%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG081+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 0.22s 0.59s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : RNG081+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.36  % Computer : n002.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Sun Aug 27 02:08:48 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.59  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.fCRPbvRUSO/cvc5---1.0.5_1219.p...
% 0.22/0.59  ------- get file name : TPTP file name is RNG081+1
% 0.22/0.59  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1219.smt2...
% 0.22/0.59  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.59  % SZS status Theorem for RNG081+1
% 0.22/0.59  % SZS output start Proof for RNG081+1
% 0.22/0.59  (
% 0.22/0.59  (let ((_let_1 (tptp.sdtasasdt0 tptp.xt tptp.xt))) (let ((_let_2 (tptp.sdtasasdt0 tptp.xs tptp.xs))) (let ((_let_3 (tptp.sdtasdt0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtasasdt0 tptp.xs tptp.xt))) (let ((_let_5 (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_4 _let_4) _let_3))) (let ((_let_6 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_7 (not (=> (=> (not (= _let_6 tptp.sz00)) (exists ((W0 $$unsorted)) (and (tptp.aVector0 W0) (= W0 (tptp.sziznziztdt0 tptp.xs)) (exists ((W1 $$unsorted)) (and (tptp.aVector0 W1) (= W1 (tptp.sziznziztdt0 tptp.xt)) (exists ((W2 $$unsorted)) (and (tptp.aScalar0 W2) (= W2 (tptp.sdtlbdtrb0 tptp.xs (tptp.aDimensionOf0 tptp.xs))) (exists ((W3 $$unsorted)) (and (tptp.aScalar0 W3) (= W3 (tptp.sdtlbdtrb0 tptp.xt (tptp.aDimensionOf0 tptp.xt))) (exists ((W4 $$unsorted)) (and (tptp.aScalar0 W4) (= W4 (tptp.sdtasasdt0 W0 W0)) (exists ((W5 $$unsorted)) (and (tptp.aScalar0 W5) (= W5 (tptp.sdtasasdt0 W1 W1)) (exists ((W6 $$unsorted)) (and (tptp.aScalar0 W6) (= W6 (tptp.sdtasasdt0 W0 W1)) (exists ((W7 $$unsorted)) (and (tptp.aScalar0 W7) (= W7 (tptp.sdtasdt0 W2 W2)) (exists ((W8 $$unsorted)) (and (tptp.aScalar0 W8) (= W8 (tptp.sdtasdt0 W3 W3)) (exists ((W9 $$unsorted)) (and (tptp.aScalar0 W9) (= W9 (tptp.sdtasdt0 W2 W3)) (exists ((W10 $$unsorted)) (and (tptp.aScalar0 W10) (= W10 (tptp.sdtasdt0 W4 W8)) (exists ((W11 $$unsorted)) (and (tptp.aScalar0 W11) (= W11 (tptp.sdtasdt0 W6 W9)) (exists ((W12 $$unsorted)) (and (tptp.aScalar0 W12) (= W12 (tptp.sdtasdt0 W7 W5)) (exists ((W13 $$unsorted)) (let ((_let_1 (tptp.sdtasasdt0 tptp.xs tptp.xt))) (let ((_let_2 (tptp.sdtpldt0 W6 W9))) (and (tptp.aScalar0 W13) (= W13 (tptp.sdtasdt0 W10 W12)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W6 W6) (tptp.sdtasdt0 W4 W5)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W11 W11) (tptp.sdtpldt0 W10 W12)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_2 _let_2) (tptp.sdtasdt0 (tptp.sdtpldt0 W4 W7) (tptp.sdtpldt0 W5 W8))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_1 _let_1) (tptp.sdtasdt0 (tptp.sdtasasdt0 tptp.xs tptp.xs) (tptp.sdtasasdt0 tptp.xt tptp.xt)))))))))))))))))))))))))))))))))) _let_5)))) (let ((_let_8 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_9 (= _let_6 _let_8))) (let ((_let_10 (tptp.aVector0 tptp.xt))) (let ((_let_11 (tptp.aVector0 tptp.xs))) (let ((_let_12 (and _let_11 _let_10))) (let ((_let_13 (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W0 W0)))))) (let ((_let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= (tptp.aDimensionOf0 W0) _let_1) (= _let_1 tptp.sz00)) (= (tptp.sdtasasdt0 W0 W1) tptp.sz0z00))))))) (let ((_let_15 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (= (tptp.aDimensionOf0 W0) (tptp.aDimensionOf0 W1)) (tptp.aScalar0 (tptp.sdtasasdt0 W0 W1))))))) (let ((_let_16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 tptp.sz0z00 W0) (tptp.sdtlseqdt0 tptp.sz0z00 W1)) (and (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtpldt0 W0 W1)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W1)))))))) (let ((_let_17 (forall ((W0 $$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))))))) (let ((_let_18 (tptp.aScalar0 tptp.sz0z00))) (let ((_let_19 (= tptp.sz0z00 _let_2))) (let ((_let_20 (= tptp.sz0z00 (tptp.sdtasdt0 tptp.sz0z00 tptp.sz0z00)))) (let ((_let_21 (tptp.sdtlseqdt0 tptp.sz0z00 _let_3))) (let ((_let_22 (= tptp.sz0z00 _let_4))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (NOT_IMPLIES_ELIM2 _let_23))) (let ((_let_25 (= tptp.sz00 _let_6))) (let ((_let_26 (not _let_25))) (let ((_let_27 (not _let_11))) (let ((_let_28 (or _let_27 _let_26 _let_19))) (let ((_let_29 (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))) (not (= tptp.sz00 _let_1)) (= tptp.sz0z00 (tptp.sdtasasdt0 W0 W1))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (_let_29))) (let ((_let_32 ((not (= (tptp.sdtasasdt0 W0 W1) tptp.sz0z00))))) (let ((_let_33 (ASSUME :args (_let_12)))) (let ((_let_34 (AND_ELIM _let_33 :args (0)))) (let ((_let_35 (tptp.sziznziztdt0 tptp.xt))) (let ((_let_36 (tptp.sdtasasdt0 _let_35 _let_35))) (let ((_let_37 (tptp.sdtlbdtrb0 tptp.xs _let_6))) (let ((_let_38 (tptp.sdtasdt0 _let_37 _let_37))) (let ((_let_39 (tptp.sdtasdt0 _let_38 _let_36))) (let ((_let_40 (tptp.sdtlbdtrb0 tptp.xt _let_8))) (let ((_let_41 (tptp.sdtasdt0 _let_40 _let_40))) (let ((_let_42 (tptp.sziznziztdt0 tptp.xs))) (let ((_let_43 (tptp.sdtasasdt0 _let_42 _let_42))) (let ((_let_44 (tptp.sdtasdt0 _let_43 _let_41))) (let ((_let_45 (tptp.sdtasdt0 _let_37 _let_40))) (let ((_let_46 (tptp.sdtasasdt0 _let_42 _let_35))) (let ((_let_47 (tptp.sdtasdt0 _let_46 _let_45))) (let ((_let_48 (tptp.sdtpldt0 _let_46 _let_45))) (let ((_let_49 (not _let_5))) (let ((_let_50 (or _let_49 (not (tptp.aScalar0 _let_40)) (not (tptp.aScalar0 _let_41)) (not (tptp.aScalar0 _let_37)) (not (tptp.aScalar0 _let_38)) (not (tptp.aScalar0 _let_45)) (not (tptp.aVector0 _let_35)) (not (tptp.aScalar0 _let_36)) (not (tptp.aScalar0 _let_39)) (not (tptp.aVector0 _let_42)) (not (tptp.aScalar0 _let_43)) (not (tptp.aScalar0 _let_44)) (not (tptp.aScalar0 _let_46)) (not (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_46 _let_46) (tptp.sdtasdt0 _let_43 _let_36))) (not (tptp.aScalar0 _let_47)) (not (tptp.aScalar0 (tptp.sdtasdt0 _let_44 _let_39))) (not (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_48 _let_48) (tptp.sdtasdt0 (tptp.sdtpldt0 _let_43 _let_38) (tptp.sdtpldt0 _let_36 _let_41)))) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 _let_47 _let_47) (tptp.sdtpldt0 _let_44 _let_39)))))) (let ((_let_51 (or))) (let ((_let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_5))))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (NOT_IMPLIES_ELIM1 _let_23)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) (REFL :args ((not _let_50))) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 0)) (CONG (REFL :args (_let_50)) _let_52 :args _let_51)) :args ((or _let_5 _let_50))) _let_24 :args (_let_50 true _let_5)) :args (_let_25 false _let_50)))) (let ((_let_54 (tptp.smndt0 tptp.sz0z00))) (let ((_let_55 (= tptp.sz0z00 (tptp.sdtpldt0 tptp.sz0z00 tptp.sz0z00)))) (let ((_let_56 (and _let_55 _let_55 _let_20 _let_20 (= tptp.sz0z00 (tptp.sdtpldt0 tptp.sz0z00 _let_54)) (= tptp.sz0z00 (tptp.sdtpldt0 _let_54 tptp.sz0z00)) (= tptp.sz0z00 (tptp.smndt0 _let_54)) (= tptp.sz0z00 _let_54)))) (let ((_let_57 (not _let_18))) (let ((_let_58 (or _let_57 _let_56))) (let ((_let_59 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (or (not (tptp.aScalar0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz0z00)) (= W0 (tptp.sdtpldt0 tptp.sz0z00 W0)) (= tptp.sz0z00 (tptp.sdtasdt0 W0 tptp.sz0z00)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.sz0z00 W0)) (= tptp.sz0z00 (tptp.sdtpldt0 W0 _let_1)) (= tptp.sz0z00 (tptp.sdtpldt0 _let_1 W0)) (= W0 (tptp.smndt0 _let_1)) (= tptp.sz0z00 (tptp.smndt0 tptp.sz0z00)))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (and (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtpldt0 _let_2 _let_1)) _let_21))) (let ((_let_62 (tptp.sdtlseqdt0 tptp.sz0z00 _let_1))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.sdtlseqdt0 tptp.sz0z00 _let_2))) (let ((_let_65 (not _let_64))) (let ((_let_66 (tptp.aScalar0 _let_1))) (let ((_let_67 (not _let_66))) (let ((_let_68 (tptp.aScalar0 _let_2))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_67 _let_65 _let_63 _let_61))) (let ((_let_71 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (not (tptp.sdtlseqdt0 tptp.sz0z00 W0)) (not (tptp.sdtlseqdt0 tptp.sz0z00 W1)) (and (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtpldt0 W0 W1)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W1))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (not _let_10))) (let ((_let_74 (or _let_73 _let_62))) (let ((_let_75 (forall ((W0 $$unsorted)) (or (not (tptp.aVector0 W0)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W0 W0)))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (_let_75))) (let ((_let_78 ((not (= (tptp.aVector0 W0) false))))) (let ((_let_79 (AND_ELIM _let_33 :args (1)))) (let ((_let_80 (or _let_27 _let_64))) (let ((_let_81 (or _let_73 _let_66))) (let ((_let_82 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aVector0 W0)) (not (tptp.aVector0 W1)) (not (= (tptp.aDimensionOf0 W0) (tptp.aDimensionOf0 W1))) (tptp.aScalar0 (tptp.sdtasasdt0 W0 W1)))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (_let_82))) (let ((_let_85 ((tptp.sdtasasdt0 W0 W1)))) (let ((_let_86 (or _let_27 _let_68))) (let ((_let_87 (= tptp.sz00 _let_8))) (let ((_let_88 (not _let_87))) (let ((_let_89 (not _let_9))) (let ((_let_90 (or _let_27 _let_73 _let_89 _let_88 _let_22))) (let ((_let_91 (ASSUME :args (_let_9)))) (let ((_let_92 (and _let_9 _let_25))) (let ((_let_93 (_let_9 _let_25))) (let ((_let_94 (ASSUME :args (_let_25)))) (let ((_let_95 (ASSUME :args (_let_21)))) (let ((_let_96 (ASSUME :args (_let_20)))) (let ((_let_97 (APPLY_UF tptp.sdtasdt0))) (let ((_let_98 (ASSUME :args (_let_19)))) (let ((_let_99 (SYMM _let_98))) (let ((_let_100 (ASSUME :args (_let_22)))) (let ((_let_101 (TRANS (SYMM _let_100) _let_98))) (let ((_let_102 (ASSUME :args (_let_49)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_95 _let_96 _let_98 _let_100 _let_102) :args (_let_49 _let_20 _let_21 _let_22 _let_19)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_102)) (CONG (TRANS (CONG _let_101 _let_101 :args _let_97) (CONG _let_99 _let_99 :args _let_97) (SYMM _let_96)) (REFL :args (_let_3)) :args (APPLY_UF tptp.sdtlseqdt0)) (TRUE_INTRO _let_95))) :args (_let_21 _let_20 _let_19 _let_22 _let_49)) :args ((not (and _let_49 _let_20 _let_21 _let_22 _let_19)) SB_LITERAL))) (CONG _let_52 (REFL :args ((not _let_20))) (REFL :args ((not _let_21))) (REFL :args ((not _let_22))) (REFL :args ((not _let_19))) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_27 _let_73 _let_89 _let_88 _let_22 (not _let_90)))) _let_34 _let_79 _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_92)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_91 _let_94) (SCOPE (TRANS (SYMM (SYMM _let_94)) (SYMM (SYMM _let_91))) :args _let_93)) :args _let_93)) :args (true _let_92)) :args ((or _let_26 _let_89 _let_87))) _let_53 _let_91 :args (_let_87 false _let_25 false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.xs tptp.xt QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31))) _let_30 :args (_let_90 false _let_29)) :args (_let_22 false _let_11 false _let_10 false _let_9 false _let_87 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_61 1)) :args ((or _let_21 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_67 _let_65 _let_63 _let_61 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_27 _let_68 (not _let_86)))) _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_83 :args (tptp.xs tptp.xs QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84))) _let_83 :args (_let_86 false _let_82)) :args (_let_68 false _let_11 false _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_73 _let_66 (not _let_81)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_83 :args (tptp.xt tptp.xt QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84))) _let_83 :args (_let_81 false _let_82)) :args (_let_66 false _let_10 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_27 _let_64 (not _let_80)))) _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (tptp.xs QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_80 false _let_75)) :args (_let_64 false _let_11 false _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_73 _let_62 (not _let_74)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (tptp.xt QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_74 false _let_75)) :args (_let_62 false _let_10 false _let_74)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_2 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_61 false _let_68 false _let_66 false _let_64 false _let_62 false _let_70)) :args (_let_21 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_56 2)) :args ((or _let_20 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_56 (not _let_58)))) (ASSUME :args (_let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.sz0z00 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aScalar0 W0) false))))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_56 false _let_18 false _let_58)) :args (_let_20 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_26 _let_27 _let_19 (not _let_28)))) _let_53 _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.xs tptp.xs QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31))) _let_30 :args (_let_28 false _let_29)) :args (_let_19 false _let_25 false _let_11 false _let_28)) _let_24 :args (false false _let_22 false _let_21 false _let_20 false _let_19 true _let_5)) :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)) _let_18 (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 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.aScalar0 (tptp.smndt0 W0)))) _let_17 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)))) _let_16 (forall ((W0 $$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 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= (tptp.aDimensionOf0 W0) _let_1) (not (= _let_1 tptp.sz00))) (= (tptp.aDimensionOf0 (tptp.sziznziztdt0 W0)) (tptp.aDimensionOf0 (tptp.sziznziztdt0 W1))))))) _let_15 _let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= _let_2 _let_1) (not (= _let_1 tptp.sz00))) (= (tptp.sdtasasdt0 W0 W1) (tptp.sdtpldt0 (tptp.sdtasasdt0 (tptp.sziznziztdt0 W0) (tptp.sziznziztdt0 W1)) (tptp.sdtasdt0 (tptp.sdtlbdtrb0 W0 _let_2) (tptp.sdtlbdtrb0 W1 _let_1))))))))) _let_13 _let_12 (forall ((W0 $$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_9 _let_7 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.59  )
% 0.22/0.59  % SZS output end Proof for RNG081+1
% 0.22/0.59  % cvc5---1.0.5 exiting
% 0.22/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------