%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET596+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:25:57 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET596+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 05:29:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(subset_type, type, (
% 0.20/0.37 subset: ( $i * $i ) > $o)).
% 0.20/0.37 tff(empty_set_type, type, (
% 0.20/0.37 empty_set: $i)).
% 0.20/0.37 tff(intersection_type, type, (
% 0.20/0.37 intersection: ( $i * $i ) > $i)).
% 0.20/0.37 tff(tptp_fun_D_3_type, type, (
% 0.20/0.37 tptp_fun_D_3: $i)).
% 0.20/0.37 tff(tptp_fun_B_5_type, type, (
% 0.20/0.37 tptp_fun_B_5: $i)).
% 0.20/0.37 tff(tptp_fun_C_4_type, type, (
% 0.20/0.37 tptp_fun_C_4: $i)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 ((~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & (intersection(C, D) = empty_set))) | (intersection(B, D) = empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & (intersection(C, D) = empty_set))) | (intersection(B, D) = empty_set)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 ((~![B: $i, C: $i, D: $i] : ((subset(B, C) & (intersection(C, D) = empty_set)) => (intersection(B, D) = empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & (intersection(C, D) = empty_set))) | (intersection(B, D) = empty_set)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(3,axiom,(~![B: $i, C: $i, D: $i] : ((subset(B, C) & (intersection(C, D) = empty_set)) => (intersection(B, D) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th55')).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & (intersection(C, D) = empty_set))) | (intersection(B, D) = empty_set))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & (intersection(C, D) = empty_set))) | (intersection(B, D) = empty_set))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & (intersection(C, D) = empty_set))) | (intersection(B, D) = empty_set))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & (intersection(C, D) = empty_set))) | (intersection(B, D) = empty_set))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.37 tff(8,plain,(
% 0.20/0.37 ~((~(subset(B!5, C!4) & (intersection(C!4, D!3) = empty_set))) | (intersection(B!5, D!3) = empty_set))),
% 0.20/0.37 inference(skolemize,[status(sab)],[7])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (subset(B!5, C!4) & (intersection(C!4, D!3) = empty_set)),
% 0.20/0.37 inference(or_elim,[status(thm)],[8])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (intersection(C!4, D!3) = empty_set),
% 0.20/0.37 inference(and_elim,[status(thm)],[9])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (empty_set = intersection(C!4, D!3)),
% 0.20/0.37 inference(symmetry,[status(thm)],[10])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (subset(intersection(B!5, D!3), empty_set) <=> subset(intersection(B!5, D!3), intersection(C!4, D!3))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[11])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (subset(intersection(B!5, D!3), intersection(C!4, D!3)) <=> subset(intersection(B!5, D!3), empty_set)),
% 0.20/0.37 inference(symmetry,[status(thm)],[12])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (subset(B!5, C!4)),
% 0.20/0.37 inference(and_elim,[status(thm)],[9])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (^[B: $i, C: $i, D: $i] : refl(((~subset(B, C)) | subset(intersection(B, D), intersection(C, D))) <=> ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (^[B: $i, C: $i, D: $i] : rewrite((subset(B, C) => subset(intersection(B, D), intersection(C, D))) <=> ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (![B: $i, C: $i, D: $i] : (subset(B, C) => subset(intersection(B, D), intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.37 tff(20,axiom,(![B: $i, C: $i, D: $i] : (subset(B, C) => subset(intersection(B, D), intersection(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_of_subset')).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.37 tff(23,plain,(
% 0.20/0.37 ![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[22])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))) | ((~subset(B!5, C!4)) | subset(intersection(B!5, D!3), intersection(C!4, D!3)))) <=> ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))) | (~subset(B!5, C!4)) | subset(intersection(B!5, D!3), intersection(C!4, D!3)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))) | ((~subset(B!5, C!4)) | subset(intersection(B!5, D!3), intersection(C!4, D!3)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(intersection(B, D), intersection(C, D)))) | (~subset(B!5, C!4)) | subset(intersection(B!5, D!3), intersection(C!4, D!3))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (subset(intersection(B!5, D!3), intersection(C!4, D!3))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (subset(intersection(B!5, D!3), empty_set)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[28, 13])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (~(intersection(B!5, D!3) = empty_set)),
% 0.20/0.37 inference(or_elim,[status(thm)],[8])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (^[B: $i] : refl(((~subset(B, empty_set)) | (B = empty_set)) <=> ((~subset(B, empty_set)) | (B = empty_set)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (![B: $i] : ((~subset(B, empty_set)) | (B = empty_set)) <=> ![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (![B: $i] : ((~subset(B, empty_set)) | (B = empty_set)) <=> ![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 (^[B: $i] : rewrite((subset(B, empty_set) => (B = empty_set)) <=> ((~subset(B, empty_set)) | (B = empty_set)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 (![B: $i] : (subset(B, empty_set) => (B = empty_set)) <=> ![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.37 tff(36,axiom,(![B: $i] : (subset(B, empty_set) => (B = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_of_empty_set_is_empty_set')).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 (![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.37 tff(39,plain,(
% 0.20/0.37 ![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.20/0.37 inference(skolemize,[status(sab)],[38])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 (![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 (((~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))) | ((~subset(intersection(B!5, D!3), empty_set)) | (intersection(B!5, D!3) = empty_set))) <=> ((~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))) | (~subset(intersection(B!5, D!3), empty_set)) | (intersection(B!5, D!3) = empty_set))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(42,plain,
% 0.20/0.37 ((~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))) | ((~subset(intersection(B!5, D!3), empty_set)) | (intersection(B!5, D!3) = empty_set))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 ((~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))) | (~subset(intersection(B!5, D!3), empty_set)) | (intersection(B!5, D!3) = empty_set)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 (~subset(intersection(B!5, D!3), empty_set)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[43, 40, 30])).
% 0.20/0.37 tff(45,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[44, 29])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------