TSTP Solution File: SWV181+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 21:49:37 EDT 2023
% Result : Theorem 0.19s 0.68s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 06:11:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.19/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.68 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.xjGLdoMl5R/cvc5---1.0.5_11932.p...
% 0.19/0.68 ------- get file name : TPTP file name is SWV181+1
% 0.19/0.68 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11932.smt2...
% 0.19/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.68 % SZS status Theorem for SWV181+1
% 0.19/0.68 % SZS output start Proof for SWV181+1
% 0.19/0.68 (
% 0.19/0.68 (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_3 tptp.n3))) (let ((_let_5 (= _let_2 tptp.n2))) (let ((_let_6 (= _let_1 tptp.n1))) (let ((_let_7 (tptp.succ _let_3))) (let ((_let_8 (= _let_7 tptp.n4))) (let ((_let_9 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_10 (tptp.gt tptp.n1 tptp.n0))) (let ((_let_11 (tptp.gt tptp.loopcounter tptp.n0))) (let ((_let_12 (tptp.gt tptp.n1 tptp.loopcounter))) (let ((_let_13 (tptp.leq tptp.n1 tptp.loopcounter))) (let ((_let_14 (not (=> (and (tptp.leq tptp.tptp_float_0_001 tptp.pv76) _let_13 _let_12 (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select3 tptp.center_init C tptp.n0) tptp.init))) (=> _let_11 (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select2 tptp.mu_init D) tptp.init)))) (=> _let_11 (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.rho_init E) tptp.init)))) (=> _let_11 (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select2 tptp.sigma_init F) tptp.init))))) (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init))))))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))))) (let ((_let_16 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_17 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_18 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))))) (let ((_let_19 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_20 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))))) (let ((_let_21 (tptp.succ tptp.tptp_minus_1))) (let ((_let_22 (= _let_21 tptp.n0))) (let ((_let_23 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))) (let ((_let_24 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_25 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_26 (forall ((X $$unsorted)) (not (tptp.gt X X))))) (let ((_let_27 (= tptp.n0 _let_21))) (let ((_let_28 (= tptp.n0 (tptp.pred _let_1)))) (let ((_let_29 (= tptp.tptp_minus_1 (tptp.pred _let_21)))) (let ((_let_30 (tptp.gt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.tptp_minus_1))) (let ((_let_31 (tptp.gt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (= tptp.n0 _let_1))) (let ((_let_33 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_34 (SYMM (ASSUME :args (_let_22))))) (let ((_let_35 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (_let_35))) (let ((_let_38 ((tptp.succ X)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_37)) _let_36 :args (_let_28 false _let_35)))) (let ((_let_40 (tptp.leq _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_30))) (let ((_let_43 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.leq (tptp.succ X) Y)) (tptp.gt Y X))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_46 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n4))) (let ((_let_47 (not _let_46))) (let ((_let_48 (not _let_45))) (let ((_let_49 (or _let_48 _let_47 (= tptp.init (tptp.a_select2 tptp.muold_init SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_50 (forall ((G $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq G tptp.n4)) (= tptp.init (tptp.a_select2 tptp.muold_init G)))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (or))) (let ((_let_54 (not _let_50))) (let ((_let_55 (_let_54))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_55)) :args _let_55)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_50))) (REFL :args (_let_51)) :args _let_53)) (NOT_IMPLIES_ELIM2 _let_52) :args (_let_51 true _let_50)))) (let ((_let_57 (REFL :args (_let_49)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 0)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_45))) :args _let_53)) :args ((or _let_45 _let_49))) _let_56 :args (_let_45 true _let_49)))) (let ((_let_59 (and _let_27 _let_45))) (let ((_let_60 (ASSUME :args (_let_45)))) (let ((_let_61 (APPLY_UF tptp.leq))) (let ((_let_62 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_63 (SYMM (SYMM _let_34)))) (let ((_let_64 (not _let_31))) (let ((_let_65 (_let_26))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (tptp.leq _let_1 tptp.n0))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.leq tptp.n0 _let_1))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_70 _let_68 _let_32))) (let ((_let_72 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (_let_72))) (let ((_let_75 ((not (= (tptp.leq tptp.n0 X) false))))) (let ((_let_76 (tptp.leq tptp.n1 tptp.n0))) (let ((_let_77 (= tptp.n1 _let_1))) (let ((_let_78 (tptp.leq tptp.loopcounter tptp.n0))) (let ((_let_79 (not _let_78))) (let ((_let_80 (not _let_13))) (let ((_let_81 (or _let_80 _let_79 _let_76))) (let ((_let_82 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq X Y)) (not (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (tptp.leq tptp.loopcounter (tptp.pred tptp.n1)))) (let ((_let_85 (= _let_12 _let_84))) (let ((_let_86 (_let_23))) (let ((_let_87 (ASSUME :args _let_86))) (let ((_let_88 (NOT_IMPLIES_ELIM1 _let_52))) (let ((_let_89 (SYMM (ASSUME :args (_let_6))))) (let ((_let_90 (not _let_28))) (let ((_let_91 (not _let_77))) (let ((_let_92 (and _let_77 _let_84 _let_28))) (let ((_let_93 (ASSUME :args (_let_84)))) (let ((_let_94 (APPLY_UF tptp.pred))) (let ((_let_95 (SYMM _let_89))) (let ((_let_96 (ASSUME :args (_let_28)))) (let ((_let_97 (SYMM (SYMM _let_96)))) (let ((_let_98 (and _let_77 _let_76))) (let ((_let_99 (ASSUME :args (_let_76)))) (let ((_let_100 (REFL :args (tptp.n0)))) (let ((_let_101 (tptp.leq tptp.n0 tptp.n1))) (let ((_let_102 (not _let_10))) (let ((_let_103 (or _let_102 _let_101))) (let ((_let_104 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (and _let_77 _let_101))) (let ((_let_107 (ASSUME :args (_let_101)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_70 _let_68 _let_32 (not _let_71)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_106)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_107 _let_89) (SCOPE (TRUE_ELIM (TRANS (CONG _let_100 _let_95 :args _let_61) (TRUE_INTRO _let_107))) :args (_let_101 _let_77))) :args (_let_77 _let_101))) :args (true _let_106)) :args ((or _let_91 _let_69 (not _let_101)))) _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_102 _let_101 (not _let_103)))) (ASSUME :args (_let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.n0 tptp.n1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_104))) _let_105 :args (_let_103 false _let_104)) :args (_let_101 false _let_10 false _let_103)) :args (_let_69 false _let_77 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_98)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_99 _let_89) (SCOPE (TRUE_ELIM (TRANS (CONG _let_95 _let_100 :args _let_61) (TRUE_INTRO _let_99))) :args (_let_76 _let_77))) :args (_let_77 _let_76))) :args (true _let_98)) :args ((or _let_91 _let_67 (not _let_76)))) _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_80 _let_79 _let_76 (not _let_81)))) (AND_ELIM _let_88 :args (1)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_92)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_93 _let_89 _let_96) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (tptp.loopcounter)) (TRANS _let_97 (CONG _let_95 :args _let_94)) :args _let_61) (TRUE_INTRO _let_93))) :args (_let_84 _let_77 _let_28))) :args (_let_77 _let_84 _let_28))) :args (true _let_92)) :args ((or _let_91 _let_78 (not _let_84) _let_90))) _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_85)) :args ((or (not _let_12) _let_84 (not _let_85)))) (AND_ELIM _let_88 :args (2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_87 :args (tptp.loopcounter tptp.n1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.gt Y X)))) :args _let_86))) _let_87 :args (_let_85 false _let_23)) :args (_let_84 false _let_12 false _let_85)) _let_39 :args (_let_78 false _let_77 false _let_84 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (tptp.n1 tptp.loopcounter tptp.n0 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.leq X Y) false)) (not (= (tptp.leq Y Z) false))))) :args (_let_82))) _let_83 :args (_let_81 false _let_82)) :args (_let_76 false _let_13 false _let_78 false _let_81)) :args (_let_67 false _let_77 false _let_76)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_71 false _let_72)) :args (_let_32 false _let_69 false _let_67 false _let_71)))) (let ((_let_109 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n0))) (let ((_let_110 (not _let_109))) (let ((_let_111 (or _let_48 _let_110 _let_33))) (let ((_let_112 (= _let_3 (tptp.plus tptp.n3 tptp.n0)))) (let ((_let_113 (= _let_2 (tptp.plus tptp.n2 tptp.n0)))) (let ((_let_114 (= _let_1 (tptp.plus tptp.n1 tptp.n0)))) (let ((_let_115 (= _let_7 (tptp.plus _let_3 tptp.n1)))) (let ((_let_116 (= _let_3 (tptp.plus _let_2 tptp.n1)))) (let ((_let_117 (= _let_2 (tptp.plus _let_1 tptp.n1)))) (let ((_let_118 (= tptp.n3 _let_3))) (let ((_let_119 (= tptp.n2 _let_2))) (let ((_let_120 (= tptp.n4 _let_7))) (let ((_let_121 (_let_17))) (let ((_let_122 (ASSUME :args _let_121))) (let ((_let_123 (_let_18))) (let ((_let_124 (ASSUME :args _let_123))) (let ((_let_125 (_let_19))) (let ((_let_126 (ASSUME :args _let_125))) (let ((_let_127 (_let_20))) (let ((_let_128 (ASSUME :args _let_127))) (let ((_let_129 ((tptp.succ X)))) (let ((_let_130 (SYMM (ASSUME :args (_let_4))))) (let ((_let_131 (SYMM (ASSUME :args (_let_5))))) (let ((_let_132 (SYMM (ASSUME :args (_let_8))))) (let ((_let_133 (not _let_32))) (let ((_let_134 (and _let_120 _let_77 _let_119 _let_118 _let_46 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_32))) (let ((_let_135 (ASSUME :args (_let_46)))) (let ((_let_136 (ASSUME :args (_let_115)))) (let ((_let_137 (APPLY_UF tptp.plus))) (let ((_let_138 (ASSUME :args (_let_32)))) (let ((_let_139 (SYMM _let_138))) (let ((_let_140 (SYMM _let_139))) (let ((_let_141 (ASSUME :args (_let_112)))) (let ((_let_142 (ASSUME :args (_let_116)))) (let ((_let_143 (ASSUME :args (_let_113)))) (let ((_let_144 (ASSUME :args (_let_117)))) (let ((_let_145 (ASSUME :args (_let_114)))) (let ((_let_146 (ASSUME :args (_let_30)))) (let ((_let_147 (APPLY_UF tptp.gt))) (let ((_let_148 (ASSUME :args (_let_29)))) (let ((_let_149 (ASSUME :args (_let_33)))) (let ((_let_150 (ASSUME :args (_let_64)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_146 _let_148 _let_34 _let_138 _let_96 _let_149 _let_150) :args (_let_27 _let_33 _let_28 _let_29 _let_30 _let_64 _let_32)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_150)) (CONG _let_62 (SYMM _let_149) :args _let_147) (CONG _let_62 (TRANS _let_97 (CONG _let_139 :args _let_94) (CONG _let_63 :args _let_94) (SYMM _let_148)) :args _let_147) (TRUE_INTRO _let_146))) :args (_let_30 _let_29 _let_27 _let_32 _let_28 _let_33 _let_64)) :args ((not (and _let_27 _let_33 _let_28 _let_29 _let_30 _let_64 _let_32)) SB_LITERAL))) (CONG (REFL :args ((not _let_27))) (REFL :args ((not _let_33))) (REFL :args (_let_90)) (REFL :args ((not _let_29))) (REFL :args ((not _let_30))) (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_31))) (REFL :args (_let_133)) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_48 _let_33 _let_110 (not _let_111)))) _let_58 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_134)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_135 _let_132 _let_136 _let_130 _let_89 _let_138 _let_141 _let_142 _let_131 _let_143 _let_144 _let_145) (SCOPE (TRUE_ELIM (TRANS (CONG _let_62 (TRANS _let_140 _let_95) :args _let_61) (CONG _let_62 (TRANS _let_89 (SYMM (SYMM _let_145)) (CONG (REFL :args (tptp.n1)) _let_140 :args _let_137) (CONG _let_89 _let_95 :args _let_137) (SYMM _let_144) (SYMM (SYMM _let_143)) (CONG (REFL :args (tptp.n2)) _let_140 :args _let_137) (CONG (SYMM (SYMM _let_131)) _let_95 :args _let_137) (SYMM _let_142) (SYMM (SYMM _let_141)) (CONG (REFL :args (tptp.n3)) _let_140 :args _let_137) (CONG (SYMM (SYMM _let_130)) _let_95 :args _let_137) (SYMM _let_136) (SYMM _let_132)) :args _let_61) (TRUE_INTRO _let_135))) :args (_let_46 _let_120 _let_115 _let_118 _let_77 _let_32 _let_112 _let_116 _let_119 _let_113 _let_117 _let_114))) :args (_let_120 _let_77 _let_119 _let_118 _let_46 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_32))) :args (true _let_134)) :args ((or (not _let_120) _let_91 (not _let_119) (not _let_118) _let_47 _let_109 (not _let_117) (not _let_116) (not _let_115) (not _let_114) (not _let_113) (not _let_112) _let_133))) _let_132 _let_89 _let_131 _let_130 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_53)) :args ((or _let_46 _let_49))) _let_56 :args (_let_46 true _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_128 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_129)) :args _let_127))) _let_128 :args (_let_117 false _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_128 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_129)) :args _let_127))) _let_128 :args (_let_116 false _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_128 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_129)) :args _let_127))) _let_128 :args (_let_115 false _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_126 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args _let_125))) _let_126 :args (_let_114 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_124 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING ((tptp.succ (tptp.succ X))))) :args _let_123))) _let_124 :args (_let_113 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_122 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING ((tptp.succ (tptp.succ (tptp.succ X)))))) :args _let_121))) _let_122 :args (_let_112 false _let_17)) _let_108 :args (_let_109 false _let_120 false _let_77 false _let_119 false _let_118 false _let_46 false _let_117 false _let_116 false _let_115 false _let_114 false _let_113 false _let_112 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_111 false _let_72)) :args (_let_33 false _let_45 false _let_109 false _let_111)) _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt X X) false))))) :args _let_65)) _let_66 :args (_let_64 false _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_30 (not _let_42)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_59)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_34) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_63) _let_62 :args _let_61) (TRUE_INTRO _let_60))) :args (_let_45 _let_27))) :args (_let_27 _let_45))) :args (true _let_59)) _let_34 _let_58 :args (_let_40 false _let_27 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.tptp_minus_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.leq (tptp.succ X) Y) false))))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_30 false _let_40 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_37)) _let_36 :args (_let_29 false _let_35)) _let_39 _let_34 :args (false false _let_33 false _let_32 true _let_31 false _let_30 false _let_29 false _let_28 false _let_27)) :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))) _let_26 (forall ((X $$unsorted)) (tptp.leq X X)) _let_25 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))) _let_24 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))) _let_23 (forall ((X $$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_22 _let_20 _let_19 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) _let_18 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) _let_17 (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 $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) _let_16 (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))) _let_15 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))) (forall ((I $$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_14 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n135299 tptp.n4) (tptp.gt tptp.n135299 tptp.n5) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n135299 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.n135299 tptp.n0) _let_10 (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.n135299 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.n135299 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n135299 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)))) _let_9 (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_8 (= (tptp.succ _let_7) tptp.n5) _let_6 _let_5 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.68 )
% 0.19/0.68 % SZS output end Proof for SWV181+1
% 0.19/0.68 % cvc5---1.0.5 exiting
% 0.19/0.69 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------