%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV163+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n031.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 : Thu Aug 31 21:49:33 EDT 2023

% Result   : Theorem 0.19s 0.68s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem    : SWV163+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n031.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   : Tue Aug 29 04:02:41 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.19/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.68  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.dUcDx6ojHt/cvc5---1.0.5_6884.p...
% 0.19/0.68  ------- get file name : TPTP file name is SWV163+1
% 0.19/0.68  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_6884.smt2...
% 0.19/0.68  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.68  % SZS status Theorem for SWV163+1
% 0.19/0.68  % SZS output start Proof for SWV163+1
% 0.19/0.68  (
% 0.19/0.68  (let ((_let_1 (tptp.succ tptp.n0))) (let ((_let_2 (tptp.succ _let_1))) (let ((_let_3 (tptp.succ _let_2))) (let ((_let_4 (tptp.succ _let_3))) (let ((_let_5 (tptp.succ _let_4))) (let ((_let_6 (= _let_5 tptp.n5))) (let ((_let_7 (= _let_4 tptp.n4))) (let ((_let_8 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_9 (tptp.gt tptp.n0 tptp.tptp_minus_1))) (let ((_let_10 (tptp.gt tptp.n5 tptp.n4))) (let ((_let_11 (not (=> (and (tptp.leq tptp.n0 tptp.pv10) (tptp.leq tptp.pv10 tptp.n135299) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q A tptp.tptp_sum_index)) tptp.n1)))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center B tptp.n0) _let_1))) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.tptp_minus_1)) (= (tptp.a_select3 tptp.q tptp.pv10 B) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times _let_2 _let_2)))))))))))))) (let ((_let_12 (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))) (let ((_let_13 (tptp.succ tptp.tptp_minus_1))) (let ((_let_14 (= _let_13 tptp.n0))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_16 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_17 (forall ((X $$unsorted)) (not (tptp.gt X X))))) (let ((_let_18 (= tptp.n0 _let_13))) (let ((_let_19 (= tptp.n4 _let_4))) (let ((_let_20 (= tptp.n5 _let_5))) (let ((_let_21 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ _let_13)))) (tptp.plus tptp.n5 tptp.tptp_minus_1)))) (let ((_let_22 (= _let_5 (tptp.plus tptp.n5 tptp.n0)))) (let ((_let_23 (= tptp.n0 tptp.tptp_minus_1))) (let ((_let_24 (tptp.gt tptp.n4 tptp.n4))) (let ((_let_25 (SYMM (ASSUME :args (_let_14))))) (let ((_let_26 (ASSUME :args (_let_10)))) (let ((_let_27 (SYMM (ASSUME :args (_let_7))))) (let ((_let_28 (SYMM (ASSUME :args (_let_6))))) (let ((_let_29 (_let_12))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_32 (tptp.leq tptp.tptp_minus_1 tptp.n0))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.leq tptp.n0 tptp.tptp_minus_1))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_23))) (let ((_let_37 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (not _let_9))) (let ((_let_40 (or _let_39 _let_32))) (let ((_let_41 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.tptp_minus_1))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_34))) (let ((_let_48 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq X Y)) (not (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_51 (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) _let_50))) (let ((_let_52 (tptp.minus (tptp.a_select3 tptp.center SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n0) _let_50))) (let ((_let_53 (or _let_46 _let_44 (= (tptp.a_select3 tptp.q tptp.pv10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.divide (tptp.sqrt (tptp.times _let_52 _let_52)) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times _let_51 _let_51)))))))) (let ((_let_54 (forall ((B $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center B tptp.n0) _let_1))) (or (not (tptp.leq tptp.n0 B)) (not (tptp.leq B tptp.tptp_minus_1)) (= (tptp.a_select3 tptp.q tptp.pv10 B) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times _let_2 _let_2)))))))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (or))) (let ((_let_57 (not _let_54))) (let ((_let_58 (_let_57))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_54))) (REFL :args (_let_55)) :args _let_56)) (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)))) :args (_let_55 true _let_54)))) (let ((_let_60 (REFL :args (_let_53)))) (let ((_let_61 (not _let_24))) (let ((_let_62 (_let_17))) (let ((_let_63 (ASSUME :args _let_62))) (let ((_let_64 (not _let_23))) (let ((_let_65 (not _let_22))) (let ((_let_66 (not _let_21))) (let ((_let_67 (not _let_20))) (let ((_let_68 (not _let_19))) (let ((_let_69 (not _let_10))) (let ((_let_70 (not _let_18))) (let ((_let_71 (ASSUME :args (_let_61)))) (let ((_let_72 (APPLY_UF tptp.succ))) (let ((_let_73 (ASSUME :args (_let_21)))) (let ((_let_74 (ASSUME :args (_let_23)))) (let ((_let_75 (ASSUME :args (_let_22)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_71 _let_27 _let_25 _let_73 _let_74 _let_75 _let_28 _let_26) :args (_let_10 _let_18 _let_19 _let_20 _let_21 _let_22 _let_23 _let_61)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_26)) (CONG (TRANS (SYMM (SYMM _let_28)) (SYMM (SYMM _let_75)) (CONG (REFL :args (tptp.n5)) (SYMM (SYMM _let_74)) :args (APPLY_UF tptp.plus)) (SYMM _let_73) (CONG (CONG (CONG (CONG (SYMM _let_25) :args _let_72) :args _let_72) :args _let_72) :args _let_72) (SYMM _let_27)) (REFL :args (tptp.n4)) :args (APPLY_UF tptp.gt)) (FALSE_INTRO _let_71))) :args (_let_61 _let_19 _let_18 _let_21 _let_23 _let_22 _let_20 _let_10)) :args ((not (and _let_10 _let_18 _let_19 _let_20 _let_21 _let_22 _let_23 _let_61)) SB_LITERAL))) (CONG (REFL :args (_let_69)) (REFL :args (_let_70)) (REFL :args (_let_68)) (REFL :args (_let_67)) (REFL :args (_let_66)) (REFL :args (_let_65)) (REFL :args (_let_64)) (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_24))) :args _let_56)) :args ((or _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_24))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (tptp.n4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt X X) false))))) :args _let_62)) _let_63 :args (_let_61 false _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_33 _let_23 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_44 _let_34 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_56)) :args ((or _let_45 _let_53))) _let_59 :args (_let_45 true _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_56)) :args ((or _let_43 _let_53))) _let_59 :args (_let_43 true _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.leq X Y) false)) (not (= (tptp.leq Y Z) false))))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_34 false _let_45 false _let_43 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_32 (not _let_40)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.tptp_minus_1 tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_41))) _let_42 :args (_let_40 false _let_41)) :args (_let_32 false _let_9 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_37))) _let_38 :args (_let_36 false _let_37)) :args (_let_23 false _let_34 false _let_32 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_31)) :args _let_29))) _let_30 :args (_let_22 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_31)) :args _let_29))) _let_30 :args (_let_21 false _let_12)) _let_28 _let_27 _let_26 _let_25 :args (false true _let_24 false _let_23 false _let_22 false _let_21 false _let_20 false _let_19 false _let_10 false _let_18)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))) _let_17 (forall ((X $$unsorted)) (tptp.leq X X)) _let_16 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))) _let_15 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))) (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq (tptp.uniform_int_rnd C X) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq tptp.n0 (tptp.uniform_int_rnd C X)))) (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim L U) Val) I) Val))) (forall ((I $$unsorted) (L1 $$unsorted) (U1 $$unsorted) (J $$unsorted) (L2 $$unsorted) (U2 $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L1 I) (tptp.leq I U1) (tptp.leq L2 J) (tptp.leq J U2)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim L1 U1) (tptp.dim L2 U2) Val) I J) Val))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.trans A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.inv A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted) (VAL $$unsorted)) (let ((_let_1 (tptp.tptp_update3 A K K VAL))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N) (tptp.leq tptp.n0 K) (tptp.leq K N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_madd A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_msub A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 D I J) (tptp.a_select3 D J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 F I J) (tptp.a_select3 F J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)) (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) _let_14 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) _let_12 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)) (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.minus X Y) X) (tptp.leq tptp.n0 Y))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V) VAL)) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= J V) (= (tptp.a_select3 X U V) VAL)) (= (tptp.a_select3 (tptp.tptp_update3 X I J VAL2) U V) VAL))) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))) tptp.true (not (= tptp.def tptp.use)) _let_11 _let_10 (tptp.gt tptp.n135299 tptp.n4) (tptp.gt tptp.n135299 tptp.n5) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n135299 tptp.tptp_minus_1) _let_9 (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) (tptp.gt tptp.n135299 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n135299 tptp.n1) (tptp.gt tptp.n2 tptp.n1) (tptp.gt tptp.n3 tptp.n1) (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n135299 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n135299 tptp.n3) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n5)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5)))) _let_8 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n3)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3)))) _let_7 _let_6 (= _let_1 tptp.n1) (= _let_2 tptp.n2) (= _let_3 tptp.n3) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.68  )
% 0.19/0.68  % SZS output end Proof for SWV163+1
% 0.19/0.68  % cvc5---1.0.5 exiting
% 0.19/0.68  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------