%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW616_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.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 00:21:42 EDT 2023

% Result   : Theorem 15.37s 15.74s
% Output   : Proof 15.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWW616_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun Aug 27 18:06:55 EDT 2023
% 0.20/0.36  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_ARI
% 15.37/15.74  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.uTQw6KFu1N/cvc5---1.0.5_16343.p...
% 15.37/15.74  ------- get file name : TPTP file name is SWW616_2
% 15.37/15.74  ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16343.smt2...
% 15.37/15.74  --- Run --finite-model-find --decision=internal at 15...
% 15.37/15.74  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.37/15.74  % SZS status Theorem for SWW616_2
% 15.37/15.74  % SZS output start Proof for SWW616_2
% 15.37/15.74  (
% 15.37/15.74  (let ((_let_1 (not (forall ((A Int) (A1 tptp.map_int_int) (L Int) (H Int)) (=> (and (<= 0 A) (<= 0 L) (<= L H) (<= H A)) (=> (not (= H L)) (forall ((Lo Int)) (=> (= Lo (+ L (tptp.div (- H L) 2))) (forall ((Hi Int)) (let ((_let_1 (+ L (tptp.div (- H L) 2)))) (=> (= Hi _let_1) (=> (<= L (- _let_1 1)) (forall ((S Int) (Ms Int) (Lo1 Int)) (let ((_let_1 (+ L (tptp.div (- H L) 2)))) (=> (and (<= L Lo1) (<= Lo1 _let_1) (= _let_1 Hi) (= Ms (tptp.sum A1 Lo1 Hi)) (forall ((Lqt Int)) (let ((_let_1 (+ L (tptp.div (- H L) 2)))) (=> (and (< (- L 1) Lqt) (<= Lqt _let_1)) (<= (tptp.sum A1 Lqt _let_1) Ms)))) (= S (tptp.sum A1 (+ (- L 1) 1) _let_1))) (=> (forall ((Lqt Int)) (let ((_let_1 (+ L (tptp.div (- H L) 2)))) (=> (and (<= L Lqt) (<= Lqt _let_1)) (<= (tptp.sum A1 Lqt _let_1) (tptp.sum A1 Lo1 _let_1))))) (forall ((S1 Int)) (=> (= S1 Ms) (=> (<= (+ L (tptp.div (- H L) 2)) (- H 1)) (forall ((Lqt Int) (Hqt Int)) (let ((_let_1 (+ L (tptp.div (- H L) 2)))) (=> (and (<= L Lqt) (<= Lqt _let_1) (<= _let_1 Hqt) (<= Hqt _let_1)) (<= (tptp.sum A1 Lqt Hqt) Ms))))))))))))))))))))))) (let ((_let_2 (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_3 (tptp.div (+ (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) 2))) (let ((_let_4 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_3))) (let ((_let_5 (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_4))) (let ((_let_6 (+ _let_5 (* (- 1) _let_2)))) (let ((_let_7 (>= _let_6 0))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (* (- 1) _let_3))))) (let ((_let_9 (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_4))) (let ((_let_10 (* (- 1) _let_9))) (let ((_let_11 (>= (+ _let_5 _let_10) 0))) (let ((_let_12 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_3))) (let ((_let_13 (>= _let_12 0))) (let ((_let_14 (not _let_13))) (let ((_let_15 (>= _let_12 1))) (let ((_let_16 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_17 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16 _let_3) 0))) (let ((_let_18 (not _let_17))) (let ((_let_19 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16) 1))) (let ((_let_20 (forall ((Lqt Int)) (let ((_let_1 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_2 (tptp.div (+ _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) 2))) (let ((_let_3 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_2))) (or (not (>= (+ Lqt _let_1) 0)) (>= (+ Lqt _let_1 (* (- 1) _let_2)) 1) (not (>= (+ (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Lqt _let_3) (* (- 1) (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_3))) 1))))))))) (let ((_let_21 (not _let_20))) (let ((_let_22 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_23 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22 _let_3) 0)))) (let ((_let_24 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22) 1))) (let ((_let_25 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_26 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_25 _let_3) 0))) (let ((_let_27 (not (>= _let_3 1)))) (let ((_let_28 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_25) 1))) (let ((_let_30 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 0)))) (let ((_let_31 (or _let_30 _let_29 _let_28 _let_27 _let_26 _let_24 _let_23 _let_21 (not (forall ((Lqt Int)) (let ((_let_1 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_2 (tptp.div (+ _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) 2))) (let ((_let_3 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_2))) (or (not (>= (+ Lqt _let_1) 0)) (>= (+ Lqt _let_1 (* (- 1) _let_2)) 1) (>= (+ (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_3) (* (- 1) (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Lqt _let_3))) 0))))))) _let_19 _let_18 _let_15 _let_14 _let_7))) (let ((_let_32 (not _let_7))) (let ((_let_33 (forall ((A1 tptp.map_int_int) (L Int) (H Int) (BOUND_VARIABLE_2244 Int) (BOUND_VARIABLE_2242 Int) (BOUND_VARIABLE_2240 Int)) (let ((_let_1 (tptp.div (+ (* (- 1) L) H) 2))) (let ((_let_2 (+ L (* (- 1) BOUND_VARIABLE_2242) _let_1))) (let ((_let_3 (* (- 1) BOUND_VARIABLE_2240))) (let ((_let_4 (* (- 1) BOUND_VARIABLE_2244))) (let ((_let_5 (* (- 1) H))) (or (not (>= L 0)) (>= (+ L _let_5) 1) (= L H) (not (>= _let_1 1)) (>= (+ L _let_5 _let_1) 0) (>= (+ L _let_4) 1) (not (>= (+ L _let_4 _let_1) 0)) (not (forall ((Lqt Int)) (let ((_let_1 (tptp.div (+ (* (- 1) L) H) 2))) (let ((_let_2 (+ L _let_1))) (let ((_let_3 (* (- 1) Lqt))) (or (>= (+ L _let_3) 1) (not (>= (+ L _let_3 _let_1) 0)) (not (>= (+ (tptp.sum A1 Lqt _let_2) (* (- 1) (tptp.sum A1 BOUND_VARIABLE_2244 _let_2))) 1)))))))) (not (forall ((Lqt Int)) (let ((_let_1 (tptp.div (+ (* (- 1) L) H) 2))) (let ((_let_2 (+ L _let_1))) (let ((_let_3 (* (- 1) Lqt))) (or (>= (+ L _let_3) 1) (not (>= (+ L _let_3 _let_1) 0)) (not (>= (+ (tptp.sum A1 Lqt _let_2) (* (- 1) (tptp.sum A1 BOUND_VARIABLE_2244 _let_2))) 1)))))))) (>= (+ L _let_3) 1) (not (>= (+ L _let_3 _let_1) 0)) (>= _let_2 1) (not (>= _let_2 0)) (>= (+ (tptp.sum A1 BOUND_VARIABLE_2244 (+ L _let_1)) (* (- 1) (tptp.sum A1 BOUND_VARIABLE_2240 BOUND_VARIABLE_2242))) 0)))))))))) (let ((_let_34 (not _let_31))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (or))) (let ((_let_37 (not _let_33))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_35) :args (_let_37)) (REWRITE :args ((=> _let_37 (not (or _let_30 _let_29 _let_28 _let_27 _let_26 _let_24 _let_23 (not (forall ((Lqt Int)) (let ((_let_1 (tptp.div (+ (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) 2))) (let ((_let_2 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_1))) (let ((_let_3 (* (- 1) Lqt))) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_3) 1) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_3 _let_1) 0)) (not (>= (+ (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Lqt _let_2) (* (- 1) (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_2))) 1)))))))) (not (forall ((Lqt Int)) (let ((_let_1 (tptp.div (+ (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) 2))) (let ((_let_2 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_1))) (let ((_let_3 (* (- 1) Lqt))) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_3) 1) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_3 _let_1) 0)) (not (>= (+ (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Lqt _let_2) (* (- 1) (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_2))) 1)))))))) _let_19 _let_18 _let_15 _let_14 _let_7))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_33))) (REFL :args (_let_34)) :args _let_36)) _let_35 :args (_let_34 true _let_33)))) (let ((_let_39 (not _let_15))) (let ((_let_40 (REFL :args (_let_31)))) (let ((_let_41 (not _let_8))) (let ((_let_42 (= _let_12 0))) (let ((_let_43 ((not _let_42)))) (let ((_let_44 (_let_41))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 (ASSUME :args (_let_13)))) (let ((_let_47 (ASSUME :args (_let_39)))) (let ((_let_48 (or _let_19 _let_18 _let_11))) (let ((_let_49 (_let_20))) (let ((_let_50 (= _let_2 _let_9))) (let ((_let_51 (= (+ _let_2 _let_10) 0))) (let ((_let_52 ((not _let_51)))) (let ((_let_53 (_let_51))) (let ((_let_54 (ASSUME :args (_let_11)))) (let ((_let_55 (ASSUME :args (_let_32)))) (let ((_let_56 ((= _let_9 _let_2)))) (let ((_let_57 ((= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_4)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_54 _let_55 (MODUS_PONENS (MODUS_PONENS (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_8)) :args _let_57) (SCOPE (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (SYMM (ASSUME :args _let_57)) :args (APPLY_UF tptp.sum)) :args _let_57)) (SCOPE (SYMM (ASSUME :args _let_56)) :args _let_56))) :args (_let_32 _let_8 _let_11)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_50)) :args _let_53) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_53) (MACRO_SR_PRED_TRANSFORM _let_55 :args ((< _let_6 0))) _let_54 :args (1.0 1.0 (- 1.0))) :args (false)) :args _let_53) :args _let_52) :args _let_52)) :args (_let_11 _let_32 _let_50)) :args ((not (and _let_32 _let_8 _let_11)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_7))) (REFL :args _let_44) (REFL :args ((not _let_11))) :args _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_19 _let_18 _let_11 (not _let_48)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 9)) _let_38 :args ((not _let_19) true _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 10)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_36)) :args ((or _let_17 _let_31))) _let_38 :args (_let_17 true _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_49) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Lqt _let_4)))) :args _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 7)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_36)) :args ((or _let_20 _let_31))) _let_38 :args (_let_20 true _let_31)) :args (_let_48 false _let_20)) :args (_let_11 true _let_19 false _let_17 false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_45 _let_47 _let_46) :args (_let_13 _let_39 _let_41)) (SCOPE (CONTRA (ARITH_TRICHOTOMY (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_47 :args ((< _let_12 1)))) _let_46 :args (_let_42)) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM _let_45 :args _let_43) :args _let_43)) :args (_let_41 _let_39 _let_13)) :args ((not (and _let_13 _let_39 _let_41)) SB_LITERAL))) (CONG (REFL :args (_let_14)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_15))) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_8))) :args _let_36)) :args ((or _let_15 _let_14 _let_8))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 12)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_36)) :args ((or _let_13 _let_31))) _let_38 :args (_let_13 true _let_31)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 11)) _let_38 :args (_let_39 true _let_31)) :args (_let_8 false _let_13 true _let_15)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 13)) _let_38 :args (_let_32 true _let_31)) :args (false false _let_11 false _let_8 true _let_7)) :args ((forall ((A tptp.ty)) (tptp.sort A (tptp.witness A))) (forall ((A tptp.ty) (X tptp.bool) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort A (tptp.match_bool A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort A Z) (= (tptp.match_bool A tptp.true Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort A Z1) (= (tptp.match_bool A tptp.false Z Z1) Z1))) (not (= tptp.true tptp.false)) (forall ((U tptp.bool)) (or (= U tptp.true) (= U tptp.false))) (forall ((U tptp.tuple0)) (= U tptp.tuple02)) (forall ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort (tptp.ref A) (tptp.mk_ref A X))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort A (tptp.contents A X))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort A U) (= (tptp.contents A (tptp.mk_ref A U)) U))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort (tptp.ref A) U) (= U (tptp.mk_ref A (tptp.contents A U))))) (forall ((X Int)) (let ((_let_1 (tptp.abs X))) (let ((_let_2 (<= 0 X))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (- X))))))) (forall ((X Int) (Y Int)) (= (<= (tptp.abs X) Y) (and (<= (- Y) X) (<= X Y)))) (forall ((X Int)) (<= 0 (tptp.abs X))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (= X (+ (* Y (tptp.div X Y)) (tptp.mod X Y))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.div X Y))) (=> (and (<= 0 X) (< 0 Y)) (and (<= 0 _let_1) (<= _let_1 X))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.abs Y))) (let ((_let_2 (tptp.mod 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.div X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (< 0 Y)) (<= (tptp.div X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (not (= Y 0))) (<= 0 (tptp.mod X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (not (= Y 0))) (<= (tptp.mod X Y) 0))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (<= (tptp.abs (* (tptp.div X Y) Y)) (tptp.abs X)))) (forall ((X Int)) (= (tptp.div X 1) X)) (forall ((X Int)) (= (tptp.mod X 1) 0)) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.div X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.mod X Y) X))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.div (+ (* X Y) Z) X) (+ Y (tptp.div Z X))))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.mod (+ (* X Y) Z) X) (tptp.mod Z X)))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort B (tptp.get B A X X1))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort (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.sort 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.sort A A1) (=> (tptp.sort 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.sort (tptp.map A B) (tptp.const B A X))) (forall ((A tptp.ty) (B tptp.ty) (B1 tptp.uni) (A1 tptp.uni)) (=> (tptp.sort B B1) (= (tptp.get B A (tptp.const B A B1) A1) B1))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort (tptp.array A) (tptp.mk_array A X X1))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length A (tptp.mk_array A U U1)) U)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort (tptp.map tptp.int A) (tptp.elts A X))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (=> (tptp.sort (tptp.map tptp.int A) U1) (= (tptp.elts A (tptp.mk_array A U U1)) U1))) (forall ((A tptp.ty) (U tptp.uni)) (= U (tptp.mk_array A (tptp.length A U) (tptp.elts A U)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int)) (tptp.sort A (tptp.get1 A X X1))) (forall ((X Int)) (tptp.sort 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.get1 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.sort (tptp.array A) (tptp.set1 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.uni) (I Int) (V tptp.uni)) (= (tptp.set1 A A1 I V) (tptp.mk_array A (tptp.length 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.sort (tptp.array A) (tptp.make A X X1))) (forall ((A tptp.ty) (N Int) (V tptp.uni)) (= (tptp.make A N V) (tptp.mk_array A N (tptp.const A tptp.int V)))) (forall ((C tptp.map_int_int) (I Int) (J Int)) (=> (<= J I) (= (tptp.sum C I J) 0))) (forall ((X tptp.map_int_int)) (tptp.sort (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.sum C I J) (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C) (tptp.t2tb I))) (tptp.sum C (+ I 1) J))))) (forall ((C tptp.map_int_int) (I Int) (J Int)) (let ((_let_1 (- J 1))) (=> (< I J) (= (tptp.sum C I J) (+ (tptp.sum 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.sum C I J) (+ (tptp.sum C I K) (tptp.sum 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.sum C1 I J) (tptp.sum C2 I J)))) (forall ((X tptp.array_int)) (tptp.sort (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.sum1 A L H) (tptp.sum (tptp.tb2t1 (tptp.elts tptp.int (tptp.t2tb2 A))) L H))) (forall ((A tptp.array_int) (Maxlo Int) (S Int)) (= (tptp.maxsublo A Maxlo S) (forall ((L Int) (H Int)) (=> (and (<= 0 L) (< L Maxlo)) (=> (and (<= L H) (<= H (tptp.length tptp.int (tptp.t2tb2 A)))) (<= (tptp.sum1 A L H) S)))))) (forall ((A tptp.array_int) (S Int)) (= (tptp.maxsub A S) (forall ((L Int) (H Int)) (=> (and (<= 0 L) (<= L H) (<= H (tptp.length tptp.int (tptp.t2tb2 A)))) (<= (tptp.sum1 A L H) S))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.37/15.74  )
% 15.37/15.74  % SZS output end Proof for SWW616_2
% 15.37/15.74  % cvc5---1.0.5 exiting
% 15.37/15.74  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------