%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV042+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n022.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 21:49:04 EDT 2023

% Result   : Theorem 0.16s 0.61s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14  % Problem    : SWV042+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.05/0.15  % Command    : do_cvc5 %s %d
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 07:21:39 EDT 2023
% 0.12/0.35  % CPUTime    : 
% 0.16/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.16/0.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.tt3oClA8Bk/cvc5---1.0.5_24364.p...
% 0.16/0.61  ------- get file name : TPTP file name is SWV042+1
% 0.16/0.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24364.smt2...
% 0.16/0.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.16/0.61  % SZS status Theorem for SWV042+1
% 0.16/0.61  % SZS output start Proof for SWV042+1
% 0.16/0.61  (
% 0.16/0.61  (let ((_let_1 (tptp.succ tptp.n0))) (let ((_let_2 (tptp.succ _let_1))) (let ((_let_3 (tptp.succ _let_2))) (let ((_let_4 (= _let_2 tptp.n2))) (let ((_let_5 (tptp.succ _let_3))) (let ((_let_6 (tptp.gt tptp.loopcounter tptp.n1))) (let ((_let_7 (=> _let_6 (and (= tptp.pvar1400_init tptp.init) (= tptp.pvar1401_init tptp.init) (= tptp.pvar1402_init tptp.init))))) (let ((_let_8 (not (=> (and (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n2)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n3)) (= (tptp.a_select3 tptp.simplex7_init B A) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n3)) (= (tptp.a_select2 tptp.s_values7_init C) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D (tptp.minus (tptp.plus tptp.n1 tptp.n2) tptp.n1))) (= (tptp.a_select2 tptp.s_center7_init D) tptp.init))) _let_7) (and (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n2)) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n3)) (= (tptp.a_select3 tptp.simplex7_init F E) tptp.init))))) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n3)) (= (tptp.a_select2 tptp.s_values7_init G) tptp.init))) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n2)) (= (tptp.a_select2 tptp.s_center7_init H) tptp.init))) _let_7))))) (let ((_let_9 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_10 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))) (let ((_let_11 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_12 (and (= tptp.init tptp.pvar1400_init) (= tptp.init tptp.pvar1401_init) (= tptp.init tptp.pvar1402_init)))) (let ((_let_13 (=> _let_6 _let_12))) (let ((_let_14 (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.n2)) (= tptp.init (tptp.a_select2 tptp.s_center7_init H)))))) (let ((_let_15 (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n3)) (= tptp.init (tptp.a_select2 tptp.s_values7_init G)))))) (let ((_let_16 (forall ((E $$unsorted) (BOUND_VARIABLE_2176 $$unsorted)) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq E tptp.n2)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2176)) (not (tptp.leq BOUND_VARIABLE_2176 tptp.n3)) (= tptp.init (tptp.a_select3 tptp.simplex7_init BOUND_VARIABLE_2176 E)))))) (let ((_let_17 (= tptp.init (tptp.a_select2 tptp.s_center7_init SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_18 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_17))) (let ((_let_23 (tptp.plus tptp.n1 tptp.n2))) (let ((_let_24 (tptp.minus _let_23 tptp.n1))) (let ((_let_25 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_24))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_21 _let_26 _let_17))) (let ((_let_28 (= tptp.n2 _let_2))) (let ((_let_29 (= _let_3 (tptp.plus tptp.n1 _let_2)))) (let ((_let_30 (= _let_2 (tptp.pred _let_3)))) (let ((_let_31 (= _let_24 (tptp.pred _let_23)))) (let ((_let_32 (or))) (let ((_let_33 (REFL :args (_let_22)))) (let ((_let_34 (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D (tptp.minus (tptp.plus tptp.n1 tptp.n2) tptp.n1))) (= tptp.init (tptp.a_select2 tptp.s_center7_init D)))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (NOT_IMPLIES_ELIM1 _let_35))) (let ((_let_37 (_let_34))) (let ((_let_38 (SYMM (ASSUME :args (_let_4))))) (let ((_let_39 (_let_11))) (let ((_let_40 (ASSUME :args _let_39))) (let ((_let_41 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_10))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 (and _let_28 _let_18 _let_29 _let_30 _let_31))) (let ((_let_46 (ASSUME :args (_let_18)))) (let ((_let_47 (ASSUME :args (_let_30)))) (let ((_let_48 (ASSUME :args (_let_29)))) (let ((_let_49 (ASSUME :args (_let_31)))) (let ((_let_50 (not _let_14))) (let ((_let_51 (_let_50))) (let ((_let_52 (forall ((C $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.n3)) (= tptp.init (tptp.a_select2 tptp.s_values7_init C)))))) (let ((_let_53 (forall ((A $$unsorted) (BOUND_VARIABLE_2121 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n2)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2121)) (not (tptp.leq BOUND_VARIABLE_2121 tptp.n3)) (= tptp.init (tptp.a_select3 tptp.simplex7_init BOUND_VARIABLE_2121 A)))))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_IMPLIES_ELIM2 _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_53 (= BOUND_VARIABLE_2121 BOUND_VARIABLE_2176) (= A E)))) :args ((or _let_16 (not _let_53)))) (AND_ELIM _let_36 :args (0)) :args (_let_16 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_52 (= C G)))) :args ((or _let_15 (not _let_52)))) (AND_ELIM _let_36 :args (1)) :args (_let_15 false _let_52)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_51)) :args _let_51)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_14))) (REFL :args ((not _let_22))) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_45)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_46 _let_38 _let_47 _let_48 _let_49) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (TRANS (SYMM (SYMM _let_49)) (CONG (TRANS (CONG (REFL :args (tptp.n1)) _let_38 :args (APPLY_UF tptp.plus)) (SYMM _let_48)) :args (APPLY_UF tptp.pred)) (SYMM _let_47) (SYMM _let_38)) :args (APPLY_UF tptp.leq)) (TRUE_INTRO _let_46))) :args (_let_18 _let_28 _let_30 _let_29 _let_31))) :args (_let_28 _let_18 _let_29 _let_30 _let_31))) :args (true _let_45)) :args ((or (not _let_28) _let_19 _let_25 (not _let_29) (not _let_30) (not _let_31)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (_let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minus X tptp.n1)))) :args _let_43)) _let_44 :args (_let_31 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args (_let_41))) _let_42 :args (_let_30 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args _let_39))) _let_40 :args (_let_29 false _let_11)) _let_38 (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_21 _let_17 _let_26 (not _let_27)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_37) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 D) false))))) :args _let_37)) (AND_ELIM _let_36 :args (2)) :args (_let_27 false _let_34)) (CNF_OR_NEG :args (_let_22 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_32)) :args ((or _let_18 _let_22))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_32)) :args ((or _let_20 _let_22))) :args (_let_22 false _let_31 false _let_30 false _let_29 false _let_28 true _let_25 false _let_27 true _let_17 false _let_18 false _let_20)) :args (_let_14 false _let_22)) :args ((not _let_13) false _let_16 false _let_15 false _let_14)))) (let ((_let_55 (_let_13))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (AND_ELIM _let_36 :args (3))) :args ((or _let_12 (not _let_6)))) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args _let_55) _let_54 :args ((not _let_12) true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_55) :args ((or _let_6 _let_13))) _let_54 :args (_let_6 true _let_13)) :args (false true _let_12 false _let_6)) :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_11 (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_10 _let_9 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))) tptp.true (not (= tptp.def tptp.use)) _let_8 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n0 tptp.tptp_minus_1) (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n2 tptp.n1) (tptp.gt tptp.n3 tptp.n1) (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (forall ((X $$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.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_5 tptp.n4) (= (tptp.succ _let_5) tptp.n5) (= _let_1 tptp.n1) _let_4 (= _let_3 tptp.n3) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.16/0.62  )
% 0.16/0.62  % SZS output end Proof for SWV042+1
% 0.16/0.62  % cvc5---1.0.5 exiting
% 0.16/0.62  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------