TSTP Solution File: SWV196+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV196+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 21:49:40 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV196+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.18/0.35 % Computer : n012.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Aug 29 06:55:09 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.61 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.sApmDikbnt/cvc5---1.0.5_32491.p...
% 0.20/0.61 ------- get file name : TPTP file name is SWV196+1
% 0.20/0.61 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32491.smt2...
% 0.20/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.61 % SZS status Theorem for SWV196+1
% 0.20/0.61 % SZS output start Proof for SWV196+1
% 0.20/0.61 (
% 0.20/0.61 (let ((_let_1 (tptp.succ tptp.n0))) (let ((_let_2 (tptp.succ _let_1))) (let ((_let_3 (tptp.succ _let_2))) (let ((_let_4 (tptp.succ _let_3))) (let ((_let_5 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_6 (tptp.gt tptp.pv5 tptp.n0))) (let ((_let_7 (tptp.leq tptp.pv5 tptp.n0))) (let ((_let_8 (tptp.leq tptp.n0 tptp.pv5))) (let ((_let_9 (not (=> (and (= (tptp.a_select2 tptp.rho_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.rho_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.rho_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n5) tptp.use) _let_8 _let_7 (tptp.leq tptp.pv5 tptp.n998) _let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A tptp.n2) (tptp.leq B (tptp.pred tptp.pv5))) (= (tptp.a_select3 tptp.u_defuse A B) tptp.use))) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq tptp.n0 D) (tptp.leq C tptp.n2) (tptp.leq D (tptp.pred tptp.pv5))) (= (tptp.a_select3 tptp.z_defuse C D) tptp.use)))) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (= tptp.pv5 F))) (=> (and (tptp.leq tptp.n0 E) (tptp.leq tptp.n0 F) (tptp.leq E tptp.n2) (tptp.leq F tptp.pv5)) (=> (and (not (and (= tptp.n0 E) _let_1)) (not (and (= tptp.n1 E) _let_1)) (not (and (= tptp.n2 E) _let_1))) (= (tptp.a_select3 tptp.z_defuse E F) tptp.use))))))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))) (let ((_let_11 (tptp.pred tptp.pv5))) (let ((_let_12 (tptp.leq tptp.n0 _let_11))) (let ((_let_13 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11))) (let ((_let_14 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (= _let_6 _let_12))) (let ((_let_16 (_let_10))) (let ((_let_17 (ASSUME :args _let_16))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (NOT_IMPLIES_ELIM1 _let_18))) (let ((_let_20 (= tptp.use (tptp.a_select3 tptp.z_defuse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_21 (not _let_13))) (let ((_let_22 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_21 _let_20))) (let ((_let_29 (forall ((C $$unsorted) (D $$unsorted)) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq tptp.n0 D)) (not (tptp.leq C tptp.n2)) (not (tptp.leq D (tptp.pred tptp.pv5))) (= tptp.use (tptp.a_select3 tptp.z_defuse C D)))))) (let ((_let_30 (_let_29))) (let ((_let_31 (= tptp.pv5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_32 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.pv5))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_27 _let_25 _let_23 _let_33 (and (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_31) (and (= tptp.n1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_31) (and (= tptp.n2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_31) _let_20))) (let ((_let_35 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (= tptp.pv5 F))) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq tptp.n0 F)) (not (tptp.leq E tptp.n2)) (not (tptp.leq F tptp.pv5)) (and (= tptp.n0 E) _let_1) (and (= tptp.n1 E) _let_1) (and (= tptp.n2 E) _let_1) (= tptp.use (tptp.a_select3 tptp.z_defuse E F))))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (or))) (let ((_let_38 (not _let_35))) (let ((_let_39 (_let_38))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_39)) :args _let_39)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_35))) (REFL :args (_let_36)) :args _let_37)) (NOT_IMPLIES_ELIM2 _let_18) :args (_let_36 true _let_35)))) (let ((_let_41 (REFL :args (_let_34)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 1)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_37)) :args ((or _let_24 _let_34))) _let_40 :args (_let_24 true _let_34)))) (let ((_let_43 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.n0))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_25 _let_44 _let_14))) (let ((_let_46 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (_let_46))) (let ((_let_49 ((not (= (tptp.leq tptp.n0 X) false))))) (let ((_let_50 (= tptp.n0 tptp.pv5))) (let ((_let_51 (not _let_7))) (let ((_let_52 (not _let_8))) (let ((_let_53 (or _let_52 _let_51 _let_50))) (let ((_let_54 (and _let_32 _let_50))) (let ((_let_55 (_let_32 _let_50))) (let ((_let_56 (ASSUME :args (_let_32)))) (let ((_let_57 (APPLY_UF tptp.leq))) (let ((_let_58 (ASSUME :args (_let_50)))) (let ((_let_59 (not _let_12))) (let ((_let_60 (not _let_14))) (let ((_let_61 (ASSUME :args (_let_12)))) (let ((_let_62 (ASSUME :args (_let_14)))) (let ((_let_63 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_61 _let_62 _let_63) :args (_let_14 _let_12 _let_21)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_63)) (CONG (SYMM _let_62) (REFL :args (_let_11)) :args _let_57) (TRUE_INTRO _let_61))) :args (_let_12 _let_14 _let_21)) :args ((not (and _let_14 _let_12 _let_21)) SB_LITERAL))) (CONG (REFL :args (_let_60)) (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_13))) :args _let_37)) :args ((or _let_13 _let_60 _let_59))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_25 _let_14 _let_44 (not _let_45)))) _let_42 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_54)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_56 _let_58) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (SYMM (SYMM _let_58)) :args _let_57) (TRUE_INTRO _let_56))) :args _let_55)) :args _let_55)) :args (true _let_54)) :args ((or _let_33 _let_43 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 3)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_37)) :args ((or _let_32 _let_34))) _let_40 :args (_let_32 true _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_52 _let_51 _let_50 (not _let_53)))) (AND_ELIM _let_19 :args (27)) (AND_ELIM _let_19 :args (28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.pv5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_53 false _let_46)) :args (_let_50 false _let_8 false _let_7 false _let_53)) :args (_let_43 false _let_32 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_45 false _let_46)) :args (_let_14 false _let_24 false _let_43 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_25 _let_23 _let_20 _let_21 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_37)) :args ((or _let_26 _let_34))) _let_40 :args (_let_26 true _let_34)) _let_42 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 2)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_37)) :args ((or _let_22 _let_34))) _let_40 :args (_let_22 true _let_34)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 7)) _let_40 :args ((not _let_20) true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_30) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.a_select3 tptp.z_defuse C D) tptp.use))))) :args _let_30)) (AND_ELIM _let_19 :args (32)) :args (_let_28 false _let_29)) :args (_let_21 false _let_26 false _let_24 false _let_22 true _let_20 false _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_15)) :args ((or (not _let_6) _let_12 (not _let_15)))) (AND_ELIM _let_19 :args (30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_17 :args (tptp.n0 tptp.pv5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.gt Y X)))) :args _let_16))) _let_17 :args (_let_15 false _let_10)) :args (_let_12 false _let_6 false _let_15)) :args (false false _let_14 true _let_13 false _let_12)) :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))) _let_10 (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))) (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))))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$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_9 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n998 tptp.n4) (tptp.gt tptp.n998 tptp.n5) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n998 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.n998 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.n998 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.n998 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n998 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_5 (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) (= (tptp.succ _let_4) tptp.n5) (= _let_1 tptp.n1) (= _let_2 tptp.n2) (= _let_3 tptp.n3) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.61 )
% 0.20/0.61 % SZS output end Proof for SWV196+1
% 0.20/0.61 % cvc5---1.0.5 exiting
% 0.20/0.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------