%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV117+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n018.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 21:49:23 EDT 2023

% Result   : Theorem 0.21s 0.65s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SWV117+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 29 03:40:17 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.65  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2K32L0LILO/cvc5---1.0.5_8829.p...
% 0.21/0.65  ------- get file name : TPTP file name is SWV117+1
% 0.21/0.65  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_8829.smt2...
% 0.21/0.65  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.65  % SZS status Theorem for SWV117+1
% 0.21/0.65  % SZS output start Proof for SWV117+1
% 0.21/0.65  (
% 0.21/0.65  (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 (tptp.succ _let_5))) (let ((_let_7 (= _let_6 tptp.n6))) (let ((_let_8 (= _let_5 tptp.n5))) (let ((_let_9 (tptp.leq tptp.pv5 (tptp.minus tptp.n999 tptp.n1)))) (let ((_let_10 (tptp.leq tptp.n0 tptp.pv5))) (let ((_let_11 (not (=> (and _let_10 _let_9 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A _let_1) (tptp.leq B _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter A B) (tptp.a_select3 tptp.q_ds1_filter B A))))) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (=> (and (tptp.leq tptp.n0 C) (tptp.leq tptp.n0 D) (tptp.leq C _let_1) (tptp.leq D _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter C D) (tptp.a_select3 tptp.r_ds1_filter D C))))) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 E) (tptp.leq tptp.n0 F) (tptp.leq E _let_1) (tptp.leq F _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter E F) (tptp.a_select3 tptp.pminus_ds1_filter F E))))) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G (tptp.minus (tptp.plus tptp.n1 (tptp.minus tptp.n6 tptp.n1)) tptp.n1))) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter G H) (tptp.a_select3 tptp.id_ds1_filter H G))))))) (and _let_10 _let_9 (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq tptp.n0 J) (tptp.leq I _let_1) (tptp.leq J _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter I J) (tptp.a_select3 tptp.q_ds1_filter J I))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (=> (and (tptp.leq tptp.n0 K) (tptp.leq tptp.n0 L) (tptp.leq K _let_1) (tptp.leq L _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter K L) (tptp.a_select3 tptp.r_ds1_filter L K))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 M) (tptp.leq tptp.n0 N) (tptp.leq M _let_1) (tptp.leq N _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter M N) (tptp.a_select3 tptp.pminus_ds1_filter N M))))) (forall ((O $$unsorted)) (=> (and (tptp.leq tptp.n0 O) (tptp.leq O (tptp.minus tptp.n6 tptp.n1))) (forall ((P $$unsorted)) (=> (and (tptp.leq tptp.n0 P) (tptp.leq P (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter O P) (tptp.a_select3 tptp.id_ds1_filter P O))))))))))) (let ((_let_12 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_13 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))) (let ((_let_14 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_15 (= tptp.n5 _let_5))) (let ((_let_16 (= tptp.n6 _let_6))) (let ((_let_17 (tptp.minus tptp.n6 tptp.n1))) (let ((_let_18 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_17))) (let ((_let_19 (= _let_6 (tptp.plus tptp.n1 _let_5)))) (let ((_let_20 (= _let_17 (tptp.pred tptp.n6)))) (let ((_let_21 (= _let_5 (tptp.pred _let_6)))) (let ((_let_22 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.minus (tptp.plus tptp.n1 _let_17) tptp.n1)))) (let ((_let_23 (SYMM (ASSUME :args (_let_8))))) (let ((_let_24 (SYMM (ASSUME :args (_let_7))))) (let ((_let_25 (= (tptp.a_select3 tptp.id_ds1_filter SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.a_select3 tptp.id_ds1_filter SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_26 (not _let_18))) (let ((_let_27 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_17))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30 _let_28 _let_26 _let_25))) (let ((_let_34 (forall ((O $$unsorted) (BOUND_VARIABLE_2270 $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 O)) (not (tptp.leq O _let_1)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2270)) (not (tptp.leq BOUND_VARIABLE_2270 _let_1)) (= (tptp.a_select3 tptp.id_ds1_filter O BOUND_VARIABLE_2270) (tptp.a_select3 tptp.id_ds1_filter BOUND_VARIABLE_2270 O))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 M)) (not (tptp.leq tptp.n0 N)) (not (tptp.leq M _let_1)) (not (tptp.leq N _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter M N) (tptp.a_select3 tptp.pminus_ds1_filter N M))))))) (let ((_let_37 (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (or (not (tptp.leq tptp.n0 K)) (not (tptp.leq tptp.n0 L)) (not (tptp.leq K _let_1)) (not (tptp.leq L _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter K L) (tptp.a_select3 tptp.r_ds1_filter L K))))))) (let ((_let_38 (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq tptp.n0 J)) (not (tptp.leq I _let_1)) (not (tptp.leq J _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter I J) (tptp.a_select3 tptp.q_ds1_filter J I))))))) (let ((_let_39 (not _let_34))) (let ((_let_40 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq tptp.n0 F)) (not (tptp.leq E _let_1)) (not (tptp.leq F _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter E F) (tptp.a_select3 tptp.pminus_ds1_filter F E))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (NOT_IMPLIES_ELIM1 _let_41))) (let ((_let_43 (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq tptp.n0 D)) (not (tptp.leq C _let_1)) (not (tptp.leq D _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter C D) (tptp.a_select3 tptp.r_ds1_filter D C))))))) (let ((_let_44 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq tptp.n0 B)) (not (tptp.leq A _let_1)) (not (tptp.leq B _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter A B) (tptp.a_select3 tptp.q_ds1_filter B A))))))) (let ((_let_45 (or))) (let ((_let_46 (_let_39))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_34))) (REFL :args (_let_35)) :args _let_45)) (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_IMPLIES_ELIM2 _let_41)) (AND_ELIM _let_42 :args (0)) (AND_ELIM _let_42 :args (1)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_44 (= A I) (= B J)))) :args ((or _let_38 (not _let_44)))) (AND_ELIM _let_42 :args (2)) :args (_let_38 false _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_43 (= C K) (= D L)))) :args ((or _let_37 (not _let_43)))) (AND_ELIM _let_42 :args (3)) :args (_let_37 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_40 (= E M) (= F N)))) :args ((or _let_36 (not _let_40)))) (AND_ELIM _let_42 :args (4)) :args (_let_36 false _let_40)) :args (_let_39 false _let_10 false _let_9 false _let_38 false _let_37 false _let_36)) :args (_let_35 true _let_34)))) (let ((_let_48 (REFL :args (_let_33)))) (let ((_let_49 (_let_14))) (let ((_let_50 (ASSUME :args _let_49))) (let ((_let_51 (_let_13))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (not _let_22))) (let ((_let_56 (or _let_28 _let_55 _let_32 _let_30 _let_25))) (let ((_let_57 (forall ((G $$unsorted) (BOUND_VARIABLE_2216 $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G (tptp.minus (tptp.plus tptp.n1 _let_1) tptp.n1))) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2216)) (not (tptp.leq BOUND_VARIABLE_2216 _let_1)) (= (tptp.a_select3 tptp.id_ds1_filter G BOUND_VARIABLE_2216) (tptp.a_select3 tptp.id_ds1_filter BOUND_VARIABLE_2216 G))))))) (let ((_let_58 (_let_57))) (let ((_let_59 (and _let_15 _let_16 _let_18 _let_19 _let_20 _let_21))) (let ((_let_60 (ASSUME :args (_let_18)))) (let ((_let_61 (APPLY_UF tptp.leq))) (let ((_let_62 (ASSUME :args (_let_20)))) (let ((_let_63 (SYMM _let_24))) (let ((_let_64 (CONG _let_63 :args (APPLY_UF tptp.pred)))) (let ((_let_65 (ASSUME :args (_let_21)))) (let ((_let_66 (SYMM _let_65))) (let ((_let_67 (SYMM _let_23))) (let ((_let_68 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_69 (SYMM _let_64))) (let ((_let_70 (REFL :args (tptp.n1)))) (let ((_let_71 (ASSUME :args (_let_19)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_59)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_62 _let_71 _let_60 _let_24 _let_65 _let_23) (SCOPE (TRUE_ELIM (TRANS (CONG _let_68 (TRANS (CONG (TRANS (CONG _let_70 (TRANS _let_62 _let_69 _let_66) :args (APPLY_UF tptp.plus)) (SYMM _let_71) _let_63) _let_70 :args (APPLY_UF tptp.minus)) _let_62 _let_69 _let_66 _let_67) :args _let_61) (CONG _let_68 (TRANS (SYMM _let_67) (SYMM _let_66) _let_64 (SYMM _let_62)) :args _let_61) (TRUE_INTRO _let_60))) :args (_let_20 _let_19 _let_18 _let_16 _let_21 _let_15))) :args (_let_15 _let_16 _let_18 _let_19 _let_20 _let_21))) :args (true _let_59)) :args ((or (not _let_15) (not _let_16) _let_26 _let_22 (not _let_19) (not _let_20) (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_32 _let_30 _let_28 _let_25 _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_45)) :args ((or _let_31 _let_33))) _let_47 :args (_let_31 true _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 1)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_45)) :args ((or _let_29 _let_33))) _let_47 :args (_let_29 true _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 2)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_45)) :args ((or _let_27 _let_33))) _let_47 :args (_let_27 true _let_33)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 4)) _let_47 :args ((not _let_25) true _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_58) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.a_select3 tptp.id_ds1_filter G BOUND_VARIABLE_2216)))) :args _let_58))) (AND_ELIM _let_42 :args (5)) :args (_let_56 false _let_57)) :args (_let_55 false _let_31 false _let_29 false _let_27 true _let_25 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args (_let_53))) _let_54 :args (_let_21 false _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.n6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minus X tptp.n1)))) :args _let_51)) _let_52 :args (_let_20 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args _let_49))) _let_50 :args (_let_19 false _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 3)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_18))) :args _let_45)) :args ((or _let_18 _let_33))) _let_47 :args (_let_18 true _let_33)) _let_24 _let_23 :args (false true _let_22 false _let_21 false _let_20 false _let_19 false _let_18 false _let_16 false _let_15)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))) (forall ((X $$unsorted)) (not (tptp.gt X X))) (forall ((X $$unsorted)) (tptp.leq X X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))) (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))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))) (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 $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) (= (tptp.succ tptp.tptp_minus_1) tptp.n0) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) _let_14 (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 $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) _let_13 _let_12 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))) tptp.true (not (= tptp.def tptp.use)) _let_11 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n6 tptp.n4) (tptp.gt tptp.n999 tptp.n4) (tptp.gt tptp.n6 tptp.n5) (tptp.gt tptp.n999 tptp.n5) (tptp.gt tptp.n999 tptp.n6) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n6 tptp.tptp_minus_1) (tptp.gt tptp.n999 tptp.tptp_minus_1) (tptp.gt tptp.n0 tptp.tptp_minus_1) (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) (tptp.gt tptp.n6 tptp.n0) (tptp.gt tptp.n999 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n6 tptp.n1) (tptp.gt tptp.n999 tptp.n1) (tptp.gt tptp.n2 tptp.n1) (tptp.gt tptp.n3 tptp.n1) (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n6 tptp.n2) (tptp.gt tptp.n999 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n6 tptp.n3) (tptp.gt tptp.n999 tptp.n3) (forall ((X $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n5)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n6)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5) (= X tptp.n6)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))) (forall ((X $$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_4 tptp.n4) _let_8 _let_7 (= _let_1 tptp.n1) (= _let_2 tptp.n2) (= _let_3 tptp.n3) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.65  )
% 0.21/0.65  % SZS output end Proof for SWV117+1
% 0.21/0.65  % cvc5---1.0.5 exiting
% 0.21/0.66  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------