TSTP Solution File: SWV191+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV191+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 21:49:39 EDT 2023
% Result : Theorem 0.20s 0.67s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWV191+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n008.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 06:44:02 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.67 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.NZTba7QA0z/cvc5---1.0.5_9003.p...
% 0.20/0.67 ------- get file name : TPTP file name is SWV191+1
% 0.20/0.67 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9003.smt2...
% 0.20/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.67 % SZS status Theorem for SWV191+1
% 0.20/0.67 % SZS output start Proof for SWV191+1
% 0.20/0.67 (
% 0.20/0.67 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_9 (tptp.gt tptp.n0 tptp.tptp_minus_1))) (let ((_let_10 (tptp.gt tptp.n5 tptp.n4))) (let ((_let_11 (not (=> (and (= (tptp.a_select2 tptp.rho_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.rho_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.rho_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n5) tptp.use)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A tptp.n2) (tptp.leq B tptp.tptp_minus_1)) (= (tptp.a_select3 tptp.z_defuse A B) tptp.use))))))) (let ((_let_12 (forall ((X $$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.gt tptp.n4 tptp.n4))) (let ((_let_19 (_let_17))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 (= tptp.n0 tptp.tptp_minus_1))) (let ((_let_22 (= _let_5 (tptp.plus tptp.n5 tptp.n0)))) (let ((_let_23 (= (tptp.succ (tptp.succ (tptp.succ (tptp.succ _let_13)))) (tptp.plus tptp.n5 tptp.tptp_minus_1)))) (let ((_let_24 (= tptp.n5 _let_5))) (let ((_let_25 (= tptp.n4 _let_4))) (let ((_let_26 (= tptp.n0 _let_13))) (let ((_let_27 (tptp.leq tptp.tptp_minus_1 tptp.n0))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.leq tptp.n0 tptp.tptp_minus_1))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28 _let_21))) (let ((_let_32 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (not _let_9))) (let ((_let_35 (or _let_34 _let_27))) (let ((_let_36 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.tptp_minus_1))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_39 _let_29))) (let ((_let_43 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq X Y)) (not (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (or (not (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) _let_41 (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2)) _let_39 (= tptp.use (tptp.a_select3 tptp.z_defuse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_46 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq tptp.n0 B)) (not (tptp.leq A tptp.n2)) (not (tptp.leq B tptp.tptp_minus_1)) (= tptp.use (tptp.a_select3 tptp.z_defuse A B)))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (or))) (let ((_let_49 (not _let_46))) (let ((_let_50 (_let_49))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_50)) :args _let_50)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_46))) (REFL :args (_let_47)) :args _let_48)) (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)))) :args (_let_47 true _let_46)))) (let ((_let_52 (REFL :args (_let_45)))) (let ((_let_53 (_let_12))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_56 (SYMM (ASSUME :args (_let_6))))) (let ((_let_57 (SYMM (ASSUME :args (_let_7))))) (let ((_let_58 (ASSUME :args (_let_10)))) (let ((_let_59 (SYMM (ASSUME :args (_let_14))))) (let ((_let_60 (and _let_10 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21))) (let ((_let_61 (ASSUME :args (_let_22)))) (let ((_let_62 (ASSUME :args (_let_21)))) (let ((_let_63 (ASSUME :args (_let_23)))) (let ((_let_64 (APPLY_UF tptp.succ))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (tptp.n4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt X X) false))))) :args _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_60)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_58 _let_56 _let_61 _let_62 _let_63 _let_59 _let_57) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (SYMM (SYMM _let_57)) (CONG (CONG (CONG (CONG (SYMM (SYMM _let_59)) :args _let_64) :args _let_64) :args _let_64) :args _let_64) (SYMM (SYMM _let_63)) (CONG (REFL :args (tptp.n5)) (SYMM _let_62) :args (APPLY_UF tptp.plus)) (SYMM _let_61) (SYMM _let_56)) (REFL :args (tptp.n4)) :args (APPLY_UF tptp.gt)) (TRUE_INTRO _let_58))) :args (_let_10 _let_24 _let_22 _let_21 _let_23 _let_26 _let_25))) :args (_let_10 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21))) :args (true _let_60)) :args ((or (not _let_26) (not _let_10) (not _let_25) (not _let_24) (not _let_23) (not _let_22) (not _let_21) _let_18))) _let_59 _let_58 _let_57 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_55)) :args _let_53))) _let_54 :args (_let_23 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_55)) :args _let_53))) _let_54 :args (_let_22 false _let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_28 _let_21 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_39 _let_29 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_48)) :args ((or _let_40 _let_45))) _let_51 :args (_let_40 true _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 3)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_48)) :args ((or _let_38 _let_45))) _let_51 :args (_let_38 true _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.leq X Y) false)) (not (= (tptp.leq Y Z) false))))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_29 false _let_40 false _let_38 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_27 (not _let_35)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.tptp_minus_1 tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_36))) _let_37 :args (_let_35 false _let_36)) :args (_let_27 false _let_9 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_32))) _let_33 :args (_let_31 false _let_32)) :args (_let_21 false _let_29 false _let_27 false _let_31)) :args (_let_18 false _let_26 false _let_10 false _let_25 false _let_24 false _let_23 false _let_22 false _let_21)) _let_20 :args (false false _let_18 false _let_17)) :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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))) tptp.true (not (= tptp.def tptp.use)) _let_11 _let_10 (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) _let_9 (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n2 tptp.n1) (tptp.gt tptp.n3 tptp.n1) (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (forall ((X $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n5)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5)))) _let_8 (forall ((X $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.68 )
% 0.20/0.68 % SZS output end Proof for SWV191+1
% 0.20/0.68 % cvc5---1.0.5 exiting
% 0.20/0.68 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------