TSTP Solution File: SWV041+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV041+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 0.47s 0.64s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWV041+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.10/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n007.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 08:12:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.47/0.64 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.2rjoTJOOoU/cvc5---1.0.5_10940.p...
% 0.47/0.64 ------- get file name : TPTP file name is SWV041+1
% 0.47/0.64 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10940.smt2...
% 0.47/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.47/0.64 % SZS status Theorem for SWV041+1
% 0.47/0.64 % SZS output start Proof for SWV041+1
% 0.47/0.64 (
% 0.47/0.64 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_9 (tptp.gt tptp.n0 tptp.tptp_minus_1))) (let ((_let_10 (tptp.gt tptp.n5 tptp.n4))) (let ((_let_11 (not (=> (and (tptp.geq (tptp.minus tptp.n330 tptp.n1) tptp.n0) (tptp.geq (tptp.minus tptp.n410 tptp.n1) tptp.n0)) (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n2)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.minus tptp.n0 tptp.n1))) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim tptp.n0 tptp.n3) (tptp.dim tptp.n0 tptp.n2) tptp.uninit) B A) tptp.init))))))))) (let ((_let_12 (forall ((X $$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.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))) (let ((_let_15 (tptp.succ tptp.tptp_minus_1))) (let ((_let_16 (= _let_15 tptp.n0))) (let ((_let_17 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_19 (forall ((X $$unsorted)) (not (tptp.gt X X))))) (let ((_let_20 (= tptp.n0 _let_15))) (let ((_let_21 (= tptp.n4 _let_4))) (let ((_let_22 (= tptp.n5 _let_5))) (let ((_let_23 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ _let_15)))) (tptp.plus tptp.n5 tptp.tptp_minus_1)))) (let ((_let_24 (= _let_5 (tptp.plus tptp.n5 tptp.n0)))) (let ((_let_25 (tptp.minus tptp.n0 tptp.n1))) (let ((_let_26 (= _let_25 (tptp.pred tptp.n0)))) (let ((_let_27 (= tptp.tptp_minus_1 (tptp.pred _let_15)))) (let ((_let_28 (= tptp.n0 _let_25))) (let ((_let_29 (tptp.gt tptp.n4 tptp.n4))) (let ((_let_30 (SYMM (ASSUME :args (_let_16))))) (let ((_let_31 (ASSUME :args (_let_10)))) (let ((_let_32 (SYMM (ASSUME :args (_let_7))))) (let ((_let_33 (SYMM (ASSUME :args (_let_6))))) (let ((_let_34 (_let_14))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_37 (_let_13))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minus X tptp.n1)))) :args _let_37)) _let_38 :args (_let_26 false _let_13)))) (let ((_let_40 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args (_let_40))) _let_41 :args (_let_27 false _let_40)))) (let ((_let_43 (tptp.leq _let_25 tptp.n0))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.leq tptp.n0 _let_25))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_28))) (let ((_let_48 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_25))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51 _let_45))) (let ((_let_55 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq X Y)) (not (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or (not (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2)) _let_53 _let_51 (= tptp.init (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim tptp.n0 tptp.n3) (tptp.dim tptp.n0 tptp.n2) tptp.uninit) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_58 (forall ((A $$unsorted) (BOUND_VARIABLE_2079 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n2)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2079)) (not (tptp.leq BOUND_VARIABLE_2079 (tptp.minus tptp.n0 tptp.n1))) (= tptp.init (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim tptp.n0 tptp.n3) (tptp.dim tptp.n0 tptp.n2) tptp.uninit) BOUND_VARIABLE_2079 A)))))) (let ((_let_59 (not _let_57))) (let ((_let_60 (or))) (let ((_let_61 (not _let_58))) (let ((_let_62 (_let_61))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_62)) :args _let_62)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_58))) (REFL :args (_let_59)) :args _let_60)) (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)))) :args (_let_59 true _let_58)))) (let ((_let_64 (REFL :args (_let_57)))) (let ((_let_65 (tptp.leq tptp.tptp_minus_1 tptp.n0))) (let ((_let_66 (not _let_9))) (let ((_let_67 (or _let_66 _let_65))) (let ((_let_68 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (not _let_27))) (let ((_let_71 (not _let_26))) (let ((_let_72 (not _let_20))) (let ((_let_73 (and _let_20 _let_65 _let_26 _let_27))) (let ((_let_74 (ASSUME :args (_let_65)))) (let ((_let_75 (ASSUME :args (_let_27)))) (let ((_let_76 (SYMM _let_75))) (let ((_let_77 (APPLY_UF tptp.pred))) (let ((_let_78 (SYMM _let_30))) (let ((_let_79 (ASSUME :args (_let_26)))) (let ((_let_80 (SYMM (SYMM _let_79)))) (let ((_let_81 (not _let_29))) (let ((_let_82 (_let_19))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (not _let_28))) (let ((_let_85 (not _let_24))) (let ((_let_86 (not _let_23))) (let ((_let_87 (not _let_22))) (let ((_let_88 (not _let_21))) (let ((_let_89 (not _let_10))) (let ((_let_90 (ASSUME :args (_let_81)))) (let ((_let_91 (APPLY_UF tptp.succ))) (let ((_let_92 (ASSUME :args (_let_23)))) (let ((_let_93 (ASSUME :args (_let_28)))) (let ((_let_94 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_90 _let_32 _let_30 _let_92 _let_75 _let_79 _let_93 _let_94 _let_33 _let_31) :args (_let_10 _let_20 _let_21 _let_22 _let_23 _let_24 _let_26 _let_27 _let_28 _let_81)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_31)) (CONG (TRANS (SYMM (SYMM _let_33)) (SYMM (SYMM _let_94)) (CONG (REFL :args (tptp.n5)) (TRANS (SYMM (SYMM _let_93)) _let_80 (CONG _let_30 :args _let_77) _let_76) :args (APPLY_UF tptp.plus)) (SYMM _let_92) (CONG (CONG (CONG (CONG _let_78 :args _let_91) :args _let_91) :args _let_91) :args _let_91) (SYMM _let_32)) (REFL :args (tptp.n4)) :args (APPLY_UF tptp.gt)) (FALSE_INTRO _let_90))) :args (_let_81 _let_21 _let_20 _let_23 _let_27 _let_26 _let_28 _let_24 _let_22 _let_10)) :args ((not (and _let_10 _let_20 _let_21 _let_22 _let_23 _let_24 _let_26 _let_27 _let_28 _let_81)) SB_LITERAL))) (CONG (REFL :args (_let_89)) (REFL :args (_let_72)) (REFL :args (_let_88)) (REFL :args (_let_87)) (REFL :args (_let_86)) (REFL :args (_let_85)) (REFL :args (_let_71)) (REFL :args (_let_70)) (REFL :args (_let_84)) (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_29))) :args _let_60)) :args ((or _let_72 _let_89 _let_88 _let_87 _let_86 _let_85 _let_71 _let_70 _let_84 _let_29))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (tptp.n4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt X X) false))))) :args _let_82)) _let_83 :args (_let_81 false _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_44 _let_46 _let_28 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_73)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_74 _let_75 _let_30 _let_79) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS _let_80 (CONG (SYMM _let_78) :args _let_77) _let_76) (REFL :args (tptp.n0)) :args (APPLY_UF tptp.leq)) (TRUE_INTRO _let_74))) :args (_let_65 _let_27 _let_20 _let_26))) :args (_let_20 _let_65 _let_26 _let_27))) :args (true _let_73)) :args ((or _let_72 _let_43 (not _let_65) _let_71 _let_70))) _let_30 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_65 (not _let_67)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.tptp_minus_1 tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_65 false _let_9 false _let_67)) _let_39 _let_42 :args (_let_43 false _let_20 false _let_65 false _let_26 false _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_51 _let_45 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 2)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_60)) :args ((or _let_52 _let_57))) _let_63 :args (_let_52 true _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 3)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_60)) :args ((or _let_50 _let_57))) _let_63 :args (_let_50 true _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_25 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.leq X Y) false)) (not (= (tptp.leq Y Z) false))))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_45 false _let_52 false _let_50 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_28 false _let_43 false _let_45 false _let_47)) _let_42 _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_36)) :args _let_34))) _let_35 :args (_let_24 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_36)) :args _let_34))) _let_35 :args (_let_23 false _let_14)) _let_33 _let_32 _let_31 _let_30 :args (false true _let_29 false _let_28 false _let_27 false _let_26 false _let_24 false _let_23 false _let_22 false _let_21 false _let_10 false _let_20)) :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_19 (forall ((X $$unsorted)) (tptp.leq X X)) _let_18 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))) _let_17 (forall ((X $$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_16 (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 $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) _let_14 _let_13 _let_12 (forall ((X $$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 _let_10 (tptp.gt tptp.n330 tptp.n4) (tptp.gt tptp.n410 tptp.n4) (tptp.gt tptp.n330 tptp.n5) (tptp.gt tptp.n410 tptp.n5) (tptp.gt tptp.n410 tptp.n330) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n330 tptp.tptp_minus_1) (tptp.gt tptp.n410 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.n330 tptp.n0) (tptp.gt tptp.n410 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.n330 tptp.n1) (tptp.gt tptp.n410 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.n330 tptp.n2) (tptp.gt tptp.n410 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n330 tptp.n3) (tptp.gt tptp.n410 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.47/0.64 )
% 0.47/0.64 % SZS output end Proof for SWV041+1
% 0.47/0.64 % cvc5---1.0.5 exiting
% 0.47/0.64 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------