0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : do_cvc5 %s %d 0.13/0.34 % Computer : n004.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 05:11:50 EDT 2022 0.13/0.35 % CPUTime : 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF 0.46/0.67 ------- cvc5-fof casc J11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 0.46/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 0.46/0.67 % SZS status Theorem for theBenchmark 0.46/0.67 % SZS output start Proof for theBenchmark 0.46/0.67 (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (E $$unsorted)) (=> (and (subset A E) (subset B E)) (= (subset A B) (subset (intersection A (difference E B)) (intersection C (difference E C))))))))) (let ((_let_2 (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (and (not (member B A)) (member B E)) (member B (difference E A)))))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (and (member X B) (member X A)) (member X (intersection A B)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (subset A B) (forall ((X $$unsorted)) (=> (member X A) (member X B))))))) (let ((_let_5 (difference skv_5 skv_3))) (let ((_let_6 (member skv_6 _let_5))) (let ((_let_7 (member skv_6 skv_5))) (let ((_let_8 (member skv_6 skv_3))) (let ((_let_9 (not _let_8))) (let ((_let_10 (and _let_9 _let_7))) (let ((_let_11 (= _let_6 _let_10))) (let ((_let_12 (member skv_6 skv_2))) (let ((_let_13 (and _let_6 _let_12))) (let ((_let_14 (not _let_6))) (let ((_let_15 (intersection skv_2 _let_5))) (let ((_let_16 (member skv_6 _let_15))) (let ((_let_17 (= _let_16 _let_13))) (let ((_let_18 (not _let_13))) (let ((_let_19 (_let_3))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 ((member X (intersection A B))))) (let ((_let_22 (not _let_16))) (let ((_let_23 (or _let_22 _let_8))) (let ((_let_24 (forall ((X $$unsorted)) (or (not (member X (intersection skv_2 (difference skv_5 skv_3)))) (member X skv_3))))) (let ((_let_25 (member skv_24 _let_15))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 (member skv_24 skv_3)))) (let ((_let_28 (difference skv_5 skv_4))) (let ((_let_29 (intersection skv_4 _let_28))) (let ((_let_30 (member skv_24 _let_29))) (let ((_let_31 (or _let_26 _let_30))) (let ((_let_32 (forall ((X $$unsorted)) (or (not (member X (intersection skv_2 (difference skv_5 skv_3)))) (member X (intersection skv_4 (difference skv_5 skv_4))))))) (let ((_let_33 (subset _let_15 _let_29))) (let ((_let_34 (= _let_33 _let_32))) (let ((_let_35 (forall ((A $$unsorted) (B $$unsorted)) (= (subset A B) (forall ((X $$unsorted)) (or (not (member X A)) (member X B))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (_let_35))) (let ((_let_38 ((subset A B)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_15 _let_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_37)) _let_36 :args (_let_34 false _let_35)))) (let ((_let_40 (subset skv_2 skv_3))) (let ((_let_41 (= _let_40 _let_33))) (let ((_let_42 (forall ((X $$unsorted)) (or (not (member X skv_2)) (member X skv_3))))) (let ((_let_43 (= _let_40 _let_42))) (let ((_let_44 (member skv_20 _let_15))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 (member skv_20 _let_29)))) (let ((_let_47 (member skv_20 skv_3))) (let ((_let_48 (member skv_20 skv_2))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47))) (let ((_let_51 (member skv_20 _let_5))) (let ((_let_52 (and _let_51 _let_48))) (let ((_let_53 (= _let_44 _let_52))) (let ((_let_54 (not _let_47))) (let ((_let_55 (and _let_54 (member skv_20 skv_5)))) (let ((_let_56 (= _let_51 _let_55))) (let ((_let_57 (subset skv_2 skv_5))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 (not (subset skv_3 skv_5)) _let_41))) (let ((_let_60 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (E $$unsorted)) (or (not (subset A E)) (not (subset B E)) (= (subset A B) (subset (intersection A (difference E B)) (intersection C (difference E C)))))))) (let ((_let_61 (not _let_59))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (OR))) (let ((_let_64 (not _let_60))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_62) :args (_let_64))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_60))) (REFL :args (_let_61)) :args _let_63)) _let_62 :args (_let_61 true _let_60)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_59 2)) _let_65 :args ((not _let_41) true _let_59)))) (let ((_let_67 (_let_41))) (let ((_let_68 (not _let_34))) (let ((_let_69 (not _let_32))) (let ((_let_70 (_let_34))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (skv_2 skv_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_37)) _let_36 :args (_let_43 false _let_35)))) (let ((_let_72 (not _let_43))) (let ((_let_73 (not _let_40))) (let ((_let_74 (_let_43))) (let ((_let_75 (_let_69))) (let ((_let_76 (_let_42))) (let ((_let_77 ((not (= (member X skv_2) false))))) (let ((_let_78 (not _let_52))) (let ((_let_79 (_let_2))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 ((member B (difference E A))))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_55 0)) :args ((or _let_54 (not _let_55)))) (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_47 (not _let_50)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_56)) :args ((or (not _let_51) _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (skv_20 skv_3 skv_5 QUANTIFIERS_INST_E_MATCHING _let_81)) :args _let_79))) _let_80 :args (_let_56 false _let_2)) (REORDERING (CNF_AND_POS :args (_let_52 1)) :args ((or _let_48 _let_78))) (REORDERING (CNF_AND_POS :args (_let_52 0)) :args ((or _let_51 _let_78))) (REORDERING (CNF_EQUIV_POS1 :args (_let_53)) :args ((or _let_45 _let_52 (not _let_53)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_20 :args (skv_20 skv_2 _let_5 QUANTIFIERS_INST_E_MATCHING _let_21)) :args _let_19))) _let_20 :args (_let_53 false _let_3)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_63)) :args ((or _let_44 _let_46))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_76) :args (skv_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_77)) :args _let_76)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_75)) :args _let_75)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_32))) (REFL :args ((not _let_46))) :args _let_63)) (REORDERING (CNF_EQUIV_POS1 :args _let_74) :args ((or _let_73 _let_42 _let_72))) _let_71 (REORDERING (CNF_EQUIV_POS2 :args _let_70) :args ((or _let_33 _let_69 _let_68))) _let_39 (REORDERING (CNF_EQUIV_NEG1 :args _let_67) :args ((or _let_40 _let_33 _let_41))) _let_66 :args (_let_33 false _let_47 false _let_55 false _let_56 false _let_48 false _let_51 false _let_52 false _let_53 false _let_44 false _let_50 true _let_46 false _let_42 false _let_43 true _let_32 false _let_34 false _let_40 true _let_41)))) (let ((_let_83 (_let_32))) (let ((_let_84 (member skv_24 skv_4))) (let ((_let_85 (member skv_24 _let_28))) (let ((_let_86 (and _let_85 _let_84))) (let ((_let_87 (= _let_30 _let_86))) (let ((_let_88 (not _let_30))) (let ((_let_89 (not _let_84))) (let ((_let_90 (and _let_89 (member skv_24 skv_5)))) (let ((_let_91 (= _let_85 _let_90))) (let ((_let_92 (not _let_86))) (let ((_let_93 (not _let_24))) (let ((_let_94 (_let_93))) (let ((_let_95 (_let_24))) (let ((_let_96 (not _let_12))) (let ((_let_97 (or _let_96 _let_8))) (let ((_let_98 (not _let_97))) (let ((_let_99 (not _let_42))) (let ((_let_100 (_let_99))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_100)) :args _let_100)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_99) _let_42))) (REFL :args (_let_98)) :args _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_74) :args ((or _let_40 _let_99 _let_72))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_67) _let_66 _let_82 :args (_let_73 true _let_41 false _let_33)) _let_71 :args (_let_99 true _let_40 false _let_43)) :args (_let_98 true _let_42)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_97 1)) _let_101 :args (_let_9 true _let_97)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_97 0)) (CONG (REFL :args (_let_97)) (MACRO_SR_PRED_INTRO :args ((= (not _let_96) _let_12))) :args _let_63)) :args ((or _let_12 _let_97))) _let_101 :args (_let_12 true _let_97)))) (let ((_let_104 (or _let_96 _let_7))) (let ((_let_105 (forall ((X $$unsorted)) (or (not (member X skv_2)) (member X skv_5))))) (let ((_let_106 (= _let_57 _let_105))) (let ((_let_107 (_let_105))) (let ((_let_108 (not _let_7))) (let ((_let_109 (_let_10))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_11)) :args ((or _let_6 (not _let_10) (not _let_11)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (skv_6 skv_3 skv_5 QUANTIFIERS_INST_E_MATCHING _let_81)) :args _let_79))) _let_80 :args (_let_11 false _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_109) (CONG (REFL :args _let_109) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) (REFL :args (_let_108)) :args _let_63)) :args ((or _let_8 _let_108 _let_10))) _let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_96 _let_7 (not _let_104)))) _let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_107) :args (skv_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_77)) :args _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_106)) :args ((or _let_58 _let_105 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_63)) :args ((or _let_57 _let_59))) _let_65 :args (_let_57 true _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (skv_2 skv_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_37)) _let_36 :args (_let_106 false _let_35)) :args (_let_105 false _let_57 false _let_106)) :args (_let_104 false _let_105)) :args (_let_7 false _let_12 false _let_104)) :args (_let_10 true _let_8 false _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_13)) :args ((or _let_96 _let_13 _let_14))) _let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_17)) :args ((or _let_16 _let_18 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_8 _let_22 (not _let_23)))) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_95) :args (skv_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (member X skv_3) true))))) :args _let_95)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_94)) :args _let_94)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_24))) (REFL :args ((not _let_27))) :args _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG (REFL :args (_let_27)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_63)) :args ((or _let_25 _let_27))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_26 _let_30 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_87)) :args ((or _let_88 _let_86 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 0)) :args ((or _let_89 (not _let_90)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_91)) :args ((or (not _let_85) _let_90 (not _let_91)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (skv_24 skv_4 skv_5 QUANTIFIERS_INST_E_MATCHING _let_81)) :args _let_79))) _let_80 :args (_let_91 false _let_2)) (REORDERING (CNF_AND_POS :args (_let_86 1)) :args ((or _let_84 _let_92))) (REORDERING (CNF_AND_POS :args (_let_86 0)) :args ((or _let_85 _let_92))) :args (_let_92 false _let_90 false _let_91 false _let_84 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_20 :args (skv_24 skv_4 _let_28 QUANTIFIERS_INST_E_MATCHING _let_21)) :args _let_19))) _let_20 :args (_let_87 false _let_3)) :args (_let_88 true _let_86 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_83) :args (skv_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (member X _let_15) false))))) :args _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_70) :args ((or (not _let_33) _let_32 _let_68))) _let_82 _let_39 :args (_let_32 false _let_33 false _let_34)) :args (_let_31 false _let_32)) :args (_let_26 true _let_30 false _let_31)) :args (_let_27 true _let_25)) :args (_let_24 false _let_27)) :args (_let_23 false _let_24)) :args (_let_22 true _let_8 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_20 :args (skv_6 skv_2 _let_5 QUANTIFIERS_INST_E_MATCHING _let_21)) :args _let_19))) _let_20 :args (_let_17 false _let_3)) :args (_let_18 true _let_16 false _let_17)) :args (_let_14 false _let_12 true _let_13)) :args (false false _let_11 false _let_10 true _let_6)) :args ((forall ((X $$unsorted) (A $$unsorted)) (= (forall ((Y $$unsorted)) (=> (member Y A) (member X Y))) (member X (product A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (member X (singleton A)) (= A X))) (forall ((A $$unsorted) (B $$unsorted)) (= (and (subset A B) (subset B A)) (equal_set A B))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (member X (unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted)) (not (member X empty_set))) (forall ((X $$unsorted) (A $$unsorted)) (= (exists ((Y $$unsorted)) (and (member Y A) (member X Y))) (member X (sum A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (subset X A) (member X (power_set A)))) _let_4 _let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (member X (union A B)) (or (member X B) (member X A)))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.46/0.68 % SZS output end Proof for theBenchmark 0.46/0.68 EOF