D!2, symmetric_difference(B!4, C!3)) = union(difference(D!2, symmetric_difference(B!4, C!3)), difference(symmetric_difference(B!4, C!3), D!2)))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(170,plain,
% 0.14/0.34 (symmetric_difference(D!2, symmetric_difference(B!4, C!3)) = union(difference(D!2, symmetric_difference(B!4, C!3)), difference(symmetric_difference(B!4, C!3), D!2))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[169, 16])).
% 0.14/0.34 tff(171,plain,
% 0.14/0.34 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))) | (symmetric_difference(D!2, symmetric_difference(B!4, C!3)) = symmetric_difference(symmetric_difference(B!4, C!3), D!2))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(172,plain,
% 0.14/0.34 (symmetric_difference(D!2, symmetric_difference(B!4, C!3)) = symmetric_difference(symmetric_difference(B!4, C!3), D!2)),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[171, 7])).
% 0.14/0.34 tff(173,plain,
% 0.14/0.34 (symmetric_difference(symmetric_difference(B!4, C!3), D!2) = symmetric_difference(D!2, symmetric_difference(B!4, C!3))),
% 0.14/0.34 inference(symmetry,[status(thm)],[172])).
% 0.14/0.34 tff(174,plain,
% 0.14/0.34 (symmetric_difference(symmetric_difference(B!4, C!3), D!2) = symmetric_difference(B!4, symmetric_difference(C!3, D!2))),
% 0.14/0.34 inference(transitivity,[status(thm)],[173, 170, 168, 163, 160, 157, 154, 150, 47, 37, 19, 9])).
% 0.14/0.34 tff(175,plain,
% 0.14/0.34 ((~![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))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(176,axiom,(~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th99')).
% 0.14/0.34 tff(177,plain,
% 0.14/0.34 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.14/0.34 tff(178,plain,
% 0.14/0.34 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[177, 175])).
% 0.14/0.34 tff(179,plain,
% 0.14/0.34 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[178, 175])).
% 0.14/0.34 tff(180,plain,
% 0.14/0.34 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.14/0.34 tff(181,plain,
% 0.14/0.34 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[180, 175])).
% 0.14/0.34 tff(182,plain,
% 0.14/0.34 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[181, 175])).
% 0.14/0.34 tff(183,plain,
% 0.14/0.34 (~![B: $i, C: $i, D: $i] : (symmetric_difference(symmetric_difference(B, C), D) = symmetric_difference(B, symmetric_difference(C, D)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.14/0.34 tff(184,plain,(
% 0.14/0.34 ~(symmetric_difference(symmetric_difference(B!4, C!3), D!2) = symmetric_difference(B!4, symmetric_difference(C!3, D!2)))),
% 0.14/0.34 inference(skolemize,[status(sab)],[183])).
% 0.14/0.34 tff(185,plain,
% 0.14/0.34 ($false),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[184, 174])).
% 0.14/0.34 % SZS output end Proof
%------------------------------------------------------------------------------