0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : do_cvc5 %s %d 0.11/0.32 % Computer : n023.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 04:51:12 EDT 2022 0.11/0.32 % CPUTime : 0.16/0.44 %----Proving TF0_ARI 46.35/46.62 ------- cvc5-tfa casc j11 : /export/starexec/sandbox/benchmark/theBenchmark.p at /export/starexec/sandbox/benchmark/theBenchmark.p... 46.35/46.62 --- Run --finite-model-find --decision=internal at 15... 46.35/46.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... 46.35/46.62 --- Run --no-e-matching --full-saturate-quant at 15... 46.35/46.62 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15... 46.35/46.62 % SZS status Theorem for theBenchmark 46.35/46.62 % SZS output start Proof for theBenchmark 46.35/46.62 (let ((_let_1 (forall ((U regexp1) (U1 regexp1) (V regexp1)) (not (= (concat1 U U1) (star1 V)))))) (let ((_let_2 (forall ((U char2) (V regexp1) (V1 regexp1)) (not (= (char3 U) (concat1 V V1)))))) (let ((_let_3 (forall ((A ty) (L uni)) (<= 0 (length1 A L))))) (let ((_let_4 (forall ((A ty) (L2 uni)) (and (= (infix_plpl A (nil A) L2) L2) (forall ((X uni) (X1 uni)) (= (infix_plpl A (cons A X X1) L2) (cons A X (infix_plpl A X1 L2)))))))) (let ((_let_5 (not (forall ((X regexp1) (X1 regexp1) (Result bool1)) (let ((_let_1 (= Result true1))) (=> (= _let_1 (mem2 (tb2t (nil char1)) X)) (=> _let_1 (forall ((Result1 bool1)) (let ((_let_1 (= Result1 true1))) (let ((_let_2 (tb2t (nil char1)))) (=> (= _let_1 (mem2 _let_2 X1)) (=> (mem2 _let_2 (concat1 X X1)) _let_1)))))))))))) (let ((_let_6 (forall ((U regexp1) (U1 regexp1)) (= (concat_proj_21 (concat1 U U1)) U1)))) (let ((_let_7 (forall ((V regexp1) (V1 regexp1)) (not (= epsilon1 (concat1 V V1)))))) (let ((_let_8 (forall ((J uni)) (= (t2tb (tb2t J)) J)))) (let ((_let_9 (forall ((A ty) (L uni)) (= (= L (nil A)) (= (length1 A L) 0))))) (let ((_let_10 (forall ((I list_char)) (= (tb2t (t2tb I)) I)))) (let ((_let_11 (forall ((A ty) (L1 uni) (L2 uni)) (= (length1 A (infix_plpl A L1 L2)) (+ (length1 A L1) (length1 A L2)))))) (let ((_let_12 (forall ((A ty)) (and (= (length1 A (nil A)) 0) (forall ((X uni) (X1 uni)) (= (length1 A (cons A X X1)) (+ 1 (length1 A X1)))))))) (let ((_let_13 (forall ((U regexp1) (U1 regexp1) (V regexp1) (V1 regexp1)) (not (= (alt1 U U1) (concat1 V V1)))))) (let ((_let_14 (forall ((Z list_char) (Z1 regexp1)) (=> (mem2 Z Z1) (or (and (= Z1 epsilon1) (= Z (tb2t (nil char1)))) (exists ((W list_char) (R1 regexp1) (R2 regexp1)) (and (= Z1 (alt1 R1 R2)) (= Z W) (mem2 W R2))) (exists ((W1 list_char) (W2 list_char) (R1 regexp1) (R2 regexp1)) (and (mem2 W2 R2) (= Z1 (concat1 R1 R2)) (= Z (tb2t (infix_plpl char1 (t2tb W1) (t2tb W2)))) (mem2 W1 R1))) (exists ((W1 list_char) (W2 list_char) (R regexp1)) (let ((_let_1 (star1 R))) (and (= Z (tb2t (infix_plpl char1 (t2tb W1) (t2tb W2)))) (= Z1 _let_1) (mem2 W2 _let_1) (mem2 W1 R)))) (exists ((R regexp1)) (and (= Z1 (star1 R)) (= Z (tb2t (nil char1))))) (exists ((W list_char) (R1 regexp1) (R2 regexp1)) (and (mem2 W R1) (= Z W) (= Z1 (alt1 R1 R2)))) (exists ((C char2)) (and (= Z (tb2t (cons char1 (t2tb1 C) (nil char1)))) (= Z1 (char3 C))))))))) (let ((_let_15 (nil char1))) (let ((_let_16 (tb2t _let_15))) (let ((_let_17 (= (length1 char1 _let_15) 0))) (let ((_let_18 (= _let_15 (t2tb _let_16)))) (let ((_let_19 (t2tb skv_100))) (let ((_let_20 (t2tb skv_99))) (let ((_let_21 (infix_plpl char1 _let_20 _let_19))) (let ((_let_22 (tb2t _let_21))) (let ((_let_23 (= _let_21 (t2tb _let_22)))) (let ((_let_24 (length1 char1 _let_21))) (let ((_let_25 (length1 char1 _let_19))) (let ((_let_26 (length1 char1 _let_20))) (let ((_let_27 (= _let_26 (+ (* (- 1) _let_25) _let_24)))) (let ((_let_28 (= _let_16 _let_22))) (let ((_let_29 (= _let_25 0))) (let ((_let_30 (>= _let_26 0))) (let ((_let_31 (>= _let_25 0))) (let ((_let_32 (forall ((BOUND_VARIABLE_1292 ty)) (= (length1 BOUND_VARIABLE_1292 (nil BOUND_VARIABLE_1292)) 0)))) (let ((_let_33 (0))) (let ((_let_34 (_let_32))) (let ((_let_35 (forall ((J uni)) (= J (t2tb (tb2t J)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (_let_35))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tb2t J)))) :args _let_37)) _let_36 :args (_let_18 false _let_35)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_21 QUANTIFIERS_INST_CBQI_PROP)) :args _let_37)) _let_36 :args (_let_23 false _let_35)))) (let ((_let_40 (forall ((A ty) (L1 uni) (L2 uni)) (= (length1 A L1) (+ (* (- 1) (length1 A L2)) (length1 A (infix_plpl A L1 L2))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (not (mem2 skv_99 skv_101)))) (let ((_let_43 (not _let_28))) (let ((_let_44 (concat1 skv_101 skv_102))) (let ((_let_45 (concat1 skv_82 skv_83))) (let ((_let_46 (= _let_45 _let_44))) (let ((_let_47 (not _let_46))) (let ((_let_48 (mem2 skv_100 skv_102))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47 _let_43 _let_42))) (let ((_let_51 (forall ((W1 list_char) (W2 list_char) (R1 regexp1) (R2 regexp1)) (or (not (mem2 W2 R2)) (not (= (concat1 R1 R2) (concat1 skv_82 skv_83))) (not (= (tb2t (nil char1)) (tb2t (infix_plpl char1 (t2tb W1) (t2tb W2))))) (not (mem2 W1 R1)))))) (let ((_let_52 (not _let_50))) (let ((_let_53 (forall ((C char2)) (let ((_let_1 (nil char1))) (or (not (= (tb2t _let_1) (tb2t (cons char1 (t2tb1 C) _let_1)))) (not (= (char3 C) (concat1 skv_82 skv_83)))))))) (let ((_let_54 (not _let_53))) (let ((_let_55 (forall ((R1 regexp1) (R2 regexp1)) (or (not (mem2 (tb2t (nil char1)) R1)) (not (= (alt1 R1 R2) (concat1 skv_82 skv_83))))))) (let ((_let_56 (not _let_55))) (let ((_let_57 (forall ((R regexp1)) (not (= (star1 R) (concat1 skv_82 skv_83)))))) (let ((_let_58 (not _let_57))) (let ((_let_59 (forall ((W1 list_char) (W2 list_char) (R regexp1)) (let ((_let_1 (star1 R))) (or (not (= (tb2t (nil char1)) (tb2t (infix_plpl char1 (t2tb W1) (t2tb W2))))) (not (= _let_1 (concat1 skv_82 skv_83))) (not (mem2 W2 _let_1)) (not (mem2 W1 R))))))) (let ((_let_60 (not _let_59))) (let ((_let_61 (not _let_51))) (let ((_let_62 (forall ((R1 regexp1) (R2 regexp1)) (or (not (= (alt1 R1 R2) (concat1 skv_82 skv_83))) (not (mem2 (tb2t (nil char1)) R2)))))) (let ((_let_63 (not _let_62))) (let ((_let_64 (= epsilon1 _let_45))) (let ((_let_65 (mem2 _let_16 _let_45))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_66 _let_64 _let_63 _let_61 _let_60 _let_58 _let_56 _let_54))) (let ((_let_68 (forall ((Z list_char) (Z1 regexp1)) (let ((_let_1 (= (tb2t (nil char1)) Z))) (or (not (mem2 Z Z1)) (and (= epsilon1 Z1) _let_1) (not (forall ((R1 regexp1) (R2 regexp1)) (or (not (= Z1 (alt1 R1 R2))) (not (mem2 Z R2))))) (not (forall ((W1 list_char) (W2 list_char) (R1 regexp1) (R2 regexp1)) (or (not (mem2 W2 R2)) (not (= Z1 (concat1 R1 R2))) (not (= Z (tb2t (infix_plpl char1 (t2tb W1) (t2tb W2))))) (not (mem2 W1 R1))))) (not (forall ((W1 list_char) (W2 list_char) (R regexp1)) (let ((_let_1 (star1 R))) (or (not (= Z (tb2t (infix_plpl char1 (t2tb W1) (t2tb W2))))) (not (= Z1 _let_1)) (not (mem2 W2 _let_1)) (not (mem2 W1 R)))))) (and _let_1 (not (forall ((R regexp1)) (not (= Z1 (star1 R)))))) (not (forall ((R1 regexp1) (R2 regexp1)) (or (not (mem2 Z R1)) (not (= Z1 (alt1 R1 R2)))))) (not (forall ((C char2)) (or (not (= Z (tb2t (cons char1 (t2tb1 C) (nil char1))))) (not (= Z1 (char3 C))))))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (char3 skv_141))) (let ((_let_71 (= _let_45 _let_70))) (let ((_let_72 (not _let_71))) (let ((_let_73 (not (= _let_16 (tb2t (cons char1 (t2tb1 skv_141) _let_15)))))) (let ((_let_74 (or _let_73 _let_72))) (let ((_let_75 (forall ((U char2) (V regexp1) (V1 regexp1)) (not (= (concat1 V V1) (char3 U)))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (OR))) (let ((_let_78 (_let_54))) (let ((_let_79 (alt1 skv_139 skv_140))) (let ((_let_80 (= _let_45 _let_79))) (let ((_let_81 (not _let_80))) (let ((_let_82 (not (mem2 _let_16 skv_139)))) (let ((_let_83 (or _let_82 _let_81))) (let ((_let_84 (forall ((U regexp1) (U1 regexp1) (V regexp1) (V1 regexp1)) (not (= (concat1 V V1) (alt1 U U1)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (_let_84))) (let ((_let_87 (_let_56))) (let ((_let_88 (star1 skv_138))) (let ((_let_89 (= _let_45 _let_88))) (let ((_let_90 (forall ((U regexp1) (U1 regexp1) (V regexp1)) (not (= (star1 V) (concat1 U U1)))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (_let_90))) (let ((_let_93 (_let_58))) (let ((_let_94 (not (mem2 skv_135 skv_137)))) (let ((_let_95 (star1 skv_137))) (let ((_let_96 (not (mem2 skv_136 _let_95)))) (let ((_let_97 (= _let_45 _let_95))) (let ((_let_98 (not _let_97))) (let ((_let_99 (not (= _let_16 (tb2t (infix_plpl char1 (t2tb skv_135) (t2tb skv_136))))))) (let ((_let_100 (or _let_99 _let_98 _let_96 _let_94))) (let ((_let_101 (_let_60))) (let ((_let_102 (not (mem2 _let_16 skv_98)))) (let ((_let_103 (alt1 skv_97 skv_98))) (let ((_let_104 (= _let_45 _let_103))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_105 _let_102))) (let ((_let_107 (_let_63))) (let ((_let_108 (_let_7))) (let ((_let_109 (ASSUME :args _let_108))) (let ((_let_110 (= true1 skv_84))) (let ((_let_111 (mem2 _let_16 skv_83))) (let ((_let_112 (not _let_111))) (let ((_let_113 (= _let_112 _let_110))) (let ((_let_114 (or (not (mem2 _let_16 skv_82)) _let_66 _let_113 _let_110))) (let ((_let_115 (forall ((X regexp1) (X1 regexp1) (BOUND_VARIABLE_1501 bool1)) (let ((_let_1 (= true1 BOUND_VARIABLE_1501))) (let ((_let_2 (tb2t (nil char1)))) (or (not (mem2 _let_2 X)) (not (mem2 _let_2 (concat1 X X1))) (= (not (mem2 _let_2 X1)) _let_1) _let_1)))))) (let ((_let_116 (not _let_114))) (let ((_let_117 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_118 (not _let_115))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_117) :args (_let_118))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_118) _let_115))) (REFL :args (_let_116)) :args _let_77)) _let_117 :args (_let_116 true _let_115)))) (let ((_let_120 (_let_61))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_120)) :args _let_120) (REWRITE :args ((=> 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(mem2 W1 R1) (=> (mem2 W2 R2) (mem2 (tb2t (infix_plpl char1 (t2tb W1) (t2tb W2))) (concat1 R1 R2))))) _let_11 (forall ((A ty) (U uni) (U1 uni)) (= (cons_proj_2 A (cons A U U1)) U1)) (forall ((A ty) (Z uni) (Z1 uni) (Z2 uni) (Z3 uni) (Z4 uni) (Z5 uni) (U regexp1) (U1 regexp1)) (=> (sort1 A Z3) (= (match_regexp1 A (alt1 U U1) Z Z1 Z2 Z3 Z4 Z5) Z3))) (forall ((U char2) (V regexp1) (V1 regexp1)) (not (= (char3 U) (alt1 V V1)))) (forall ((A ty) (Z uni) (Z1 uni) (Z2 uni) (Z3 uni) (Z4 uni) (Z5 uni) (U regexp1)) (=> (sort1 A Z5) (= (match_regexp1 A (star1 U) Z Z1 Z2 Z3 Z4 Z5) Z5))) (forall ((A ty) (X uni)) (sort1 A (cons_proj_1 A X))) (forall ((A ty) (X uni)) (=> (sort1 A X) (and (forall ((X1 uni) (X2 uni)) (=> (sort1 A X1) (= (or (= X X1) (mem A X X2)) (mem A X (cons A X1 X2))))) (not (mem A X (nil A)))))) (forall ((A ty) (Z uni) (Z1 uni)) (=> (sort1 A Z) (= (match_bool1 A true1 Z Z1) Z))) (forall ((V regexp1) (V1 regexp1)) (not (= empty1 (alt1 V V1)))) (forall ((X Int) (Y Int) (Z Int)) (=> 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(not (= (char3 U) (star1 V)))) (forall ((U bool1)) (or (= U true1) (= U false1))) _let_7 (forall ((C char2)) (mem2 (tb2t (cons char1 (t2tb1 C) (nil char1))) (char3 C))) (forall ((A ty) (X bool1) (X1 uni) (X2 uni)) (sort1 A (match_bool1 A X X1 X2))) (forall ((A ty) (X regexp1) (X1 uni) (X2 uni) (X3 uni) (X4 uni) (X5 uni) (X6 uni)) (sort1 A (match_regexp1 A X X1 X2 X3 X4 X5 X6))) _let_6 (forall ((A ty) (A1 ty) (X uni) (X1 uni) (X2 uni)) (sort1 A1 (match_list A1 A X X1 X2))) (forall ((V regexp1) (V1 regexp1)) (not (= epsilon1 (alt1 V V1)))) (forall ((A ty) (U uni) (U1 uni)) (=> (sort1 A U) (= (cons_proj_1 A (cons A U U1)) U))) (forall ((R regexp1)) (mem2 (tb2t (nil char1)) (star1 R))) (forall ((J uni)) (=> (sort1 char1 J) (= (t2tb1 (tb2t1 J)) J))) (forall ((V char2)) (not (= epsilon1 (char3 V)))) _let_5 (forall ((U tuple02)) (= U tuple03)) (forall ((A ty) (Z uni) (Z1 uni) (Z2 uni) (Z3 uni) (Z4 uni) (Z5 uni)) (=> (sort1 A Z1) (= (match_regexp1 A epsilon1 Z Z1 Z2 Z3 Z4 Z5) Z1))) _let_4 (forall ((A ty) (Z uni) (Z1 uni)) (=> (sort1 A Z1) (= (match_bool1 A false1 Z Z1) Z1))) (forall ((V regexp1)) (not (= epsilon1 (star1 V)))) (forall ((U regexp1) (U1 regexp1)) (= (alt_proj_11 (alt1 U U1)) U)) (forall ((X char2)) (sort1 char1 (t2tb1 X))) (forall ((U regexp1) (U1 regexp1) (V regexp1)) (not (= (alt1 U U1) (star1 V)))) _let_3 (forall ((A ty) (Z uni) (Z1 uni) (Z2 uni) (Z3 uni) (Z4 uni) (Z5 uni)) (=> (sort1 A Z) (= (match_regexp1 A empty1 Z Z1 Z2 Z3 Z4 Z5) Z))) _let_2 (forall ((A ty) (L1 uni) (L2 uni) (L3 uni)) (= (infix_plpl A L1 (infix_plpl A L2 L3)) (infix_plpl A (infix_plpl A L1 L2) L3))) (forall ((A ty) (X uni) (L1 uni) (L2 uni)) (= (mem A X (infix_plpl A L1 L2)) (or (mem A X L1) (mem A X L2)))) (forall ((A ty) (L uni)) (= (infix_plpl A L (nil A)) L)) _let_1 (forall ((A ty) (V uni) (V1 uni)) (not (= (nil A) (cons A V V1)))) (not (= true1 false1)) (forall ((V regexp1) (V1 regexp1)) (not (= empty1 (concat1 V V1)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 46.35/46.63 % SZS output end Proof for theBenchmark 46.35/46.63 EOF