%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV104+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 0.21s 0.64s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWV104+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n014.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 29 08:55:15 EDT 2023
% 0.21/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.64  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.J2wnXkOylo/cvc5---1.0.5_25406.p...
% 0.21/0.64  ------- get file name : TPTP file name is SWV104+1
% 0.21/0.64  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25406.smt2...
% 0.21/0.64  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.64  % SZS status Theorem for SWV104+1
% 0.21/0.64  % SZS output start Proof for SWV104+1
% 0.21/0.64  (
% 0.21/0.64  (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 (tptp.succ _let_7))) (let ((_let_9 (= _let_8 tptp.n5))) (let ((_let_10 (= _let_7 tptp.n4))) (let ((_let_11 (tptp.tptp_update2 tptp.xinit_defuse tptp.n3 tptp.use))) (let ((_let_12 (tptp.tptp_update2 _let_11 tptp.n4 tptp.use))) (let ((_let_13 (tptp.tptp_update2 _let_12 tptp.n5 tptp.use))) (let ((_let_14 (tptp.a_select2 _let_13 tptp.n5))) (let ((_let_15 (tptp.a_select2 _let_13 tptp.n4))) (let ((_let_16 (tptp.a_select2 _let_13 tptp.n3))) (let ((_let_17 (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0))) (let ((_let_18 (= _let_17 tptp.use))) (let ((_let_19 (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0))) (let ((_let_20 (= _let_19 tptp.use))) (let ((_let_21 (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0))) (let ((_let_22 (= _let_21 tptp.use))) (let ((_let_23 (not (=> (and _let_22 _let_20 _let_18 (= (tptp.a_select2 tptp.xinit_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_defuse tptp.n5) tptp.use)) (and _let_22 _let_20 _let_18 (= _let_16 tptp.use) (= _let_15 tptp.use) (= _let_14 tptp.use)))))) (let ((_let_24 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))))) (let ((_let_25 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)))) (let ((_let_26 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_27 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_28 (= tptp.n4 _let_7))) (let ((_let_29 (= tptp.n5 _let_8))) (let ((_let_30 (= tptp.n1 _let_1))) (let ((_let_31 (= tptp.n2 _let_2))) (let ((_let_32 (= tptp.n3 _let_3))) (let ((_let_33 (= _let_7 (tptp.plus tptp.n1 _let_3)))) (let ((_let_34 (= _let_8 (tptp.plus tptp.n1 _let_7)))) (let ((_let_35 (= _let_2 (tptp.pred _let_3)))) (let ((_let_36 (= _let_3 (tptp.pred _let_7)))) (let ((_let_37 (= tptp.n4 tptp.n5))) (let ((_let_38 (= tptp.n3 tptp.n4))) (let ((_let_39 (SYMM (ASSUME :args (_let_10))))) (let ((_let_40 (SYMM (ASSUME :args (_let_9))))) (let ((_let_41 (SYMM (ASSUME :args (_let_6))))) (let ((_let_42 (SYMM (ASSUME :args (_let_5))))) (let ((_let_43 (SYMM (ASSUME :args (_let_4))))) (let ((_let_44 (_let_27))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 ((tptp.succ X)))) (let ((_let_47 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (_let_47))) (let ((_let_50 ((tptp.succ X)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_36 false _let_47)))) (let ((_let_52 (tptp.a_select2 _let_12 tptp.n4))) (let ((_let_53 (= _let_15 _let_52))) (let ((_let_54 (= tptp.use _let_52))) (let ((_let_55 (= _let_7 (tptp.pred _let_8)))) (let ((_let_56 (= tptp.use _let_16))) (let ((_let_57 (not _let_37))) (let ((_let_58 (or _let_37 _let_53))) (let ((_let_59 (= tptp.use _let_14))) (let ((_let_60 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 ((tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (let ((_let_64 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (_let_64))) (let ((_let_67 ((tptp.tptp_update2 X U VAL)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_11 tptp.n4 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_54 false _let_64)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_12 tptp.n5 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) :args ((or _let_59 (not _let_64)))) _let_65 :args (_let_59 false _let_64)))) (let ((_let_70 (not _let_54))) (let ((_let_71 (not _let_59))) (let ((_let_72 (and _let_59 _let_54 _let_37))) (let ((_let_73 (ASSUME :args (_let_54)))) (let ((_let_74 (SYMM (SYMM _let_73)))) (let ((_let_75 (ASSUME :args (_let_59)))) (let ((_let_76 (SYMM _let_75))) (let ((_let_77 (APPLY_UF tptp.a_select2))) (let ((_let_78 (ASSUME :args (_let_37)))) (let ((_let_79 (SYMM _let_78))) (let ((_let_80 (REFL :args (_let_13)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_72)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_73 _let_75 _let_78) (SCOPE (TRANS (CONG _let_80 (SYMM _let_79) :args _let_77) _let_76 _let_74) :args (_let_54 _let_59 _let_37))) :args (_let_59 _let_54 _let_37))) :args (true _let_72)) :args ((or _let_71 _let_53 _let_70 _let_57))) _let_69 _let_68 (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_37 _let_53 (not _let_58)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.n5 tptp.n4 _let_12 tptp.use QUANTIFIERS_INST_E_MATCHING _let_63)) :args _let_62))) _let_61 :args (_let_58 false _let_60)) :args (_let_53 false _let_59 false _let_54 false _let_37 false _let_58)))) (let ((_let_82 (= tptp.use _let_15))) (let ((_let_83 (not _let_56))) (let ((_let_84 (not _let_53))) (let ((_let_85 (and _let_54 _let_53))) (let ((_let_86 (ASSUME :args (_let_53)))) (let ((_let_87 (SYMM _let_86))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (NOT_IMPLIES_ELIM1 _let_88))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_IMPLIES_ELIM2 _let_88)) (AND_ELIM _let_89 :args (0)) (AND_ELIM _let_89 :args (1)) (AND_ELIM _let_89 :args (2)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_85)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_86 _let_73) (SCOPE (TRANS _let_74 _let_87) :args (_let_53 _let_54))) :args (_let_54 _let_53))) :args (true _let_85)) :args ((or _let_82 _let_70 _let_84))) _let_68 _let_81 :args (_let_82 false _let_54 false _let_53)) _let_69 :args (_let_83 false (= tptp.use _let_21) false (= tptp.use _let_19) false (= tptp.use _let_17) false _let_82 false _let_59)))) (let ((_let_91 (not _let_36))) (let ((_let_92 (not _let_32))) (let ((_let_93 (not _let_29))) (let ((_let_94 (not _let_28))) (let ((_let_95 (and _let_28 _let_29 _let_32 _let_36 _let_55 _let_54 _let_37 _let_53))) (let ((_let_96 (SYMM _let_43))) (let ((_let_97 (ASSUME :args (_let_36)))) (let ((_let_98 (SYMM _let_97))) (let ((_let_99 (APPLY_UF tptp.pred))) (let ((_let_100 (SYMM (SYMM _let_39)))) (let ((_let_101 (SYMM _let_40))) (let ((_let_102 (ASSUME :args (_let_55)))) (let ((_let_103 (tptp.a_select2 _let_12 tptp.n3))) (let ((_let_104 (tptp.a_select2 _let_11 tptp.n3))) (let ((_let_105 (= _let_104 _let_103))) (let ((_let_106 (or _let_38 _let_105))) (let ((_let_107 (= _let_16 _let_103))) (let ((_let_108 (= tptp.use _let_104))) (let ((_let_109 (not _let_105))) (let ((_let_110 (= tptp.n3 tptp.n5))) (let ((_let_111 (or _let_110 _let_107))) (let ((_let_112 (not _let_110))) (let ((_let_113 (and _let_59 _let_110))) (let ((_let_114 (ASSUME :args (_let_110)))) (let ((_let_115 (or))) (let ((_let_116 (and _let_83 _let_108 _let_107))) (let ((_let_117 (ASSUME :args (_let_83)))) (let ((_let_118 (ASSUME :args (_let_107)))) (let ((_let_119 (ASSUME :args (_let_108)))) (let ((_let_120 (not _let_38))) (let ((_let_121 (not _let_35))) (let ((_let_122 (not _let_34))) (let ((_let_123 (not _let_33))) (let ((_let_124 (not _let_31))) (let ((_let_125 (not _let_30))) (let ((_let_126 (= tptp.n2 tptp.n5))) (let ((_let_127 (= tptp.n2 _let_3))) (let ((_let_128 (ASSUME :args (_let_38)))) (let ((_let_129 (SYMM (SYMM _let_128)))) (let ((_let_130 (ASSUME :args (_let_57)))) (let ((_let_131 (ASSUME :args (_let_34)))) (let ((_let_132 (APPLY_UF tptp.plus))) (let ((_let_133 (ASSUME :args (_let_33)))) (let ((_let_134 (CONG (TRANS _let_129 _let_100) :args _let_99))) (let ((_let_135 (CONG _let_96 :args _let_99))) (let ((_let_136 (ASSUME :args (_let_35)))) (let ((_let_137 (SYMM (SYMM _let_136)))) (let ((_let_138 (SYMM (SYMM _let_42)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_39 _let_128 _let_43 (MODUS_PONENS (AND_INTRO _let_97 _let_39 _let_128 _let_43 _let_136 _let_42) (SCOPE (TRANS _let_138 _let_137 _let_135 _let_134 _let_98) :args (_let_36 _let_28 _let_38 _let_32 _let_35 _let_31))) (MODUS_PONENS (AND_INTRO _let_40 _let_131 _let_41 _let_39 _let_128 _let_43 _let_133 _let_97 _let_136 _let_42) (SCOPE (TRANS _let_138 _let_137 _let_135 _let_134 _let_98 _let_96 _let_129 _let_100 (SYMM (SYMM _let_133)) (CONG _let_41 _let_96 :args _let_132) (CONG (REFL :args (_let_1)) _let_129 :args _let_132) (CONG (SYMM _let_41) _let_100 :args _let_132) (SYMM _let_131) _let_101) :args (_let_29 _let_34 _let_30 _let_28 _let_38 _let_32 _let_33 _let_36 _let_35 _let_31))) _let_130) :args (_let_28 _let_29 _let_30 _let_31 _let_32 _let_33 _let_34 _let_35 _let_36 _let_57 _let_38)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_130)) (TRUE_INTRO (TRANS _let_100 (SYMM (TRANS (SYMM (ASSUME :args (_let_126))) (SYMM (SYMM (ASSUME :args (_let_127)))) _let_96 _let_129 _let_100)))))) :args (_let_28 _let_38 _let_32 _let_127 _let_126 _let_57)) :args ((not (and _let_28 _let_29 _let_30 _let_31 _let_32 _let_33 _let_34 _let_35 _let_36 _let_57 _let_38)) SB_LITERAL))) (CONG (REFL :args (_let_94)) (REFL :args (_let_93)) (REFL :args (_let_125)) (REFL :args (_let_124)) (REFL :args (_let_92)) (REFL :args (_let_123)) (REFL :args (_let_122)) (REFL :args (_let_121)) (REFL :args (_let_91)) (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_37))) (REFL :args (_let_120)) :args _let_115)) :args ((or _let_94 _let_93 _let_125 _let_124 _let_92 _let_37 _let_123 _let_122 _let_121 _let_91 _let_120))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_38 _let_105 (not _let_106)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_116)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_119 _let_117 _let_118) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_119) (SYMM _let_118) :args (=)) (FALSE_INTRO _let_117))) :args (_let_108 _let_83 _let_107))) :args (_let_83 _let_108 _let_107))) :args (true _let_116)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_56))) (REFL :args ((not _let_108))) (REFL :args ((not _let_107))) (REFL :args (_let_109)) :args _let_115)) _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.xinit_defuse tptp.n3 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_108 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_110 _let_107 (not _let_111)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_113)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_114 _let_75) (SCOPE (TRANS (SYMM _let_76) (CONG _let_80 (SYMM _let_114) :args _let_77)) :args (_let_110 _let_59))) :args (_let_59 _let_110))) :args (true _let_113)) :args ((or _let_56 _let_71 _let_112))) _let_90 _let_69 :args (_let_112 true _let_56 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.n5 tptp.n3 _let_12 tptp.use QUANTIFIERS_INST_E_MATCHING _let_63)) :args _let_62))) _let_61 :args (_let_111 false _let_60)) :args (_let_107 true _let_110 false _let_111)) :args (_let_109 true _let_56 false _let_108 false _let_107)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.n4 tptp.n3 _let_11 tptp.use QUANTIFIERS_INST_E_MATCHING _let_63)) :args _let_62))) _let_61 :args (_let_106 false _let_60)) :args (_let_38 true _let_105 false _let_106)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_95)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_43 _let_97 _let_39 _let_78 _let_40 _let_102 _let_86 _let_73) (SCOPE (TRANS _let_74 _let_87 (CONG _let_80 (TRANS _let_100 (SYMM (SYMM _let_102)) (CONG _let_101 :args _let_99) (CONG (TRANS _let_79 _let_100) :args _let_99) _let_98 _let_96) :args _let_77)) :args (_let_32 _let_36 _let_28 _let_37 _let_29 _let_55 _let_53 _let_54))) :args (_let_28 _let_29 _let_32 _let_36 _let_55 _let_54 _let_37 _let_53))) :args (true _let_95)) :args ((or _let_56 _let_94 _let_93 _let_92 _let_91 (not _let_55) _let_70 _let_57 _let_84))) _let_90 _let_39 _let_40 _let_43 _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_55 false _let_47)) _let_68 _let_81 :args (_let_57 true _let_56 false _let_28 false _let_29 false _let_32 false _let_36 false _let_55 false _let_54 false _let_53)) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_35 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (_let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_44))) _let_45 :args (_let_34 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_44))) _let_45 :args (_let_33 false _let_27)) _let_43 _let_42 _let_41 _let_40 _let_39 :args (false false _let_38 true _let_37 false _let_36 false _let_35 false _let_34 false _let_33 false _let_32 false _let_31 false _let_30 false _let_29 false _let_28)) :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 $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) (= (tptp.succ tptp.tptp_minus_1) tptp.n0) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) _let_27 (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 $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) _let_26 (forall ((X $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))) _let_25 _let_24 (forall ((I $$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_23 (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_10 _let_9 _let_6 _let_5 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.64  )
% 0.21/0.64  % SZS output end Proof for SWV104+1
% 0.21/0.64  % cvc5---1.0.5 exiting
% 0.21/0.65  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------