TSTP Solution File: RNG059+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG059+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 13:49:45 EDT 2023
% Result : Theorem 0.97s 1.15s
% Output : Proof 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : RNG059+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 02:29:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.97/1.15 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Sm0rYg97RM/cvc5---1.0.5_26490.p...
% 0.97/1.15 ------- get file name : TPTP file name is RNG059+2
% 0.97/1.15 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_26490.smt2...
% 0.97/1.15 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.97/1.15 % SZS status Theorem for RNG059+2
% 0.97/1.15 % SZS output start Proof for RNG059+2
% 0.97/1.15 (
% 0.97/1.15 (let ((_let_1 (tptp.smndt0 tptp.xS))) (let ((_let_2 (tptp.sdtasdt0 _let_1 tptp.xR))) (let ((_let_3 (= _let_2 (tptp.smndt0 tptp.xN)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.sdtasdt0 tptp.xR tptp.xS))) (let ((_let_6 (= tptp.xN _let_5))) (let ((_let_7 (and (tptp.aScalar0 tptp.xN) _let_6))) (let ((_let_8 (tptp.aScalar0 tptp.xS))) (let ((_let_9 (and _let_8 (= tptp.xS (tptp.sdtasdt0 tptp.xF tptp.xD))))) (let ((_let_10 (tptp.aScalar0 tptp.xR))) (let ((_let_11 (and _let_10 (= tptp.xR (tptp.sdtasdt0 tptp.xC tptp.xG))))) (let ((_let_12 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_13 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (= (tptp.sdtasdt0 (tptp.smndt0 W0) (tptp.smndt0 W1)) (tptp.sdtasdt0 W0 W1)))))) (let ((_let_15 (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))))))) (let ((_let_16 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtpldt0 _let_2 W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))) (= _let_2 (tptp.sdtpldt0 W1 W0)) (= (tptp.sdtasdt0 _let_1 W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))) (= _let_1 (tptp.sdtasdt0 W1 W0))))))))) (let ((_let_17 (forall ((W0 $$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 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.aScalar0 (tptp.smndt0 W0)))))) (let ((_let_19 (tptp.aScalar0 tptp.sz0z00))) (let ((_let_20 (tptp.smndt0 tptp.xR))) (let ((_let_21 (tptp.smndt0 _let_20))) (let ((_let_22 (= tptp.xR _let_21))) (let ((_let_23 (tptp.smndt0 _let_1))) (let ((_let_24 (= tptp.xS _let_23))) (let ((_let_25 (tptp.sdtasdt0 tptp.xS tptp.xR))) (let ((_let_26 (tptp.smndt0 _let_25))) (let ((_let_27 (= _let_2 _let_26))) (let ((_let_28 (= (tptp.sdtasdt0 _let_1 _let_20) (tptp.sdtasdt0 _let_23 _let_21)))) (let ((_let_29 (= _let_5 _let_25))) (let ((_let_30 (= tptp.sz0z00 (tptp.smndt0 tptp.sz0z00)))) (let ((_let_31 (and (= tptp.xR (tptp.sdtpldt0 tptp.xR tptp.sz0z00)) (= tptp.xR (tptp.sdtpldt0 tptp.sz0z00 tptp.xR)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.xR tptp.sz0z00)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.sz0z00 tptp.xR)) (= tptp.sz0z00 (tptp.sdtpldt0 tptp.xR _let_20)) (= tptp.sz0z00 (tptp.sdtpldt0 _let_20 tptp.xR)) _let_22 _let_30))) (let ((_let_32 (not _let_10))) (let ((_let_33 (or _let_32 _let_31))) (let ((_let_34 (forall ((W0 $$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_35 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (_let_34))) (let ((_let_37 ((not (= (tptp.aScalar0 W0) false))))) (let ((_let_38 (0))) (let ((_let_39 (AND_ELIM (ASSUME :args (_let_11)) :args _let_38))) (let ((_let_40 (tptp.sdtasdt0 tptp.xS tptp.sz0z00))) (let ((_let_41 (tptp.sdtpldt0 tptp.xS tptp.sz0z00))) (let ((_let_42 (and (= tptp.xS _let_41) (= tptp.xS (tptp.sdtpldt0 tptp.sz0z00 tptp.xS)) (= tptp.sz0z00 _let_40) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.sz0z00 tptp.xS)) (= tptp.sz0z00 (tptp.sdtpldt0 tptp.xS _let_1)) (= tptp.sz0z00 (tptp.sdtpldt0 _let_1 tptp.xS)) _let_24 _let_30))) (let ((_let_43 (not _let_8))) (let ((_let_44 (or _let_43 _let_42))) (let ((_let_45 (AND_ELIM (ASSUME :args (_let_9)) :args _let_38))) (let ((_let_46 (and (= _let_26 (tptp.sdtasdt0 tptp.xS _let_20)) _let_27))) (let ((_let_47 (or _let_43 _let_32 _let_46))) (let ((_let_48 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.smndt0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (and (= _let_1 (tptp.sdtasdt0 W0 (tptp.smndt0 W1))) (= _let_1 (tptp.sdtasdt0 (tptp.smndt0 W0) W1)))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (tptp.aScalar0 _let_20))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.aScalar0 _let_1))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51 _let_28))) (let ((_let_55 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (= (tptp.sdtasdt0 (tptp.smndt0 W0) (tptp.smndt0 W1)) (tptp.sdtasdt0 W0 W1)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or _let_32 _let_50))) (let ((_let_58 (forall ((W0 $$unsorted)) (or (not (tptp.aScalar0 W0)) (tptp.aScalar0 (tptp.smndt0 W0)))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (_let_58))) (let ((_let_61 ((tptp.smndt0 W0)))) (let ((_let_62 (or _let_43 _let_52))) (let ((_let_63 (tptp.sdtpldt0 tptp.xR tptp.xS))) (let ((_let_64 (and (= (tptp.sdtpldt0 _let_63 tptp.sz0z00) (tptp.sdtpldt0 tptp.xR _let_41)) (= _let_63 (tptp.sdtpldt0 tptp.xS tptp.xR)) (= (tptp.sdtasdt0 _let_5 tptp.sz0z00) (tptp.sdtasdt0 tptp.xR _let_40)) _let_29))) (let ((_let_65 (not _let_19))) (let ((_let_66 (or _let_32 _let_43 _let_65 _let_64))) (let ((_let_67 (forall ((W0 $$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_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (and _let_6 _let_22 _let_24 _let_27 _let_29 _let_28))) (let ((_let_70 (APPLY_UF tptp.smndt0))) (let ((_let_71 (ASSUME :args (_let_6)))) (let ((_let_72 (ASSUME :args (_let_29)))) (let ((_let_73 (ASSUME :args (_let_22)))) (let ((_let_74 (ASSUME :args (_let_24)))) (let ((_let_75 (CONG (SYMM _let_74) (SYMM _let_73) :args (APPLY_UF tptp.sdtasdt0)))) (let ((_let_76 (ASSUME :args (_let_28)))) (let ((_let_77 (SYMM _let_76))) (let ((_let_78 (ASSUME :args (_let_27)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_69)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_71 _let_72 _let_74 _let_73 _let_76 _let_78) (SCOPE (TRANS (SYMM (SYMM _let_78)) (CONG (TRANS (SYMM _let_75) _let_77) :args _let_70) (CONG (TRANS (SYMM _let_77) _let_75 (SYMM _let_72) (SYMM _let_71)) :args _let_70)) :args (_let_6 _let_29 _let_24 _let_22 _let_28 _let_27))) :args (_let_6 _let_22 _let_24 _let_27 _let_29 _let_28))) :args (true _let_69)) :args ((or _let_3 (not _let_6) (not _let_22) (not _let_24) (not _let_27) (not _let_29) (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_64 3)) :args ((or _let_29 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_32 _let_43 _let_64 (not _let_66)))) (ASSUME :args (_let_19)) _let_39 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.xR tptp.xS tptp.sz0z00 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_64 false _let_19 false _let_10 false _let_8 false _let_66)) :args (_let_29 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_51 _let_28 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_43 _let_52 (not _let_62)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_61)) :args _let_60)) _let_59 :args (_let_62 false _let_58)) :args (_let_52 false _let_8 false _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_32 _let_50 (not _let_57)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (tptp.xR QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_61)) :args _let_60)) _let_59 :args (_let_57 false _let_58)) :args (_let_50 false _let_10 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_1 _let_20 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 (tptp.smndt0 W0) (tptp.smndt0 W1))))) :args (_let_55)))) _let_56 :args (_let_54 false _let_55)) :args (_let_28 false _let_52 false _let_50 false _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_46 1)) :args ((or _let_27 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_32 _let_43 _let_46 (not _let_47)))) _let_39 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.xS tptp.xR QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 (tptp.smndt0 W0) W1)))) :args (_let_48)))) _let_49 :args (_let_47 false _let_48)) :args (_let_46 false _let_10 false _let_8 false _let_47)) :args (_let_27 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 6)) :args ((or _let_24 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_42 (not _let_44)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_44 false _let_34)) :args (_let_42 false _let_8 false _let_44)) :args (_let_24 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 6)) :args ((or _let_22 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_31 (not _let_33)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.xR QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_33 false _let_34)) :args (_let_31 false _let_10 false _let_33)) :args (_let_22 false _let_31)) (ASSUME :args (_let_4)) (AND_ELIM (ASSUME :args (_let_7)) :args (1)) :args (false false _let_29 false _let_28 false _let_27 false _let_24 false _let_22 true _let_3 false _let_6)) :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_19 (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)))) _let_18 _let_17 _let_16 (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 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W2 W3)) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W0 W3)) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W2) (tptp.sdtasdt0 W1 W3)))))) _let_15 _let_14 (forall ((W0 $$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_13 _let_12) (not (= _let_13 tptp.sz00)) (and (tptp.aVector0 tptp.xp) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xp)) _let_13) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xp W0) (tptp.sdtlbdtrb0 tptp.xs W0)))) (= tptp.xp (tptp.sziznziztdt0 tptp.xs))) (and (tptp.aVector0 tptp.xq) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xq)) _let_12) (forall ((W0 $$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_13))) (and (tptp.aScalar0 tptp.xB) (= tptp.xB (tptp.sdtlbdtrb0 tptp.xt _let_12))) (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_11 (and (tptp.aScalar0 tptp.xP) (= tptp.xP (tptp.sdtasdt0 tptp.xE tptp.xH))) _let_9 _let_7 (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_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.97/1.16 )
% 0.97/1.16 % SZS output end Proof for RNG059+2
% 0.97/1.16 % cvc5---1.0.5 exiting
% 0.97/1.16 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------