%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG057+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n025.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 13:49:44 EDT 2023

% Result   : Theorem 25.55s 26.10s
% Output   : Proof 25.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG057+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n025.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   : Sun Aug 27 02:07:54 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 25.55/26.10  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.jCJaHUTNuc/cvc5---1.0.5_14357.p...
% 25.55/26.10  ------- get file name : TPTP file name is RNG057+2
% 25.55/26.10  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14357.smt2...
% 25.55/26.10  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.55/26.10  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.55/26.10  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.55/26.10  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.55/26.10  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.55/26.10  % SZS status Theorem for RNG057+2
% 25.55/26.10  % SZS output start Proof for RNG057+2
% 25.55/26.10  (
% 25.55/26.10  (let ((_let_1 (tptp.sdtasdt0 tptp.xP tptp.xP))) (let ((_let_2 (not (tptp.sdtlseqdt0 _let_1 tptp.xN)))) (let ((_let_3 (tptp.sdtasdt0 tptp.xC tptp.xD))) (let ((_let_4 (tptp.sdtasdt0 tptp.xH tptp.xH))) (let ((_let_5 (= tptp.xN (tptp.sdtasdt0 _let_4 _let_3)))) (let ((_let_6 (tptp.sdtasdt0 tptp.xE tptp.xE))) (let ((_let_7 (= _let_1 (tptp.sdtasdt0 _let_4 _let_6)))) (let ((_let_8 (tptp.sdtlseqdt0 _let_6 _let_3))) (let ((_let_9 (= tptp.xN (tptp.sdtasdt0 tptp.xR tptp.xS)))) (let ((_let_10 (and (tptp.aScalar0 tptp.xN) _let_9))) (let ((_let_11 (= tptp.xS (tptp.sdtasdt0 tptp.xF tptp.xD)))) (let ((_let_12 (and (tptp.aScalar0 tptp.xS) _let_11))) (let ((_let_13 (= tptp.xP (tptp.sdtasdt0 tptp.xE tptp.xH)))) (let ((_let_14 (and (tptp.aScalar0 tptp.xP) _let_13))) (let ((_let_15 (= tptp.xR (tptp.sdtasdt0 tptp.xC tptp.xG)))) (let ((_let_16 (and (tptp.aScalar0 tptp.xR) _let_15))) (let ((_let_17 (= tptp.xH (tptp.sdtasdt0 tptp.xA tptp.xB)))) (let ((_let_18 (and (tptp.aScalar0 tptp.xH) _let_17))) (let ((_let_19 (= tptp.xG (tptp.sdtasdt0 tptp.xB tptp.xB)))) (let ((_let_20 (and (tptp.aScalar0 tptp.xG) _let_19))) (let ((_let_21 (= tptp.xF (tptp.sdtasdt0 tptp.xA tptp.xA)))) (let ((_let_22 (and (tptp.aScalar0 tptp.xF) _let_21))) (let ((_let_23 (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq)))) (let ((_let_24 (and (tptp.aScalar0 tptp.xE) _let_23))) (let ((_let_25 (= tptp.xD (tptp.sdtasasdt0 tptp.xq tptp.xq)))) (let ((_let_26 (and (tptp.aScalar0 tptp.xD) _let_25))) (let ((_let_27 (= tptp.xC (tptp.sdtasasdt0 tptp.xp tptp.xp)))) (let ((_let_28 (and (tptp.aScalar0 tptp.xC) _let_27))) (let ((_let_29 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_30 (tptp.sdtlbdtrb0 tptp.xt _let_29))) (let ((_let_31 (and (tptp.aScalar0 tptp.xB) (= tptp.xB _let_30)))) (let ((_let_32 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_33 (tptp.sdtlbdtrb0 tptp.xs _let_32))) (let ((_let_34 (and (tptp.aScalar0 tptp.xA) (= tptp.xA _let_33)))) (let ((_let_35 (tptp.sziznziztdt0 tptp.xt))) (let ((_let_36 (and (tptp.aVector0 tptp.xq) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xq)) _let_29) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xq W0) (tptp.sdtlbdtrb0 tptp.xt W0)))) (= tptp.xq _let_35)))) (let ((_let_37 (tptp.sziznziztdt0 tptp.xs))) (let ((_let_38 (and (tptp.aVector0 tptp.xp) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xp)) _let_32) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xp W0) (tptp.sdtlbdtrb0 tptp.xs W0)))) (= tptp.xp _let_37)))) (let ((_let_39 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W0)))))) (let ((_let_40 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 tptp.sz0z00 W2) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W1 W3))))))) (let ((_let_41 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_42 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_43 (tptp.sdtasdt0 _let_33 _let_30))) (let ((_let_44 (tptp.sdtasasdt0 _let_37 _let_35))) (let ((_let_45 (tptp.sdtasdt0 _let_44 _let_43))) (let ((_let_46 (tptp.sdtasdt0 _let_45 _let_45))) (let ((_let_47 (tptp.sdtasdt0 _let_44 _let_44))) (let ((_let_48 (tptp.sdtasdt0 _let_43 _let_43))) (let ((_let_49 (tptp.sdtasdt0 _let_48 _let_47))) (let ((_let_50 (= _let_49 _let_46))) (let ((_let_51 (tptp.sdtasasdt0 _let_35 _let_35))) (let ((_let_52 (tptp.sdtasasdt0 _let_37 _let_37))) (let ((_let_53 (tptp.sdtasdt0 _let_52 _let_51))) (let ((_let_54 (tptp.sdtasdt0 _let_48 _let_53))) (let ((_let_55 (tptp.sdtasdt0 (tptp.sdtasdt0 _let_52 (tptp.sdtasdt0 _let_30 _let_30)) (tptp.sdtasdt0 (tptp.sdtasdt0 _let_33 _let_33) _let_51)))) (let ((_let_56 (= _let_55 _let_54))) (let ((_let_57 (tptp.sdtlseqdt0 _let_46 _let_55))) (let ((_let_58 (tptp.sdtlseqdt0 _let_49 _let_54))) (let ((_let_59 (3))) (let ((_let_60 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))) :args _let_59))) (let ((_let_61 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))) :args _let_59))) (let ((_let_62 (1))) (let ((_let_63 (AND_ELIM (ASSUME :args (_let_34)) :args _let_62))) (let ((_let_64 (AND_ELIM (ASSUME :args (_let_31)) :args _let_62))) (let ((_let_65 (ASSUME :args (_let_28)))) (let ((_let_66 (EQ_RESOLVE (AND_ELIM _let_65 :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_64 _let_63 _let_61 _let_60) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (ASSUME :args (_let_26)))) (let ((_let_68 (EQ_RESOLVE (AND_ELIM _let_67 :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (ASSUME :args (_let_24)))) (let ((_let_70 (EQ_RESOLVE (AND_ELIM _let_69 :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_68 _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_22)) :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_70 _let_68 _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_20)) :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_71 _let_70 _let_68 _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (ASSUME :args (_let_18)))) (let ((_let_74 (EQ_RESOLVE (AND_ELIM _let_73 :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_72 _let_71 _let_70 _let_68 _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_16)) :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_74 _let_72 _let_71 _let_70 _let_68 _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_14)) :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_75 _let_74 _let_72 _let_71 _let_70 _let_68 _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_12)) :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_76 _let_75 _let_74 _let_72 _let_71 _let_70 _let_68 _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (AND_INTRO (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_10)) :args _let_62) (MACRO_SR_EQ_INTRO (AND_INTRO _let_77 _let_76 _let_75 _let_74 _let_72 _let_71 _let_70 _let_68 _let_66 _let_64 _let_63 _let_61 _let_60) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) _let_77 _let_76 _let_75 _let_74 _let_72 _let_71 _let_70 _let_68 _let_66 _let_64 _let_63 _let_61 _let_60))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO _let_78 :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO _let_78 :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO _let_78 :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (tptp.sdtlseqdt0 _let_47 _let_53))) (let ((_let_83 (not _let_82))) (let ((_let_84 (tptp.sdtlseqdt0 tptp.sz0z00 _let_47))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.sdtlseqdt0 _let_48 _let_48))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.aScalar0 _let_53))) (let ((_let_89 (not _let_88))) (let ((_let_90 (tptp.aScalar0 _let_47))) (let ((_let_91 (not _let_90))) (let ((_let_92 (tptp.aScalar0 _let_48))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_93 _let_93 _let_91 _let_89 _let_87 _let_85 _let_83 _let_58))) (let ((_let_95 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (not (tptp.aScalar0 W2)) (not (tptp.aScalar0 W3)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 tptp.sz0z00 W2)) (not (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W1 W3)))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (or _let_93 _let_86))) (let ((_let_98 (forall ((W0 $$unsorted)) (or (not (tptp.aScalar0 W0)) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (tptp.aScalar0 _let_43))) (let ((_let_101 (not _let_100))) (let ((_let_102 (or _let_101 _let_101 _let_92))) (let ((_let_103 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (_let_103))) (let ((_let_106 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_102))) :args ((or _let_101 _let_92 (not _let_102)))) (EQ_RESOLVE _let_73 (MACRO_SR_EQ_INTRO _let_78 :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_43 _let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_102 false _let_103)) :args (_let_92 false _let_100 false _let_102)))) (let ((_let_108 (tptp.aScalar0 _let_44))) (let ((_let_109 (not _let_108))) (let ((_let_110 (or _let_109 _let_84))) (let ((_let_111 (forall ((W0 $$unsorted)) (or (not (tptp.aScalar0 W0)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W0)))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (EQ_RESOLVE _let_69 (MACRO_SR_EQ_INTRO _let_78 :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (tptp.aScalar0 _let_51))) (let ((_let_115 (not _let_114))) (let ((_let_116 (tptp.aScalar0 _let_52))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or _let_117 _let_115 _let_88))) (let ((_let_119 (or _let_109 _let_109 _let_90))) (let ((_let_120 (not _let_58))) (let ((_let_121 (not _let_56))) (let ((_let_122 (not _let_50))) (let ((_let_123 (not _let_57))) (let ((_let_124 (ASSUME :args (_let_58)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_124 _let_79 _let_80 _let_81) :args (_let_50 _let_56 _let_123 _let_58)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_81)) (CONG (SYMM _let_79) (SYMM (SYMM _let_80)) :args (APPLY_UF tptp.sdtlseqdt0)) (TRUE_INTRO _let_124))) :args (_let_58 _let_50 _let_56 _let_123)) :args ((not (and _let_50 _let_56 _let_123 _let_58)) SB_LITERAL))) (CONG (REFL :args (_let_122)) (REFL :args (_let_121)) (MACRO_SR_PRED_INTRO :args ((= (not _let_123) _let_57))) (REFL :args (_let_120)) :args (or))) :args ((or _let_57 _let_122 _let_121 _let_120))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_94))) :args ((or _let_83 _let_93 _let_91 _let_89 _let_85 _let_87 _let_58 (not _let_94)))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO _let_78 :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) _let_107 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_119))) :args ((or _let_109 _let_90 (not _let_119)))) _let_113 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_44 _let_44 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_119 false _let_103)) :args (_let_90 false _let_108 false _let_119)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_117 _let_115 _let_88 (not _let_118)))) (EQ_RESOLVE _let_65 (MACRO_SR_EQ_INTRO _let_78 :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE _let_67 (MACRO_SR_EQ_INTRO _let_78 :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_52 _let_51 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_118 false _let_103)) :args (_let_88 false _let_116 false _let_114 false _let_118)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_109 _let_84 (not _let_110)))) _let_113 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (_let_44 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aScalar0 W0) false))))) :args (_let_111))) _let_112 :args (_let_110 false _let_111)) :args (_let_84 false _let_108 false _let_110)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_97)) :args ((or _let_93 _let_86 (not _let_97)))) _let_107 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (_let_48 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_98))) _let_99 :args (_let_97 false _let_98)) :args (_let_86 false _let_92 false _let_97)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (_let_48 _let_48 _let_47 _let_53 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_95))) _let_96 :args (_let_94 false _let_95)) :args (_let_58 false _let_82 false _let_92 false _let_90 false _let_88 false _let_84 false _let_86 false _let_94)) _let_81 _let_80 _let_79 :args (false false _let_58 true _let_57 false _let_56 false _let_50)) :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)))) _let_42 (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))) _let_41 (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 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 W2) (tptp.sdtpldt0 W1 W3))))) _let_40 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 tptp.sz0z00 W0) (tptp.sdtlseqdt0 tptp.sz0z00 W1)) (and (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtpldt0 W0 W1)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W1)))))) _let_39 (forall ((W0 $$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))))) (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))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W0 W0)))) (and (tptp.aVector0 tptp.xs) (tptp.aVector0 tptp.xt)) (forall ((W0 $$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_32 _let_29) (not (= _let_32 tptp.sz00)) _let_38 _let_36 _let_34 _let_31 _let_28 _let_26 _let_24 _let_22 _let_20 _let_18 _let_16 _let_14 _let_12 _let_10 _let_8 _let_7 _let_5 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.55/26.10  )
% 25.55/26.10  % SZS output end Proof for RNG057+2
% 25.55/26.10  % cvc5---1.0.5 exiting
% 25.55/26.10  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------