TSTP Solution File: SET580+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET580+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 05:07:06 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET580+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 06:56:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(member_type, type, (
% 0.12/0.39 member: ( $i * $i ) > $o)).
% 0.12/0.39 tff(difference_type, type, (
% 0.12/0.39 difference: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_C_2_type, type, (
% 0.12/0.39 tptp_fun_C_2: $i)).
% 0.12/0.39 tff(tptp_fun_D_1_type, type, (
% 0.12/0.39 tptp_fun_D_1: $i)).
% 0.12/0.39 tff(tptp_fun_B_3_type, type, (
% 0.12/0.39 tptp_fun_B_3: $i)).
% 0.12/0.39 tff(union_type, type, (
% 0.12/0.39 union: ( $i * $i ) > $i)).
% 0.12/0.39 tff(symmetric_difference_type, type, (
% 0.12/0.39 symmetric_difference: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = symmetric_difference(C, B)) <=> (symmetric_difference(B, C) = symmetric_difference(C, B)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_symmetric_difference')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))) | (symmetric_difference(D!1, C!2) = symmetric_difference(C!2, D!1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (symmetric_difference(D!1, C!2) = symmetric_difference(C!2, D!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B))) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(13,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetric_difference_defn')).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.39 tff(15,plain,(
% 0.12/0.39 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[14])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(D!1, C!2) = union(difference(D!1, C!2), difference(C!2, D!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (symmetric_difference(D!1, C!2) = union(difference(D!1, C!2), difference(C!2, D!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (union(difference(D!1, C!2), difference(C!2, D!1)) = symmetric_difference(D!1, C!2)),
% 0.12/0.39 inference(symmetry,[status(thm)],[18])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (union(difference(D!1, C!2), difference(C!2, D!1)) = symmetric_difference(C!2, D!1)),
% 0.19/0.39 inference(transitivity,[status(thm)],[19, 9])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))) <=> member(B!3, symmetric_difference(C!2, D!1))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (member(B!3, symmetric_difference(C!2, D!1)) <=> member(B!3, union(difference(D!1, C!2), difference(C!2, D!1)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~member(B!3, symmetric_difference(C!2, D!1))) <=> (~member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.39 tff(24,assumption,(~member(B!3, symmetric_difference(C!2, D!1))), introduced(assumption)).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (~member(B!3, union(difference(D!1, C!2), difference(C!2, D!1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.39 tff(31,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.39 tff(34,plain,(
% 0.19/0.39 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))) <=> (member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))) <=> (member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~(member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))) <=> (member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))))) | member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))) | (~(member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))) | (~(member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (~(member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 25])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))) | (~member(B!3, difference(D!1, C!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (~member(B!3, difference(D!1, C!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.40 tff(43,assumption,(~(member(B!3, difference(D!1, C!2)) <=> (~((~member(B!3, D!1)) | member(B!3, C!2))))), introduced(assumption)).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : refl((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : rewrite((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(49,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,(
% 0.19/0.40 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(B!3, difference(D!1, C!2)) <=> (~((~member(B!3, D!1)) | member(B!3, C!2))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 53, 43])).
% 0.19/0.40 tff(56,plain,(member(B!3, difference(D!1, C!2)) <=> (~((~member(B!3, D!1)) | member(B!3, C!2)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~(member(B!3, difference(D!1, C!2)) <=> (~((~member(B!3, D!1)) | member(B!3, C!2))))) | member(B!3, difference(D!1, C!2)) | ((~member(B!3, D!1)) | member(B!3, C!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (member(B!3, difference(D!1, C!2)) | ((~member(B!3, D!1)) | member(B!3, C!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((~member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[58, 42])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~(member(B!3, symmetric_difference(C!2, D!1)) <=> ((~member(B!3, C!2)) <=> member(B!3, D!1)))) <=> ((~member(B!3, symmetric_difference(C!2, D!1))) <=> ((~member(B!3, C!2)) <=> member(B!3, D!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D)))) <=> (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> (~(member(B, C) <=> member(B, D))))) <=> (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(63,axiom,(~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> (~(member(B, C) <=> member(B, D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th23')).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 61])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 61])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (~![B: $i, C: $i, D: $i] : (member(B, symmetric_difference(C, D)) <=> ((~member(B, C)) <=> member(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 61])).
% 0.19/0.40 tff(71,plain,(
% 0.19/0.40 ~(member(B!3, symmetric_difference(C!2, D!1)) <=> ((~member(B!3, C!2)) <=> member(B!3, D!1)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[70])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~member(B!3, symmetric_difference(C!2, D!1))) <=> ((~member(B!3, C!2)) <=> member(B!3, D!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[71, 60])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (member(B!3, symmetric_difference(C!2, D!1)) | ((~member(B!3, C!2)) <=> member(B!3, D!1)) | (~((~member(B!3, symmetric_difference(C!2, D!1))) <=> ((~member(B!3, C!2)) <=> member(B!3, D!1))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (member(B!3, symmetric_difference(C!2, D!1)) | ((~member(B!3, C!2)) <=> member(B!3, D!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~member(B!3, C!2)) <=> member(B!3, D!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 24])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(B!3, difference(C!2, D!1)) <=> (~((~member(B!3, C!2)) | member(B!3, D!1))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (member(B!3, difference(C!2, D!1)) <=> (~((~member(B!3, C!2)) | member(B!3, D!1)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 53])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))) | (~member(B!3, difference(C!2, D!1)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (~member(B!3, difference(C!2, D!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 40])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((~(member(B!3, difference(C!2, D!1)) <=> (~((~member(B!3, C!2)) | member(B!3, D!1))))) | member(B!3, difference(C!2, D!1)) | ((~member(B!3, C!2)) | member(B!3, D!1))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~(member(B!3, difference(C!2, D!1)) <=> (~((~member(B!3, C!2)) | member(B!3, D!1))))) | ((~member(B!3, C!2)) | member(B!3, D!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 77])).
% 0.19/0.40 tff(83,assumption,((~member(B!3, C!2)) | member(B!3, D!1)), introduced(assumption)).
% 0.19/0.40 tff(84,assumption,(~member(B!3, D!1)), introduced(assumption)).
% 0.19/0.40 tff(85,assumption,((~member(B!3, C!2)) <=> member(B!3, D!1)), introduced(assumption)).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((~((~member(B!3, C!2)) <=> member(B!3, D!1))) | member(B!3, C!2) | member(B!3, D!1)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (member(B!3, C!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[86, 84, 85])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~((~member(B!3, C!2)) | member(B!3, D!1))) | (~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[88, 87, 84, 83])).
% 0.19/0.40 tff(90,plain,(member(B!3, D!1) | (~((~member(B!3, C!2)) | member(B!3, D!1))) | (~((~member(B!3, C!2)) <=> member(B!3, D!1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (member(B!3, D!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[90, 82, 75])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~((~member(B!3, C!2)) <=> member(B!3, D!1))) | (~member(B!3, C!2)) | (~member(B!3, D!1))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (~member(B!3, C!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 91, 75])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ((~((~member(B!3, D!1)) | member(B!3, C!2))) | (~member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 93, 91, 59])).
% 0.19/0.40 tff(96,plain,(member(B!3, symmetric_difference(C!2, D!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (member(B!3, union(difference(D!1, C!2), difference(C!2, D!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[96, 22])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~(member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))) <=> (member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))))) | (~member(B!3, union(difference(D!1, C!2), difference(C!2, D!1)))) | (member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((~member(B!3, union(difference(D!1, C!2), difference(C!2, D!1)))) | (member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 37])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 97])).
% 0.19/0.40 tff(101,assumption,(~(member(B!3, difference(C!2, D!1)) <=> (~((~member(B!3, C!2)) | member(B!3, D!1))))), introduced(assumption)).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 53, 101])).
% 0.19/0.40 tff(103,plain,(member(B!3, difference(C!2, D!1)) <=> (~((~member(B!3, C!2)) | member(B!3, D!1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 ((~member(B!3, symmetric_difference(C!2, D!1))) | (~((~member(B!3, C!2)) <=> member(B!3, D!1))) | (~((~member(B!3, symmetric_difference(C!2, D!1))) <=> ((~member(B!3, C!2)) <=> member(B!3, D!1))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~member(B!3, symmetric_difference(C!2, D!1))) | (~((~member(B!3, C!2)) <=> member(B!3, D!1)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[104, 72])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (~((~member(B!3, C!2)) <=> member(B!3, D!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[105, 96])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (((~member(B!3, C!2)) <=> member(B!3, D!1)) | (~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (~member(B!3, C!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[107, 84, 106])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (((~member(B!3, C!2)) | member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 ((~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(C!2, D!1) = union(difference(C!2, D!1), difference(D!1, C!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (symmetric_difference(C!2, D!1) = union(difference(C!2, D!1), difference(D!1, C!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 16])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (union(difference(C!2, D!1), difference(D!1, C!2)) = symmetric_difference(C!2, D!1)),
% 0.19/0.40 inference(symmetry,[status(thm)],[112])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (member(B!3, union(difference(C!2, D!1), difference(D!1, C!2))) <=> member(B!3, symmetric_difference(C!2, D!1))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (member(B!3, symmetric_difference(C!2, D!1)) <=> member(B!3, union(difference(C!2, D!1), difference(D!1, C!2)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[114])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (member(B!3, union(difference(C!2, D!1), difference(D!1, C!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[96, 115])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(B!3, union(difference(C!2, D!1), difference(D!1, C!2))) <=> (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (member(B!3, union(difference(C!2, D!1), difference(D!1, C!2))) <=> (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[117, 35])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~(member(B!3, union(difference(C!2, D!1), difference(D!1, C!2))) <=> (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1))))) | (~member(B!3, union(difference(C!2, D!1), difference(D!1, C!2)))) | (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 ((~member(B!3, union(difference(C!2, D!1), difference(D!1, C!2)))) | (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[120, 116])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (((~member(B!3, D!1)) | member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((~member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[122, 84])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ((~(member(B!3, difference(D!1, C!2)) <=> (~((~member(B!3, D!1)) | member(B!3, C!2))))) | (~member(B!3, difference(D!1, C!2))) | (~((~member(B!3, D!1)) | member(B!3, C!2)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~member(B!3, difference(D!1, C!2))) | (~((~member(B!3, D!1)) | member(B!3, C!2)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[124, 56])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (~member(B!3, difference(D!1, C!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 123])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 ((~(member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1)))) | member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (member(B!3, difference(C!2, D!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 126, 121])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 ((~(member(B!3, difference(C!2, D!1)) <=> (~((~member(B!3, C!2)) | member(B!3, D!1))))) | (~member(B!3, difference(C!2, D!1))) | (~((~member(B!3, C!2)) | member(B!3, D!1)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[129, 128, 110, 103])).
% 0.19/0.41 tff(131,plain,(member(B!3, D!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (((~member(B!3, C!2)) | member(B!3, D!1)) | (~member(B!3, D!1))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 ((~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (~member(B!3, difference(C!2, D!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[129, 133, 103])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (((~member(B!3, C!2)) <=> member(B!3, D!1)) | member(B!3, C!2) | (~member(B!3, D!1))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 (member(B!3, C!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[135, 131, 106])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (((~member(B!3, D!1)) | member(B!3, C!2)) | (~member(B!3, C!2))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 ((~member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 (~member(B!3, difference(D!1, C!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 138])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 ((~(member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2)))) | member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[140, 139, 134, 100])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------