TSTP Solution File: SWW662_2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW662_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:21:52 EDT 2023
% Result : Theorem 0.65s 0.92s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWW662_2 : TPTP v8.1.2. Released v6.1.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 19:34:11 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_ARI
% 0.65/0.92 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.yXrrBrl3Fc/cvc5---1.0.5_11120.p...
% 0.65/0.92 ------- get file name : TPTP file name is SWW662_2
% 0.65/0.92 ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11120.smt2...
% 0.65/0.92 --- Run --finite-model-find --decision=internal at 15...
% 0.65/0.92 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.65/0.92 % SZS status Theorem for SWW662_2
% 0.65/0.92 % SZS output start Proof for SWW662_2
% 0.65/0.92 (
% 0.65/0.92 (let ((_let_1 (not (forall ((X Int)) (=> (tptp.is_power_of_21 X) (=> (< 1 X) (= (* 2 (tptp.div1 X 2)) X))))))) (let ((_let_2 (forall ((X Int)) (= (tptp.is_power_of_21 X) (exists ((K Int)) (and (<= 0 K) (= X (tptp.power1 2 K)))))))) (let ((_let_3 (forall ((X Int)) (let ((_let_1 (* 2 (tptp.div1 X 2)))) (=> (<= 0 X) (and (<= _let_1 X) (<= (- X 1) _let_1))))))) (let ((_let_4 (forall ((X Int) (N Int)) (=> (< 0 N) (= (tptp.power1 X N) (* X (tptp.power1 X (- N 1)))))))) (let ((_let_5 (forall ((X Int)) (= (tptp.power1 X 0) 1)))) (let ((_let_6 (tptp.div1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 2))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (* 2 _let_6)))) (let ((_let_8 (tptp.power1 2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8))) (let ((_let_10 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (* (- 2) _let_6)))) (let ((_let_11 (>= _let_10 0))) (let ((_let_12 (>= _let_10 2))) (let ((_let_13 (= _let_8 (* 2 (tptp.power1 2 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83)))))) (let ((_let_14 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 2))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.is_power_of_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_7))) (let ((_let_19 (not _let_7))) (let ((_let_20 (forall ((X Int)) (or (not (tptp.is_power_of_21 X)) (not (>= X 2)) (= X (* 2 (tptp.div1 X 2))))))) (let ((_let_21 (not _let_18))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (or))) (let ((_let_24 (not _let_20))) (let ((_let_25 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_22) :args (_let_24))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_20))) (REFL :args (_let_21)) :args _let_23)) _let_22 :args (_let_21 true _let_20)))) (let ((_let_26 (not _let_9))) (let ((_let_27 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 0))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26))) (let ((_let_30 (forall ((K Int)) (or (not (>= K 0)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.power1 2 K))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (not _let_30))) (let ((_let_33 (= _let_16 _let_32))) (let ((_let_34 (forall ((X Int)) (= (tptp.is_power_of_21 X) (not (forall ((K Int)) (or (not (>= K 0)) (not (= X (tptp.power1 2 K)))))))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (REFL :args (_let_18)))) (let ((_let_37 (_let_32))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_37)) :args _let_37)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_30))) (REFL :args (_let_31)) :args _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or _let_17 _let_32 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_23)) :args ((or _let_16 _let_18))) _let_25 :args (_let_16 true _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.is_power_of_21 X)))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_32 false _let_16 false _let_33)) :args (_let_31 true _let_30)))) (let ((_let_39 (REFL :args (_let_29)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_9))) :args _let_23)) :args ((or _let_9 _let_29))) _let_38 :args (_let_9 true _let_29)))) (let ((_let_41 (not _let_12))) (let ((_let_42 (and _let_11 _let_41))) (let ((_let_43 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 0))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42))) (let ((_let_46 (forall ((X Int)) (let ((_let_1 (+ X (* (- 2) (tptp.div1 X 2))))) (or (not (>= X 0)) (and (>= _let_1 0) (not (>= _let_1 2)))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_23)) :args ((or _let_14 _let_18))) _let_25 :args (_let_14 true _let_18)))) (let ((_let_49 (REFL :args (_let_15)))) (let ((_let_50 (> SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (- 1)))) (let ((_let_51 (ASSUME :args (_let_44)))) (let ((_let_52 ((<= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (- 1))))) (let ((_let_53 (false))) (let ((_let_54 (1.0 (- 1.0)))) (let ((_let_55 (ASSUME :args (_let_14)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_42 (not _let_45)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_51 _let_55) :args (_let_14 _let_44)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_52) _let_55 :args _let_54) :args _let_53) :args _let_52) :args (_let_50)) (MACRO_SR_PRED_TRANSFORM (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_51 :args ((< SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 0)))) :args ((not _let_50)))) :args (_let_44 _let_14)) :args ((not (and _let_14 _let_44)) SB_LITERAL))) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_23)) _let_48 :args (_let_43 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.div1 X 2)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_42 false _let_43 false _let_45)))) (let ((_let_57 (not _let_42))) (let ((_let_58 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 1))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_13))) (let ((_let_61 (forall ((X Int) (N Int)) (or (not (>= N 1)) (= (tptp.power1 X N) (* X (tptp.power1 X (+ (- 1) N)))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.power1 2 0))) (let ((_let_64 (= _let_63 1))) (let ((_let_65 (_let_5))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (REFL :args (_let_26)))) (let ((_let_68 (= 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_69 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 1))) (let ((_let_70 (_let_69))) (let ((_let_71 (= 1 _let_63))) (let ((_let_72 (= 0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_73 (ASSUME :args (_let_9)))) (let ((_let_74 (_let_64))) (let ((_let_75 (ASSUME :args _let_74))) (let ((_let_76 ((= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 0)))) (let ((_let_77 (_let_27 _let_59))) (let ((_let_78 (ASSUME :args (_let_59)))) (let ((_let_79 (ASSUME :args (_let_27)))) (let ((_let_80 (not _let_13))) (let ((_let_81 (not _let_11))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_73 (ASSUME :args (_let_41)) (ASSUME :args (_let_19)) (ASSUME :args (_let_11)) (ASSUME :args (_let_13))) :args (_let_19 _let_11 _let_41 _let_9 _let_13)) (THEORY_LEMMA :args ((not (and _let_9 _let_41 _let_19 _let_11 _let_13)) THEORY_ARITH)) :args ((not (and _let_19 _let_11 _let_41 _let_9 _let_13)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_7))) (REFL :args (_let_81)) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_12))) _let_67 (REFL :args (_let_80)) :args _let_23)) :args ((or _let_7 _let_12 _let_81 _let_26 _let_80))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_59 _let_13 (not _let_60)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_73 (MODUS_PONENS (MODUS_PONENS (AND_INTRO _let_79 _let_78) (SCOPE (MACRO_SR_PRED_TRANSFORM (SCOPE (SYMM (ARITH_TRICHOTOMY _let_79 (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_78 :args ((< SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 1)))) :args _let_76)) :args _let_77) (TRUE_INTRO _let_79) (TRUE_INTRO _let_78) :args _let_76) :args _let_77)) (SCOPE (SYMM (ASSUME :args _let_76)) :args _let_76)) (MODUS_PONENS _let_75 (SCOPE (SYMM _let_75) :args _let_74))) (SCOPE (TRANS (SYMM (SYMM (ASSUME :args (_let_71)))) (CONG (REFL :args (2)) (SYMM (SYMM (ASSUME :args (_let_72)))) :args (APPLY_UF tptp.power1)) (SYMM _let_73)) :args (_let_9 _let_72 _let_71))) _let_55) :args (_let_14 _let_27 _let_9 _let_59 _let_64)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_68)) :args _let_70) :args _let_70) (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_70) _let_55 :args _let_54) :args _let_53) :args _let_70) :args ((not _let_69)))) :args (_let_68 _let_14)) :args ((not (and _let_14 _let_27 _let_9 _let_59 _let_64)) SB_LITERAL))) (CONG _let_49 (REFL :args (_let_28)) _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_58))) (REFL :args ((not _let_64))) :args _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.power1 X 0) 1))))) :args _let_65)) _let_66 :args (_let_64 false _let_5)) _let_40 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_23)) :args ((or _let_27 _let_29))) _let_38 :args (_let_27 true _let_29)) _let_48 :args (_let_58 false _let_64 false _let_9 false _let_27 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.power1 X N)))) :args (_let_61)))) _let_62 :args (_let_60 false _let_61)) :args (_let_13 false _let_58 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 1)) :args ((or _let_41 _let_57))) _let_56 :args (_let_41 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 0)) :args ((or _let_11 _let_57))) _let_56 :args (_let_11 false _let_42)) _let_40 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_18 2)) _let_25 :args (_let_19 true _let_18)) :args (false false _let_13 true _let_12 false _let_11 false _let_9 true _let_7)) :args ((forall ((A tptp.ty)) (tptp.sort1 A (tptp.witness1 A))) (forall ((A tptp.ty) (X tptp.bool1) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A (tptp.match_bool1 A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z) (= (tptp.match_bool1 A tptp.true1 Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z1) (= (tptp.match_bool1 A tptp.false1 Z Z1) Z1))) (not (= tptp.true1 tptp.false1)) (forall ((U tptp.bool1)) (or (= U tptp.true1) (= U tptp.false1))) (forall ((U tptp.tuple02)) (= U tptp.tuple03)) (forall ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))) (forall ((X Int)) (let ((_let_1 (tptp.abs1 X))) (let ((_let_2 (<= 0 X))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (- X))))))) (forall ((X Int) (Y Int)) (= (<= (tptp.abs1 X) Y) (and (<= (- Y) X) (<= X Y)))) (forall ((X Int)) (<= 0 (tptp.abs1 X))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (= X (+ (* Y (tptp.div1 X Y)) (tptp.mod1 X Y))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.div1 X Y))) (=> (and (<= 0 X) (< 0 Y)) (and (<= 0 _let_1) (<= _let_1 X))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.abs1 Y))) (let ((_let_2 (tptp.mod1 X Y))) (=> (not (= Y 0)) (and (< (- _let_1) _let_2) (< _let_2 _let_1)))))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< 0 Y)) (<= 0 (tptp.div1 X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (< 0 Y)) (<= (tptp.div1 X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (not (= Y 0))) (<= 0 (tptp.mod1 X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (not (= Y 0))) (<= (tptp.mod1 X Y) 0))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (<= (tptp.abs1 (* (tptp.div1 X Y) Y)) (tptp.abs1 X)))) (forall ((X Int)) (= (tptp.div1 X 1) X)) (forall ((X Int)) (= (tptp.mod1 X 1) 0)) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.div1 X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.mod1 X Y) X))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.div1 (+ (* X Y) Z) X) (+ Y (tptp.div1 Z X))))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.mod1 (+ (* X Y) Z) X) (tptp.mod1 Z X)))) _let_5 (forall ((X Int) (N Int)) (=> (<= 0 N) (= (tptp.power1 X (+ N 1)) (* X (tptp.power1 X N))))) _let_4 (forall ((X Int)) (= (tptp.power1 X 1) X)) (forall ((X Int) (N Int) (M Int)) (=> (<= 0 N) (=> (<= 0 M) (= (tptp.power1 X (+ N M)) (* (tptp.power1 X N) (tptp.power1 X M)))))) (forall ((X Int) (N Int) (M Int)) (=> (<= 0 N) (=> (<= 0 M) (= (tptp.power1 X (* N M)) (tptp.power1 (tptp.power1 X N) M))))) (forall ((X Int) (Y Int) (N Int)) (=> (<= 0 N) (= (tptp.power1 (* X Y) N) (* (tptp.power1 X N) (tptp.power1 Y N))))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 B (tptp.get B A X X1))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.set B A X X1 X2))) (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A1 tptp.uni) (A2 tptp.uni) (B1 tptp.uni)) (=> (tptp.sort1 B B1) (=> (= A1 A2) (= (tptp.get B A (tptp.set B A M A1 B1) A2) B1)))) (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A1 tptp.uni) (A2 tptp.uni)) (=> (tptp.sort1 A A1) (=> (tptp.sort1 A A2) (forall ((B1 tptp.uni)) (=> (not (= A1 A2)) (= (tptp.get B A (tptp.set B A M A1 B1) A2) (tptp.get B A M A2))))))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.const B A X))) (forall ((A tptp.ty) (B tptp.ty) (B1 tptp.uni) (A1 tptp.uni)) (=> (tptp.sort1 B B1) (= (tptp.get B A (tptp.const B A B1) A1) B1))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.mk_array1 A X X1))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length1 A (tptp.mk_array1 A U U1)) U)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map tptp.int A) (tptp.elts A X))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (=> (tptp.sort1 (tptp.map tptp.int A) U1) (= (tptp.elts A (tptp.mk_array1 A U U1)) U1))) (forall ((A tptp.ty) (U tptp.uni)) (= U (tptp.mk_array1 A (tptp.length1 A U) (tptp.elts A U)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int)) (tptp.sort1 A (tptp.get2 A X X1))) (forall ((X Int)) (tptp.sort1 tptp.int (tptp.t2tb X))) (forall ((I Int)) (= (tptp.tb2t (tptp.t2tb I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb (tptp.tb2t J)) J)) (forall ((A tptp.ty) (A1 tptp.uni) (I Int)) (= (tptp.get2 A A1 I) (tptp.get A tptp.int (tptp.elts A A1) (tptp.t2tb I)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int) (X2 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.set2 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.uni) (I Int) (V tptp.uni)) (= (tptp.set2 A A1 I V) (tptp.mk_array1 A (tptp.length1 A A1) (tptp.set A tptp.int (tptp.elts A A1) (tptp.t2tb I) V)))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.make1 A X X1))) (forall ((A tptp.ty) (N Int) (V tptp.uni)) (= (tptp.make1 A N V) (tptp.mk_array1 A N (tptp.const A tptp.int V)))) (forall ((C tptp.map_int_int) (I Int) (J Int)) (=> (<= J I) (= (tptp.sum2 C I J) 0))) (forall ((X tptp.map_int_int)) (tptp.sort1 (tptp.map tptp.int tptp.int) (tptp.t2tb1 X))) (forall ((I tptp.map_int_int)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb1 (tptp.tb2t1 J)) J)) (forall ((C tptp.map_int_int) (I Int) (J Int)) (=> (< I J) (= (tptp.sum2 C I J) (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C) (tptp.t2tb I))) (tptp.sum2 C (+ I 1) J))))) (forall ((C tptp.map_int_int) (I Int) (J Int)) (let ((_let_1 (- J 1))) (=> (< I J) (= (tptp.sum2 C I J) (+ (tptp.sum2 C I _let_1) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C) (tptp.t2tb _let_1)))))))) (forall ((C tptp.map_int_int) (I Int) (K Int) (J Int)) (=> (and (<= I K) (<= K J)) (= (tptp.sum2 C I J) (+ (tptp.sum2 C I K) (tptp.sum2 C K J))))) (forall ((C1 tptp.map_int_int) (C2 tptp.map_int_int) (I Int) (J Int)) (=> (forall ((K Int)) (let ((_let_1 (tptp.t2tb K))) (=> (and (<= I K) (< K J)) (= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C1) _let_1)) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C2) _let_1)))))) (= (tptp.sum2 C1 I J) (tptp.sum2 C2 I J)))) (forall ((X tptp.array_int)) (tptp.sort1 (tptp.array tptp.int) (tptp.t2tb2 X))) (forall ((I tptp.array_int)) (= (tptp.tb2t2 (tptp.t2tb2 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)) (forall ((A tptp.array_int) (L Int) (H Int)) (= (tptp.sum3 A L H) (tptp.sum2 (tptp.tb2t1 (tptp.elts tptp.int (tptp.t2tb2 A))) L H))) _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.65/0.92 )
% 0.65/0.92 % SZS output end Proof for SWW662_2
% 0.65/0.92 % cvc5---1.0.5 exiting
% 0.65/0.93 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------