%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET585+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 05:25:55 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET585+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % 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 05:29:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(subset_type, type, (
% 0.12/0.36 subset: ( $i * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun_B_4_type, type, (
% 0.12/0.36 tptp_fun_B_4: $i)).
% 0.12/0.36 tff(intersection_type, type, (
% 0.12/0.36 intersection: ( $i * $i ) > $i)).
% 0.12/0.36 tff(tptp_fun_C_3_type, type, (
% 0.12/0.36 tptp_fun_C_3: $i)).
% 0.12/0.36 tff(union_type, type, (
% 0.12/0.36 union: ( $i * $i ) > $i)).
% 0.12/0.36 tff(tptp_fun_D_2_type, type, (
% 0.12/0.36 tptp_fun_D_2: $i)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (^[B: $i, C: $i] : refl(subset(intersection(B, C), B) <=> subset(intersection(B, C), B))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![B: $i, C: $i] : subset(intersection(B, C), B) <=> ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![B: $i, C: $i] : subset(intersection(B, C), B) <=> ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(4,axiom,(![B: $i, C: $i] : subset(intersection(B, C), B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_is_subset')).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.36 tff(6,plain,(
% 0.12/0.36 ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.36 inference(skolemize,[status(sab)],[5])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 ((~![B: $i, C: $i] : subset(intersection(B, C), B)) | subset(intersection(B!4, C!3), B!4)),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (subset(intersection(B!4, C!3), B!4)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (^[B: $i, C: $i] : refl(subset(B, union(B, C)) <=> subset(B, union(B, C)))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (![B: $i, C: $i] : subset(B, union(B, C)) <=> ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (![B: $i, C: $i] : subset(B, union(B, C)) <=> ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(13,axiom,(![B: $i, C: $i] : subset(B, union(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_of_union')).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (![B: $i, C: $i] : subset(B, union(B, C))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.36 tff(15,plain,(
% 0.12/0.36 ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.12/0.36 inference(skolemize,[status(sab)],[14])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (![B: $i, C: $i] : subset(B, union(B, C))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 ((~![B: $i, C: $i] : subset(B, union(B, C))) | subset(B!4, union(B!4, D!2))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (subset(B!4, union(B!4, D!2))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 ((~![B: $i, C: $i, D: $i] : subset(intersection(B, C), union(B, D))) <=> (~![B: $i, C: $i, D: $i] : subset(intersection(B, C), union(B, D)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(20,axiom,(~![B: $i, C: $i, D: $i] : subset(intersection(B, C), union(B, D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_intersection_subset_of_union')).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (~![B: $i, C: $i, D: $i] : subset(intersection(B, C), union(B, D))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 (~![B: $i, C: $i, D: $i] : subset(intersection(B, C), union(B, D))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (~![B: $i, C: $i, D: $i] : subset(intersection(B, C), union(B, D))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 (~![B: $i, C: $i, D: $i] : subset(intersection(B, C), union(B, D))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.12/0.36 tff(25,plain,(
% 0.12/0.36 ~subset(intersection(B!4, C!3), union(B!4, D!2))),
% 0.12/0.36 inference(skolemize,[status(sab)],[24])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C))) <=> ![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(27,plain,
% 0.12/0.36 (^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(B, C) & subset(C, D)) <=> (~((~subset(C, D)) | (~subset(B, C))))), ((~(subset(B, C) & subset(C, D))) <=> (~(~((~subset(C, D)) | (~subset(B, C))))))), rewrite((~(~((~subset(C, D)) | (~subset(B, C))))) <=> ((~subset(C, D)) | (~subset(B, C)))), ((~(subset(B, C) & subset(C, D))) <=> ((~subset(C, D)) | (~subset(B, C))))), (((~(subset(B, C) & subset(C, D))) | subset(B, D)) <=> (((~subset(C, D)) | (~subset(B, C))) | subset(B, D)))), rewrite((((~subset(C, D)) | (~subset(B, C))) | subset(B, D)) <=> (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))), (((~(subset(B, C) & subset(C, D))) | subset(B, D)) <=> (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D)) <=> ![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D)) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (^[B: $i, C: $i, D: $i] : rewrite(((subset(B, C) & subset(C, D)) => subset(B, D)) <=> ((~(subset(B, C) & subset(C, D))) | subset(B, D)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(C, D)) => subset(B, D)) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.37 tff(32,axiom,(![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(C, D)) => subset(B, D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity_of_subset')).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.37 tff(35,plain,(
% 0.12/0.37 ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.12/0.37 inference(skolemize,[status(sab)],[34])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (((~![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))) | (subset(intersection(B!4, C!3), union(B!4, D!2)) | (~subset(B!4, union(B!4, D!2))) | (~subset(intersection(B!4, C!3), B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))) | subset(intersection(B!4, C!3), union(B!4, D!2)) | (~subset(B!4, union(B!4, D!2))) | (~subset(intersection(B!4, C!3), B!4)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((~![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))) | (subset(intersection(B!4, C!3), union(B!4, D!2)) | (~subset(B!4, union(B!4, D!2))) | (~subset(intersection(B!4, C!3), B!4)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~![B: $i, C: $i, D: $i] : (subset(B, D) | (~subset(C, D)) | (~subset(B, C)))) | subset(intersection(B!4, C!3), union(B!4, D!2)) | (~subset(B!4, union(B!4, D!2))) | (~subset(intersection(B!4, C!3), B!4))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[40, 37, 25, 18, 9])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------