%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET580+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:54 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET580+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:28:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(member_type, type, (
% 0.12/0.37 member: ( $i * $i ) > $o)).
% 0.12/0.37 tff(difference_type, type, (
% 0.12/0.37 difference: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_D_1_type, type, (
% 0.12/0.37 tptp_fun_D_1: $i)).
% 0.12/0.37 tff(tptp_fun_C_2_type, type, (
% 0.12/0.37 tptp_fun_C_2: $i)).
% 0.12/0.37 tff(tptp_fun_B_3_type, type, (
% 0.12/0.37 tptp_fun_B_3: $i)).
% 0.12/0.37 tff(union_type, type, (
% 0.12/0.37 union: ( $i * $i ) > $i)).
% 0.12/0.37 tff(symmetric_difference_type, type, (
% 0.12/0.37 symmetric_difference: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,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')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![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)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (symmetric_difference(C!2, D!1) = union(difference(C!2, D!1), difference(D!1, C!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (union(difference(C!2, D!1), difference(D!1, C!2)) = symmetric_difference(C!2, D!1)),
% 0.12/0.37 inference(symmetry,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (member(B!3, union(difference(C!2, D!1), difference(D!1, C!2))) <=> member(B!3, symmetric_difference(C!2, D!1))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (member(B!3, symmetric_difference(C!2, D!1)) <=> member(B!3, union(difference(C!2, D!1), difference(D!1, C!2)))),
% 0.12/0.37 inference(symmetry,[status(thm)],[11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![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, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,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')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(B!3, D!1)) | member(B!3, C!2)) <=> member(B!3, difference(D!1, C!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (~(((~member(B!3, D!1)) | member(B!3, C!2)) <=> member(B!3, difference(D!1, C!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = symmetric_difference(C, B)) <=> (symmetric_difference(B, C) = symmetric_difference(C, B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,axiom,(![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_symmetric_difference')).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,(
% 0.12/0.38 ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.38 inference(skolemize,[status(sab)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))) | (symmetric_difference(D!1, C!2) = symmetric_difference(C!2, D!1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (symmetric_difference(D!1, C!2) = symmetric_difference(C!2, D!1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![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)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (symmetric_difference(D!1, C!2) = union(difference(D!1, C!2), difference(C!2, D!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[34, 7])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (union(difference(D!1, C!2), difference(C!2, D!1)) = symmetric_difference(D!1, C!2)),
% 0.12/0.38 inference(symmetry,[status(thm)],[35])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (union(difference(D!1, C!2), difference(C!2, D!1)) = symmetric_difference(C!2, D!1)),
% 0.12/0.38 inference(transitivity,[status(thm)],[36, 33])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))) <=> member(B!3, symmetric_difference(C!2, D!1))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (member(B!3, symmetric_difference(C!2, D!1)) <=> member(B!3, union(difference(D!1, C!2), difference(C!2, D!1)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((~member(B!3, symmetric_difference(C!2, D!1))) <=> (~member(B!3, union(difference(D!1, C!2), difference(C!2, D!1))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[39])).
% 0.12/0.38 tff(41,assumption,(~member(B!3, symmetric_difference(C!2, D!1))), introduced(assumption)).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (~member(B!3, union(difference(D!1, C!2), difference(C!2, D!1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,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')).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.12/0.38 tff(51,plain,(
% 0.12/0.38 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 ((~![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))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (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)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 ((~(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))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (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))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (~(member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[56, 42])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 ((member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))) | (~member(B!3, difference(D!1, C!2)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (~member(B!3, difference(D!1, C!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 ((((~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)) | member(B!3, difference(D!1, C!2))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 ((((~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))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 ((~member(B!3, D!1)) | member(B!3, C!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[61, 24])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : (~((member(B, C) <=> member(B, D)) <=> member(B, symmetric_difference(C, D))))) <=> (~![B: $i, C: $i, D: $i] : (~((member(B, C) <=> member(B, D)) <=> member(B, symmetric_difference(C, D)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 ((~![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, C) <=> member(B, D)) <=> member(B, symmetric_difference(C, D)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(65,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')).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : (~((member(B, C) <=> member(B, D)) <=> member(B, symmetric_difference(C, D))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : (~((member(B, C) <=> member(B, D)) <=> member(B, symmetric_difference(C, D))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[66, 63])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : (~((member(B, C) <=> member(B, D)) <=> member(B, symmetric_difference(C, D))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 (~![B: $i, C: $i, D: $i] : (~((member(B, C) <=> member(B, D)) <=> member(B, symmetric_difference(C, D))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[68, 63])).
% 0.12/0.38 tff(70,plain,(
% 0.12/0.38 (member(B!3, C!2) <=> member(B!3, D!1)) <=> member(B!3, symmetric_difference(C!2, D!1))),
% 0.12/0.38 inference(skolemize,[status(sab)],[69])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 ((~(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)) <=> member(B!3, symmetric_difference(C!2, D!1))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 ((~(member(B!3, C!2) <=> member(B!3, D!1))) | member(B!3, symmetric_difference(C!2, D!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 (~(member(B!3, C!2) <=> member(B!3, D!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[72, 41])).
% 0.12/0.38 tff(74,plain,
% 0.12/0.38 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(B!3, C!2)) | member(B!3, D!1)) <=> member(B!3, difference(C!2, D!1))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 (~(((~member(B!3, C!2)) | member(B!3, D!1)) <=> member(B!3, difference(C!2, D!1)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[74, 22])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 ((member(B!3, difference(C!2, D!1)) | member(B!3, difference(D!1, C!2))) | (~member(B!3, difference(C!2, D!1)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(77,plain,
% 0.12/0.38 (~member(B!3, difference(C!2, D!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[76, 57])).
% 0.12/0.38 tff(78,plain,
% 0.12/0.38 ((((~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)) | member(B!3, difference(C!2, D!1))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 ((((~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))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 ((~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[79, 75])).
% 0.19/0.39 tff(81,assumption,((~member(B!3, C!2)) | member(B!3, D!1)), introduced(assumption)).
% 0.19/0.39 tff(82,assumption,(~member(B!3, D!1)), introduced(assumption)).
% 0.19/0.39 tff(83,assumption,(~(member(B!3, C!2) <=> member(B!3, D!1))), introduced(assumption)).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 ((member(B!3, C!2) <=> member(B!3, D!1)) | member(B!3, C!2) | member(B!3, D!1)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (member(B!3, C!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[84, 82, 83])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((~((~member(B!3, C!2)) | member(B!3, D!1))) | (~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[86, 85, 82, 81])).
% 0.19/0.39 tff(88,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,[]))).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (member(B!3, D!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[88, 80, 73])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 ((member(B!3, C!2) <=> member(B!3, D!1)) | (~member(B!3, C!2)) | (~member(B!3, D!1))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (~member(B!3, C!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[90, 89, 73])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 ((~((~member(B!3, D!1)) | member(B!3, C!2))) | (~member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[92, 91, 89, 62])).
% 0.19/0.39 tff(94,plain,(member(B!3, symmetric_difference(C!2, D!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (member(B!3, union(difference(C!2, D!1), difference(D!1, C!2)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[94, 12])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(B!3, union(difference(C!2, D!1), difference(D!1, C!2))) <=> (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (member(B!3, union(difference(C!2, D!1), difference(D!1, C!2))) <=> (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[96, 52])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 ((~(member(B!3, union(difference(C!2, D!1), difference(D!1, C!2))) <=> (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1))))) | (~member(B!3, union(difference(C!2, D!1), difference(D!1, C!2)))) | (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~member(B!3, union(difference(C!2, D!1), difference(D!1, C!2)))) | (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (member(B!3, difference(D!1, C!2)) | member(B!3, difference(C!2, D!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.19/0.39 tff(101,assumption,(((~member(B!3, D!1)) | member(B!3, C!2)) <=> member(B!3, difference(D!1, C!2))), introduced(assumption)).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[23, 22, 101])).
% 0.19/0.39 tff(103,plain,(~(((~member(B!3, D!1)) | member(B!3, C!2)) <=> member(B!3, difference(D!1, C!2)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(104,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)],[94, 39])).
% 0.19/0.39 tff(105,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(106,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)],[105, 54])).
% 0.19/0.39 tff(107,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)],[106, 104])).
% 0.19/0.39 tff(108,assumption,(((~member(B!3, C!2)) | member(B!3, D!1)) <=> member(B!3, difference(C!2, D!1))), introduced(assumption)).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[74, 22, 108])).
% 0.19/0.39 tff(110,plain,(~(((~member(B!3, C!2)) | member(B!3, D!1)) <=> member(B!3, difference(C!2, D!1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(111,assumption,(~member(B!3, C!2)), introduced(assumption)).
% 0.19/0.39 tff(112,plain,
% 0.19/0.39 (((~member(B!3, C!2)) | member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 ((~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 ((((~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))) | (~member(B!3, difference(C!2, D!1)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(115,plain,
% 0.19/0.39 (~member(B!3, difference(C!2, D!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[114, 113, 110])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 ((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)) <=> member(B!3, symmetric_difference(C!2, D!1))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(117,plain,
% 0.19/0.39 ((member(B!3, C!2) <=> member(B!3, D!1)) | (~member(B!3, symmetric_difference(C!2, D!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[116, 70])).
% 0.19/0.39 tff(118,plain,
% 0.19/0.39 (member(B!3, C!2) <=> member(B!3, D!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[117, 94])).
% 0.19/0.39 tff(119,plain,
% 0.19/0.39 ((~(member(B!3, C!2) <=> member(B!3, D!1))) | member(B!3, C!2) | (~member(B!3, D!1))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(120,plain,
% 0.19/0.39 (~member(B!3, D!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[119, 111, 118])).
% 0.19/0.39 tff(121,plain,
% 0.19/0.39 (((~member(B!3, D!1)) | member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(122,plain,
% 0.19/0.39 ((~member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.39 tff(123,plain,
% 0.19/0.39 ((((~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))) | (~member(B!3, difference(D!1, C!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(124,plain,
% 0.19/0.39 (~member(B!3, difference(D!1, C!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[123, 122, 103])).
% 0.19/0.39 tff(125,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(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(126,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[125, 124, 115, 107])).
% 0.19/0.39 tff(127,plain,(member(B!3, C!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(128,plain,
% 0.19/0.39 (((~member(B!3, D!1)) | member(B!3, C!2)) | (~member(B!3, C!2))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(129,plain,
% 0.19/0.39 ((~member(B!3, D!1)) | member(B!3, C!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.39 tff(130,plain,
% 0.19/0.39 (~member(B!3, difference(D!1, C!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[123, 129, 103])).
% 0.19/0.39 tff(131,plain,
% 0.19/0.39 ((~(member(B!3, C!2) <=> member(B!3, D!1))) | (~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(132,plain,
% 0.19/0.39 (member(B!3, D!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[131, 127, 118])).
% 0.19/0.39 tff(133,plain,
% 0.19/0.39 (((~member(B!3, C!2)) | member(B!3, D!1)) | (~member(B!3, D!1))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(134,plain,
% 0.19/0.39 ((~member(B!3, C!2)) | member(B!3, D!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.39 tff(135,plain,
% 0.19/0.39 (~member(B!3, difference(C!2, D!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[114, 134, 110])).
% 0.19/0.39 tff(136,plain,
% 0.19/0.39 ((~(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))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(137,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[136, 135, 130, 100])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------