TSTP Solution File: RNG061+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG061+2 : 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 13:49:46 EDT 2023
% Result : Theorem 1.07s 1.28s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG061+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 02:32:50 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 1.07/1.28 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.I2HuknvHXX/cvc5---1.0.5_11680.p...
% 1.07/1.28 ------- get file name : TPTP file name is RNG061+2
% 1.07/1.28 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11680.smt2...
% 1.07/1.28 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.07/1.28 % SZS status Theorem for RNG061+2
% 1.07/1.28 % SZS output start Proof for RNG061+2
% 1.07/1.28 (
% 1.07/1.28 (let ((_let_1 (tptp.smndt0 tptp.xN))) (let ((_let_2 (tptp.sdtasdt0 tptp.xS tptp.xS))) (let ((_let_3 (tptp.sdtpldt0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtasdt0 tptp.xR tptp.xR))) (let ((_let_5 (tptp.sdtpldt0 _let_4 _let_1))) (let ((_let_6 (tptp.smndt0 tptp.xS))) (let ((_let_7 (tptp.sdtpldt0 tptp.xR _let_6))) (let ((_let_8 (tptp.sdtasdt0 _let_7 _let_7))) (let ((_let_9 (= _let_8 (tptp.sdtpldt0 _let_5 _let_3)))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.sdtpldt0 _let_1 _let_2))) (let ((_let_12 (= _let_8 (tptp.sdtpldt0 _let_5 _let_11)))) (let ((_let_13 (tptp.sdtasdt0 _let_6 _let_6))) (let ((_let_14 (= _let_13 _let_2))) (let ((_let_15 (tptp.sdtasdt0 _let_6 tptp.xR))) (let ((_let_16 (tptp.sdtasdt0 tptp.xR _let_6))) (let ((_let_17 (and (= _let_16 _let_1) (= _let_15 _let_1) _let_14))) (let ((_let_18 (tptp.aScalar0 tptp.xN))) (let ((_let_19 (and _let_18 (= tptp.xN (tptp.sdtasdt0 tptp.xR tptp.xS))))) (let ((_let_20 (tptp.aScalar0 tptp.xS))) (let ((_let_21 (and _let_20 (= tptp.xS (tptp.sdtasdt0 tptp.xF tptp.xD))))) (let ((_let_22 (tptp.aScalar0 tptp.xR))) (let ((_let_23 (and _let_22 (= tptp.xR (tptp.sdtasdt0 tptp.xC tptp.xG))))) (let ((_let_24 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_25 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W2))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) _let_1)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 _let_1 (tptp.sdtasdt0 W1 W2))))))))) (let ((_let_27 (forall ((W0 $$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_28 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.aScalar0 (tptp.smndt0 W0)))))) (let ((_let_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_30 (= _let_1 _let_16))) (let ((_let_31 (= _let_1 _let_15))) (let ((_let_32 (= (tptp.sdtasdt0 _let_7 _let_6) (tptp.sdtpldt0 _let_16 _let_13)))) (let ((_let_33 (= (tptp.sdtasdt0 _let_7 tptp.xR) (tptp.sdtpldt0 _let_4 _let_15)))) (let ((_let_34 (= _let_11 _let_3))) (let ((_let_35 (0))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (ASSUME :args (_let_12)))) (let ((_let_38 (and (= (tptp.sdtpldt0 _let_16 _let_16) (tptp.sdtasdt0 tptp.xR (tptp.sdtpldt0 _let_6 _let_6))) _let_32))) (let ((_let_39 (tptp.aScalar0 _let_6))) (let ((_let_40 (not _let_39))) (let ((_let_41 (not _let_22))) (let ((_let_42 (or _let_41 _let_40 _let_40 _let_38))) (let ((_let_43 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W2))) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (not (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))))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (_let_43))) (let ((_let_46 ((tptp.sdtpldt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W1 W2))))) (let ((_let_47 (not _let_20))) (let ((_let_48 (or _let_47 _let_39))) (let ((_let_49 (forall ((W0 $$unsorted)) (or (not (tptp.aScalar0 W0)) (tptp.aScalar0 (tptp.smndt0 W0)))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (_let_49))) (let ((_let_52 ((tptp.smndt0 W0)))) (let ((_let_53 (AND_ELIM (ASSUME :args (_let_21)) :args _let_35))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_39 (not _let_48)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_51)) _let_50 :args (_let_48 false _let_49)) :args (_let_39 false _let_20 false _let_48)))) (let ((_let_55 (AND_ELIM (ASSUME :args (_let_23)) :args _let_35))) (let ((_let_56 (and (= (tptp.sdtasdt0 tptp.xR (tptp.sdtpldt0 _let_6 tptp.xR)) (tptp.sdtpldt0 _let_16 _let_4)) _let_33))) (let ((_let_57 (or _let_41 _let_40 _let_41 _let_56))) (let ((_let_58 (tptp.sdtasdt0 _let_1 _let_2))) (let ((_let_59 (and (= (tptp.sdtpldt0 _let_11 _let_16) (tptp.sdtpldt0 _let_1 (tptp.sdtpldt0 _let_2 _let_16))) _let_34 (= (tptp.sdtasdt0 _let_58 _let_16) (tptp.sdtasdt0 _let_1 (tptp.sdtasdt0 _let_2 _let_16))) (= _let_58 (tptp.sdtasdt0 _let_2 _let_1))))) (let ((_let_60 (tptp.aScalar0 _let_16))) (let ((_let_61 (not _let_60))) (let ((_let_62 (tptp.aScalar0 _let_2))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.aScalar0 _let_1))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63 _let_61 _let_59))) (let ((_let_67 (forall ((W0 $$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_68 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (or _let_41 _let_40 _let_60))) (let ((_let_70 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_70))) (let ((_let_73 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_74 (or _let_47 _let_47 _let_62))) (let ((_let_75 (not _let_18))) (let ((_let_76 (or _let_75 _let_64))) (let ((_let_77 (and _let_14 _let_12 _let_30 _let_31 _let_32 _let_33 _let_34))) (let ((_let_78 (APPLY_UF tptp.sdtpldt0))) (let ((_let_79 (ASSUME :args (_let_34)))) (let ((_let_80 (ASSUME :args (_let_14)))) (let ((_let_81 (ASSUME :args (_let_30)))) (let ((_let_82 (CONG (SYMM _let_81) (SYMM (SYMM _let_80)) :args _let_78))) (let ((_let_83 (ASSUME :args (_let_32)))) (let ((_let_84 (SYMM _let_83))) (let ((_let_85 (ASSUME :args (_let_31)))) (let ((_let_86 (ASSUME :args (_let_33)))) (let ((_let_87 (TRANS (SYMM (SYMM _let_86)) (CONG (REFL :args (_let_4)) (SYMM _let_85) :args _let_78)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_77)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_85 _let_86 _let_79 _let_81 _let_80 _let_83 _let_37) (SCOPE (TRANS (SYMM (SYMM _let_37)) (CONG (SYMM _let_87) (TRANS (SYMM _let_82) _let_84) :args _let_78) (CONG _let_87 (TRANS (SYMM _let_84) _let_82 (SYMM (SYMM _let_79))) :args _let_78)) :args (_let_31 _let_33 _let_34 _let_30 _let_14 _let_32 _let_12))) :args (_let_14 _let_12 _let_30 _let_31 _let_32 _let_33 _let_34))) :args (true _let_77)) :args ((or _let_9 (not _let_30) (not _let_31) (not _let_14) (not _let_12) (not _let_32) (not _let_33) (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_59 1)) :args ((or _let_34 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_63 _let_61 _let_59 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_75 _let_64 (not _let_76)))) (AND_ELIM (ASSUME :args (_let_19)) :args _let_35) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.xN QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_51)) _let_50 :args (_let_76 false _let_49)) :args (_let_64 false _let_18 false _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_74))) :args ((or _let_47 _let_62 (not _let_74)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.xS tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_72)) _let_71 :args (_let_74 false _let_70)) :args (_let_62 false _let_20 false _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_41 _let_40 _let_60 (not _let_69)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.xR _let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_72)) _let_71 :args (_let_69 false _let_70)) :args (_let_60 false _let_22 false _let_39 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_1 _let_2 _let_16 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_59 false _let_64 false _let_62 false _let_60 false _let_66)) :args (_let_34 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_56 1)) :args ((or _let_33 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_57))) :args ((or _let_41 _let_40 _let_56 (not _let_57)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.xR _let_6 tptp.xR QUANTIFIERS_INST_E_MATCHING _let_46)) :args _let_45)) _let_44 :args (_let_57 false _let_43)) :args (_let_56 false _let_22 false _let_39 false _let_57)) :args (_let_33 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_38 1)) :args ((or _let_32 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_42))) :args ((or _let_41 _let_40 _let_38 (not _let_42)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.xR _let_6 _let_6 QUANTIFIERS_INST_E_MATCHING _let_46)) :args _let_45))) _let_44 :args (_let_42 false _let_43)) :args (_let_38 false _let_22 false _let_39 false _let_42)) :args (_let_32 false _let_38)) (ASSUME :args (_let_10)) _let_37 (AND_ELIM _let_36 :args (2)) (AND_ELIM _let_36 :args (1)) (AND_ELIM _let_36 :args _let_35) :args (false false _let_34 false _let_33 false _let_32 true _let_9 false _let_12 false _let_14 false _let_31 false _let_30)) :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_29 _let_28 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aScalar0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz0z00) W0) (= (tptp.sdtpldt0 tptp.sz0z00 W0) W0) (= (tptp.sdtasdt0 W0 tptp.sz0z00) tptp.sz0z00) (= (tptp.sdtasdt0 tptp.sz0z00 W0) tptp.sz0z00) (= (tptp.sdtpldt0 W0 _let_1) tptp.sz0z00) (= (tptp.sdtpldt0 _let_1 W0) tptp.sz0z00) (= (tptp.smndt0 _let_1) W0) (= (tptp.smndt0 tptp.sz0z00) tptp.sz0z00))))) _let_27 _let_26 (forall ((W0 $$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_25 _let_24) (not (= _let_25 tptp.sz00)) (and (tptp.aVector0 tptp.xp) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xp)) _let_25) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xp W0) (tptp.sdtlbdtrb0 tptp.xs W0)))) (= tptp.xp (tptp.sziznziztdt0 tptp.xs))) (and (tptp.aVector0 tptp.xq) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xq)) _let_24) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xq W0) (tptp.sdtlbdtrb0 tptp.xt W0)))) (= tptp.xq (tptp.sziznziztdt0 tptp.xt))) (and (tptp.aScalar0 tptp.xA) (= tptp.xA (tptp.sdtlbdtrb0 tptp.xs _let_25))) (and (tptp.aScalar0 tptp.xB) (= tptp.xB (tptp.sdtlbdtrb0 tptp.xt _let_24))) (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))) (and (tptp.aScalar0 tptp.xE) (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq))) (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))) (and (tptp.aScalar0 tptp.xH) (= tptp.xH (tptp.sdtasdt0 tptp.xA tptp.xB))) _let_23 (and (tptp.aScalar0 tptp.xP) (= tptp.xP (tptp.sdtasdt0 tptp.xE tptp.xH))) _let_21 _let_19 (tptp.sdtlseqdt0 (tptp.sdtasdt0 tptp.xE tptp.xE) (tptp.sdtasdt0 tptp.xC tptp.xD)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 tptp.xP tptp.xP) tptp.xN) _let_17 _let_12 _let_10 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.07/1.28 )
% 1.07/1.28 % SZS output end Proof for RNG061+2
% 1.07/1.28 % cvc5---1.0.5 exiting
% 1.07/1.29 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------