0.11/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : do_cvc5 %s %d 0.12/0.34 % Computer : n019.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 : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 05:05:21 EDT 2022 0.12/0.34 % CPUTime : 0.19/0.47 %----Proving TF0_NAR, FOF, or CNF 10.33/10.77 ------- cvc5-fof casc J11 : /export/starexec/sandbox/benchmark/theBenchmark.p at /export/starexec/sandbox/benchmark/theBenchmark.p... 10.33/10.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 10.33/10.77 --- Run --no-e-matching --full-saturate-quant at 5... 10.33/10.77 % SZS status Theorem for theBenchmark 10.33/10.77 % SZS output start Proof for theBenchmark 10.33/10.77 (let ((_let_1 (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (=> (and (int_less I J) (int_less J K)) (int_less I K))))) (let ((_let_2 (forall ((I $$unsorted) (J $$unsorted)) (=> (int_less I J) (not (= J I)))))) (let ((_let_3 (forall ((I $$unsorted) (J $$unsorted)) (=> (and (int_leq int_one I) (int_leq J n) (int_leq int_one J) (int_leq I n)) (and (forall ((C $$unsorted)) (=> (and (= I (plus J C)) (int_less int_zero C)) (forall ((K $$unsorted)) (=> (and (int_leq int_one K) (int_leq K J)) (= (a (plus K C) K) real_zero))))) (forall ((K $$unsorted)) (=> (and (int_leq K J) (int_leq int_one K)) (= (a K K) real_one))) (forall ((C $$unsorted)) (=> (and (int_less int_zero C) (= (plus I C) J)) (forall ((K $$unsorted)) (=> (and (int_leq K I) (int_leq int_one K)) (= (a K (plus K C)) real_zero)))))))))) (let ((_let_4 (not (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (a I J))) (=> (and (int_leq int_one J) (int_leq J n) (int_leq I n) (int_leq int_one I)) (and (=> (= I J) (= _let_1 real_one)) (=> (int_less J I) (= _let_1 real_zero)) (=> (int_less I J) (= real_zero _let_1))))))))) (let ((_let_5 (forall ((I $$unsorted) (J $$unsorted)) (or (int_less I J) (int_leq J I))))) (let ((_let_6 (forall ((I $$unsorted) (J $$unsorted)) (= (exists ((K $$unsorted)) (and (= (plus I K) J) (int_less int_zero K))) (int_less I J))))) (let ((_let_7 (a skv_2 skv_3))) (let ((_let_8 (= real_zero _let_7))) (let ((_let_9 (plus skv_2 skv_7))) (let ((_let_10 (= skv_3 _let_9))) (let ((_let_11 (= real_zero (a skv_2 _let_9)))) (let ((_let_12 (int_less skv_2 skv_3))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_8))) (let ((_let_15 (not _let_8))) (let ((_let_16 (int_less skv_3 skv_2))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_8))) (let ((_let_19 (= real_one _let_7))) (let ((_let_20 (= skv_2 skv_3))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19))) (let ((_let_23 (and _let_22 _let_18 _let_14))) (let ((_let_24 (int_less skv_2 skv_2))) (let ((_let_25 (or _let_13 _let_17 _let_24))) (let ((_let_26 (forall ((K $$unsorted)) (or (not (= skv_2 (plus skv_3 K))) (not (int_less int_zero K)))))) (let ((_let_27 (not _let_26))) (let ((_let_28 (= _let_16 _let_27))) (let ((_let_29 (int_less int_zero skv_6))) (let ((_let_30 (not _let_29))) (let ((_let_31 (plus skv_3 skv_6))) (let ((_let_32 (= skv_2 _let_31))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_30))) (let ((_let_35 (int_leq int_one skv_3))) (let ((_let_36 (int_leq skv_3 skv_3))) (let ((_let_37 (= real_zero (a _let_31 skv_3)))) (let ((_let_38 (not _let_36))) (let ((_let_39 (not _let_35))) (let ((_let_40 (or _let_33 _let_30 _let_39 _let_38 _let_37))) (let ((_let_41 (forall ((J $$unsorted)) (not (int_less J J))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (skv_2 QUANTIFIERS_INST_ENUM)) :args _let_43)) _let_42 :args ((not _let_24) false _let_41)))) (let ((_let_45 (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (or (not (int_less I J)) (not (int_less J K)) (int_less I K))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (forall ((I $$unsorted) (J $$unsorted)) (= (int_less I J) (not (forall ((K $$unsorted)) (or (not (= J (plus I K))) (not (int_less int_zero K))))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (_let_47))) (let ((_let_50 (OR))) (let ((_let_51 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG (REFL :args (_let_14)) (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_50)) :args ((or _let_12 _let_14))))) (let ((_let_52 (_let_27))) (let ((_let_53 (int_leq int_one skv_2))) (let ((_let_54 (not _let_53))) (let ((_let_55 (int_leq skv_2 n))) (let ((_let_56 (not _let_55))) (let ((_let_57 (int_leq skv_3 n))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_39 _let_58 _let_56 _let_54 _let_23))) (let ((_let_60 (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (a I J))) (let ((_let_2 (= _let_1 real_zero))) (or (not (int_leq int_one J)) (not (int_leq J n)) (not (int_leq I n)) (not (int_leq int_one I)) (and (or (not (= I J)) (= real_one _let_1)) (or (not (int_less J I)) _let_2) (or (not (int_less I J)) _let_2)))))))) (let ((_let_61 (not _let_59))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (not _let_60))) (let ((_let_64 (= _let_7 real_zero))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_62) :args (_let_63)) (REWRITE :args ((=> _let_63 (not (or _let_39 _let_58 _let_56 _let_54 (and _let_22 (or _let_17 _let_64) (or _let_13 _let_64))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_60))) (REFL :args (_let_61)) :args _let_50)) _let_62 :args (_let_61 true _let_60)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_59 4)) _let_65 :args ((not _let_23) true _let_59)))) (let ((_let_67 (int_less skv_3 skv_3))) (let ((_let_68 (int_leq skv_2 skv_3))) (let ((_let_69 (or _let_16 _let_68))) (let ((_let_70 (= real_one (a skv_3 skv_3)))) (let ((_let_71 (or _let_38 _let_39 _let_70))) (let ((_let_72 (not _let_67))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (skv_3 QUANTIFIERS_INST_ENUM)) :args _let_43)) _let_42 :args (_let_72 false _let_41)))) (let ((_let_74 (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_67))))) (let ((_let_75 (REFL :args (_let_21)))) (let ((_let_76 (and _let_20 _let_72))) (let ((_let_77 (true _let_76))) (let ((_let_78 (_let_20 _let_72))) (let ((_let_79 (_let_72 _let_20))) (let ((_let_80 (ASSUME :args (_let_72)))) (let ((_let_81 (FALSE_INTRO _let_80))) (let ((_let_82 (APPLY_UF int_less))) (let ((_let_83 (ASSUME :args (_let_20)))) (let ((_let_84 (SYMM _let_83))) (let ((_let_85 (SYMM _let_84))) (let ((_let_86 (REFL :args (skv_3)))) (let ((_let_87 (AND_INTRO _let_80 _let_83))) (let ((_let_88 (CNF_AND_NEG :args (_let_76)))) (let ((_let_89 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG (REFL :args (_let_18)) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_50)) :args ((or _let_16 _let_18))))) (let ((_let_90 (_let_5))) (let ((_let_91 (ASSUME :args _let_90))) (let ((_let_92 (CNF_AND_NEG :args (_let_23)))) (let ((_let_93 (and _let_20 _let_68))) (let ((_let_94 (ASSUME :args (_let_68)))) (let ((_let_95 (not _let_19))) (let ((_let_96 (and _let_20 _let_95))) (let ((_let_97 (ASSUME :args (_let_95)))) (let ((_let_98 (EQUAL))) (let ((_let_99 (APPLY_UF a))) (let ((_let_100 (REFL :args (_let_59)))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG _let_100 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) :args _let_50)) :args ((or _let_35 _let_59))) _let_65 :args (_let_35 true _let_59)))) (let ((_let_102 (plus int_zero int_zero))) (let ((_let_103 (= real_zero (a int_zero _let_102)))) (let ((_let_104 (not (int_leq int_one int_zero)))) (let ((_let_105 (not (int_leq int_zero skv_3)))) (let ((_let_106 (plus skv_3 int_zero))) (let ((_let_107 (not (= skv_3 _let_106)))) (let ((_let_108 (not (int_less int_zero int_zero)))) (let ((_let_109 (= real_zero (a _let_102 int_zero)))) (let ((_let_110 (and (or _let_107 _let_108 _let_104 _let_105 _let_109) _let_71 (or _let_108 _let_107 _let_105 _let_104 _let_103)))) (let ((_let_111 (or _let_39 _let_58 _let_39 _let_58 _let_110))) (let ((_let_112 (forall ((I $$unsorted) (J $$unsorted) (BOUND_VARIABLE_644 $$unsorted) (BOUND_VARIABLE_655 $$unsorted) (BOUND_VARIABLE_629 $$unsorted) (BOUND_VARIABLE_653 $$unsorted) (BOUND_VARIABLE_627 $$unsorted)) (or (not (int_leq int_one I)) (not (int_leq J n)) (not (int_leq int_one J)) (not (int_leq I n)) (and (or (not (= I (plus J BOUND_VARIABLE_627))) (not (int_less int_zero BOUND_VARIABLE_627)) (not (int_leq int_one 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(CNF_OR_NEG :args (_let_22 0)) (CONG (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_50)) :args ((or _let_20 _let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_39 _let_38 _let_70 (not _let_71)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_110 1)) :args ((or _let_71 (not _let_110)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_111))) :args ((or _let_39 _let_58 _let_110 (not _let_111)))) _let_101 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (skv_3 skv_3 skv_3 int_zero int_zero int_zero int_zero QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_114)) _let_113 :args (_let_111 false _let_112)) :args (_let_110 false _let_35 false _let_57 false _let_111)) :args (_let_71 false _let_110)) _let_101 (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_96)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_97 _let_83) (SCOPE (FALSE_ELIM (TRANS 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(IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) (REFL :args ((not _let_34))) :args _let_50)) _let_51 (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or _let_17 _let_27 (not _let_28)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (skv_3 skv_2 QUANTIFIERS_INST_ENUM)) :args _let_49)) _let_48 :args (_let_28 false _let_47)) (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_17 _let_13 _let_24 (not _let_25)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (skv_2 skv_3 skv_2 QUANTIFIERS_INST_ENUM)) :args (_let_45))) _let_46 :args (_let_25 false _let_45)) _let_44 :args (_let_17 false _let_37 false _let_40 false _let_36 false _let_35 true _let_8 false _let_29 false _let_32 true _let_18 false _let_22 true _let_23 true _let_34 false _let_14 true _let_26 false _let_28 true _let_12 false _let_25 true _let_24)) :args (_let_18 true _let_16)) :args ((not _let_14) true _let_23 false _let_22 false _let_18)))) (let ((_let_132 (int_less int_zero skv_7))) (let ((_let_133 (not _let_132))) (let ((_let_134 (not _let_10))) (let ((_let_135 (or _let_134 _let_133))) (let ((_let_136 (forall ((K $$unsorted)) (or (not (= skv_3 (plus skv_2 K))) (not (int_less int_zero K)))))) (let ((_let_137 (not _let_135))) (let ((_let_138 (not _let_136))) (let ((_let_139 (= _let_12 _let_138))) (let ((_let_140 (_let_138))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_140)) :args _let_140)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_138) _let_136))) (REFL :args (_let_137)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_139)) :args ((or _let_13 _let_138 (not _let_139)))) (MACRO_RESOLUTION_TRUST _let_51 _let_131 :args (_let_12 true _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (skv_2 skv_3 QUANTIFIERS_INST_ENUM)) :args _let_49)) _let_48 :args (_let_139 false _let_47)) :args (_let_138 false _let_12 false _let_139)) :args (_let_137 true _let_136)))) (let ((_let_142 (REFL :args (_let_135)))) (let ((_let_143 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_135 0)) (CONG _let_142 (MACRO_SR_PRED_INTRO :args ((= (not _let_134) _let_10))) :args _let_50)) :args ((or _let_10 _let_135))) _let_141 :args (_let_10 true _let_135)))) (let ((_let_144 (int_leq skv_2 skv_2))) (let ((_let_145 (not _let_144))) (let ((_let_146 (or _let_133 _let_134 _let_145 _let_54 _let_11))) (let ((_let_147 (and (or (not (= skv_2 _let_106)) _let_108 _let_104 _let_105 _let_109) _let_119 _let_146))) (let ((_let_148 (or _let_54 _let_58 _let_39 _let_56 _let_147))) (let ((_let_149 (or _let_24 _let_144))) (let ((_let_150 (not _let_11))) (let ((_let_151 (_let_150))) (let ((_let_152 (ASSUME :args (_let_11)))) (let ((_let_153 (ASSUME :args (_let_10)))) (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_152 (MODUS_PONENS (AND_INTRO _let_127 _let_153) (SCOPE (FALSE_ELIM (TRANS (CONG _let_130 (CONG (REFL :args (skv_2)) (SYMM _let_153) :args _let_99) :args _let_98) _let_128)) :args (_let_15 _let_10)))) :args (_let_15 _let_10 _let_11)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_151))) (TRUE_INTRO (SYMM (SYMM _let_152))))) :args (_let_11 _let_150)) :args ((not (and _let_15 _let_10 _let_11)) SB_LITERAL))) (CONG _let_124 (REFL :args (_let_134)) (REFL :args _let_151) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_146)) :args ((or _let_54 _let_145 _let_134 _let_133 _let_11 (not _let_146)))) _let_122 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_149)) :args ((or _let_144 _let_24 (not _let_149)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (skv_2 skv_2 QUANTIFIERS_INST_CBQI_PROP)) :args _let_90)) _let_91 :args (_let_149 false _let_5)) :args (_let_144 true _let_24 false _let_149)) _let_143 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_135 1)) (CONG _let_142 (MACRO_SR_PRED_INTRO :args ((= (not _let_133) _let_132))) :args _let_50)) :args ((or _let_132 _let_135))) _let_141 :args (_let_132 true _let_135)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_147 2)) :args ((or _let_146 (not _let_147)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_148)) :args ((or _let_56 _let_54 _let_39 _let_58 _let_147 (not _let_148)))) _let_123 _let_122 _let_101 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (skv_2 skv_3 int_zero skv_2 int_zero skv_7 int_zero QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_114)) _let_113 :args (_let_148 false _let_112)) :args (_let_147 false _let_55 false _let_53 false _let_35 false _let_57 false _let_148)) :args (_let_146 false _let_147)) :args (_let_11 false _let_53 false _let_144 false _let_10 false _let_132 false _let_146)) _let_143 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_14 1)) _let_131 :args (_let_15 true _let_14)) :args (false false _let_11 false _let_10 true _let_8)) :args ((forall ((I $$unsorted) (J $$unsorted)) (= (plus I J) (plus J I))) (forall ((I1 $$unsorted) (J1 $$unsorted) (I2 $$unsorted) (J2 $$unsorted)) (=> (and (int_less I1 J1) (int_leq I2 J2)) (int_leq (plus I1 I2) (plus J1 J2)))) (forall ((I $$unsorted)) (= (int_leq int_one I) (int_less int_zero I))) (int_less int_zero int_one) _let_6 _let_5 _let_4 _let_3 (forall ((I $$unsorted) (J $$unsorted)) (= (or (= J I) (int_less I J)) (int_leq I J))) _let_2 (forall ((I $$unsorted)) (= I (plus I int_zero))) (not (= real_zero real_one)) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.33/10.77 % SZS output end Proof for theBenchmark 10.33/10.77 EOF