%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET581+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET581+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:28:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(member_type, type, (
% 0.20/0.39 member: ( $i * $i ) > $o)).
% 0.20/0.39 tff(intersection_type, type, (
% 0.20/0.39 intersection: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_C_3_type, type, (
% 0.20/0.39 tptp_fun_C_3: $i)).
% 0.20/0.39 tff(tptp_fun_D_2_type, type, (
% 0.20/0.39 tptp_fun_D_2: $i)).
% 0.20/0.39 tff(tptp_fun_B_4_type, type, (
% 0.20/0.39 tptp_fun_B_4: $i)).
% 0.20/0.39 tff(empty_set_type, type, (
% 0.20/0.39 empty_set: $i)).
% 0.20/0.39 tff(not_equal_type, type, (
% 0.20/0.39 not_equal: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[B: $i, C: $i] : refl((~((B = C) <=> not_equal(B, C))) <=> (~((B = C) <=> not_equal(B, C))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C))) <=> ![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C))) <=> ![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (^[B: $i, C: $i] : trans(rewrite((not_equal(B, C) <=> (~(B = C))) <=> (~((B = C) <=> not_equal(B, C)))), rewrite((~((B = C) <=> not_equal(B, C))) <=> (~((B = C) <=> not_equal(B, C)))), ((not_equal(B, C) <=> (~(B = C))) <=> (~((B = C) <=> not_equal(B, C)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C))) <=> ![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.39 tff(6,axiom,(![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_equal_defn')).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.39 tff(9,plain,(
% 0.20/0.39 ![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[8])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 ((~![B: $i, C: $i] : (~((B = C) <=> not_equal(B, C)))) | (~((intersection(C!3, D!2) = empty_set) <=> not_equal(intersection(C!3, D!2), empty_set)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~((intersection(C!3, D!2) = empty_set) <=> not_equal(intersection(C!3, D!2), empty_set))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : ((member(B, C) & member(B, D)) => not_equal(intersection(C, D), empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(15,axiom,(~![B: $i, C: $i, D: $i] : ((member(B, C) & member(B, D)) => not_equal(intersection(C, D), empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th24')).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.20/0.39 tff(20,plain,(
% 0.20/0.39 ~((~(member(B!4, C!3) & member(B!4, D!2))) | not_equal(intersection(C!3, D!2), empty_set))),
% 0.20/0.39 inference(skolemize,[status(sab)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (~not_equal(intersection(C!3, D!2), empty_set)),
% 0.20/0.39 inference(or_elim,[status(thm)],[20])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (((intersection(C!3, D!2) = empty_set) <=> not_equal(intersection(C!3, D!2), empty_set)) | (intersection(C!3, D!2) = empty_set) | not_equal(intersection(C!3, D!2), empty_set)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (((intersection(C!3, D!2) = empty_set) <=> not_equal(intersection(C!3, D!2), empty_set)) | (intersection(C!3, D!2) = empty_set)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (intersection(C!3, D!2) = empty_set),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(28,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.39 tff(30,plain,(
% 0.20/0.39 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.39 inference(skolemize,[status(sab)],[29])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, D!2) = intersection(D!2, C!3))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 0.20/0.39 inference(symmetry,[status(thm)],[33])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (intersection(D!2, C!3) = empty_set),
% 0.20/0.39 inference(transitivity,[status(thm)],[34, 24])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (member(B!4, intersection(D!2, C!3)) <=> member(B!4, empty_set)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (member(B!4, empty_set) <=> member(B!4, intersection(D!2, C!3))),
% 0.20/0.39 inference(symmetry,[status(thm)],[36])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ((~member(B!4, empty_set)) <=> (~member(B!4, intersection(D!2, C!3)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(42,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (![B: $i] : (~member(B, empty_set))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.39 tff(44,plain,(
% 0.20/0.39 ![B: $i] : (~member(B, empty_set))),
% 0.20/0.39 inference(skolemize,[status(sab)],[43])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![B: $i] : (~member(B, empty_set))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~![B: $i] : (~member(B, empty_set))) | (~member(B!4, empty_set))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (~member(B!4, empty_set)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (~member(B!4, intersection(D!2, C!3))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 38])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, C)) | (~member(D, B))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(54,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_defn')).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.39 tff(56,plain,(
% 0.20/0.39 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[55])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~member(B!4, C!3)) | (~member(B!4, D!2))) <=> member(B!4, intersection(D!2, C!3))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (~(((~member(B!4, C!3)) | (~member(B!4, D!2))) <=> member(B!4, intersection(D!2, C!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (member(B!4, C!3) & member(B!4, D!2)),
% 0.20/0.39 inference(or_elim,[status(thm)],[20])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (member(B!4, D!2)),
% 0.20/0.39 inference(and_elim,[status(thm)],[61])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (member(B!4, C!3)),
% 0.20/0.39 inference(and_elim,[status(thm)],[61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((~((~member(B!4, C!3)) | (~member(B!4, D!2)))) | (~member(B!4, C!3)) | (~member(B!4, D!2))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (~((~member(B!4, C!3)) | (~member(B!4, D!2)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[64, 63, 62])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((((~member(B!4, C!3)) | (~member(B!4, D!2))) <=> member(B!4, intersection(D!2, C!3))) | ((~member(B!4, C!3)) | (~member(B!4, D!2))) | member(B!4, intersection(D!2, C!3))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((((~member(B!4, C!3)) | (~member(B!4, D!2))) <=> member(B!4, intersection(D!2, C!3))) | member(B!4, intersection(D!2, C!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (member(B!4, intersection(D!2, C!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[67, 60])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[68, 48])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------