TSTP Solution File: SWV092+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV092+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 21:49:16 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 : SWV092+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n027.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 04:25:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.64 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.uWaVd7qTu4/cvc5---1.0.5_20676.p...
% 0.21/0.64 ------- get file name : TPTP file name is SWV092+1
% 0.21/0.64 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20676.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 SWV092+1
% 0.21/0.64 % SZS output start Proof for SWV092+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 (tptp.succ _let_3))) (let ((_let_5 (= _let_4 tptp.n4))) (let ((_let_6 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_7 (tptp.gt tptp.n4 tptp.n0))) (let ((_let_8 (tptp.gt tptp.n0 tptp.tptp_minus_1))) (let ((_let_9 (tptp.a_select2 tptp.xinit_noise_defuse tptp.n5))) (let ((_let_10 (= _let_9 tptp.use))) (let ((_let_11 (tptp.a_select2 tptp.xinit_noise_defuse tptp.n4))) (let ((_let_12 (= _let_11 tptp.use))) (let ((_let_13 (tptp.a_select2 tptp.xinit_noise_defuse tptp.n3))) (let ((_let_14 (= _let_13 tptp.use))) (let ((_let_15 (tptp.a_select2 tptp.xinit_noise_defuse tptp.n2))) (let ((_let_16 (= _let_15 tptp.use))) (let ((_let_17 (tptp.a_select2 tptp.xinit_noise_defuse tptp.n1))) (let ((_let_18 (= _let_17 tptp.use))) (let ((_let_19 (tptp.a_select2 tptp.xinit_noise_defuse tptp.n0))) (let ((_let_20 (= _let_19 tptp.use))) (let ((_let_21 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n5))) (let ((_let_22 (= _let_21 tptp.use))) (let ((_let_23 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n4))) (let ((_let_24 (= _let_23 tptp.use))) (let ((_let_25 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n3))) (let ((_let_26 (= _let_25 tptp.use))) (let ((_let_27 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n2))) (let ((_let_28 (= _let_27 tptp.use))) (let ((_let_29 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n1))) (let ((_let_30 (= _let_29 tptp.use))) (let ((_let_31 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n0))) (let ((_let_32 (= _let_31 tptp.use))) (let ((_let_33 (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (let ((_let_34 (= _let_33 tptp.use))) (let ((_let_35 (tptp.a_select2 tptp.xinit_defuse tptp.n4))) (let ((_let_36 (= _let_35 tptp.use))) (let ((_let_37 (tptp.a_select2 tptp.xinit_defuse tptp.n3))) (let ((_let_38 (= _let_37 tptp.use))) (let ((_let_39 (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0))) (let ((_let_40 (= _let_39 tptp.use))) (let ((_let_41 (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0))) (let ((_let_42 (= _let_41 tptp.use))) (let ((_let_43 (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0))) (let ((_let_44 (= _let_43 tptp.use))) (let ((_let_45 (tptp.a_select2 tptp.sigma_defuse tptp.n5))) (let ((_let_46 (= _let_45 tptp.use))) (let ((_let_47 (tptp.a_select2 tptp.sigma_defuse tptp.n4))) (let ((_let_48 (= _let_47 tptp.use))) (let ((_let_49 (tptp.a_select2 tptp.sigma_defuse tptp.n3))) (let ((_let_50 (= _let_49 tptp.use))) (let ((_let_51 (tptp.a_select2 tptp.sigma_defuse tptp.n2))) (let ((_let_52 (= _let_51 tptp.use))) (let ((_let_53 (tptp.a_select2 tptp.sigma_defuse tptp.n1))) (let ((_let_54 (= _let_53 tptp.use))) (let ((_let_55 (tptp.a_select2 tptp.sigma_defuse tptp.n0))) (let ((_let_56 (= _let_55 tptp.use))) (let ((_let_57 (tptp.a_select2 tptp.rho_defuse tptp.n2))) (let ((_let_58 (= _let_57 tptp.use))) (let ((_let_59 (tptp.a_select2 tptp.rho_defuse tptp.n1))) (let ((_let_60 (= _let_59 tptp.use))) (let ((_let_61 (tptp.a_select2 tptp.rho_defuse tptp.n0))) (let ((_let_62 (= _let_61 tptp.use))) (let ((_let_63 (not (=> (and _let_62 _let_60 _let_58 _let_56 _let_54 _let_52 _let_50 _let_48 _let_46 _let_44 _let_42 _let_40 _let_38 _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 _let_10) (and _let_62 _let_60 _let_58 _let_56 _let_54 _let_52 _let_50 _let_48 _let_46 _let_44 _let_42 _let_40 _let_38 _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 _let_10 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A tptp.n2) (tptp.leq B (tptp.minus tptp.n0 tptp.n1))) (and (= (tptp.a_select3 tptp.u_defuse A B) tptp.use) (= (tptp.a_select3 tptp.z_defuse A B) tptp.use))))))))) (let ((_let_64 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_65 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))) (let ((_let_66 (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_67 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_68 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))))) (let ((_let_69 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_70 (tptp.succ tptp.tptp_minus_1))) (let ((_let_71 (= _let_70 tptp.n0))) (let ((_let_72 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_73 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_74 (forall ((X $$unsorted)) (not (tptp.gt X X))))) (let ((_let_75 (= tptp.n0 _let_70))) (let ((_let_76 (= tptp.n4 _let_4))) (let ((_let_77 (= _let_1 (tptp.plus tptp.n1 tptp.n0)))) (let ((_let_78 (= _let_70 (tptp.plus tptp.n1 tptp.tptp_minus_1)))) (let ((_let_79 (tptp.succ _let_70))) (let ((_let_80 (= _let_79 (tptp.plus tptp.n2 tptp.tptp_minus_1)))) (let ((_let_81 (= _let_2 (tptp.plus tptp.n2 tptp.n0)))) (let ((_let_82 (tptp.succ _let_79))) (let ((_let_83 (= _let_82 (tptp.plus tptp.n3 tptp.tptp_minus_1)))) (let ((_let_84 (= _let_3 (tptp.plus tptp.n3 tptp.n0)))) (let ((_let_85 (= (tptp.succ _let_82) (tptp.plus tptp.n4 tptp.tptp_minus_1)))) (let ((_let_86 (= _let_4 (tptp.plus tptp.n4 tptp.n0)))) (let ((_let_87 (tptp.minus tptp.n0 tptp.n1))) (let ((_let_88 (= _let_87 (tptp.pred tptp.n0)))) (let ((_let_89 (= tptp.tptp_minus_1 (tptp.pred _let_70)))) (let ((_let_90 (tptp.gt tptp.n4 tptp.n4))) (let ((_let_91 (= tptp.n0 _let_87))) (let ((_let_92 (SYMM (ASSUME :args (_let_71))))) (let ((_let_93 (ASSUME :args (_let_7)))) (let ((_let_94 (SYMM (ASSUME :args (_let_5))))) (let ((_let_95 (_let_69))) (let ((_let_96 (ASSUME :args _let_95))) (let ((_let_97 ((tptp.succ X)))) (let ((_let_98 (_let_68))) (let ((_let_99 (ASSUME :args _let_98))) (let ((_let_100 ((tptp.succ (tptp.succ X))))) (let ((_let_101 (_let_67))) (let ((_let_102 (ASSUME :args _let_101))) (let ((_let_103 ((tptp.succ (tptp.succ (tptp.succ X)))))) (let ((_let_104 (_let_66))) (let ((_let_105 (ASSUME :args _let_104))) (let ((_let_106 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_107 (_let_65))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minus X tptp.n1)))) :args _let_107)) _let_108 :args (_let_88 false _let_65)))) (let ((_let_110 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.succ X)))) :args (_let_110))) _let_111 :args (_let_89 false _let_110)))) (let ((_let_113 (not _let_90))) (let ((_let_114 (_let_74))) (let ((_let_115 (ASSUME :args _let_114))) (let ((_let_116 (tptp.leq _let_87 tptp.n0))) (let ((_let_117 (not _let_116))) (let ((_let_118 (tptp.leq tptp.n0 _let_87))) (let ((_let_119 (not _let_118))) (let ((_let_120 (or _let_119 _let_117 _let_91))) (let ((_let_121 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_87))) (let ((_let_124 (not _let_123))) (let ((_let_125 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_126 (not _let_125))) (let ((_let_127 (or _let_126 _let_124 _let_118))) (let ((_let_128 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq X Y)) (not (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_129 (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO :args (_let_73 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_130 (or (not (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) _let_126 (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2)) _let_124 (and (= tptp.use (tptp.a_select3 tptp.u_defuse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (= tptp.use (tptp.a_select3 tptp.z_defuse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_131 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq tptp.n0 B)) (not (tptp.leq A tptp.n2)) (not (tptp.leq B (tptp.minus tptp.n0 tptp.n1))) (and (= tptp.use (tptp.a_select3 tptp.u_defuse A B)) (= tptp.use (tptp.a_select3 tptp.z_defuse A B))))))) (let ((_let_132 (not _let_130))) (let ((_let_133 (not _let_131))) (let ((_let_134 (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO :args (_let_63 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_135 (NOT_IMPLIES_ELIM1 _let_134))) (let ((_let_136 (or))) (let ((_let_137 (_let_133))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_137)) :args _let_137)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_133) _let_131))) (REFL :args (_let_132)) :args _let_136)) (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_IMPLIES_ELIM2 _let_134)) (AND_ELIM _let_135 :args (0)) (AND_ELIM _let_135 :args (1)) (AND_ELIM _let_135 :args (2)) (AND_ELIM _let_135 :args (3)) (AND_ELIM _let_135 :args (4)) (AND_ELIM _let_135 :args (5)) (AND_ELIM _let_135 :args (6)) (AND_ELIM _let_135 :args (7)) (AND_ELIM _let_135 :args (8)) (AND_ELIM _let_135 :args (9)) (AND_ELIM _let_135 :args (10)) (AND_ELIM _let_135 :args (11)) (AND_ELIM _let_135 :args (12)) (AND_ELIM _let_135 :args (13)) (AND_ELIM _let_135 :args (14)) (AND_ELIM _let_135 :args (15)) (AND_ELIM _let_135 :args (16)) (AND_ELIM _let_135 :args (17)) (AND_ELIM _let_135 :args (18)) (AND_ELIM _let_135 :args (19)) (AND_ELIM _let_135 :args (20)) (AND_ELIM _let_135 :args (21)) (AND_ELIM _let_135 :args (22)) (AND_ELIM _let_135 :args (23)) (AND_ELIM _let_135 :args (24)) (AND_ELIM _let_135 :args (25)) (AND_ELIM _let_135 :args (26)) :args (_let_133 false (= tptp.use _let_61) false (= tptp.use _let_59) false (= tptp.use _let_57) false (= tptp.use _let_55) false (= tptp.use _let_53) false (= tptp.use _let_51) false (= tptp.use _let_49) false (= tptp.use _let_47) false (= tptp.use _let_45) false (= tptp.use _let_43) false (= tptp.use _let_41) false (= tptp.use _let_39) false (= tptp.use _let_37) 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 (= tptp.use _let_11) false (= tptp.use _let_9))) :args (_let_132 true _let_131)))) (let ((_let_139 (REFL :args (_let_130)))) (let ((_let_140 (tptp.leq tptp.tptp_minus_1 tptp.n0))) (let ((_let_141 (not _let_8))) (let ((_let_142 (or _let_141 _let_140))) (let ((_let_143 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_144 (EQ_RESOLVE (ASSUME :args (_let_72)) (MACRO_SR_EQ_INTRO :args (_let_72 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_145 (not _let_89))) (let ((_let_146 (not _let_88))) (let ((_let_147 (not _let_75))) (let ((_let_148 (and _let_75 _let_140 _let_88 _let_89))) (let ((_let_149 (ASSUME :args (_let_140)))) (let ((_let_150 (ASSUME :args (_let_89)))) (let ((_let_151 (SYMM _let_150))) (let ((_let_152 (APPLY_UF tptp.pred))) (let ((_let_153 (SYMM _let_92))) (let ((_let_154 (ASSUME :args (_let_88)))) (let ((_let_155 (SYMM (SYMM _let_154)))) (let ((_let_156 (not _let_91))) (let ((_let_157 (not _let_86))) (let ((_let_158 (not _let_85))) (let ((_let_159 (not _let_84))) (let ((_let_160 (not _let_83))) (let ((_let_161 (not _let_81))) (let ((_let_162 (not _let_80))) (let ((_let_163 (not _let_78))) (let ((_let_164 (not _let_77))) (let ((_let_165 (not _let_76))) (let ((_let_166 (not _let_7))) (let ((_let_167 (APPLY_UF tptp.gt))) (let ((_let_168 (ASSUME :args (_let_78)))) (let ((_let_169 (APPLY_UF tptp.plus))) (let ((_let_170 (ASSUME :args (_let_91)))) (let ((_let_171 (TRANS (SYMM (SYMM _let_170)) _let_155 (CONG _let_92 :args _let_152) _let_151))) (let ((_let_172 (ASSUME :args (_let_77)))) (let ((_let_173 (APPLY_UF tptp.succ))) (let ((_let_174 (CONG _let_153 :args _let_173))) (let ((_let_175 (ASSUME :args (_let_80)))) (let ((_let_176 (ASSUME :args (_let_81)))) (let ((_let_177 (CONG _let_174 :args _let_173))) (let ((_let_178 (ASSUME :args (_let_83)))) (let ((_let_179 (ASSUME :args (_let_84)))) (let ((_let_180 (ASSUME :args (_let_85)))) (let ((_let_181 (REFL :args (tptp.n4)))) (let ((_let_182 (ASSUME :args (_let_86)))) (let ((_let_183 (SYMM _let_94))) (let ((_let_184 (SYMM _let_183))) (let ((_let_185 (ASSUME :args (_let_113)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_93 _let_176 _let_92 _let_172 _let_168 _let_94 _let_175 _let_150 _let_178 _let_180 _let_154 _let_170 _let_179 _let_185 _let_182) :args (_let_7 _let_75 _let_76 _let_77 _let_78 _let_80 _let_81 _let_83 _let_84 _let_85 _let_86 _let_88 _let_89 _let_113 _let_91)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_185)) (CONG _let_184 _let_181 :args _let_167) (CONG _let_183 (TRANS _let_184 (SYMM (SYMM _let_182)) (CONG _let_181 _let_171 :args _let_169) (SYMM _let_180) (CONG _let_177 :args _let_173) (SYMM (SYMM _let_179)) (CONG (REFL :args (tptp.n3)) _let_171 :args _let_169) (SYMM _let_178) _let_177 (SYMM (SYMM _let_176)) (CONG (REFL :args (tptp.n2)) _let_171 :args _let_169) (SYMM _let_175) _let_174 (SYMM (SYMM _let_172)) (CONG (REFL :args (tptp.n1)) _let_171 :args _let_169) (SYMM _let_168) _let_153) :args _let_167) (TRUE_INTRO _let_93))) :args (_let_7 _let_81 _let_75 _let_77 _let_78 _let_76 _let_80 _let_89 _let_83 _let_85 _let_88 _let_91 _let_84 _let_113 _let_86)) :args ((not (and _let_7 _let_75 _let_76 _let_77 _let_78 _let_80 _let_81 _let_83 _let_84 _let_85 _let_86 _let_88 _let_89 _let_113 _let_91)) SB_LITERAL))) (CONG (REFL :args (_let_166)) (REFL :args (_let_147)) (REFL :args (_let_165)) (REFL :args (_let_164)) (REFL :args (_let_163)) (REFL :args (_let_162)) (REFL :args (_let_161)) (REFL :args (_let_160)) (REFL :args (_let_159)) (REFL :args (_let_158)) (REFL :args (_let_157)) (REFL :args (_let_146)) (REFL :args (_let_145)) (MACRO_SR_PRED_INTRO :args ((= (not _let_113) _let_90))) (REFL :args (_let_156)) :args _let_136)) :args ((or _let_147 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_146 _let_145 _let_90 _let_156))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_117 _let_119 _let_91 (not _let_120)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_148)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_149 _let_150 _let_92 _let_154) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS _let_155 (CONG (SYMM _let_153) :args _let_152) _let_151) (REFL :args (tptp.n0)) :args (APPLY_UF tptp.leq)) (TRUE_INTRO _let_149))) :args (_let_140 _let_89 _let_75 _let_88))) :args (_let_75 _let_140 _let_88 _let_89))) :args (true _let_148)) :args ((or _let_147 _let_116 (not _let_140) _let_146 _let_145))) _let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_142)) :args ((or _let_141 _let_140 (not _let_142)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_144 :args (tptp.tptp_minus_1 tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_143))) _let_144 :args (_let_142 false _let_143)) :args (_let_140 false _let_8 false _let_142)) _let_109 _let_112 :args (_let_116 false _let_75 false _let_140 false _let_88 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_127)) :args ((or _let_126 _let_124 _let_118 (not _let_127)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_130 1)) (CONG _let_139 (MACRO_SR_PRED_INTRO :args ((= (not _let_126) _let_125))) :args _let_136)) :args ((or _let_125 _let_130))) _let_138 :args (_let_125 true _let_130)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_130 3)) (CONG _let_139 (MACRO_SR_PRED_INTRO :args ((= (not _let_124) _let_123))) :args _let_136)) :args ((or _let_123 _let_130))) _let_138 :args (_let_123 true _let_130)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_129 :args (tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_87 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.leq X Y) false)) (not (= (tptp.leq Y Z) false))))) :args (_let_128))) _let_129 :args (_let_127 false _let_128)) :args (_let_118 false _let_125 false _let_123 false _let_127)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args (_let_87 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_121))) _let_122 :args (_let_120 false _let_121)) :args (_let_91 false _let_116 false _let_118 false _let_120)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (tptp.n4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt X X) false))))) :args _let_114)) _let_115 :args (_let_113 false _let_74)) _let_112 _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_106)) :args _let_104))) _let_105 :args (_let_86 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_106)) :args _let_104))) _let_105 :args (_let_85 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_102 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_103)) :args _let_101))) _let_102 :args (_let_84 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_102 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_103)) :args _let_101))) _let_102 :args (_let_83 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_99 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_100)) :args _let_98))) _let_99 :args (_let_81 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_99 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_100)) :args _let_98))) _let_99 :args (_let_80 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_96 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_95))) _let_96 :args (_let_78 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_96 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_95))) _let_96 :args (_let_77 false _let_69)) _let_94 _let_93 _let_92 :args (false false _let_91 true _let_90 false _let_89 false _let_88 false _let_86 false _let_85 false _let_84 false _let_83 false _let_81 false _let_80 false _let_78 false _let_77 false _let_76 false _let_7 false _let_75)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))) _let_74 (forall ((X $$unsorted)) (tptp.leq X X)) _let_73 (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_72 (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 $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) _let_71 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) _let_69 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) _let_68 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) _let_67 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) _let_66 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) _let_65 _let_64 (forall ((X $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))) (forall ((X $$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_63 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) _let_8 (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) _let_7 (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)))) _let_6 (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_5 (= (tptp.succ _let_4) tptp.n5) (= _let_1 tptp.n1) (= _let_2 tptp.n2) (= _let_3 tptp.n3) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.65 )
% 0.21/0.65 % SZS output end Proof for SWV092+1
% 0.21/0.65 % cvc5---1.0.5 exiting
% 0.21/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------