0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : do_cvc5 %s %d 0.13/0.33 % Computer : n015.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 05:43:41 EDT 2022 0.13/0.33 % CPUTime : 0.18/0.47 %----Proving TF0_ARI 47.31/47.51 ------- cvc5-tfa casc j11 : /export/starexec/sandbox/benchmark/theBenchmark.p at /export/starexec/sandbox/benchmark/theBenchmark.p... 47.31/47.51 --- Run --finite-model-find --decision=internal at 15... 47.31/47.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... 47.31/47.51 --- Run --no-e-matching --full-saturate-quant at 15... 47.31/47.51 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15... 47.31/47.51 % SZS status Theorem for theBenchmark 47.31/47.51 % SZS output start Proof for theBenchmark 47.31/47.51 (let ((_let_1 (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))))) (let ((_let_2 (forall ((A ty) (N Int) (X uni) (L uni)) (=> (< 0 N) (= (prefix A N (cons A X L)) (cons A X (prefix A (- N 1) L))))))) (let ((_let_3 (not (forall ((N Int) (L list_elt)) (=> (and (<= 2 N) (<= N (length elt1 (t2tb L)))) (=> (not (= N 2)) (=> (= N 3) (forall ((X elt) (X1 list_elt)) (=> (= L (tb2t (cons elt1 (t2tb1 X) (t2tb X1)))) (forall ((X2 elt) (X3 list_elt)) (=> (= X1 (tb2t (cons elt1 (t2tb1 X2) (t2tb X3)))) (forall ((X4 elt) (X5 list_elt)) (let ((_let_1 (prefix elt1 N (t2tb L)))) (let ((_let_2 (cons elt1 (t2tb1 X) (nil elt1)))) (let ((_let_3 (t2tb1 X4))) (let ((_let_4 (t2tb1 X2))) (let ((_let_5 (le X2 X4))) (=> (= X3 (tb2t (cons elt1 _let_3 (t2tb X5)))) (=> (not (le X X2)) (=> (not (le X X4)) (and (=> (not _let_5) (permut elt1 (cons elt1 _let_3 (cons elt1 _let_4 _let_2)) _let_1)) (=> _let_5 (permut elt1 (cons elt1 _let_4 (cons elt1 _let_3 _let_2)) _let_1))))))))))))))))))))))) (let ((_let_4 (forall ((A ty) (L1 uni) (L2 uni)) (permut A (infix_plpl A L1 L2) (infix_plpl A L2 L1))))) (let ((_let_5 (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_6 (forall ((A ty) (X uni) (Y uni) (L uni)) (permut A (cons A X (cons A Y L)) (cons A Y (cons A X L)))))) (let ((_let_7 (nil elt1))) (let ((_let_8 (forall ((J uni)) (= (t2tb (tb2t J)) J)))) (let ((_let_9 (forall ((A ty) (L uni)) (= (prefix A 0 L) (nil A))))) (let ((_let_10 (forall ((A ty)) (let ((_let_1 (nil A))) (and (forall ((X uni) (X1 uni)) (= (reverse A (cons A X X1)) (infix_plpl A (reverse A X1) (cons A X (nil A))))) (= (reverse A _let_1) _let_1)))))) (let ((_let_11 (forall ((A ty) (L1 uni) (L2 uni)) (let ((_let_1 (permut A L1 L2))) (and (=> (forall ((X uni)) (=> (sort A X) (= (num_occ A X L1) (num_occ A X L2)))) _let_1) (=> _let_1 (forall ((X uni)) (= (num_occ A X L1) (num_occ A X L2))))))))) (let ((_let_12 (t2tb1 skv_117))) (let ((_let_13 (cons elt1 _let_12 _let_7))) (let ((_let_14 (t2tb1 skv_116))) (let ((_let_15 (t2tb1 skv_114))) (let ((_let_16 (cons elt1 _let_15 (cons elt1 _let_14 _let_13)))) (let ((_let_17 (num_occ elt1 skv_126 _let_16))) (let ((_let_18 (cons elt1 _let_15 _let_13))) (let ((_let_19 (cons elt1 _let_14 _let_18))) (let ((_let_20 (num_occ elt1 skv_126 _let_19))) (let ((_let_21 (= _let_20 _let_17))) (let ((_let_22 (t2tb skv_115))) (let ((_let_23 (cons elt1 _let_14 _let_22))) (let ((_let_24 (t2tb (tb2t _let_23)))) (let ((_let_25 (cons elt1 _let_15 _let_24))) (let ((_let_26 (t2tb (tb2t _let_25)))) (let ((_let_27 (cons elt1 _let_12 _let_26))) (let ((_let_28 (t2tb (tb2t _let_27)))) (let ((_let_29 (prefix elt1 3 _let_28))) (let ((_let_30 (num_occ elt1 skv_126 _let_29))) (let ((_let_31 (= _let_30 _let_20))) (let ((_let_32 (= _let_30 _let_17))) (let ((_let_33 (permut elt1 _let_16 _let_19))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_21))) (let ((_let_36 (forall ((BOUND_VARIABLE_1613 ty) (BOUND_VARIABLE_1615 uni) (BOUND_VARIABLE_1617 uni) (BOUND_VARIABLE_1629 uni)) (or (not (permut BOUND_VARIABLE_1613 BOUND_VARIABLE_1615 BOUND_VARIABLE_1617)) (= (num_occ BOUND_VARIABLE_1613 BOUND_VARIABLE_1629 BOUND_VARIABLE_1617) (num_occ BOUND_VARIABLE_1613 BOUND_VARIABLE_1629 BOUND_VARIABLE_1615)))))) (let ((_let_37 (1))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (AND_ELIM _let_38 :args _let_37))) (let ((_let_40 (_let_36))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (_let_6))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 (or (not (sort elt1 skv_126)) _let_31))) (let ((_let_45 (not _let_31))) (let ((_let_46 (forall ((X uni)) (let ((_let_1 (t2tb1 skv_117))) (let ((_let_2 (t2tb1 skv_114))) (let ((_let_3 (t2tb1 skv_116))) (or (not (sort elt1 X)) (= 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((_let_77 (= (infix_plpl elt1 _let_76 _let_62) _let_67))) (let ((_let_78 (= (prefix elt1 2 _let_25) (cons elt1 _let_15 (prefix elt1 1 _let_24))))) (let ((_let_79 (= (cons elt1 _let_12 _let_74) (infix_plpl elt1 _let_13 _let_65)))) (let ((_let_80 (reverse elt1 _let_7))) (let ((_let_81 (infix_plpl elt1 _let_80 _let_13))) (let ((_let_82 (= (cons elt1 _let_14 _let_81) (infix_plpl elt1 (cons elt1 _let_14 _let_80) _let_13)))) (let ((_let_83 (= _let_13 (infix_plpl elt1 _let_7 _let_13)))) (let ((_let_84 (= (prefix elt1 3 _let_27) (cons elt1 _let_12 (prefix elt1 2 _let_26))))) (let ((_let_85 (= _let_7 _let_80))) (let ((_let_86 (= _let_61 _let_81))) (let ((_let_87 (= _let_76 (reverse elt1 _let_18)))) (let ((_let_88 (= _let_27 _let_28))) (let ((_let_89 (= _let_25 _let_26))) (let ((_let_90 (= _let_23 _let_24))) (let ((_let_91 (forall ((A ty) (L uni)) (= (nil A) (prefix A 0 L))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let 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X (prefix A (+ (- 1) N) L))))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (_let_100))) (let ((_let_103 ((prefix A N (cons A X L))))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_101 :args (elt1 1 _let_14 _let_22 QUANTIFIERS_INST_E_MATCHING _let_103)) :args _let_102))) _let_101 :args (_let_64 false _let_100)))) (let ((_let_105 (_let_4))) (let ((_let_106 (ASSUME :args _let_105))) (let ((_let_107 ((infix_plpl BOUND_VARIABLE_2217 (cons BOUND_VARIABLE_2217 X X1) BOUND_VARIABLE_2219)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (elt1 _let_62 _let_12 _let_65 QUANTIFIERS_INST_E_MATCHING _let_107)) :args _let_97)) _let_96 :args (_let_70 false _let_94)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_98 :args (elt1 _let_62 _let_15 _let_7 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((A ty) (X uni) (L1 uni) (L2 uni)) (permut A (infix_plpl A (cons A X L1) L2) (infix_plpl A L1 (cons A X L2)))) (forall ((A ty) (L1 uni) (L2 uni) (L3 uni)) (=> (permut A L1 L2) (=> (permut A L2 L3) (permut A L1 L3)))) (forall ((A ty) (X uni) (L1 uni) (L2 uni)) (= (num_occ A X (infix_plpl A L1 L2)) (+ (num_occ A X L1) (num_occ A X L2)))) _let_3 (forall ((A ty) (L uni)) (= (= (length A L) 0) (= L (nil A)))) (forall ((A ty) (R uni) (S uni) (T uni)) (= (rev_append A (infix_plpl A R S) T) (rev_append A S (rev_append A R T)))) (forall ((X elt) (Y elt)) (or (le Y X) (le X Y))) (forall ((A ty) (X uni)) (sort (list A) (cons_proj_2 A X))) (forall ((A ty) (L uni)) (= (reverse A (reverse A L)) L)) (forall ((X Int) (Y Int)) (=> (and (not (= Y 0)) (<= 0 X)) (<= 0 (mod X Y)))) _let_2 (forall ((A ty) (X uni) (X1 uni)) (sort (list A) (rev_append A X X1))) (forall ((J uni)) (=> (sort elt1 J) (= (t2tb1 (tb2t1 J)) J))) (forall ((A ty) (X uni) (L1 uni) (L2 uni)) (=> (permut A L1 L2) (=> (mem A X L1) (mem A X L2)))) (forall ((X Int) (Y Int)) (let ((_let_1 (mod X Y))) (let ((_let_2 (abs Y))) (=> (not (= Y 0)) (and (< _let_1 _let_2) (< (- _let_2) _let_1)))))) (forall ((A ty) (L1 uni) (L2 uni) (X uni)) (= (infix_plpl A (reverse A (cons A X L1)) L2) (infix_plpl A (reverse A L1) (cons A X L2)))) (forall ((A ty) (U uni)) (or (= U (nil A)) (= U (cons A (cons_proj_1 A U) (cons_proj_2 A U))))) (forall ((A ty) (X Int) (X1 uni)) (sort (list A) (prefix A X X1))) _let_1 (forall ((A ty) (Z uni) (Z1 uni)) (=> (sort A Z1) (= (match_bool A false Z Z1) Z1))) (forall ((A ty) (T uni)) (and (= (rev_append A (nil A) T) T) (forall ((X uni) (R uni)) (= (rev_append A (cons A X R) T) (rev_append A R (cons A X T)))))) (forall ((A ty) (X bool) (X1 uni) (X2 uni)) (sort A (match_bool A X X1 X2))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 47.31/47.52 % SZS output end Proof for theBenchmark 47.31/47.52 EOF