0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : do_cvc5 %s %d 0.13/0.33 % Computer : n016.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 960 0.13/0.33 % WCLimit : 120 0.13/0.33 % DateTime : Tue Aug 9 05:26:12 EDT 2022 0.13/0.33 % CPUTime : 0.19/0.47 %----Proving TF0_ARI 31.96/32.23 ------- cvc5-tfa casc j11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 31.96/32.23 --- Run --finite-model-find --decision=internal at 15... 31.96/32.23 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... 31.96/32.23 --- Run --no-e-matching --full-saturate-quant at 15... 31.96/32.23 % SZS status Theorem for theBenchmark 31.96/32.23 % SZS output start Proof for theBenchmark 31.96/32.23 (let ((_let_1 (not (forall ((Left Int) (Right Int) (A0 Int) (A01 map_int_int) (A Int) (A1 map_int_int)) (let ((_let_1 (- Right Left))) (let ((_let_2 (- Left _let_1))) (let ((_let_3 (+ _let_2 1))) (let ((_let_4 (t2tb1 A1))) (let ((_let_5 (= (tb2t (get int int _let_4 (t2tb Right))) (sum2 A01 0 _let_3)))) (let ((_let_6 (< Right A))) (=> (and (<= 0 A0) (<= 0 A) (< Left Right) _let_6 (<= (- 1) _let_2) _let_5 (phase11 Left Right (tb2t2 (mk_array1 int A0 (t2tb1 A01))) (tb2t2 (mk_array1 int A _let_4))) (is_power_of_21 _let_1) (<= 0 Left)) (=> (and _let_6 (<= 0 Right)) (=> _let_5 (= (tb2t (get int int _let_4 (t2tb Left))) (sum2 A01 _let_3 (+ Left 1)))))))))))))))) (let ((_let_2 (forall ((A ty) (U Int) (U1 uni)) (=> (sort1 (map int A) U1) (= (elts A (mk_array1 A U U1)) U1))))) (let ((_let_3 (forall ((J uni)) (= (t2tb2 (tb2t2 J)) J)))) (let ((_let_4 (forall ((I map_int_int)) (= (tb2t1 (t2tb1 I)) I)))) (let ((_let_5 (forall ((X map_int_int)) (sort1 (map int int) (t2tb1 X))))) (let ((_let_6 (forall ((A ty) (A1 uni) (I Int)) (= (get2 A A1 I) (get A int (elts A A1) (t2tb I)))))) (let ((_let_7 (forall ((Z Int) (Z1 Int) (Z2 array_int) (Z3 array_int)) (=> (phase11 Z Z1 Z2 Z3) (or (exists ((Left Int) (Right Int) (A0 array_int) (A array_int)) (let ((_let_1 (+ Left 1))) (and (< _let_1 Right) (phase11 (go_left1 Left Right) Left A0 A) (phase11 (go_right1 Left Right) Right A0 A) (= Z1 Right) (= Z2 A0) (= Z3 A) (= Z Left) (= (tb2t (get2 int (t2tb2 A) Left)) (sum3 A0 (+ (- Left (- Right Left)) 1) _let_1))))) (exists ((Left Int) (A0 array_int) (A array_int)) (and (= Z Left) (= Z1 (+ Left 1)) (= Z3 A) (= Z2 A0) (= (tb2t (get2 int (t2tb2 A) Left)) (tb2t (get2 int (t2tb2 A0) Left)))))))))) (let ((_let_8 (forall ((A array_int) (L Int) (H Int)) (= (sum3 A L H) (sum2 (tb2t1 (elts int (t2tb2 A))) L H))))) (let ((_let_9 (forall ((C map_int_int) (I Int) (K Int) (J Int)) (=> (and (<= I K) (<= K J)) (= (sum2 C I J) (+ (sum2 C I K) (sum2 C K J))))))) (let ((_let_10 (forall ((C map_int_int) (I Int) (J Int)) (=> (< I J) (= (sum2 C I J) (+ (tb2t (get int int (t2tb1 C) (t2tb I))) (sum2 C (+ I 1) J))))))) (let ((_let_11 (forall ((C map_int_int) (I Int) (J Int)) (let ((_let_1 (- J 1))) (=> (< I J) (= (sum2 C I J) (+ (sum2 C I _let_1) (tb2t (get int int (t2tb1 C) (t2tb _let_1)))))))))) (let ((_let_12 (t2tb skv_3))) (let ((_let_13 (t2tb1 skv_8))) (let ((_let_14 (tb2t (get int int _let_13 _let_12)))) (let ((_let_15 (+ 1 skv_3))) (let ((_let_16 (* (- 1) skv_4))) (let ((_let_17 (* 2 skv_3))) (let ((_let_18 (+ 1 _let_17 _let_16))) (let ((_let_19 (sum2 skv_6 _let_18 _let_15))) (let ((_let_20 (= _let_19 _let_14))) (let ((_let_21 (t2tb1 skv_6))) (let ((_let_22 (= skv_6 (tb2t1 _let_21)))) (let ((_let_23 (mk_array1 int skv_5 _let_21))) (let ((_let_24 (tb2t2 _let_23))) (let ((_let_25 (t2tb2 _let_24))) (let ((_let_26 (= _let_23 _let_25))) (let ((_let_27 (= _let_21 (elts int _let_23)))) (let ((_let_28 (+ (- 1) skv_4))) (let ((_let_29 (tb2t (get int int _let_21 (t2tb _let_28))))) (let ((_let_30 (sum2 skv_6 skv_3 _let_28))) (let ((_let_31 (+ _let_30 _let_29))) (let ((_let_32 (= (sum2 skv_6 skv_3 skv_4) _let_31))) (let ((_let_33 (sum2 skv_8 _let_15 skv_4))) (let ((_let_34 (sum2 skv_8 skv_3 skv_4))) (let ((_let_35 (+ _let_34 (* (- 1) _let_33)))) (let ((_let_36 (= _let_14 _let_35))) (let ((_let_37 (= skv_3 _let_28))) (let ((_let_38 (* (- 1) _let_34))) (let ((_let_39 (+ _let_30 _let_29 _let_38 _let_33))) (let ((_let_40 (>= _let_39 1))) (let ((_let_41 (>= _let_39 0))) (let ((_let_42 (not (>= skv_4 0)))) (let ((_let_43 (not (>= skv_3 0)))) (let ((_let_44 (not (is_power_of_21 (+ (* (- 1) skv_3) skv_4))))) (let ((_let_45 (mk_array1 int skv_7 _let_13))) (let ((_let_46 (tb2t2 _let_45))) (let ((_let_47 (phase11 skv_3 skv_4 _let_24 _let_46))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tb2t (get int int _let_13 (t2tb skv_4))))) (let ((_let_50 (sum2 skv_6 0 _let_18))) (let ((_let_51 (not (>= (+ _let_17 _let_16) (- 1))))) (let ((_let_52 (>= (+ skv_4 (* (- 1) skv_7)) 0))) (let ((_let_53 (+ skv_3 _let_16))) (let ((_let_54 (>= _let_53 0))) (let ((_let_55 (not (>= skv_7 0)))) (let ((_let_56 (not (>= skv_5 0)))) (let ((_let_57 (or _let_56 _let_55 _let_54 _let_52 _let_51 (not (= _let_50 _let_49)) _let_48 _let_44 _let_43 _let_42 _let_20))) (let ((_let_58 (not _let_20))) (let ((_let_59 (forall ((Left Int) (Right Int) (A0 Int) (A01 map_int_int) (A Int) (A1 map_int_int)) (let ((_let_1 (* (- 1) Right))) (let ((_let_2 (* 2 Left))) (let ((_let_3 (+ 1 _let_2 _let_1))) (let ((_let_4 (t2tb1 A1))) (or (not (>= A0 0)) (not (>= A 0)) (>= (+ Left _let_1) 0) (>= (+ Right (* (- 1) A)) 0) (not (>= (+ _let_2 _let_1) (- 1))) (not (= (tb2t (get int int _let_4 (t2tb Right))) (sum2 A01 0 _let_3))) (not (phase11 Left Right (tb2t2 (mk_array1 int A0 (t2tb1 A01))) (tb2t2 (mk_array1 int A _let_4)))) (not (is_power_of_21 (+ (* (- 1) Left) Right))) (not (>= Left 0)) (not (>= Right 0)) (= (tb2t (get int int _let_4 (t2tb Left))) (sum2 A01 _let_3 (+ 1 Left))))))))))) (let ((_let_60 (not _let_57))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (OR))) (let ((_let_63 (not _let_59))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_61) :args (_let_63)) (REWRITE :args ((=> _let_63 (not (or _let_56 _let_55 _let_54 _let_52 _let_51 (not (= _let_49 _let_50)) _let_48 _let_44 _let_43 _let_42 (= _let_14 _let_19)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_59))) (REFL :args (_let_60)) :args _let_62)) _let_61 :args (_let_60 true _let_59)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_57 10)) _let_64 :args (_let_58 true _let_57)))) (let ((_let_66 (forall ((I map_int_int)) (= I (tb2t1 (t2tb1 I)))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (skv_6 QUANTIFIERS_INST_ENUM))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args _let_68) :args (_let_66))) _let_67 :args (_let_22 false _let_66)))) (let ((_let_70 (forall ((J uni)) (= J (t2tb2 (tb2t2 J)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_70))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_23 QUANTIFIERS_INST_ENUM)) :args _let_72)) _let_71 :args (_let_26 false _let_70)))) (let ((_let_74 (map int int))) (let ((_let_75 (sort1 _let_74 _let_21))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_76 _let_27))) (let ((_let_78 (forall ((A ty) (U Int) (U1 uni)) (or (not (sort1 (map int A) U1)) (= U1 (elts A (mk_array1 A U U1))))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 (_let_5))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_76 _let_27 (not 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_let_99))) (let ((_let_101 (or _let_48 _let_100 _let_97))) (let ((_let_102 (forall ((Z Int) (Z1 Int) (Z2 array_int) (Z3 array_int)) (let ((_let_1 (tb2t (get2 int (t2tb2 Z3) Z)))) (let ((_let_2 (* (- 1) Z1))) (or (not (phase11 Z Z1 Z2 Z3)) (and (not (>= (+ Z _let_2) (- 1))) (phase11 (go_left1 Z Z1) Z Z2 Z3) (phase11 (go_right1 Z Z1) Z1 Z2 Z3) (= _let_1 (sum3 Z2 (+ 1 (* 2 Z) _let_2) (+ 1 Z)))) (and (= Z (+ (- 1) Z1)) (= _let_1 (tb2t (get2 int (t2tb2 Z2) Z)))))))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (not _let_100))) (let ((_let_105 (= _let_45 _let_92))) (let ((_let_106 (elts int _let_25))) (let ((_let_107 (tb2t1 _let_106))) (let ((_let_108 (= _let_98 (sum2 _let_107 _let_18 _let_15)))) (let ((_let_109 (= _let_13 (elts int _let_45)))) (let ((_let_110 (= _let_93 (get int int (elts int _let_92) _let_12)))) (let ((_let_111 (not _let_99))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_45 QUANTIFIERS_INST_ENUM)) :args _let_72)) _let_71 :args (_let_105 false _let_70)))) (let ((_let_113 (forall ((A array_int) (L Int) (H Int)) (= (sum2 (tb2t1 (elts int (t2tb2 A))) L H) (sum3 A L H))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (sort1 _let_74 _let_13))) (let ((_let_116 (not _let_115))) (let ((_let_117 (or _let_116 _let_109))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_116 _let_109 (not _let_117)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (skv_8 QUANTIFIERS_INST_ENUM)) :args _let_81)) _let_82 :args (_let_115 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (int skv_7 _let_13 QUANTIFIERS_INST_CBQI_PROP)) :args _let_80)) _let_79 :args (_let_117 false _let_78)) :args (_let_109 false _let_115 false _let_117)))) (let ((_let_119 (forall ((A ty) (A1 uni) (I Int)) (= (get A int (elts A A1) (t2tb I)) (get2 A A1 I))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (_let_119))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_120 :args (int _let_92 skv_3 QUANTIFIERS_INST_CBQI_PROP)) :args _let_121))) _let_120 :args (_let_110 false _let_119)))) (let ((_let_123 (not _let_110))) (let ((_let_124 (not _let_109))) (let ((_let_125 (not _let_108))) (let ((_let_126 (not _let_105))) (let ((_let_127 (not _let_27))) (let ((_let_128 (not _let_26))) (let ((_let_129 (not _let_22))) (let ((_let_130 (REFL :args (_let_127)))) (let ((_let_131 (REFL :args (_let_128)))) (let ((_let_132 (REFL :args (_let_129)))) (let ((_let_133 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_20))))) (let ((_let_134 (and _let_58 _let_22 _let_26 _let_27 _let_105 _let_108 _let_109 _let_110))) (let ((_let_135 (ASSUME :args 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(CONG _let_146 _let_157 :args _let_143) _let_155))) (let ((_let_159 (TRANS (CONG _let_158 :args (APPLY_UF tb2t1)) (SYMM _let_153)))) (let ((_let_160 (ASSUME :args (_let_108)))) (let ((_let_161 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_48 _let_100 _let_97 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 6)) (CONG (REFL :args (_let_57)) (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_62)) :args ((or _let_47 _let_57))) _let_64 :args (_let_47 true _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_100 3)) :args ((or _let_99 _let_104))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_134)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_153 _let_154 _let_156 _let_160 _let_135 _let_141 _let_144 _let_147) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (TRANS (SYMM (SYMM _let_160)) (CONG _let_159 _let_152 _let_151 :args _let_150)) _let_149 :args _let_137) _let_136) :args ((= _let_99 false)))) :args (_let_22 _let_27 _let_26 _let_108 _let_58 _let_109 _let_105 _let_110))) :args (_let_58 _let_22 _let_26 _let_27 _let_105 _let_108 _let_109 _let_110))) :args (true _let_134)) (CONG _let_133 _let_132 _let_131 _let_130 (REFL :args (_let_126)) (REFL :args (_let_125)) (REFL :args (_let_124)) (REFL :args (_let_123)) (REFL :args (_let_111)) :args _let_62)) :args ((or _let_20 _let_129 _let_128 _let_127 _let_126 _let_125 _let_111 _let_124 _let_123))) _let_122 _let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (_let_24 _let_18 _let_15 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_113)))) _let_114 :args (_let_108 false _let_113)) _let_112 _let_83 _let_73 _let_69 _let_65 :args (_let_111 false _let_110 false _let_109 false _let_108 false _let_105 false _let_27 false _let_26 false _let_22 true _let_20)) :args (_let_104 true _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM 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(forall ((A ty) (B ty) (M uni) (A1 uni) (A2 uni)) (=> (sort1 A A1) (=> (sort1 A A2) (forall ((B1 uni)) (=> (not (= A1 A2)) (= (get B A (set B A M A1 B1) A2) (get B A M A2))))))) (forall ((X Int)) (=> (is_power_of_21 X) (=> (< 1 X) (= (* 2 (div1 X 2)) X)))) (forall ((X Int) (N Int)) (=> (<= 0 N) (= (power1 X (+ N 1)) (* X (power1 X N))))) (forall ((Left Int) (Right Int) (A0 array_int) (A0qt array_int) (A array_int)) (=> (and (<= 0 (length1 int (t2tb2 A0qt))) (<= 0 (length1 int (t2tb2 A))) (forall ((I Int)) (=> (and (< I Right) (< (- Left (- Right Left)) I)) (= (tb2t (get2 int (t2tb2 A0) I)) (tb2t (get2 int (t2tb2 A0qt) I))))) (phase11 Left Right A0 A) (<= 0 (length1 int (t2tb2 A0)))) (phase11 Left Right A0qt A))) (forall ((A ty) (X uni) (X1 Int) (X2 uni)) (sort1 (array A) (set2 A X X1 X2))) (forall ((X Int) (Y Int)) (=> (and (not (= Y 0)) (<= X 0)) (<= (mod1 X Y) 0))) (forall ((J uni)) (= (t2tb (tb2t J)) J)) (forall ((Left Int) (Right Int) (A0 array_int) (A array_int)) (= (forall ((I 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