TSTP Solution File: SWW664_2 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW664_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 60.82s 61.16s
% Output : Proof 60.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW664_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.19/0.36 % Computer : n001.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Sun Aug 27 18:34:33 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_ARI
% 60.82/61.16 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.OJd4DJTlxF/cvc5---1.0.5_27372.p...
% 60.82/61.16 ------- get file name : TPTP file name is SWW664_2
% 60.82/61.16 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27372.smt2...
% 60.82/61.16 --- Run --finite-model-find --decision=internal at 15...
% 60.82/61.16 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 60.82/61.16 --- Run --no-e-matching --full-saturate-quant at 15...
% 60.82/61.16 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 60.82/61.16 --- Run --macros-quant --macros-quant-mode=all --nl-ext-tplanes --full-saturate-quant...
% 60.82/61.16 % SZS status Theorem for SWW664_2
% 60.82/61.16 % SZS output start Proof for SWW664_2
% 60.82/61.16 (
% 60.82/61.16 (let ((_let_1 (not (forall ((Left Int) (Right Int) (A0 Int) (A01 tptp.map_int_int) (A Int) (A1 tptp.map_int_int)) (let ((_let_1 (- Right Left))) (let ((_let_2 (- Left _let_1))) (let ((_let_3 (+ _let_2 1))) (let ((_let_4 (tptp.t2tb1 A1))) (let ((_let_5 (= (tptp.tb2t (tptp.get tptp.int tptp.int _let_4 (tptp.t2tb Right))) (tptp.sum2 A01 0 _let_3)))) (let ((_let_6 (< Right A))) (=> (and (<= 0 A0) (<= 0 A) (<= 0 Left) (< Left Right) _let_6 (<= (- 1) _let_2) (tptp.is_power_of_21 _let_1) _let_5 (tptp.phase11 Left Right (tptp.tb2t2 (tptp.mk_array1 tptp.int A0 (tptp.t2tb1 A01))) (tptp.tb2t2 (tptp.mk_array1 tptp.int A _let_4)))) (=> (and (<= 0 Right) _let_6) (=> _let_5 (= (tptp.tb2t (tptp.get tptp.int tptp.int _let_4 (tptp.t2tb Left))) (tptp.sum2 A01 _let_3 (+ Left 1)))))))))))))))) (let ((_let_2 (forall ((Left Int) (Right Int) (A0 tptp.array_int) (A tptp.array_int)) (= (tptp.partial_sum1 Left Right A0 A) (forall ((I Int)) (=> (and (< (- Left (- Right Left)) I) (<= I Right)) (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) I)) (tptp.sum3 A0 0 I)))))))) (let ((_let_3 (forall ((Z Int) (Z1 Int) (Z2 tptp.array_int) (Z3 tptp.array_int)) (=> (tptp.phase11 Z Z1 Z2 Z3) (or (exists ((Left Int) (A0 tptp.array_int) (A tptp.array_int)) (and (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) Left)) (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A0) Left))) (= Z Left) (= Z1 (+ Left 1)) (= Z2 A0) (= Z3 A))) (exists ((Left Int) (Right Int) (A0 tptp.array_int) (A tptp.array_int)) (let ((_let_1 (+ Left 1))) (and (< _let_1 Right) (tptp.phase11 (tptp.go_left1 Left Right) Left A0 A) (tptp.phase11 (tptp.go_right1 Left Right) Right A0 A) (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) Left)) (tptp.sum3 A0 (+ (- Left (- Right Left)) 1) _let_1)) (= Z Left) (= Z1 Right) (= Z2 A0) (= Z3 A))))))))) (let ((_let_4 (forall ((Left Int) (Right Int)) (= (tptp.go_right1 Left Right) (- Right (tptp.div1 (- Right Left) 2)))))) (let ((_let_5 (forall ((Left Int) (Right Int)) (= (tptp.go_left1 Left Right) (- Left (tptp.div1 (- Right Left) 2)))))) (let ((_let_6 (forall ((X Int)) (= (tptp.is_power_of_21 X) (exists ((K Int)) (and (<= 0 K) (= X (tptp.power1 2 K)))))))) (let ((_let_7 (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 ((_let_8 (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)))) (let ((_let_9 (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))))))) (let ((_let_10 (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)))))))))) (let ((_let_11 (forall ((I tptp.map_int_int)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)))) (let ((_let_12 (forall ((X tptp.map_int_int)) (tptp.sort1 (tptp.map tptp.int tptp.int) (tptp.t2tb1 X))))) (let ((_let_13 (forall ((C tptp.map_int_int) (I Int) (J Int)) (=> (<= J I) (= (tptp.sum2 C I J) 0))))) (let ((_let_14 (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)))))) (let ((_let_15 (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)))))) (let ((_let_16 (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)))))) (let ((_let_17 (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))))) (let ((_let_18 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_18))) (let ((_let_20 (tptp.tb2t2 _let_19))) (let ((_let_21 (tptp.t2tb2 _let_20))) (let ((_let_22 (= _let_19 _let_21))) (let ((_let_23 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_24 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_23))) (let ((_let_25 (tptp.tb2t2 _let_24))) (let ((_let_26 (tptp.t2tb2 _let_25))) (let ((_let_27 (= _let_24 _let_26))) (let ((_let_28 (= _let_18 (tptp.elts tptp.int _let_19)))) (let ((_let_29 (= _let_23 (tptp.elts tptp.int _let_24)))) (let ((_let_30 (tptp.power1 2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_31 (* (- 1) _let_30))) (let ((_let_32 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_31))) (let ((_let_33 (tptp.t2tb _let_32))) (let ((_let_34 (tptp.tb2t (tptp.get tptp.int tptp.int _let_18 _let_33)))) (let ((_let_35 (* (- 2) _let_30))) (let ((_let_36 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_35))) (let ((_let_37 (tptp.sum2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_36 _let_32))) (let ((_let_38 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_31))) (let ((_let_39 (tptp.sum2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_36 _let_38))) (let ((_let_40 (= _let_39 (+ _let_37 _let_34)))) (let ((_let_41 (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.elts tptp.int _let_26) _let_33)))) (let ((_let_42 (tptp.elts tptp.int _let_21))) (let ((_let_43 (tptp.tb2t (tptp.get tptp.int tptp.int _let_42 _let_33)))) (let ((_let_44 (= _let_43 _let_41))) (let ((_let_45 (tptp.tb2t (tptp.get tptp.int tptp.int _let_23 _let_33)))) (let ((_let_46 (+ _let_45 (* (- 1) _let_39)))) (let ((_let_47 (>= _let_46 1))) (let ((_let_48 (= _let_37 0))) (let ((_let_49 (forall ((J tptp.uni)) (= J (tptp.t2tb2 (tptp.tb2t2 J)))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (_let_49))) (let ((_let_52 ((tptp.tb2t2 J)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_51)) _let_50 :args (_let_22 false _let_49)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_51)) _let_50 :args (_let_27 false _let_49)))) (let ((_let_55 (tptp.map tptp.int tptp.int))) (let ((_let_56 (tptp.sort1 _let_55 _let_18))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_28))) (let ((_let_59 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (or (not (tptp.sort1 (tptp.map tptp.int A) U1)) (= U1 (tptp.elts A (tptp.mk_array1 A U U1))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (_let_59))) (let ((_let_62 ((tptp.mk_array1 A U U1)))) (let ((_let_63 (_let_12))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 ((tptp.t2tb1 X)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_28 (not _let_58)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_65)) :args _let_63)) _let_64 :args (_let_56 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_61)) _let_60 :args (_let_58 false _let_59)) :args (_let_28 false _let_56 false _let_58)))) (let ((_let_67 (tptp.sort1 _let_55 _let_23))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_29))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_29 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_65)) :args _let_63)) _let_64 :args (_let_67 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_61)) _let_60 :args (_let_69 false _let_59)) :args (_let_29 false _let_67 false _let_69)))) (let ((_let_71 (>= _let_30 1))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_40))) (let ((_let_74 (forall ((C tptp.map_int_int) (I Int) (J Int)) (let ((_let_1 (+ (- 1) J))) (or (>= (+ I (* (- 1) J)) 0) (= (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)))))))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (= _let_45 _let_39))) (let ((_let_77 (tptp.phase11 _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_20 _let_25))) (let ((_let_78 (not _let_77))) (let ((_let_79 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_35) (- 1)))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 0)) (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 0)) (not (>= _let_32 0)) _let_72 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) 0) _let_80 (not (= (tptp.tb2t (tptp.get tptp.int tptp.int _let_23 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.sum2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0 _let_36))) _let_78 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 0)) _let_76 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 0))))) (let ((_let_82 (forall ((Right Int) (A0 Int) (A01 tptp.map_int_int) (A Int) (A1 tptp.map_int_int) (BOUND_VARIABLE_2955 Int)) (let ((_let_1 (tptp.power1 2 BOUND_VARIABLE_2955))) (let ((_let_2 (* (- 1) _let_1))) (let ((_let_3 (* (- 2) _let_1))) (let ((_let_4 (+ 1 Right _let_3))) (let ((_let_5 (+ Right _let_2))) (let ((_let_6 (tptp.t2tb1 A1))) (or (not (>= A0 0)) (not (>= A 0)) (not (>= _let_5 0)) (not (>= _let_1 1)) (>= (+ Right (* (- 1) A)) 0) (not (>= (+ Right _let_3) (- 1))) (not (= (tptp.tb2t (tptp.get tptp.int tptp.int _let_6 (tptp.t2tb Right))) (tptp.sum2 A01 0 _let_4))) (not (tptp.phase11 _let_5 Right (tptp.tb2t2 (tptp.mk_array1 tptp.int A0 (tptp.t2tb1 A01))) (tptp.tb2t2 (tptp.mk_array1 tptp.int A _let_6)))) (not (>= Right 0)) (= (tptp.tb2t (tptp.get tptp.int tptp.int _let_6 (tptp.t2tb _let_5))) (tptp.sum2 A01 _let_4 (+ 1 Right _let_2))) (not (>= BOUND_VARIABLE_2955 0)))))))))))) (let ((_let_83 (not _let_81))) (let ((_let_84 (TRUST_SUBS_EQ (ASSUME :args (_let_16)) :args ((= tptp.get2 (lambda ((BOUND_VARIABLE_2585 tptp.ty) (BOUND_VARIABLE_2586 tptp.uni) (BOUND_VARIABLE_2587 Int)) (tptp.get BOUND_VARIABLE_2585 tptp.int (tptp.elts BOUND_VARIABLE_2585 BOUND_VARIABLE_2586) (tptp.t2tb BOUND_VARIABLE_2587)))))))) (let ((_let_85 (TRUST_SUBS_EQ (ASSUME :args (_let_15)) :args ((= tptp.set2 (lambda ((BOUND_VARIABLE_2599 tptp.ty) (BOUND_VARIABLE_2600 tptp.uni) (BOUND_VARIABLE_2601 Int) (BOUND_VARIABLE_2602 tptp.uni)) (tptp.mk_array1 BOUND_VARIABLE_2599 (tptp.length1 BOUND_VARIABLE_2599 BOUND_VARIABLE_2600) (tptp.set BOUND_VARIABLE_2599 tptp.int (tptp.elts BOUND_VARIABLE_2599 BOUND_VARIABLE_2600) (tptp.t2tb BOUND_VARIABLE_2601) BOUND_VARIABLE_2602)))))))) (let ((_let_86 (TRUST_SUBS_EQ (ASSUME :args (_let_14)) :args ((= tptp.make1 (lambda ((BOUND_VARIABLE_2618 tptp.ty) (BOUND_VARIABLE_2619 Int) (BOUND_VARIABLE_2620 tptp.uni)) (tptp.mk_array1 BOUND_VARIABLE_2618 BOUND_VARIABLE_2619 (tptp.const BOUND_VARIABLE_2618 tptp.int BOUND_VARIABLE_2620)))))))) (let ((_let_87 (TRUST_SUBS_EQ (ASSUME :args (_let_7)) :args ((= tptp.sum3 (lambda ((BOUND_VARIABLE_2631 tptp.array_int) (BOUND_VARIABLE_2632 Int) (BOUND_VARIABLE_2633 Int)) (tptp.sum2 (tptp.tb2t1 (tptp.elts tptp.int (tptp.t2tb2 BOUND_VARIABLE_2631))) BOUND_VARIABLE_2632 BOUND_VARIABLE_2633))))))) (let ((_let_88 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.is_power_of_21 (lambda ((BOUND_VARIABLE_2646 Int)) (not (forall ((K Int)) (or (not (>= K 0)) (not (= BOUND_VARIABLE_2646 (tptp.power1 2 K)))))))))))) (let ((_let_89 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.go_left1 (lambda ((BOUND_VARIABLE_2695 Int) (BOUND_VARIABLE_2696 Int)) (+ BOUND_VARIABLE_2695 (* (- 1) (tptp.div1 (+ (* (- 1) BOUND_VARIABLE_2695) BOUND_VARIABLE_2696) 2))))))))) (let ((_let_90 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.go_right1 (lambda ((BOUND_VARIABLE_2708 Int) (BOUND_VARIABLE_2709 Int)) (+ BOUND_VARIABLE_2709 (* (- 1) (tptp.div1 (+ (* (- 1) BOUND_VARIABLE_2708) BOUND_VARIABLE_2709) 2))))))))) (let ((_let_91 (AND_INTRO _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (TRUST_SUBS_EQ (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO _let_91 :args ((forall ((Left Int) (Right Int) (A0 tptp.array_int) (A tptp.array_int)) (= (tptp.partial_sum1 Left Right A0 A) (forall ((I Int)) (let ((_let_1 (* (- 1) I))) (or (>= (+ (* 2 Left) (* (- 1) Right) _let_1) 0) (not (>= (+ Right _let_1) 0)) (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) I)) (tptp.sum3 A0 0 I))))))) SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.partial_sum1 (lambda ((BOUND_VARIABLE_2886 Int) (BOUND_VARIABLE_2887 Int) (BOUND_VARIABLE_2888 tptp.array_int) (BOUND_VARIABLE_2889 tptp.array_int)) (forall ((I Int)) (let ((_let_1 (* (- 1) I))) (or (>= (+ (* 2 BOUND_VARIABLE_2886) (* (- 1) BOUND_VARIABLE_2887) _let_1) 0) (not (>= (+ BOUND_VARIABLE_2887 _let_1) 0)) (= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.elts tptp.int (tptp.t2tb2 BOUND_VARIABLE_2889)) (tptp.t2tb I))) (tptp.sum2 (tptp.tb2t1 (tptp.elts tptp.int (tptp.t2tb2 BOUND_VARIABLE_2888))) 0 I))))))))) _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84) :args ((not (forall ((Left Int) (Right Int) (A0 Int) (A01 tptp.map_int_int) (A Int) (A1 tptp.map_int_int)) (let ((_let_1 (* (- 1) Right))) (let ((_let_2 (* 2 Left))) (let ((_let_3 (+ 1 _let_2 _let_1))) (let ((_let_4 (tptp.t2tb1 A1))) (or (not (>= A0 0)) (not (>= A 0)) (not (>= Left 0)) (>= (+ Left _let_1) 0) (>= (+ Right (* (- 1) A)) 0) (not (>= (+ _let_2 _let_1) (- 1))) (not (tptp.is_power_of_21 (+ (* (- 1) Left) Right))) (not (= (tptp.tb2t (tptp.get tptp.int tptp.int _let_4 (tptp.t2tb Right))) (tptp.sum2 A01 0 _let_3))) (not (tptp.phase11 Left Right (tptp.tb2t2 (tptp.mk_array1 tptp.int A0 (tptp.t2tb1 A01))) (tptp.tb2t2 (tptp.mk_array1 tptp.int A _let_4)))) (not (>= Right 0)) (= (tptp.tb2t (tptp.get tptp.int tptp.int _let_4 (tptp.t2tb Left))) (tptp.sum2 A01 _let_3 (+ 1 Left)))))))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_93 (or))) (let ((_let_94 (not _let_82))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_92) :args (_let_94))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_82))) (REFL :args (_let_83)) :args _let_93)) _let_92 :args (_let_83 true _let_82)))) (let ((_let_96 (REFL :args (_let_81)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_40 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_81 3)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_71))) :args _let_93)) :args ((or _let_71 _let_81))) _let_95 :args (_let_71 true _let_81)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_36 _let_38 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sum2 C I J)))) :args (_let_74)))) _let_75 :args (_let_73 false _let_74)) :args (_let_40 false _let_71 false _let_73)))) (let ((_let_98 (= _let_30 1))) (let ((_let_99 (and _let_44 _let_98))) (let ((_let_100 (tptp.sum2 (tptp.tb2t1 _let_42) _let_36 _let_38))) (let ((_let_101 (= _let_41 _let_100))) (let ((_let_102 (* (- 1) (tptp.div1 _let_30 2)))) (let ((_let_103 (>= _let_30 2))) (let ((_let_104 (and _let_103 (tptp.phase11 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_31 _let_102) _let_32 _let_20 _let_25) (tptp.phase11 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_102) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_20 _let_25) _let_101))) (let ((_let_105 (or _let_78 _let_99 _let_104))) (let ((_let_106 (forall ((Z Int) (Z1 Int) (Z2 tptp.array_int) (Z3 tptp.array_int)) (let ((_let_1 (* (- 1) Z1))) (let ((_let_2 (tptp.elts tptp.int (tptp.t2tb2 Z2)))) (let ((_let_3 (tptp.t2tb Z))) (let ((_let_4 (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.elts tptp.int (tptp.t2tb2 Z3)) _let_3)))) (let ((_let_5 (* (- 1) (tptp.div1 (+ (* (- 1) Z) Z1) 2)))) (or (not (tptp.phase11 Z Z1 Z2 Z3)) (and (= (tptp.tb2t (tptp.get tptp.int tptp.int _let_2 _let_3)) _let_4) (= Z (+ (- 1) Z1))) (and (not (>= (+ Z _let_1) (- 1))) (tptp.phase11 (+ Z _let_5) Z Z2 Z3) (tptp.phase11 (+ Z1 _let_5) Z1 Z2 Z3) (= _let_4 (tptp.sum2 (tptp.tb2t1 _let_2) (+ 1 (* 2 Z) _let_1) (+ 1 Z))))))))))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_91 :args ((forall ((Z Int) (Z1 Int) (Z2 tptp.array_int) (Z3 tptp.array_int)) (let ((_let_1 (* (- 1) Z1))) (let ((_let_2 (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 Z3) Z)))) (or (not (tptp.phase11 Z Z1 Z2 Z3)) (and (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 Z2) Z)) _let_2) (= Z (+ (- 1) Z1))) (and (not (>= (+ Z _let_1) (- 1))) (tptp.phase11 (tptp.go_left1 Z Z1) Z Z2 Z3) (tptp.phase11 (tptp.go_right1 Z Z1) Z1 Z2 Z3) (= _let_2 (tptp.sum3 Z2 (+ 1 (* 2 Z) _let_1) (+ 1 Z)))))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_108 (not _let_104))) (let ((_let_109 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.tb2t1 _let_18)))) (let ((_let_110 (not _let_101))) (let ((_let_111 (forall ((I tptp.map_int_int)) (= I (tptp.tb2t1 (tptp.t2tb1 I)))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (not _let_76))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_81 9)) _let_95 :args (_let_113 true _let_81)))) (let ((_let_115 (REFL :args ((not _let_27))))) (let ((_let_116 (REFL :args ((not _let_22))))) (let ((_let_117 (REFL :args ((not _let_29))))) (let ((_let_118 (REFL :args ((not _let_28))))) (let ((_let_119 (MACRO_SR_PRED_INTRO :args ((= (not _let_113) _let_76))))) (let ((_let_120 (and _let_113 _let_28 _let_29 _let_109 _let_22 _let_27))) (let ((_let_121 (= _let_100 _let_39))) (let ((_let_122 (= _let_41 _let_45))) (let ((_let_123 (ASSUME :args (_let_113)))) (let ((_let_124 (ASSUME :args (_let_122)))) (let ((_let_125 (APPLY_UF tptp.sum2))) (let ((_let_126 (REFL :args (_let_36)))) (let ((_let_127 (ASSUME :args (_let_109)))) (let ((_let_128 (ASSUME :args (_let_28)))) (let ((_let_129 (APPLY_UF tptp.elts))) (let ((_let_130 (ASSUME :args (_let_22)))) (let ((_let_131 (REFL :args (tptp.int)))) (let ((_let_132 (TRANS (CONG _let_131 (SYMM _let_130) :args _let_129) (SYMM _let_128)))) (let ((_let_133 (APPLY_UF tptp.tb2t))) (let ((_let_134 (APPLY_UF tptp.get))) (let ((_let_135 (REFL :args (_let_33)))) (let ((_let_136 (ASSUME :args (_let_29)))) (let ((_let_137 (ASSUME :args (_let_27)))) (let ((_let_138 (MODUS_PONENS (AND_INTRO _let_136 _let_137) (SCOPE (CONG (CONG _let_131 _let_131 (TRANS (CONG _let_131 (SYMM _let_137) :args _let_129) (SYMM _let_136)) _let_135 :args _let_134) :args _let_133) :args (_let_29 _let_27))))) (let ((_let_139 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_78 _let_99 _let_104 (not _let_105)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_81 7)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_77))) :args _let_93)) :args ((or _let_77 _let_81))) _let_95 :args (_let_77 true _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_104 3)) :args ((or _let_101 _let_108))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_120)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_123 _let_138 (MODUS_PONENS (AND_INTRO _let_127 _let_128 _let_130) (SCOPE (CONG (TRANS (CONG _let_132 :args (APPLY_UF tptp.tb2t1)) (SYMM _let_127)) _let_126 (REFL :args (_let_38)) :args _let_125) :args (_let_109 _let_28 _let_22)))) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM (SYMM _let_124)) (SYMM (SYMM (ASSUME :args (_let_121)))) :args (=)) (FALSE_INTRO _let_123))) :args (_let_113 _let_122 _let_121))) :args (_let_113 _let_28 _let_29 _let_109 _let_22 _let_27))) :args (true _let_120)) (CONG _let_119 _let_118 _let_117 (REFL :args ((not _let_109))) _let_116 _let_115 (REFL :args (_let_110)) :args _let_93)) _let_114 _let_66 _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.t2tb1 I)))) :args (_let_111))) _let_112 :args (_let_109 false _let_111)) _let_53 _let_54 :args (_let_110 true _let_76 false _let_28 false _let_29 false _let_109 false _let_22 false _let_27)) :args (_let_108 true _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_107 :args (_let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_20 _let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.phase11 Z Z1 Z2 Z3) false))))) :args (_let_106)))) _let_107 :args (_let_105 false _let_106)) :args (_let_99 false _let_77 true _let_104 false _let_105)))) (let ((_let_140 (not _let_99))) (let ((_let_141 (REORDERING (CNF_AND_POS :args (_let_99 0)) :args ((or _let_44 _let_140))))) (let ((_let_142 (>= _let_46 0))) (let ((_let_143 (tptp.sum2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_36 _let_36))) (let ((_let_144 (= _let_143 0))) (let ((_let_145 (REORDERING (CNF_AND_POS :args (_let_99 1)) :args ((or _let_98 _let_140))))) (let ((_let_146 (or _let_80 _let_144))) (let ((_let_147 (forall ((C tptp.map_int_int) (I Int) (K Int) (J Int)) (or (>= (+ I (* (- 1) K)) 1) (>= (+ K (* (- 1) J)) 1) (= (tptp.sum2 C I J) (+ (tptp.sum2 C I K) (tptp.sum2 C K J))))))) (let ((_let_148 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_149 (not _let_98))) (let ((_let_150 (not _let_142))) (let ((_let_151 (= 0 _let_37))) (let ((_let_152 (= _let_43 _let_34))) (let ((_let_153 ((not _let_48)))) (let ((_let_154 (_let_48))) (let ((_let_155 (false))) (let ((_let_156 (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_152)) :args ((= (+ _let_34 (* (- 1) _let_43)) 0))))) (let ((_let_157 (ASSUME :args (_let_40)))) (let ((_let_158 (MACRO_SR_PRED_TRANSFORM _let_157 :args ((= (+ _let_39 (* (- 1) _let_37) (* (- 1) _let_34)) 0))))) (let ((_let_159 (* (- 1) _let_41))) (let ((_let_160 (ASSUME :args (_let_44)))) (let ((_let_161 (MACRO_SR_PRED_TRANSFORM _let_160 :args ((= (+ _let_43 _let_159) 0))))) (let ((_let_162 ((< _let_46 0)))) (let ((_let_163 (_let_150))) (let ((_let_164 (ASSUME :args _let_163))) (let ((_let_165 (MACRO_SR_PRED_TRANSFORM _let_124 :args ((= (+ _let_45 _let_159) 0))))) (let ((_let_166 (ASSUME :args _let_154))) (let ((_let_167 (= 0 _let_143))) (let ((_let_168 (= _let_32 _let_36))) (let ((_let_169 (_let_168))) (let ((_let_170 (_let_144))) (let ((_let_171 (ASSUME :args _let_170))) (let ((_let_172 (_let_98))) (let ((_let_173 (ASSUME :args _let_172))) (let ((_let_174 (MODUS_PONENS (AND_INTRO _let_128 _let_130) (SCOPE (CONG (CONG _let_131 _let_131 _let_132 _let_135 :args _let_134) :args _let_133) :args (_let_28 _let_22))))) (let ((_let_175 (not _let_47))) (let ((_let_176 (and _let_113 _let_175))) (let ((_let_177 (_let_113 _let_175))) (let ((_let_178 (ASSUME :args (_let_175)))) (let ((_let_179 (or _let_103 _let_48))) (let ((_let_180 (forall ((C tptp.map_int_int) (I Int) (J Int)) (or (not (>= (+ I (* (- 1) J)) 0)) (= (tptp.sum2 C I J) 0))))) (let ((_let_181 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_182 (not _let_103))) (let ((_let_183 (_let_103))) (let ((_let_184 (ASSUME :args (_let_47)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_174 _let_157 _let_160 _let_184 _let_138 _let_166) :args (_let_47 _let_28 _let_29 _let_40 _let_22 _let_27 _let_44 _let_48)) (SCOPE (CONTRA _let_166 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_166 _let_165 _let_184 _let_161 _let_158 _let_156 :args ((- 1.0) 1.0 (- 1.0) (- 1.0) (- 1.0) (- 1.0))) :args _let_155) :args _let_154) :args _let_153) :args _let_153)) :args (_let_152 _let_40 _let_44 _let_47 _let_122 _let_48)) :args ((not (and _let_47 _let_28 _let_29 _let_40 _let_22 _let_27 _let_44 _let_48)) SB_LITERAL))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_179)) :args ((or _let_103 _let_48 (not _let_179)))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_173 (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_183) _let_173 :args ((- 1.0) 1.0)) :args _let_155) :args _let_183) :args ((< _let_30 2))) :args (_let_182)) :args _let_172)) :args _let_172)) :args ((or _let_182 _let_149))) (MACRO_RESOLUTION_TRUST _let_145 _let_139 :args (_let_98 false _let_99)) :args (_let_182 false _let_98)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_181 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_36 _let_32 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sum2 C I J) 0))))) :args (_let_180)))) _let_181 :args (_let_179 false _let_180)) :args (_let_48 true _let_103 false _let_179)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_176)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_123 _let_178) (SCOPE (MACRO_SR_PRED_TRANSFORM (ARITH_TRICHOTOMY (MACRO_SR_PRED_TRANSFORM _let_123 :args ((not (= _let_46 0)))) (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_178 :args ((< _let_46 1)))) :args _let_162) :args _let_163) :args _let_177)) :args _let_177)) :args (true _let_176)) (CONG _let_119 (MACRO_SR_PRED_INTRO :args ((= (not _let_175) _let_47))) (REFL :args _let_163) :args _let_93)) _let_114 (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_174 _let_157 _let_160 _let_164 _let_138 (MODUS_PONENS (AND_INTRO (MACRO_SR_PRED_TRANSFORM _let_173 :args _let_169) (MODUS_PONENS _let_171 (SCOPE (SYMM _let_171) :args _let_170))) (SCOPE (TRANS (SYMM (SYMM (ASSUME :args (_let_167)))) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_126 (SYMM (ASSUME :args _let_169)) :args _let_125)) :args (_let_168 _let_167)))) :args (_let_150 _let_28 _let_29 _let_40 _let_144 _let_22 _let_27 _let_44 _let_98)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_151)) :args _let_154) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_166 _let_165 (MACRO_SR_PRED_TRANSFORM _let_164 :args _let_162) _let_161 _let_158 _let_156 :args (1.0 (- 1.0) 1.0 1.0 1.0 1.0)) :args _let_155) :args _let_154) :args _let_153) :args _let_153)) :args (_let_152 _let_40 _let_44 _let_150 _let_122 _let_151)) :args ((not (and _let_150 _let_28 _let_29 _let_40 _let_144 _let_22 _let_27 _let_44 _let_98)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_150) _let_142))) _let_118 _let_117 (REFL :args ((not _let_40))) (REFL :args ((not _let_144))) _let_116 _let_115 (REFL :args ((not _let_44))) (REFL :args (_let_149)) :args _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_146)) :args ((or _let_80 _let_144 (not _let_146)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_81 5)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_80) _let_79))) :args _let_93)) :args ((or _let_79 _let_81))) _let_95 :args (_let_79 true _let_81)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_148 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0 _let_36 _let_36 QUANTIFIERS_INST_E_MATCHING ((tptp.sum2 C I J) (tptp.sum2 C I K)))) :args (_let_147)))) _let_148 :args (_let_146 false _let_147)) :args (_let_144 false _let_79 false _let_146)) _let_97 _let_70 _let_66 _let_54 _let_53 _let_145 _let_141 :args ((or _let_142 _let_140) false _let_144 false _let_40 false _let_29 false _let_28 false _let_27 false _let_22 false _let_98 false _let_44)) _let_139 :args (_let_142 false _let_99)) :args (_let_47 true _let_76 false _let_142)) (MACRO_RESOLUTION_TRUST _let_141 _let_139 :args (_let_44 false _let_99)) _let_97 _let_70 _let_66 _let_54 _let_53 :args (false false _let_48 false _let_47 false _let_44 false _let_40 false _let_29 false _let_28 false _let_27 false _let_22)) :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)))) (forall ((X Int)) (= (tptp.power1 X 0) 1)) (forall ((X Int) (N Int)) (=> (<= 0 N) (= (tptp.power1 X (+ N 1)) (* X (tptp.power1 X N))))) (forall ((X Int) (N Int)) (=> (< 0 N) (= (tptp.power1 X N) (* X (tptp.power1 X (- N 1)))))) (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))) _let_17 (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)) _let_16 (forall ((A tptp.ty) (X tptp.uni) (X1 Int) (X2 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.set2 A X X1 X2))) _let_15 (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.make1 A X X1))) _let_14 _let_13 _let_12 _let_11 (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))))) _let_10 _let_9 (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)) _let_8 _let_7 (forall ((X Int)) (let ((_let_1 (* 2 (tptp.div1 X 2)))) (=> (<= 0 X) (and (<= _let_1 X) (<= (- X 1) _let_1))))) _let_6 (forall ((X Int)) (=> (tptp.is_power_of_21 X) (=> (< 1 X) (= (* 2 (tptp.div1 X 2)) X)))) _let_5 _let_4 (forall ((Left Int) (Right Int) (A0 tptp.array_int) (A tptp.array_int)) (=> (= Right (+ Left 1)) (=> (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) Left)) (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A0) Left))) (tptp.phase11 Left Right A0 A)))) (forall ((Left Int) (Right Int) (A0 tptp.array_int) (A tptp.array_int)) (let ((_let_1 (+ Left 1))) (=> (< _let_1 Right) (=> (tptp.phase11 (tptp.go_left1 Left Right) Left A0 A) (=> (tptp.phase11 (tptp.go_right1 Left Right) Right A0 A) (=> (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) Left)) (tptp.sum3 A0 (+ (- Left (- Right Left)) 1) _let_1)) (tptp.phase11 Left Right A0 A))))))) _let_3 (forall ((Left Int) (Right Int) (A0 tptp.array_int) (A tptp.array_int) (Aqt tptp.array_int)) (=> (and (<= 0 (tptp.length1 tptp.int (tptp.t2tb2 A0))) (<= 0 (tptp.length1 tptp.int (tptp.t2tb2 A))) (<= 0 (tptp.length1 tptp.int (tptp.t2tb2 Aqt))) (forall ((I Int)) (=> (and (< (- Left (- Right Left)) I) (< I Right)) (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) I)) (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 Aqt) I))))) (tptp.phase11 Left Right A0 A)) (tptp.phase11 Left Right A0 Aqt))) (forall ((Left Int) (Right Int) (A0 tptp.array_int) (A0qt tptp.array_int) (A tptp.array_int)) (=> (and (<= 0 (tptp.length1 tptp.int (tptp.t2tb2 A0))) (<= 0 (tptp.length1 tptp.int (tptp.t2tb2 A0qt))) (<= 0 (tptp.length1 tptp.int (tptp.t2tb2 A))) (forall ((I Int)) (=> (and (< (- Left (- Right Left)) I) (< I Right)) (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A0) I)) (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A0qt) I))))) (tptp.phase11 Left Right A0 A)) (tptp.phase11 Left Right A0qt A))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 60.82/61.16 )
% 60.82/61.16 % SZS output end Proof for SWW664_2
% 60.82/61.16 % cvc5---1.0.5 exiting
% 60.82/61.16 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------