TSTP Solution File: RNG055+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG055+1 : 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 13:49:43 EDT 2023
% Result : Theorem 1.20s 1.51s
% Output : Proof 1.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : RNG055+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n025.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 02:57:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.18/0.48 %----Proving TF0_NAR, FOF, or CNF
% 1.20/1.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.z2Ab6M4yEZ/cvc5---1.0.5_2814.p...
% 1.20/1.51 ------- get file name : TPTP file name is RNG055+1
% 1.20/1.51 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2814.smt2...
% 1.20/1.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.20/1.51 % SZS status Theorem for RNG055+1
% 1.20/1.51 % SZS output start Proof for RNG055+1
% 1.20/1.51 (
% 1.20/1.51 (let ((_let_1 (tptp.sdtasdt0 tptp.xE tptp.xE))) (let ((_let_2 (tptp.sdtasdt0 (tptp.sdtasdt0 tptp.xH tptp.xH) _let_1))) (let ((_let_3 (= (tptp.sdtasdt0 tptp.xP tptp.xP) _let_2))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.sdtasdt0 tptp.xE tptp.xH))) (let ((_let_6 (= tptp.xP _let_5))) (let ((_let_7 (tptp.aScalar0 tptp.xP))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (tptp.sdtasdt0 tptp.xA tptp.xB))) (let ((_let_10 (= tptp.xH _let_9))) (let ((_let_11 (tptp.aScalar0 tptp.xH))) (let ((_let_12 (and _let_11 _let_10))) (let ((_let_13 (tptp.aScalar0 tptp.xE))) (let ((_let_14 (and _let_13 (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq))))) (let ((_let_15 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_16 (tptp.aScalar0 tptp.xB))) (let ((_let_17 (and _let_16 (= tptp.xB (tptp.sdtlbdtrb0 tptp.xt _let_15))))) (let ((_let_18 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_19 (tptp.aScalar0 tptp.xA))) (let ((_let_20 (and _let_19 (= tptp.xA (tptp.sdtlbdtrb0 tptp.xs _let_18))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtpldt0 _let_2 W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))) (= _let_2 (tptp.sdtpldt0 W1 W0)) (= (tptp.sdtasdt0 _let_1 W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))) (= _let_1 (tptp.sdtasdt0 W1 W0))))))))) (let ((_let_22 (forall ((W0 $$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_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_24 (tptp.smndt0 tptp.xH))) (let ((_let_25 (= tptp.xH (tptp.smndt0 _let_24)))) (let ((_let_26 (= _let_9 (tptp.sdtasdt0 tptp.xB tptp.xA)))) (let ((_let_27 (tptp.sdtasdt0 tptp.xH tptp.xE))) (let ((_let_28 (= _let_5 _let_27))) (let ((_let_29 (tptp.sdtasdt0 tptp.xE tptp.xP))) (let ((_let_30 (tptp.sdtasdt0 tptp.xP tptp.xE))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (tptp.sdtasdt0 tptp.xH _let_1))) (let ((_let_33 (= _let_2 (tptp.sdtasdt0 tptp.xH _let_32)))) (let ((_let_34 (= (tptp.sdtasdt0 _let_27 tptp.xP) (tptp.sdtasdt0 tptp.xH _let_29)))) (let ((_let_35 (= _let_32 (tptp.sdtasdt0 _let_27 tptp.xE)))) (let ((_let_36 (1))) (let ((_let_37 (ASSUME :args (_let_12)))) (let ((_let_38 (ASSUME :args (_let_8)))) (let ((_let_39 (and (= tptp.xH (tptp.sdtpldt0 tptp.xH tptp.sz0z00)) (= tptp.xH (tptp.sdtpldt0 tptp.sz0z00 tptp.xH)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.xH tptp.sz0z00)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.sz0z00 tptp.xH)) (= tptp.sz0z00 (tptp.sdtpldt0 tptp.xH _let_24)) (= tptp.sz0z00 (tptp.sdtpldt0 _let_24 tptp.xH)) _let_25 (= tptp.sz0z00 (tptp.smndt0 tptp.sz0z00))))) (let ((_let_40 (not _let_11))) (let ((_let_41 (or _let_40 _let_39))) (let ((_let_42 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (or (not (tptp.aScalar0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz0z00)) (= W0 (tptp.sdtpldt0 tptp.sz0z00 W0)) (= tptp.sz0z00 (tptp.sdtasdt0 W0 tptp.sz0z00)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.sz0z00 W0)) (= tptp.sz0z00 (tptp.sdtpldt0 W0 _let_1)) (= tptp.sz0z00 (tptp.sdtpldt0 _let_1 W0)) (= W0 (tptp.smndt0 _let_1)) (= tptp.sz0z00 (tptp.smndt0 tptp.sz0z00)))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (0))) (let ((_let_45 (AND_ELIM _let_37 :args _let_44))) (let ((_let_46 (tptp.sdtpldt0 tptp.xA tptp.xB))) (let ((_let_47 (and (= (tptp.sdtpldt0 _let_46 tptp.xH) (tptp.sdtpldt0 tptp.xA (tptp.sdtpldt0 tptp.xB tptp.xH))) (= _let_46 (tptp.sdtpldt0 tptp.xB tptp.xA)) (= (tptp.sdtasdt0 _let_9 tptp.xH) (tptp.sdtasdt0 tptp.xA (tptp.sdtasdt0 tptp.xB tptp.xH))) _let_26))) (let ((_let_48 (not _let_16))) (let ((_let_49 (not _let_19))) (let ((_let_50 (or _let_49 _let_48 _let_40 _let_47))) (let ((_let_51 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (not (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))))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (_let_51))) (let ((_let_54 ((tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2)))) (let ((_let_55 (tptp.sdtpldt0 tptp.xH tptp.xE))) (let ((_let_56 (tptp.sdtpldt0 tptp.xE tptp.xH))) (let ((_let_57 (= _let_56 _let_55))) (let ((_let_58 (and (= (tptp.sdtpldt0 _let_56 tptp.xP) (tptp.sdtpldt0 tptp.xE (tptp.sdtpldt0 tptp.xH tptp.xP))) _let_57 (= (tptp.sdtasdt0 _let_5 tptp.xP) (tptp.sdtasdt0 tptp.xE (tptp.sdtasdt0 tptp.xH tptp.xP))) _let_28))) (let ((_let_59 (not _let_7))) (let ((_let_60 (not _let_13))) (let ((_let_61 (or _let_60 _let_40 _let_59 _let_58))) (let ((_let_62 (AND_ELIM _let_38 :args _let_44))) (let ((_let_63 (AND_ELIM (ASSUME :args (_let_14)) :args _let_44))) (let ((_let_64 (tptp.sdtpldt0 tptp.xE tptp.xP))) (let ((_let_65 (tptp.sdtpldt0 tptp.xP tptp.xE))) (let ((_let_66 (and (= (tptp.sdtpldt0 _let_65 tptp.xH) (tptp.sdtpldt0 tptp.xP _let_56)) (= _let_65 _let_64) (= (tptp.sdtasdt0 _let_30 tptp.xH) (tptp.sdtasdt0 tptp.xP _let_5)) _let_31))) (let ((_let_67 (or _let_59 _let_60 _let_40 _let_66))) (let ((_let_68 ((tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (let ((_let_69 (and (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xH tptp.xH) _let_1) (tptp.sdtpldt0 tptp.xH (tptp.sdtpldt0 tptp.xH _let_1))) _let_33))) (let ((_let_70 (tptp.aScalar0 _let_1))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_40 _let_40 _let_71 _let_69))) (let ((_let_73 (or _let_60 _let_60 _let_70))) (let ((_let_74 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (and (= (tptp.sdtpldt0 _let_55 tptp.xP) (tptp.sdtpldt0 tptp.xH _let_64)) _let_57 _let_34 _let_28))) (let ((_let_77 (or _let_40 _let_60 _let_59 _let_76))) (let ((_let_78 (and (= (tptp.sdtpldt0 _let_55 tptp.xE) (tptp.sdtpldt0 tptp.xH (tptp.sdtpldt0 tptp.xE tptp.xE))) _let_57 _let_35 _let_28))) (let ((_let_79 (or _let_40 _let_60 _let_60 _let_78))) (let ((_let_80 (and _let_10 _let_6 _let_25 _let_26 _let_33 _let_28 _let_31 _let_34 _let_35))) (let ((_let_81 (ASSUME :args (_let_33)))) (let ((_let_82 (APPLY_UF tptp.sdtasdt0))) (let ((_let_83 (REFL :args (_let_32)))) (let ((_let_84 (ASSUME :args (_let_25)))) (let ((_let_85 (ASSUME :args (_let_10)))) (let ((_let_86 (ASSUME :args (_let_26)))) (let ((_let_87 (TRANS (SYMM _let_86) (SYMM _let_85)))) (let ((_let_88 (ASSUME :args (_let_35)))) (let ((_let_89 (ASSUME :args (_let_28)))) (let ((_let_90 (ASSUME :args (_let_6)))) (let ((_let_91 (TRANS (SYMM (SYMM _let_90)) (SYMM (SYMM _let_89))))) (let ((_let_92 (ASSUME :args (_let_31)))) (let ((_let_93 (ASSUME :args (_let_34)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_80)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_81 _let_84 _let_85 _let_86 _let_88 _let_89 _let_90 _let_92 _let_93) (SCOPE (TRANS (CONG _let_91 (REFL :args (tptp.xP)) :args _let_82) (SYMM (SYMM _let_93)) (CONG (SYMM _let_87) (TRANS (SYMM _let_92) (CONG _let_91 (REFL :args (tptp.xE)) :args _let_82) (SYMM _let_88)) :args _let_82) (CONG (TRANS _let_87 _let_84) _let_83 :args _let_82) (CONG (SYMM _let_84) _let_83 :args _let_82) (SYMM _let_81)) :args (_let_33 _let_25 _let_10 _let_26 _let_35 _let_28 _let_6 _let_31 _let_34))) :args (_let_10 _let_6 _let_25 _let_26 _let_33 _let_28 _let_31 _let_34 _let_35))) :args (true _let_80)) :args ((or _let_3 (not _let_10) (not _let_6) (not _let_25) (not _let_26) (not _let_33) (not _let_28) (not _let_31) (not _let_34) (not _let_35)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_78 2)) :args ((or _let_35 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_79))) :args ((or _let_60 _let_40 _let_78 (not _let_79)))) _let_63 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xH tptp.xE tptp.xE QUANTIFIERS_INST_E_MATCHING _let_68)) :args _let_53))) _let_52 :args (_let_79 false _let_51)) :args (_let_78 false _let_13 false _let_11 false _let_79)) :args (_let_35 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_76 2)) :args ((or _let_34 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_60 _let_40 _let_59 _let_76 (not _let_77)))) _let_63 _let_45 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xH tptp.xE tptp.xP QUANTIFIERS_INST_E_MATCHING ((tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))) :args _let_53))) _let_52 :args (_let_77 false _let_51)) :args (_let_76 false _let_13 false _let_11 false _let_7 false _let_77)) :args (_let_34 false _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_69 1)) :args ((or _let_33 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_72))) :args ((or _let_40 _let_71 _let_69 (not _let_72)))) _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_73))) :args ((or _let_60 _let_70 (not _let_73)))) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (tptp.xE tptp.xE QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_74))) _let_75 :args (_let_73 false _let_74)) :args (_let_70 false _let_13 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xH tptp.xH _let_1 QUANTIFIERS_INST_E_MATCHING _let_54)) :args _let_53))) _let_52 :args (_let_72 false _let_51)) :args (_let_69 false _let_11 false _let_70 false _let_72)) :args (_let_33 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 3)) :args ((or _let_31 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_60 _let_40 _let_59 _let_66 (not _let_67)))) _let_63 _let_45 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xP tptp.xE tptp.xH QUANTIFIERS_INST_E_MATCHING _let_68)) :args _let_53)) _let_52 :args (_let_67 false _let_51)) :args (_let_66 false _let_13 false _let_11 false _let_7 false _let_67)) :args (_let_31 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 3)) :args ((or _let_28 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_60 _let_40 _let_59 _let_58 (not _let_61)))) _let_63 _let_45 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xE tptp.xH tptp.xP QUANTIFIERS_INST_E_MATCHING _let_54)) :args _let_53)) _let_52 :args (_let_61 false _let_51)) :args (_let_58 false _let_13 false _let_11 false _let_7 false _let_61)) :args (_let_28 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 3)) :args ((or _let_26 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_48 _let_40 _let_47 (not _let_50)))) (AND_ELIM (ASSUME :args (_let_20)) :args _let_44) (AND_ELIM (ASSUME :args (_let_17)) :args _let_44) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xA tptp.xB tptp.xH QUANTIFIERS_INST_E_MATCHING _let_54)) :args _let_53)) _let_52 :args (_let_50 false _let_51)) :args (_let_47 false _let_19 false _let_16 false _let_11 false _let_50)) :args (_let_26 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_39 6)) :args ((or _let_25 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_39 (not _let_41)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.xH QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aScalar0 W0) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_39 false _let_11 false _let_41)) :args (_let_25 false _let_39)) (ASSUME :args (_let_4)) (AND_ELIM _let_38 :args _let_36) (AND_ELIM _let_37 :args _let_36) :args (false false _let_35 false _let_34 false _let_33 false _let_31 false _let_28 false _let_26 false _let_25 true _let_3 false _let_6 false _let_10)) :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_23 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.aScalar0 (tptp.smndt0 W0)))) _let_22 _let_21 (forall ((W0 $$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))))) (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_18 _let_15) (not (= _let_18 tptp.sz00)) (and (tptp.aVector0 tptp.xp) (= tptp.xp (tptp.sziznziztdt0 tptp.xs))) (and (tptp.aVector0 tptp.xq) (= tptp.xq (tptp.sziznziztdt0 tptp.xt))) _let_20 _let_17 (and (tptp.aScalar0 tptp.xC) (= tptp.xC (tptp.sdtasasdt0 tptp.xp tptp.xp))) (and (tptp.aScalar0 tptp.xD) (= tptp.xD (tptp.sdtasasdt0 tptp.xq tptp.xq))) _let_14 (and (tptp.aScalar0 tptp.xF) (= tptp.xF (tptp.sdtasdt0 tptp.xA tptp.xA))) (and (tptp.aScalar0 tptp.xG) (= tptp.xG (tptp.sdtasdt0 tptp.xB tptp.xB))) _let_12 (and (tptp.aScalar0 tptp.xR) (= tptp.xR (tptp.sdtasdt0 tptp.xC tptp.xG))) _let_8 (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 _let_1 (tptp.sdtasdt0 tptp.xC tptp.xD)) _let_4 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.20/1.52 )
% 1.20/1.52 % SZS output end Proof for RNG055+1
% 1.20/1.52 % cvc5---1.0.5 exiting
% 1.20/1.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------