TSTP Solution File: RNG048+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG048+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 13:49:41 EDT 2023
% Result : Theorem 10.65s 10.87s
% Output : Proof 10.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG048+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n007.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 02:58:12 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 10.65/10.87 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.vKRXRYR8NG/cvc5---1.0.5_4882.p...
% 10.65/10.87 ------- get file name : TPTP file name is RNG048+1
% 10.65/10.87 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4882.smt2...
% 10.65/10.87 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.65/10.87 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.65/10.87 % SZS status Theorem for RNG048+1
% 10.65/10.87 % SZS output start Proof for RNG048+1
% 10.65/10.87 (
% 10.65/10.87 (let ((_let_1 (not (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (=> (forall ((W1 $$unsorted)) (=> (tptp.aVector0 W1) (=> (tptp.iLess0 (tptp.aDimensionOf0 W1) (tptp.aDimensionOf0 W0)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W1 W1))))) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W0 W0)))))))) (let ((_let_2 (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 ((_let_3 (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_4 (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_5 (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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtlbdtrb0 W1 W2) (tptp.sdtlbdtrb0 W0 W2)))))))))))) (let ((_let_6 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aScalar0 (tptp.sdtlbdtrb0 W0 W1)))))) (let ((_let_7 (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.aNaturalNumber0 (tptp.aDimensionOf0 W0)))))) (let ((_let_8 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W0)))))) (let ((_let_9 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 W2) (tptp.sdtpldt0 W1 W3))))))) (let ((_let_10 (forall ((W0 $$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_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_12 (tptp.aScalar0 tptp.sz0z00))) (let ((_let_13 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_14 (tptp.sdtasasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.sdtlseqdt0 tptp.sz0z00 _let_14))) (let ((_let_16 (tptp.sdtpldt0 tptp.sz0z00 tptp.sz0z00))) (let ((_let_17 (= tptp.sz0z00 _let_16))) (let ((_let_18 (tptp.aDimensionOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_19 (tptp.sdtlbdtrb0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18))) (let ((_let_20 (tptp.sdtasdt0 _let_19 _let_19))) (let ((_let_21 (tptp.sziznziztdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (tptp.sdtasasdt0 _let_21 _let_21))) (let ((_let_23 (tptp.sdtpldt0 _let_22 _let_20))) (let ((_let_24 (= _let_14 _let_23))) (let ((_let_25 (tptp.sdtlseqdt0 _let_16 _let_23))) (let ((_let_26 (forall ((W1 $$unsorted)) (or (not (tptp.aVector0 W1)) (not (tptp.iLess0 (tptp.aDimensionOf0 W1) (tptp.aDimensionOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W1 W1)))))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.aVector0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27 _let_15))) (let ((_let_31 (not _let_15))) (let ((_let_32 (forall ((W0 $$unsorted)) (or (not (tptp.aVector0 W0)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aVector0 W1)) (not (tptp.iLess0 (tptp.aDimensionOf0 W1) (tptp.aDimensionOf0 W0))) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W1 W1))))) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W0 W0)))))) (let ((_let_33 (not _let_30))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (or))) (let ((_let_36 (not _let_32))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_34) :args (_let_36))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) (REFL :args (_let_33)) :args _let_35)) _let_34 :args (_let_33 true _let_32)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 2)) _let_37 :args (_let_31 true _let_30)))) (let ((_let_39 (tptp.smndt0 tptp.sz0z00))) (let ((_let_40 (tptp.sdtasdt0 tptp.sz0z00 tptp.sz0z00))) (let ((_let_41 (= tptp.sz0z00 _let_40))) (let ((_let_42 (and _let_17 _let_17 _let_41 _let_41 (= tptp.sz0z00 (tptp.sdtpldt0 tptp.sz0z00 _let_39)) (= tptp.sz0z00 (tptp.sdtpldt0 _let_39 tptp.sz0z00)) (= tptp.sz0z00 (tptp.smndt0 _let_39)) (= tptp.sz0z00 _let_39)))) (let ((_let_43 (not _let_12))) (let ((_let_44 (or _let_43 _let_42))) (let ((_let_45 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (or (not (tptp.aScalar0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz0z00)) (= W0 (tptp.sdtpldt0 tptp.sz0z00 W0)) (= tptp.sz0z00 (tptp.sdtasdt0 W0 tptp.sz0z00)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.sz0z00 W0)) (= tptp.sz0z00 (tptp.sdtpldt0 W0 _let_1)) (= tptp.sz0z00 (tptp.sdtpldt0 _let_1 W0)) (= W0 (tptp.smndt0 _let_1)) (= tptp.sz0z00 (tptp.smndt0 tptp.sz0z00)))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (tptp.sz0z00 QUANTIFIERS_INST_ENUM))) (let ((_let_48 (ASSUME :args (_let_12)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_42 (not _let_44)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args _let_47) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_42 false _let_12 false _let_44)))) (let ((_let_50 (not _let_42))) (let ((_let_51 (= tptp.sz00 _let_18))) (let ((_let_52 (or _let_29 _let_51 _let_24))) (let ((_let_53 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (or (not (tptp.aVector0 W0)) (not (tptp.aVector0 W1)) (not (= _let_1 _let_2)) (= tptp.sz00 _let_1) (= (tptp.sdtasasdt0 W0 W1) (tptp.sdtpldt0 (tptp.sdtasasdt0 (tptp.sziznziztdt0 W0) (tptp.sziznziztdt0 W1)) (tptp.sdtasdt0 (tptp.sdtlbdtrb0 W0 _let_2) (tptp.sdtlbdtrb0 W1 _let_1)))))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM))) (let ((_let_56 (= tptp.sz0z00 _let_14))) (let ((_let_57 (not _let_51))) (let ((_let_58 (or _let_29 _let_57 _let_56))) (let ((_let_59 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (or (not (tptp.aVector0 W0)) (not (tptp.aVector0 W1)) (not (= _let_1 (tptp.aDimensionOf0 W0))) (not (= tptp.sz00 _let_1)) (= tptp.sz0z00 (tptp.sdtasasdt0 W0 W1))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (tptp.sdtlseqdt0 tptp.sz0z00 _let_40))) (let ((_let_62 (not _let_56))) (let ((_let_63 (or _let_43 _let_61))) (let ((_let_64 (forall ((W0 $$unsorted)) (or (not (tptp.aScalar0 W0)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W0)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (_let_64))) (let ((_let_67 (not _let_61))) (let ((_let_68 (not _let_41))) (let ((_let_69 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_15))))) (let ((_let_70 (ASSUME :args (_let_61)))) (let ((_let_71 (APPLY_UF tptp.sdtlseqdt0))) (let ((_let_72 (ASSUME :args (_let_41)))) (let ((_let_73 (ASSUME :args (_let_56)))) (let ((_let_74 (ASSUME :args (_let_31)))) (let ((_let_75 (SYMM (FALSE_INTRO _let_74)))) (let ((_let_76 (REFL :args (_let_30)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_35)) :args ((or _let_28 _let_30))) _let_37 :args (_let_28 true _let_30)))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_29 _let_56 _let_57 (not _let_58)))) _let_77 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_70 _let_72 _let_73 _let_74) :args (_let_31 _let_41 _let_56 _let_61)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_75 (CONG (REFL :args (tptp.sz0z00)) (TRANS (SYMM _let_73) (SYMM (SYMM _let_72))) :args _let_71) (TRUE_INTRO _let_70))) :args (_let_61 _let_41 _let_56 _let_31)) :args ((not (and _let_31 _let_41 _let_56 _let_61)) SB_LITERAL))) (CONG _let_69 (REFL :args (_let_68)) (REFL :args (_let_62)) (REFL :args (_let_67)) :args _let_35)) :args ((or _let_15 _let_68 _let_67 _let_62))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 2)) :args ((or _let_41 _let_50))) _let_49 :args (_let_41 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_43 _let_61 (not _let_63)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args _let_47) :args _let_66)) _let_65 :args (_let_63 false _let_64)) :args (_let_61 false _let_12 false _let_63)) _let_38 :args (_let_62 false _let_41 false _let_61 true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args _let_55) :args (_let_59)))) _let_60 :args (_let_58 false _let_59)) :args (_let_57 false _let_28 true _let_56 false _let_58)))) (let ((_let_79 (tptp.sdtlseqdt0 tptp.sz0z00 _let_20))) (let ((_let_80 (not _let_79))) (let ((_let_81 (tptp.sdtlseqdt0 tptp.sz0z00 _let_22))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.aScalar0 _let_20))) (let ((_let_84 (not _let_83))) (let ((_let_85 (tptp.aScalar0 _let_22))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_43 _let_86 _let_43 _let_84 _let_82 _let_80 _let_25))) (let ((_let_88 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (not (tptp.aScalar0 W2)) (not (tptp.aScalar0 W3)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 W2) (tptp.sdtpldt0 W1 W3)))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (tptp.aScalar0 _let_19))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_79))) (let ((_let_93 (tptp.aNaturalNumber0 _let_18))) (let ((_let_94 (not _let_93))) (let ((_let_95 (or _let_29 _let_94 _let_90))) (let ((_let_96 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aVector0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aScalar0 (tptp.sdtlbdtrb0 W0 W1)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (or _let_29 _let_93))) (let ((_let_99 (forall ((W0 $$unsorted)) (or (not (tptp.aVector0 W0)) (tptp.aNaturalNumber0 (tptp.aDimensionOf0 W0)))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (_let_99))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_29 _let_94 _let_90 (not _let_95)))) _let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_29 _let_93 (not _let_98)))) _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM)) :args _let_101)) _let_100 :args (_let_98 false _let_99)) :args (_let_93 false _let_28 false _let_98)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18 QUANTIFIERS_INST_ENUM)) :args (_let_96))) _let_97 :args (_let_95 false _let_96)) :args (_let_90 false _let_28 false _let_93 false _let_95)))) (let ((_let_103 (or _let_91 _let_91 _let_83))) (let ((_let_104 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (tptp.aDimensionOf0 _let_21))) (let ((_let_107 (tptp.iLess0 _let_106 _let_18))) (let ((_let_108 (not _let_107))) (let ((_let_109 (tptp.aVector0 _let_21))) (let ((_let_110 (not _let_109))) (let ((_let_111 (or _let_110 _let_108 _let_81))) (let ((_let_112 (_let_26))) (let ((_let_113 (_let_21 QUANTIFIERS_INST_ENUM))) (let ((_let_114 (tptp.szszuzczcdt0 _let_106))) (let ((_let_115 (tptp.iLess0 _let_106 _let_114))) (let ((_let_116 (= _let_18 _let_114))) (let ((_let_117 (tptp.aNaturalNumber0 _let_106))) (let ((_let_118 (not _let_117))) (let ((_let_119 (or _let_118 _let_115))) (let ((_let_120 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (or _let_110 _let_117))) (let ((_let_123 (and _let_109 _let_116 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtlbdtrb0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 W2) (tptp.sdtlbdtrb0 (tptp.sziznziztdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) W2))))))) (let ((_let_124 (or _let_29 _let_51 _let_123))) (let ((_let_125 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1338 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W0))) (or (not (tptp.aVector0 W0)) (= tptp.sz00 _let_1) (= (= (tptp.sziznziztdt0 W0) BOUND_VARIABLE_1338) (and (tptp.aVector0 BOUND_VARIABLE_1338) (= _let_1 (tptp.szszuzczcdt0 (tptp.aDimensionOf0 BOUND_VARIABLE_1338))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtlbdtrb0 W0 W2) (tptp.sdtlbdtrb0 BOUND_VARIABLE_1338 W2))))))))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_29 _let_51 _let_123 (not _let_124)))) _let_77 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_126 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_21 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_125)))) _let_126 :args (_let_124 false _let_125)) :args (_let_123 false _let_28 true _let_51 false _let_124)))) (let ((_let_128 (not _let_123))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_123 0)) :args ((or _let_109 _let_128))) _let_127 :args (_let_109 false _let_123)))) (let ((_let_130 (and _let_116 _let_115))) (let ((_let_131 (ASSUME :args (_let_115)))) (let ((_let_132 (ASSUME :args (_let_116)))) (let ((_let_133 (or _let_110 _let_85))) (let ((_let_134 (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_135 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_136 (ASSUME :args (_let_25)))) (let ((_let_137 (ASSUME :args (_let_24)))) (let ((_let_138 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_138 _let_136 _let_137 _let_74) :args (_let_31 _let_17 _let_24 _let_25)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_75 (CONG (SYMM (SYMM _let_138)) (SYMM (SYMM _let_137)) :args _let_71) (TRUE_INTRO _let_136))) :args (_let_17 _let_25 _let_24 _let_31)) :args ((not (and _let_31 _let_17 _let_24 _let_25)) SB_LITERAL))) (CONG _let_69 (REFL :args ((not _let_17))) (REFL :args ((not _let_24))) (REFL :args ((not _let_25))) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_87))) :args ((or _let_43 _let_86 _let_82 _let_84 _let_80 _let_25 (not _let_87)))) _let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_133)) :args ((or _let_85 _let_110 (not _let_133)))) _let_129 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_135 :args (_let_21 _let_21 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_134)))) _let_135 :args (_let_133 false _let_134)) :args (_let_85 false _let_109 false _let_133)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_81 _let_110 _let_108 (not _let_111)))) _let_129 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_130)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_131 _let_132) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_106)) (SYMM (SYMM _let_132)) :args (APPLY_UF tptp.iLess0)) (TRUE_INTRO _let_131))) :args (_let_115 _let_116))) :args (_let_116 _let_115))) :args (true _let_130)) :args ((or _let_107 (not _let_116) (not _let_115)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_123 1)) :args ((or _let_116 _let_128))) _let_127 :args (_let_116 false _let_123)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_118 _let_115 (not _let_119)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_122)) :args ((or _let_110 _let_117 (not _let_122)))) _let_129 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args _let_113) :args _let_101)) _let_100 :args (_let_122 false _let_99)) :args (_let_117 false _let_109 false _let_122)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (_let_106 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_120))) _let_121 :args (_let_119 false _let_120)) :args (_let_115 false _let_117 false _let_119)) :args (_let_107 false _let_116 false _let_115)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_112) :args _let_113) :args _let_112)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 1)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_35)) :args ((or _let_26 _let_30))) _let_37 :args (_let_26 true _let_30)) :args (_let_111 false _let_26)) :args (_let_81 false _let_109 false _let_107 false _let_111)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_103))) :args ((or _let_91 _let_83 (not _let_103)))) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (_let_19 _let_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_104))) _let_105 :args (_let_103 false _let_104)) :args (_let_83 false _let_90 false _let_103)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_91 _let_79 (not _let_92)))) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_19 QUANTIFIERS_INST_ENUM)) :args _let_66)) _let_65 :args (_let_92 false _let_64)) :args (_let_79 false _let_90 false _let_92)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.sz0z00 _let_22 tptp.sz0z00 _let_20 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_25 false _let_12 false _let_85 false _let_81 false _let_83 false _let_79 false _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_29 _let_51 _let_24 (not _let_52)))) _let_77 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args _let_55) :args (_let_53)))) _let_54 :args (_let_52 false _let_53)) :args (_let_24 false _let_28 true _let_51 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 0)) :args ((or _let_17 _let_50))) _let_49 :args (_let_17 false _let_42)) _let_38 :args (false false _let_25 false _let_24 false _let_17 true _let_15)) :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_13 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) true)) _let_12 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtpldt0 W0 W1)))) _let_11 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.aScalar0 (tptp.smndt0 W0)))) _let_10 (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)))) _let_9 (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)))))) _let_8 (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 $$unsorted)) (=> (tptp.aVector0 W0) true)) _let_7 _let_6 _let_5 (forall ((W0 $$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_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.65/10.87 )
% 10.65/10.87 % SZS output end Proof for RNG048+1
% 10.65/10.87 % cvc5---1.0.5 exiting
% 10.65/10.87 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------