TSTP Solution File: SWV102+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV102+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 21:49:19 EDT 2023
% Result : Theorem 0.17s 0.62s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWV102+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.09/0.12 % Command : do_cvc5 %s %d
% 0.11/0.33 % Computer : n032.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 29 08:02:46 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.47 %----Proving TF0_NAR, FOF, or CNF
% 0.17/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.SIYkMwTVIz/cvc5---1.0.5_7666.p...
% 0.17/0.62 ------- get file name : TPTP file name is SWV102+1
% 0.17/0.62 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7666.smt2...
% 0.17/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.17/0.62 % SZS status Theorem for SWV102+1
% 0.17/0.62 % SZS output start Proof for SWV102+1
% 0.17/0.62 (
% 0.17/0.62 (let ((_let_1 (tptp.succ tptp.n0))) (let ((_let_2 (tptp.succ _let_1))) (let ((_let_3 (tptp.succ _let_2))) (let ((_let_4 (= _let_2 tptp.n2))) (let ((_let_5 (= _let_1 tptp.n1))) (let ((_let_6 (tptp.succ _let_3))) (let ((_let_7 (tptp.tptp_update2 tptp.rho_defuse tptp.n0 tptp.use))) (let ((_let_8 (tptp.tptp_update2 _let_7 tptp.n1 tptp.use))) (let ((_let_9 (tptp.tptp_update2 _let_8 tptp.n2 tptp.use))) (let ((_let_10 (tptp.a_select2 _let_9 tptp.n2))) (let ((_let_11 (tptp.a_select2 _let_9 tptp.n1))) (let ((_let_12 (tptp.a_select2 _let_9 tptp.n0))) (let ((_let_13 (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (let ((_let_14 (= _let_13 tptp.use))) (let ((_let_15 (tptp.a_select2 tptp.xinit_defuse tptp.n4))) (let ((_let_16 (= _let_15 tptp.use))) (let ((_let_17 (tptp.a_select2 tptp.xinit_defuse tptp.n3))) (let ((_let_18 (= _let_17 tptp.use))) (let ((_let_19 (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0))) (let ((_let_20 (= _let_19 tptp.use))) (let ((_let_21 (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0))) (let ((_let_22 (= _let_21 tptp.use))) (let ((_let_23 (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0))) (let ((_let_24 (= _let_23 tptp.use))) (let ((_let_25 (tptp.a_select2 tptp.sigma_defuse tptp.n5))) (let ((_let_26 (= _let_25 tptp.use))) (let ((_let_27 (tptp.a_select2 tptp.sigma_defuse tptp.n4))) (let ((_let_28 (= _let_27 tptp.use))) (let ((_let_29 (tptp.a_select2 tptp.sigma_defuse tptp.n3))) (let ((_let_30 (= _let_29 tptp.use))) (let ((_let_31 (tptp.a_select2 tptp.sigma_defuse tptp.n2))) (let ((_let_32 (= _let_31 tptp.use))) (let ((_let_33 (tptp.a_select2 tptp.sigma_defuse tptp.n1))) (let ((_let_34 (= _let_33 tptp.use))) (let ((_let_35 (tptp.a_select2 tptp.sigma_defuse tptp.n0))) (let ((_let_36 (= _let_35 tptp.use))) (let ((_let_37 (not (=> (and _let_36 _let_34 _let_32 _let_30 _let_28 _let_26 _let_24 _let_22 _let_20 _let_18 _let_16 _let_14) (and _let_36 _let_34 _let_32 _let_30 _let_28 _let_26 _let_24 _let_22 _let_20 _let_18 _let_16 _let_14 (= _let_12 tptp.use) (= _let_11 tptp.use) (= _let_10 tptp.use)))))) (let ((_let_38 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))))) (let ((_let_39 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)))) (let ((_let_40 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_41 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_42 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))))) (let ((_let_43 (tptp.succ tptp.tptp_minus_1))) (let ((_let_44 (= _let_43 tptp.n0))) (let ((_let_45 (= tptp.n0 _let_43))) (let ((_let_46 (= tptp.n1 _let_1))) (let ((_let_47 (= tptp.n2 _let_2))) (let ((_let_48 (= _let_2 (tptp.plus _let_1 tptp.n1)))) (let ((_let_49 (= _let_1 (tptp.plus tptp.n1 tptp.n0)))) (let ((_let_50 (= tptp.n0 (tptp.pred _let_1)))) (let ((_let_51 (= tptp.tptp_minus_1 (tptp.pred _let_43)))) (let ((_let_52 (= tptp.n0 tptp.n2))) (let ((_let_53 (= tptp.n0 tptp.n1))) (let ((_let_54 (SYMM (ASSUME :args (_let_44))))) (let ((_let_55 (SYMM (ASSUME :args (_let_5))))) (let ((_let_56 (SYMM (ASSUME :args (_let_4))))) (let ((_let_57 (_let_42))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 (_let_41))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 ((tptp.succ X)))) (let ((_let_65 (= tptp.use _let_10))) (let ((_let_66 (= tptp.use _let_12))) (let ((_let_67 (not _let_52))) (let ((_let_68 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (_let_68))) (let ((_let_71 ((tptp.tptp_update2 X U VAL)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (_let_8 tptp.n2 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) :args ((or _let_65 (not _let_68)))) _let_69 :args (_let_65 false _let_68)))) (let ((_let_73 (= tptp.use _let_11))) (let ((_let_74 (not _let_66))) (let ((_let_75 (tptp.a_select2 _let_8 tptp.n1))) (let ((_let_76 (= _let_11 _let_75))) (let ((_let_77 (= tptp.use _let_75))) (let ((_let_78 (= tptp.n1 tptp.n2))) (let ((_let_79 (or _let_78 _let_76))) (let ((_let_80 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (_let_7 tptp.n1 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_77 false _let_68)))) (let ((_let_85 (not _let_77))) (let ((_let_86 (not _let_65))) (let ((_let_87 (and _let_65 _let_77 _let_78))) (let ((_let_88 (ASSUME :args (_let_77)))) (let ((_let_89 (SYMM (SYMM _let_88)))) (let ((_let_90 (ASSUME :args (_let_65)))) (let ((_let_91 (SYMM _let_90))) (let ((_let_92 (APPLY_UF tptp.a_select2))) (let ((_let_93 (ASSUME :args (_let_78)))) (let ((_let_94 (REFL :args (_let_9)))) (let ((_let_95 (and _let_77 _let_76))) (let ((_let_96 (ASSUME :args (_let_76)))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (NOT_IMPLIES_ELIM1 _let_97))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_IMPLIES_ELIM2 _let_97)) (AND_ELIM _let_98 :args (0)) (AND_ELIM _let_98 :args (1)) (AND_ELIM _let_98 :args (2)) (AND_ELIM _let_98 :args (3)) (AND_ELIM _let_98 :args (4)) (AND_ELIM _let_98 :args (5)) (AND_ELIM _let_98 :args (6)) (AND_ELIM _let_98 :args (7)) (AND_ELIM _let_98 :args (8)) (AND_ELIM _let_98 :args (9)) (AND_ELIM _let_98 :args (10)) (AND_ELIM _let_98 :args (11)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_95)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_96 _let_88) (SCOPE (TRANS _let_89 (SYMM _let_96)) :args (_let_76 _let_77))) :args (_let_77 _let_76))) :args (true _let_95)) :args ((or _let_73 _let_85 (not _let_76)))) _let_84 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_88 _let_90 _let_93) (SCOPE (TRANS (CONG _let_94 (SYMM (SYMM _let_93)) :args _let_92) _let_91 _let_89) :args (_let_77 _let_65 _let_78))) :args (_let_65 _let_77 _let_78))) :args (true _let_87)) :args ((or _let_86 _let_76 _let_85 (not _let_78)))) _let_72 _let_84 (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_78 _let_76 (not _let_79)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.n2 tptp.n1 _let_8 tptp.use QUANTIFIERS_INST_E_MATCHING _let_83)) :args _let_82))) _let_81 :args (_let_79 false _let_80)) :args (_let_76 false _let_65 false _let_77 false _let_78 false _let_79)) :args (_let_73 false _let_77 false _let_76)) _let_72 :args (_let_74 false (= tptp.use _let_35) false (= tptp.use _let_33) false (= tptp.use _let_31) false (= tptp.use _let_29) false (= tptp.use _let_27) false (= tptp.use _let_25) false (= tptp.use _let_23) false (= tptp.use _let_21) false (= tptp.use _let_19) false (= tptp.use _let_17) false (= tptp.use _let_15) false (= tptp.use _let_13) false _let_73 false _let_65)))) (let ((_let_100 (and _let_65 _let_52))) (let ((_let_101 (ASSUME :args (_let_52)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_100)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_101 _let_90) (SCOPE (TRANS (SYMM _let_91) (CONG _let_94 (SYMM _let_101) :args _let_92)) :args (_let_52 _let_65))) :args (_let_65 _let_52))) :args (true _let_100)) :args ((or _let_66 _let_86 _let_67))) _let_99 _let_72 :args (_let_67 true _let_66 false _let_65)))) (let ((_let_103 (tptp.a_select2 _let_8 tptp.n0))) (let ((_let_104 (tptp.a_select2 _let_7 tptp.n0))) (let ((_let_105 (= _let_104 _let_103))) (let ((_let_106 (or _let_53 _let_105))) (let ((_let_107 (= _let_12 _let_103))) (let ((_let_108 (= tptp.use _let_104))) (let ((_let_109 (not _let_105))) (let ((_let_110 (or _let_52 _let_107))) (let ((_let_111 (or))) (let ((_let_112 (and _let_74 _let_108 _let_107))) (let ((_let_113 (ASSUME :args (_let_74)))) (let ((_let_114 (ASSUME :args (_let_107)))) (let ((_let_115 (ASSUME :args (_let_108)))) (let ((_let_116 (not _let_53))) (let ((_let_117 (not _let_51))) (let ((_let_118 (not _let_50))) (let ((_let_119 (not _let_49))) (let ((_let_120 (not _let_48))) (let ((_let_121 (not _let_47))) (let ((_let_122 (not _let_46))) (let ((_let_123 (not _let_45))) (let ((_let_124 (= tptp.tptp_minus_1 tptp.n2))) (let ((_let_125 (= tptp.tptp_minus_1 tptp.n1))) (let ((_let_126 (SYMM _let_54))) (let ((_let_127 (SYMM _let_126))) (let ((_let_128 (ASSUME :args (_let_53)))) (let ((_let_129 (SYMM _let_128))) (let ((_let_130 (ASSUME :args (_let_67)))) (let ((_let_131 (ASSUME :args (_let_48)))) (let ((_let_132 (APPLY_UF tptp.plus))) (let ((_let_133 (SYMM (SYMM _let_55)))) (let ((_let_134 (SYMM _let_129))) (let ((_let_135 (TRANS _let_134 _let_133))) (let ((_let_136 (ASSUME :args (_let_49)))) (let ((_let_137 (ASSUME :args (_let_50)))) (let ((_let_138 (SYMM _let_137))) (let ((_let_139 (APPLY_UF tptp.pred))) (let ((_let_140 (CONG _let_135 :args _let_139))) (let ((_let_141 (CONG _let_126 :args _let_139))) (let ((_let_142 (ASSUME :args (_let_51)))) (let ((_let_143 (SYMM (SYMM _let_142)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_54 _let_128 (MODUS_PONENS (AND_INTRO _let_128 _let_137 _let_55 _let_54 _let_142) (SCOPE (TRANS _let_143 _let_141 _let_140 _let_138 _let_134) :args (_let_53 _let_50 _let_46 _let_45 _let_51))) (MODUS_PONENS (AND_INTRO _let_56 _let_131 _let_55 _let_128 _let_136 _let_137 _let_54 _let_142) (SCOPE (TRANS _let_143 _let_141 _let_140 _let_138 _let_134 _let_133 (SYMM (SYMM _let_136)) (CONG (REFL :args (tptp.n1)) _let_135 :args _let_132) (CONG _let_133 (SYMM _let_133) :args _let_132) (SYMM _let_131) (SYMM _let_56)) :args (_let_47 _let_48 _let_46 _let_53 _let_49 _let_50 _let_45 _let_51))) _let_130) :args (_let_45 _let_46 _let_47 _let_48 _let_49 _let_50 _let_51 _let_67 _let_53)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_130)) (TRUE_INTRO (TRANS _let_127 (SYMM (TRANS (SYMM (ASSUME :args (_let_124))) (SYMM (SYMM (ASSUME :args (_let_125)))) _let_129 _let_127)))))) :args (_let_45 _let_53 _let_125 _let_124 _let_67)) :args ((not (and _let_45 _let_46 _let_47 _let_48 _let_49 _let_50 _let_51 _let_67 _let_53)) SB_LITERAL))) (CONG (REFL :args (_let_123)) (REFL :args (_let_122)) (REFL :args (_let_121)) (REFL :args (_let_120)) (REFL :args (_let_119)) (REFL :args (_let_118)) (REFL :args (_let_117)) (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_52))) (REFL :args (_let_116)) :args _let_111)) :args ((or _let_123 _let_122 _let_121 _let_52 _let_120 _let_119 _let_118 _let_117 _let_116))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_105 _let_53 (not _let_106)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_112)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_115 _let_113 _let_114) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_115) (SYMM _let_114) :args (=)) (FALSE_INTRO _let_113))) :args (_let_108 _let_74 _let_107))) :args (_let_74 _let_108 _let_107))) :args (true _let_112)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_66))) (REFL :args ((not _let_108))) (REFL :args ((not _let_107))) (REFL :args (_let_109)) :args _let_111)) _let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.rho_defuse tptp.n0 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_108 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_52 _let_107 (not _let_110)))) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.n2 tptp.n0 _let_8 tptp.use QUANTIFIERS_INST_E_MATCHING _let_83)) :args _let_82))) _let_81 :args (_let_110 false _let_80)) :args (_let_107 true _let_52 false _let_110)) :args (_let_109 true _let_66 false _let_108 false _let_107)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.n1 tptp.n0 _let_7 tptp.use QUANTIFIERS_INST_E_MATCHING _let_83)) :args _let_82))) _let_81 :args (_let_106 false _let_80)) :args (_let_53 true _let_105 false _let_106)) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_64)) :args _let_63)) _let_62 :args (_let_51 false _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_64)) :args _let_63)) _let_62 :args (_let_50 false _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args _let_59))) _let_60 :args (_let_49 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args _let_57))) _let_58 :args (_let_48 false _let_42)) _let_56 _let_55 _let_54 :args (false false _let_53 true _let_52 false _let_51 false _let_50 false _let_49 false _let_48 false _let_47 false _let_46 false _let_45)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))) (forall ((X $$unsorted)) (not (tptp.gt X X))) (forall ((X $$unsorted)) (tptp.leq X X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))) (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq (tptp.uniform_int_rnd C X) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq tptp.n0 (tptp.uniform_int_rnd C X)))) (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim L U) Val) I) Val))) (forall ((I $$unsorted) (L1 $$unsorted) (U1 $$unsorted) (J $$unsorted) (L2 $$unsorted) (U2 $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L1 I) (tptp.leq I U1) (tptp.leq L2 J) (tptp.leq J U2)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim L1 U1) (tptp.dim L2 U2) Val) I J) Val))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.trans A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.inv A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted) (VAL $$unsorted)) (let ((_let_1 (tptp.tptp_update3 A K K VAL))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N) (tptp.leq tptp.n0 K) (tptp.leq K N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_madd A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_msub A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 D I J) (tptp.a_select3 D J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 F I J) (tptp.a_select3 F J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)) (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) _let_44 _let_42 _let_41 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) _let_40 (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.minus X Y) X) (tptp.leq tptp.n0 Y))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V) VAL)) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= J V) (= (tptp.a_select3 X U V) VAL)) (= (tptp.a_select3 (tptp.tptp_update3 X I J VAL2) U V) VAL))) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))) _let_39 _let_38 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))) tptp.true (not (= tptp.def tptp.use)) _let_37 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n0 tptp.tptp_minus_1) (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n2 tptp.n1) (tptp.gt tptp.n3 tptp.n1) (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n5)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n3)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3)))) (= _let_6 tptp.n4) (= (tptp.succ _let_6) tptp.n5) _let_5 _let_4 (= _let_3 tptp.n3) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.17/0.62 )
% 0.17/0.62 % SZS output end Proof for SWV102+1
% 0.17/0.62 % cvc5---1.0.5 exiting
% 0.17/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------