%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET633+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:26:04 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET633+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:33:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(subset_type, type, (
% 0.19/0.37 subset: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_D_2_type, type, (
% 0.19/0.37 tptp_fun_D_2: $i)).
% 0.19/0.37 tff(union_type, type, (
% 0.19/0.37 union: ( $i * $i ) > $i)).
% 0.19/0.37 tff(difference_type, type, (
% 0.19/0.37 difference: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_C_3_type, type, (
% 0.19/0.37 tptp_fun_C_3: $i)).
% 0.19/0.37 tff(tptp_fun_B_4_type, type, (
% 0.19/0.37 tptp_fun_B_4: $i)).
% 0.19/0.37 tff(symmetric_difference_type, type, (
% 0.19/0.37 symmetric_difference: ( $i * $i ) > $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[B: $i, C: $i] : refl((symmetric_difference(B, C) = symmetric_difference(C, B)) <=> (symmetric_difference(B, C) = symmetric_difference(C, B)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B)) <=> ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 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')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,(
% 0.19/0.37 ![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.37 inference(skolemize,[status(sab)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = symmetric_difference(C, B))) | (symmetric_difference(C!3, B!4) = symmetric_difference(B!4, C!3))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (symmetric_difference(C!3, B!4) = symmetric_difference(B!4, C!3)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (^[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))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 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')).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.37 tff(15,plain,(
% 0.19/0.37 ![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[14])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 ((~![B: $i, C: $i] : (symmetric_difference(B, C) = union(difference(B, C), difference(C, B)))) | (symmetric_difference(C!3, B!4) = union(difference(C!3, B!4), difference(B!4, C!3)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (symmetric_difference(C!3, B!4) = union(difference(C!3, B!4), difference(B!4, C!3))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (union(difference(C!3, B!4), difference(B!4, C!3)) = symmetric_difference(C!3, B!4)),
% 0.19/0.37 inference(symmetry,[status(thm)],[18])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (union(difference(C!3, B!4), difference(B!4, C!3)) = symmetric_difference(B!4, C!3)),
% 0.19/0.37 inference(transitivity,[status(thm)],[19, 9])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2) <=> subset(symmetric_difference(B!4, C!3), D!2)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (subset(symmetric_difference(B!4, C!3), D!2) <=> subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2)),
% 0.19/0.37 inference(symmetry,[status(thm)],[21])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 ((~subset(symmetric_difference(B!4, C!3), D!2)) <=> (~subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((~![B: $i, C: $i, D: $i] : ((~(subset(difference(B, C), D) & subset(difference(C, B), D))) | subset(symmetric_difference(B, C), D))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(difference(B, C), D) & subset(difference(C, B), D))) | subset(symmetric_difference(B, C), D)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 ((~![B: $i, C: $i, D: $i] : ((subset(difference(B, C), D) & subset(difference(C, B), D)) => subset(symmetric_difference(B, C), D))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(difference(B, C), D) & subset(difference(C, B), D))) | subset(symmetric_difference(B, C), D)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(26,axiom,(~![B: $i, C: $i, D: $i] : ((subset(difference(B, C), D) & subset(difference(C, B), D)) => subset(symmetric_difference(B, C), D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th115')).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (~![B: $i, C: $i, D: $i] : ((~(subset(difference(B, C), D) & subset(difference(C, B), D))) | subset(symmetric_difference(B, C), D))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (~![B: $i, C: $i, D: $i] : ((~(subset(difference(B, C), D) & subset(difference(C, B), D))) | subset(symmetric_difference(B, C), D))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (~![B: $i, C: $i, D: $i] : ((~(subset(difference(B, C), D) & subset(difference(C, B), D))) | subset(symmetric_difference(B, C), D))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (~![B: $i, C: $i, D: $i] : ((~(subset(difference(B, C), D) & subset(difference(C, B), D))) | subset(symmetric_difference(B, C), D))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.19/0.37 tff(31,plain,(
% 0.19/0.37 ~((~(subset(difference(B!4, C!3), D!2) & subset(difference(C!3, B!4), D!2))) | subset(symmetric_difference(B!4, C!3), D!2))),
% 0.19/0.37 inference(skolemize,[status(sab)],[30])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (~subset(symmetric_difference(B!4, C!3), D!2)),
% 0.19/0.37 inference(or_elim,[status(thm)],[31])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (~subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[32, 23])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (subset(difference(B!4, C!3), D!2) & subset(difference(C!3, B!4), D!2)),
% 0.19/0.37 inference(or_elim,[status(thm)],[31])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (subset(difference(C!3, B!4), D!2)),
% 0.19/0.37 inference(and_elim,[status(thm)],[34])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (subset(difference(B!4, C!3), D!2)),
% 0.19/0.37 inference(and_elim,[status(thm)],[34])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (^[B: $i, C: $i, D: $i] : refl((subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))) <=> ![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(B, C) & subset(D, C)) <=> (~((~subset(B, C)) | (~subset(D, C))))), ((~(subset(B, C) & subset(D, C))) <=> (~(~((~subset(B, C)) | (~subset(D, C))))))), rewrite((~(~((~subset(B, C)) | (~subset(D, C))))) <=> ((~subset(B, C)) | (~subset(D, C)))), ((~(subset(B, C) & subset(D, C))) <=> ((~subset(B, C)) | (~subset(D, C))))), (((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> (((~subset(B, C)) | (~subset(D, C))) | subset(union(B, D), C)))), rewrite((((~subset(B, C)) | (~subset(D, C))) | subset(union(B, D), C)) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))), (((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> ![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (^[B: $i, C: $i, D: $i] : rewrite(((subset(B, C) & subset(D, C)) => subset(union(B, D), C)) <=> ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(D, C)) => subset(union(B, D), C)) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.37 tff(44,axiom,(![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(D, C)) => subset(union(B, D), C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_subset')).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.37 tff(47,plain,(
% 0.19/0.37 ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.19/0.37 inference(skolemize,[status(sab)],[46])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | ((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(C!3, B!4), D!2)) | subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(difference(B!4, C!3), D!2)) | (~subset(difference(C!3, B!4), D!2)) | subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 ((subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2) | (~subset(difference(C!3, B!4), D!2)) | (~subset(difference(B!4, C!3), D!2))) <=> ((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(C!3, B!4), D!2)) | subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2) | (~subset(difference(C!3, B!4), D!2)) | (~subset(difference(B!4, C!3), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | ((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(C!3, B!4), D!2)) | subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2) | (~subset(difference(C!3, B!4), D!2)) | (~subset(difference(B!4, C!3), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(difference(B!4, C!3), D!2)) | (~subset(difference(C!3, B!4), D!2)) | subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2))),
% 0.19/0.37 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2) | (~subset(difference(C!3, B!4), D!2)) | (~subset(difference(B!4, C!3), D!2)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(difference(B!4, C!3), D!2)) | (~subset(difference(C!3, B!4), D!2)) | subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (subset(union(difference(C!3, B!4), difference(B!4, C!3)), D!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[55, 49, 36, 35])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[56, 33])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------