TSTP Solution File: RNG052+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG052+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 13:49:42 EDT 2023
% Result : Theorem 10.37s 10.82s
% Output : Proof 10.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG052+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n009.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 01:35:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 10.37/10.82 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XPfwEs6UkS/cvc5---1.0.5_12254.p...
% 10.37/10.82 ------- get file name : TPTP file name is RNG052+1
% 10.37/10.82 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12254.smt2...
% 10.37/10.82 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.37/10.82 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.37/10.82 % SZS status Theorem for RNG052+1
% 10.37/10.82 % SZS output start Proof for RNG052+1
% 10.37/10.82 (
% 10.37/10.82 (let ((_let_1 (not (tptp.sdtlseqdt0 (tptp.sdtasdt0 tptp.xE tptp.xE) (tptp.sdtasdt0 tptp.xC tptp.xD))))) (let ((_let_2 (= tptp.xN (tptp.sdtasdt0 tptp.xR tptp.xS)))) (let ((_let_3 (and (tptp.aScalar0 tptp.xN) _let_2))) (let ((_let_4 (= tptp.xS (tptp.sdtasdt0 tptp.xF tptp.xD)))) (let ((_let_5 (and (tptp.aScalar0 tptp.xS) _let_4))) (let ((_let_6 (= tptp.xP (tptp.sdtasdt0 tptp.xE tptp.xH)))) (let ((_let_7 (and (tptp.aScalar0 tptp.xP) _let_6))) (let ((_let_8 (= tptp.xR (tptp.sdtasdt0 tptp.xC tptp.xG)))) (let ((_let_9 (and (tptp.aScalar0 tptp.xR) _let_8))) (let ((_let_10 (= tptp.xH (tptp.sdtasdt0 tptp.xA tptp.xB)))) (let ((_let_11 (and (tptp.aScalar0 tptp.xH) _let_10))) (let ((_let_12 (= tptp.xG (tptp.sdtasdt0 tptp.xB tptp.xB)))) (let ((_let_13 (and (tptp.aScalar0 tptp.xG) _let_12))) (let ((_let_14 (= tptp.xF (tptp.sdtasdt0 tptp.xA tptp.xA)))) (let ((_let_15 (and (tptp.aScalar0 tptp.xF) _let_14))) (let ((_let_16 (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq)))) (let ((_let_17 (and (tptp.aScalar0 tptp.xE) _let_16))) (let ((_let_18 (= tptp.xD (tptp.sdtasasdt0 tptp.xq tptp.xq)))) (let ((_let_19 (and (tptp.aScalar0 tptp.xD) _let_18))) (let ((_let_20 (= tptp.xC (tptp.sdtasasdt0 tptp.xp tptp.xp)))) (let ((_let_21 (and (tptp.aScalar0 tptp.xC) _let_20))) (let ((_let_22 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_23 (and (tptp.aScalar0 tptp.xB) (= tptp.xB (tptp.sdtlbdtrb0 tptp.xt _let_22))))) (let ((_let_24 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_25 (and (tptp.aScalar0 tptp.xA) (= tptp.xA (tptp.sdtlbdtrb0 tptp.xs _let_24))))) (let ((_let_26 (tptp.sziznziztdt0 tptp.xt))) (let ((_let_27 (and (tptp.aVector0 tptp.xq) (= tptp.xq _let_26)))) (let ((_let_28 (tptp.sziznziztdt0 tptp.xs))) (let ((_let_29 (and (tptp.aVector0 tptp.xp) (= tptp.xp _let_28)))) (let ((_let_30 (not (= _let_24 tptp.sz00)))) (let ((_let_31 (= _let_24 _let_22))) (let ((_let_32 (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 ((_let_33 (tptp.aVector0 tptp.xt))) (let ((_let_34 (tptp.aVector0 tptp.xs))) (let ((_let_35 (and _let_34 _let_33))) (let ((_let_36 (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))))))))) (let ((_let_37 (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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtlbdtrb0 W1 W2) (tptp.sdtlbdtrb0 W0 W2)))))))))))) (let ((_let_38 (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.aNaturalNumber0 (tptp.aDimensionOf0 W0)))))) (let ((_let_39 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_40 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.sdtasasdt0 W0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (or (not (tptp.aVector0 W0)) (not (tptp.aVector0 W1)) (not (= _let_2 (tptp.aDimensionOf0 W1))) (not (tptp.iLess0 _let_2 (tptp.aDimensionOf0 tptp.xs))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_1 _let_1) (tptp.sdtasdt0 (tptp.sdtasasdt0 W0 W0) (tptp.sdtasasdt0 W1 W1))))))))) (let ((_let_41 (tptp.sdtasasdt0 _let_28 _let_26))) (let ((_let_42 (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_41 _let_41) (tptp.sdtasdt0 (tptp.sdtasasdt0 _let_28 _let_28) (tptp.sdtasasdt0 _let_26 _let_26))))) (let ((_let_43 (tptp.aDimensionOf0 _let_28))) (let ((_let_44 (tptp.iLess0 _let_43 _let_24))) (let ((_let_45 (not _let_44))) (let ((_let_46 (= _let_43 (tptp.aDimensionOf0 _let_26)))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.aVector0 _let_26))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.aVector0 _let_28))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49 _let_47 _let_45 _let_42))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (tptp.szszuzczcdt0 _let_43))) (let ((_let_56 (= _let_24 _let_55))) (let ((_let_57 (tptp.iLess0 _let_43 _let_55))) (let ((_let_58 (and _let_50 _let_56 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtlbdtrb0 tptp.xs W2) (tptp.sdtlbdtrb0 (tptp.sziznziztdt0 tptp.xs) W2))))))) (let ((_let_59 (= tptp.sz00 _let_24))) (let ((_let_60 (not _let_34))) (let ((_let_61 (or _let_60 _let_59 _let_58))) (let ((_let_62 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1429 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W0))) (or (not (tptp.aVector0 W0)) (= tptp.sz00 _let_1) (= (= (tptp.sziznziztdt0 W0) BOUND_VARIABLE_1429) (and (tptp.aVector0 BOUND_VARIABLE_1429) (= _let_1 (tptp.szszuzczcdt0 (tptp.aDimensionOf0 BOUND_VARIABLE_1429))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtlbdtrb0 W0 W2) (tptp.sdtlbdtrb0 BOUND_VARIABLE_1429 W2))))))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (ASSUME :args (_let_35)))) (let ((_let_65 (AND_ELIM _let_64 :args (0)))) (let ((_let_66 (SYMM (ASSUME :args (_let_30))))) (let ((_let_67 (tptp.aNaturalNumber0 _let_43))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_57))) (let ((_let_70 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (or _let_51 _let_67))) (let ((_let_73 (forall ((W0 $$unsorted)) (or (not (tptp.aVector0 W0)) (tptp.aNaturalNumber0 (tptp.aDimensionOf0 W0)))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (1))) (let ((_let_76 (ASSUME :args (_let_29)))) (let ((_let_77 (AND_ELIM _let_76 :args _let_75))) (let ((_let_78 (ASSUME :args (_let_27)))) (let ((_let_79 (AND_ELIM _let_78 :args _let_75))) (let ((_let_80 (AND_ELIM (ASSUME :args (_let_25)) :args _let_75))) (let ((_let_81 (AND_ELIM (ASSUME :args (_let_23)) :args _let_75))) (let ((_let_82 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_21)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_81 _let_80 _let_79 _let_77) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_19)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_17)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_83 _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_15)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_13)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_11)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_9)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_7)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_5)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (AND_INTRO (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_3)) :args _let_75) (MACRO_SR_EQ_INTRO (AND_INTRO _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_77))) (let ((_let_92 (EQ_RESOLVE _let_76 (MACRO_SR_EQ_INTRO _let_91 :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (and _let_57 _let_56))) (let ((_let_94 (_let_57 _let_56))) (let ((_let_95 (ASSUME :args (_let_57)))) (let ((_let_96 (ASSUME :args (_let_56)))) (let ((_let_97 (= tptp.sz00 _let_22))) (let ((_let_98 (not _let_31))) (let ((_let_99 (not _let_33))) (let ((_let_100 (or _let_60 _let_99 _let_98 _let_97 _let_46))) (let ((_let_101 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (or (not (tptp.aVector0 W0)) (not (tptp.aVector0 W1)) (not (= _let_1 (tptp.aDimensionOf0 W0))) (= tptp.sz00 _let_1) (= (tptp.aDimensionOf0 (tptp.sziznziztdt0 W0)) (tptp.aDimensionOf0 (tptp.sziznziztdt0 W1)))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (not _let_97))) (let ((_let_104 (ASSUME :args (_let_31)))) (let ((_let_105 (not _let_59))) (let ((_let_106 (and _let_31 _let_105))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (_let_28 _let_26 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_40))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_42 _let_51 _let_49 _let_47 _let_45 _let_54))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO _let_91 :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) _let_92 (EQ_RESOLVE _let_78 (MACRO_SR_EQ_INTRO _let_91 :args (_let_27 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_60 _let_99 _let_98 _let_97 _let_46 (not _let_100)))) _let_65 (AND_ELIM _let_64 :args _let_75) _let_104 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_106)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_104) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.sz00)) (SYMM _let_104) :args (=)) (FALSE_INTRO _let_66))) :args (_let_105 _let_31))) :args (_let_31 _let_105))) :args (true _let_106)) (CONG (REFL :args (_let_98)) (MACRO_SR_PRED_INTRO :args ((= (not _let_105) _let_59))) (REFL :args (_let_103)) :args (or))) :args ((or _let_59 _let_98 _let_103))) _let_66 _let_104 :args (_let_103 true _let_59 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_102 :args (tptp.xs tptp.xt QUANTIFIERS_INST_ENUM)) :args (_let_101)))) _let_102 :args (_let_100 false _let_101)) :args (_let_46 false _let_34 false _let_33 false _let_31 true _let_97 false _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_93)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_95 _let_96) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_43)) (SYMM (SYMM _let_96)) :args (APPLY_UF tptp.iLess0)) (TRUE_INTRO _let_95))) :args _let_94)) :args _let_94)) :args (true _let_93)) :args ((or _let_44 (not _let_57) (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_57 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_51 _let_67 (not _let_72)))) _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_28 QUANTIFIERS_INST_ENUM)) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_67 false _let_50 false _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_43 QUANTIFIERS_INST_ENUM)) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_57 false _let_67 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 1)) :args ((or _let_56 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_59 _let_60 _let_58 (not _let_61)))) _let_66 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_63 :args (tptp.xs _let_28 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_62)))) _let_63 :args (_let_61 false _let_62)) :args (_let_58 true _let_59 false _let_34 false _let_61)) :args (_let_56 false _let_58)) :args (_let_44 false _let_57 false _let_56)) :args (_let_54 true _let_42 false _let_50 false _let_48 false _let_46 false _let_44)) _let_53 :args (false true _let_52 false _let_40)) :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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) _let_39 (forall ((W0 $$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)) _let_38 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aScalar0 (tptp.sdtlbdtrb0 W0 W1)))) _let_37 _let_36 (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)))) _let_35 _let_32 _let_31 _let_30 _let_29 _let_27 _let_25 _let_23 _let_21 _let_19 _let_17 _let_15 _let_13 _let_11 _let_9 _let_7 _let_5 _let_3 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.66/10.83 )
% 10.66/10.83 % SZS output end Proof for RNG052+1
% 10.66/10.83 % cvc5---1.0.5 exiting
% 10.66/10.83 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------