%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG080+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n016.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 13:49:55 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    : RNG080+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun Aug 27 03:25:57 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.61  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.WLu9LLcZao/cvc5---1.0.5_21658.p...
% 0.20/0.61  ------- get file name : TPTP file name is RNG080+2
% 0.20/0.61  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21658.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 RNG080+2
% 0.20/0.61  % SZS output start Proof for RNG080+2
% 0.20/0.61  (
% 0.20/0.61  (let ((_let_1 (tptp.sdtasasdt0 tptp.xt tptp.xt))) (let ((_let_2 (tptp.sdtasasdt0 tptp.xs tptp.xs))) (let ((_let_3 (tptp.sdtasasdt0 tptp.xs tptp.xt))) (let ((_let_4 (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_3 _let_3) (tptp.sdtasdt0 _let_2 _let_1)))) (let ((_let_5 (not _let_4))) (let ((_let_6 (tptp.sdtpldt0 tptp.xE tptp.xH))) (let ((_let_7 (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_6 _let_6) (tptp.sdtasdt0 (tptp.sdtpldt0 tptp.xC tptp.xF) (tptp.sdtpldt0 tptp.xD tptp.xG))))) (let ((_let_8 (= tptp.xH (tptp.sdtasdt0 tptp.xA tptp.xB)))) (let ((_let_9 (and (tptp.aScalar0 tptp.xH) _let_8))) (let ((_let_10 (= tptp.xG (tptp.sdtasdt0 tptp.xB tptp.xB)))) (let ((_let_11 (and (tptp.aScalar0 tptp.xG) _let_10))) (let ((_let_12 (= tptp.xF (tptp.sdtasdt0 tptp.xA tptp.xA)))) (let ((_let_13 (and (tptp.aScalar0 tptp.xF) _let_12))) (let ((_let_14 (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq)))) (let ((_let_15 (and (tptp.aScalar0 tptp.xE) _let_14))) (let ((_let_16 (= tptp.xD (tptp.sdtasasdt0 tptp.xq tptp.xq)))) (let ((_let_17 (and (tptp.aScalar0 tptp.xD) _let_16))) (let ((_let_18 (= tptp.xC (tptp.sdtasasdt0 tptp.xp tptp.xp)))) (let ((_let_19 (and (tptp.aScalar0 tptp.xC) _let_18))) (let ((_let_20 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_21 (tptp.sdtlbdtrb0 tptp.xt _let_20))) (let ((_let_22 (= tptp.xB _let_21))) (let ((_let_23 (and (tptp.aScalar0 tptp.xB) _let_22))) (let ((_let_24 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_25 (tptp.sdtlbdtrb0 tptp.xs _let_24))) (let ((_let_26 (= tptp.xA _let_25))) (let ((_let_27 (and (tptp.aScalar0 tptp.xA) _let_26))) (let ((_let_28 (tptp.sziznziztdt0 tptp.xt))) (let ((_let_29 (= tptp.xq _let_28))) (let ((_let_30 (and (tptp.aVector0 tptp.xq) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xq)) _let_20) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xq W0) (tptp.sdtlbdtrb0 tptp.xt W0)))) _let_29))) (let ((_let_31 (tptp.sziznziztdt0 tptp.xs))) (let ((_let_32 (= tptp.xp _let_31))) (let ((_let_33 (and (tptp.aVector0 tptp.xp) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xp)) _let_24) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xp W0) (tptp.sdtlbdtrb0 tptp.xs W0)))) _let_32))) (let ((_let_34 (not (= _let_24 tptp.sz00)))) (let ((_let_35 (= _let_24 _let_20))) (let ((_let_36 (tptp.aVector0 tptp.xt))) (let ((_let_37 (tptp.aVector0 tptp.xs))) (let ((_let_38 (and _let_37 _let_36))) (let ((_let_39 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= _let_2 _let_1) (not (= _let_1 tptp.sz00))) (= (tptp.sdtasasdt0 W0 W1) (tptp.sdtpldt0 (tptp.sdtasasdt0 (tptp.sziznziztdt0 W0) (tptp.sziznziztdt0 W1)) (tptp.sdtasdt0 (tptp.sdtlbdtrb0 W0 _let_2) (tptp.sdtlbdtrb0 W1 _let_1))))))))))) (let ((_let_40 (= _let_2 (tptp.sdtpldt0 (tptp.sdtasasdt0 _let_31 _let_31) (tptp.sdtasdt0 _let_25 _let_25))))) (let ((_let_41 (= _let_1 (tptp.sdtpldt0 (tptp.sdtasasdt0 _let_28 _let_28) (tptp.sdtasdt0 _let_21 _let_21))))) (let ((_let_42 (= _let_3 (tptp.sdtpldt0 (tptp.sdtasasdt0 _let_31 _let_28) (tptp.sdtasdt0 _let_25 _let_21))))) (let ((_let_43 (3))) (let ((_let_44 (1))) (let ((_let_45 (ASSUME :args (_let_7)))) (let ((_let_46 (ASSUME :args (_let_5)))) (let ((_let_47 (= tptp.sz00 _let_24))) (let ((_let_48 (not _let_37))) (let ((_let_49 (or _let_48 _let_47 _let_40))) (let ((_let_50 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (or (not (tptp.aVector0 W0)) (not (tptp.aVector0 W1)) (not (= _let_1 _let_2)) (= tptp.sz00 _let_1) (= (tptp.sdtasasdt0 W0 W1) (tptp.sdtpldt0 (tptp.sdtasasdt0 (tptp.sziznziztdt0 W0) (tptp.sziznziztdt0 W1)) (tptp.sdtasdt0 (tptp.sdtlbdtrb0 W0 _let_2) (tptp.sdtlbdtrb0 W1 _let_1)))))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_50))) (let ((_let_53 ((tptp.sdtasasdt0 (tptp.sziznziztdt0 W0) (tptp.sziznziztdt0 W1))))) (let ((_let_54 (ASSUME :args (_let_38)))) (let ((_let_55 (AND_ELIM _let_54 :args (0)))) (let ((_let_56 (SYMM (ASSUME :args (_let_34))))) (let ((_let_57 (= tptp.sz00 _let_20))) (let ((_let_58 (not _let_36))) (let ((_let_59 (or _let_58 _let_57 _let_41))) (let ((_let_60 (not _let_57))) (let ((_let_61 (ASSUME :args (_let_35)))) (let ((_let_62 (not _let_35))) (let ((_let_63 (or))) (let ((_let_64 (not _let_47))) (let ((_let_65 (and _let_35 _let_64))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_65)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_56 _let_61) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.sz00)) (SYMM _let_61) :args (=)) (FALSE_INTRO _let_56))) :args (_let_64 _let_35))) :args (_let_35 _let_64))) :args (true _let_65)) (CONG (REFL :args (_let_62)) (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_47))) (REFL :args (_let_60)) :args _let_63)) :args ((or _let_47 _let_62 _let_60))) _let_56 _let_61 :args (_let_60 true _let_47 false _let_35)))) (let ((_let_67 (AND_ELIM _let_54 :args _let_44))) (let ((_let_68 (or _let_48 _let_58 _let_62 _let_57 _let_42))) (let ((_let_69 (not _let_42))) (let ((_let_70 (not _let_41))) (let ((_let_71 (not _let_40))) (let ((_let_72 (not _let_7))) (let ((_let_73 (not _let_8))) (let ((_let_74 (not _let_10))) (let ((_let_75 (not _let_12))) (let ((_let_76 (not _let_14))) (let ((_let_77 (not _let_16))) (let ((_let_78 (not _let_18))) (let ((_let_79 (not _let_22))) (let ((_let_80 (not _let_26))) (let ((_let_81 (not _let_29))) (let ((_let_82 (not _let_32))) (let ((_let_83 (APPLY_UF tptp.sdtasdt0))) (let ((_let_84 (ASSUME :args (_let_41)))) (let ((_let_85 (APPLY_UF tptp.sdtpldt0))) (let ((_let_86 (ASSUME :args (_let_22)))) (let ((_let_87 (SYMM (SYMM _let_86)))) (let ((_let_88 (ASSUME :args (_let_10)))) (let ((_let_89 (APPLY_UF tptp.sdtasasdt0))) (let ((_let_90 (ASSUME :args (_let_29)))) (let ((_let_91 (SYMM (SYMM _let_90)))) (let ((_let_92 (ASSUME :args (_let_16)))) (let ((_let_93 (ASSUME :args (_let_40)))) (let ((_let_94 (ASSUME :args (_let_26)))) (let ((_let_95 (SYMM (SYMM _let_94)))) (let ((_let_96 (ASSUME :args (_let_12)))) (let ((_let_97 (ASSUME :args (_let_32)))) (let ((_let_98 (SYMM (SYMM _let_97)))) (let ((_let_99 (ASSUME :args (_let_18)))) (let ((_let_100 (ASSUME :args (_let_42)))) (let ((_let_101 (ASSUME :args (_let_8)))) (let ((_let_102 (ASSUME :args (_let_14)))) (let ((_let_103 (TRANS (CONG (TRANS (SYMM (SYMM _let_102)) (CONG _let_98 _let_91 :args _let_89)) (TRANS (SYMM (SYMM _let_101)) (CONG _let_95 _let_87 :args _let_83)) :args _let_85) (SYMM _let_100)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_46 _let_100 _let_97 _let_90 _let_102 _let_94 _let_86 _let_101 _let_93 _let_99 _let_96 _let_84 _let_92 _let_88 _let_45) :args (_let_32 _let_29 _let_26 _let_22 _let_18 _let_16 _let_14 _let_12 _let_10 _let_8 _let_7 _let_5 _let_40 _let_41 _let_42)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_45)) (CONG (CONG _let_103 _let_103 :args _let_83) (CONG (TRANS (CONG (TRANS (SYMM (SYMM _let_99)) (CONG _let_98 _let_98 :args _let_89)) (TRANS (SYMM (SYMM _let_96)) (CONG _let_95 _let_95 :args _let_83)) :args _let_85) (SYMM _let_93)) (TRANS (CONG (TRANS (SYMM (SYMM _let_92)) (CONG _let_91 _let_91 :args _let_89)) (TRANS (SYMM (SYMM _let_88)) (CONG _let_87 _let_87 :args _let_83)) :args _let_85) (SYMM _let_84)) :args _let_83) :args (APPLY_UF tptp.sdtlseqdt0)) (FALSE_INTRO _let_46))) :args (_let_5 _let_42 _let_32 _let_29 _let_14 _let_26 _let_22 _let_8 _let_40 _let_18 _let_12 _let_41 _let_16 _let_10 _let_7)) :args ((not (and _let_32 _let_29 _let_26 _let_22 _let_18 _let_16 _let_14 _let_12 _let_10 _let_8 _let_7 _let_5 _let_40 _let_41 _let_42)) SB_LITERAL))) (CONG (REFL :args (_let_82)) (REFL :args (_let_81)) (REFL :args (_let_80)) (REFL :args (_let_79)) (REFL :args (_let_78)) (REFL :args (_let_77)) (REFL :args (_let_76)) (REFL :args (_let_75)) (REFL :args (_let_74)) (REFL :args (_let_73)) (REFL :args (_let_72)) (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) (REFL :args (_let_71)) (REFL :args (_let_70)) (REFL :args (_let_69)) :args _let_63)) :args ((or _let_4 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_48 _let_58 _let_62 _let_57 _let_42 (not _let_68)))) _let_55 _let_67 _let_61 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xs tptp.xt QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_68 false _let_50)) :args (_let_42 false _let_37 false _let_36 false _let_35 true _let_57 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_58 _let_57 _let_41 (not _let_59)))) _let_67 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xt tptp.xt QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_59 false _let_50)) :args (_let_41 false _let_36 true _let_57 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_47 _let_48 _let_40 (not _let_49)))) _let_56 _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xs tptp.xs QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_49 false _let_50)) :args (_let_40 true _let_47 false _let_37 false _let_49)) _let_46 _let_45 (AND_ELIM (ASSUME :args (_let_9)) :args _let_44) (AND_ELIM (ASSUME :args (_let_11)) :args _let_44) (AND_ELIM (ASSUME :args (_let_13)) :args _let_44) (AND_ELIM (ASSUME :args (_let_15)) :args _let_44) (AND_ELIM (ASSUME :args (_let_17)) :args _let_44) (AND_ELIM (ASSUME :args (_let_19)) :args _let_44) (AND_ELIM (ASSUME :args (_let_23)) :args _let_44) (AND_ELIM (ASSUME :args (_let_27)) :args _let_44) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))) :args _let_43) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))) :args _let_43) :args (false false _let_42 false _let_41 false _let_40 true _let_4 false _let_7 false _let_8 false _let_10 false _let_12 false _let_14 false _let_16 false _let_18 false _let_22 false _let_26 false _let_29 false _let_32)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aNaturalNumber0 W0) (and (tptp.aNaturalNumber0 _let_1) (not (= _let_1 tptp.sz00)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= W0 (tptp.szszuzczcdt0 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) true)) (tptp.aScalar0 tptp.sz0z00) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.aScalar0 (tptp.smndt0 W0)))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aScalar0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz0z00) W0) (= (tptp.sdtpldt0 tptp.sz0z00 W0) W0) (= (tptp.sdtasdt0 W0 tptp.sz0z00) tptp.sz0z00) (= (tptp.sdtasdt0 tptp.sz0z00 W0) tptp.sz0z00) (= (tptp.sdtpldt0 W0 _let_1) tptp.sz0z00) (= (tptp.sdtpldt0 _let_1 W0) tptp.sz0z00) (= (tptp.smndt0 _let_1) W0) (= (tptp.smndt0 tptp.sz0z00) tptp.sz0z00))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtpldt0 _let_2 W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))) (= _let_2 (tptp.sdtpldt0 W1 W0)) (= (tptp.sdtasdt0 _let_1 W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))) (= _let_1 (tptp.sdtasdt0 W1 W0))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W2))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) _let_1)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 _let_1 (tptp.sdtasdt0 W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W2 W3)) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W0 W3)) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W2) (tptp.sdtasdt0 W1 W3)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.smndt0 (tptp.sdtasdt0 W0 W1)))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (and (= (tptp.sdtasdt0 W0 (tptp.smndt0 W1)) _let_1) (= (tptp.sdtasdt0 (tptp.smndt0 W0) W1) _let_1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (= (tptp.sdtasdt0 (tptp.smndt0 W0) (tptp.smndt0 W1)) (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 W2) (tptp.sdtpldt0 W1 W3))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 tptp.sz0z00 W2) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W1 W3))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 tptp.sz0z00 W0) (tptp.sdtlseqdt0 tptp.sz0z00 W1)) (and (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtpldt0 W0 W1)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 tptp.sz0z00 W0) (tptp.sdtlseqdt0 tptp.sz0z00 W1) (= (tptp.sdtasdt0 W0 W0) (tptp.sdtasdt0 W1 W1))) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.aNaturalNumber0 (tptp.aDimensionOf0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aScalar0 (tptp.sdtlbdtrb0 W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (=> (not (= (tptp.aDimensionOf0 W0) tptp.sz00)) (forall ((W1 $$unsorted)) (= (= W1 (tptp.sziznziztdt0 W0)) (and (tptp.aVector0 W1) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 W1)) (tptp.aDimensionOf0 W0)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtlbdtrb0 W1 W2) (tptp.sdtlbdtrb0 W0 W2)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= (tptp.aDimensionOf0 W0) _let_1) (not (= _let_1 tptp.sz00))) (= (tptp.aDimensionOf0 (tptp.sziznziztdt0 W0)) (tptp.aDimensionOf0 (tptp.sziznziztdt0 W1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (= (tptp.aDimensionOf0 W0) (tptp.aDimensionOf0 W1)) (tptp.aScalar0 (tptp.sdtasasdt0 W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= (tptp.aDimensionOf0 W0) _let_1) (= _let_1 tptp.sz00)) (= (tptp.sdtasasdt0 W0 W1) tptp.sz0z00))))) _let_39 (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W0 W0)))) _let_38 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.sdtasasdt0 W0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (= _let_2 (tptp.aDimensionOf0 W1)) (=> (tptp.iLess0 _let_2 (tptp.aDimensionOf0 tptp.xs)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_1 _let_1) (tptp.sdtasdt0 (tptp.sdtasasdt0 W0 W0) (tptp.sdtasasdt0 W1 W1))))))))) _let_35 _let_34 _let_33 _let_30 _let_27 _let_23 _let_19 _let_17 _let_15 _let_13 _let_11 _let_9 (and (tptp.aScalar0 tptp.xR) (= tptp.xR (tptp.sdtasdt0 tptp.xC tptp.xG))) (and (tptp.aScalar0 tptp.xP) (= tptp.xP (tptp.sdtasdt0 tptp.xE tptp.xH))) (and (tptp.aScalar0 tptp.xS) (= tptp.xS (tptp.sdtasdt0 tptp.xF tptp.xD))) (and (tptp.aScalar0 tptp.xN) (= tptp.xN (tptp.sdtasdt0 tptp.xR tptp.xS))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 tptp.xE tptp.xE) (tptp.sdtasdt0 tptp.xC tptp.xD)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 tptp.xP tptp.xP) (tptp.sdtpldt0 tptp.xR tptp.xS)) _let_7 _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.61  )
% 0.20/0.61  % SZS output end Proof for RNG080+2
% 0.20/0.61  % cvc5---1.0.5 exiting
% 0.20/0.62  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------