TSTP Solution File: SWV190+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV190+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 21:49:39 EDT 2023
% Result : Theorem 0.41s 0.65s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWV190+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 04:22:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.41/0.65 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Dw8Xarv3eV/cvc5---1.0.5_7948.p...
% 0.41/0.65 ------- get file name : TPTP file name is SWV190+1
% 0.41/0.65 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7948.smt2...
% 0.41/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.41/0.65 % SZS status Theorem for SWV190+1
% 0.41/0.65 % SZS output start Proof for SWV190+1
% 0.41/0.65 (
% 0.41/0.65 (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.succ _let_6))) (let ((_let_8 (= _let_7 tptp.n5))) (let ((_let_9 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))))) (let ((_let_10 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_11 (tptp.gt tptp.n0 tptp.tptp_minus_1))) (let ((_let_12 (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0))) (let ((_let_13 (not (=> (and (= (tptp.a_select2 tptp.rho_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.rho_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.rho_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.sigma_defuse tptp.n5) tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0) tptp.use) (= _let_12 tptp.use) (= (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0) tptp.use) (= (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) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_mean_defuse tptp.n5) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n0) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n1) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n2) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n3) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n4) tptp.use) (= (tptp.a_select2 tptp.xinit_noise_defuse tptp.n5) tptp.use)) (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.tptp_minus_1)) (= (tptp.a_select3 tptp.u_defuse A B) tptp.use))))))) (let ((_let_14 (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))) (let ((_let_15 (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_16 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_17 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))))) (let ((_let_18 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_19 (tptp.succ tptp.tptp_minus_1))) (let ((_let_20 (= _let_19 tptp.n0))) (let ((_let_21 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_22 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_23 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_24 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2))) (let ((_let_25 (= tptp.n2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_26 (= tptp.n1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (not _let_24))) (let ((_let_29 (not _let_23))) (let ((_let_30 (or _let_29 _let_28 _let_27 _let_26 _let_25))) (let ((_let_31 (= tptp.use (tptp.a_select3 tptp.u_defuse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_32 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.tptp_minus_1))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_29 _let_35 _let_28 _let_33 _let_31))) (let ((_let_37 (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.tptp_minus_1)) (= tptp.use (tptp.a_select3 tptp.u_defuse A B)))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (or))) (let ((_let_41 (not _let_37))) (let ((_let_42 (_let_41))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_42)) :args _let_42)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_37))) (REFL :args (_let_38)) :args _let_40)) (NOT_IMPLIES_ELIM2 _let_39) :args (_let_38 true _let_37)))) (let ((_let_44 (REFL :args (_let_36)))) (let ((_let_45 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n2)) (= tptp.n0 X) (= tptp.n1 X) (= tptp.n2 X))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_48 (= tptp.use _let_12))) (let ((_let_49 (not _let_26))) (let ((_let_50 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.n0))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_35 _let_51 _let_47))) (let ((_let_53 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 ((not (= (tptp.leq tptp.n0 X) false))))) (let ((_let_57 (tptp.leq tptp.tptp_minus_1 tptp.n0))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_33 _let_58 _let_50))) (let ((_let_60 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq X Y)) (not (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 ((not (= (tptp.leq X Y) false)) (not (= (tptp.leq Y Z) false))))) (let ((_let_64 (not _let_11))) (let ((_let_65 (or _let_64 _let_57))) (let ((_let_66 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_64 _let_57 (not _let_65)))) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.tptp_minus_1 tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_66))) _let_67 :args (_let_65 false _let_66)) :args (_let_57 false _let_11 false _let_65)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 3)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_40)) :args ((or _let_32 _let_36))) _let_43 :args (_let_32 true _let_36)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 1)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_40)) :args ((or _let_34 _let_36))) _let_43 :args (_let_34 true _let_36)))) (let ((_let_71 (and _let_48 _let_47 _let_26))) (let ((_let_72 (ASSUME :args (_let_47)))) (let ((_let_73 (ASSUME :args (_let_26)))) (let ((_let_74 (ASSUME :args (_let_48)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_71)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_73 _let_72 _let_74) (SCOPE (TRANS (SYMM (SYMM _let_74)) (CONG (REFL :args (tptp.u_defuse)) (SYMM (SYMM _let_73)) (SYMM (SYMM _let_72)) :args (APPLY_UF tptp.a_select3))) :args (_let_26 _let_47 _let_48))) :args (_let_48 _let_47 _let_26))) :args (true _let_71)) :args ((or (not _let_48) _let_31 (not _let_47) _let_49))) (AND_ELIM (NOT_IMPLIES_ELIM1 _let_39) :args (10)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_36 4)) _let_43 :args ((not _let_31) true _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_35 _let_47 _let_51 (not _let_52)))) _let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_33 _let_50 _let_58 (not _let_59)))) _let_69 _let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.tptp_minus_1 tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_63)) :args _let_62)) _let_61 :args (_let_59 false _let_60)) :args (_let_50 false _let_32 false _let_57 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_52 false _let_53)) :args (_let_47 false _let_34 false _let_50 false _let_52)) :args (_let_49 false _let_48 true _let_31 false _let_47)))) (let ((_let_76 (= tptp.n0 tptp.tptp_minus_1))) (let ((_let_77 (= _let_7 (tptp.plus tptp.n5 tptp.n0)))) (let ((_let_78 (tptp.succ _let_19))) (let ((_let_79 (tptp.succ _let_78))) (let ((_let_80 (tptp.succ _let_79))) (let ((_let_81 (= (tptp.succ _let_80) (tptp.plus tptp.n5 tptp.tptp_minus_1)))) (let ((_let_82 (= _let_6 (tptp.plus tptp.n4 tptp.n0)))) (let ((_let_83 (= _let_80 (tptp.plus tptp.n4 tptp.tptp_minus_1)))) (let ((_let_84 (= _let_3 (tptp.plus tptp.n3 tptp.n0)))) (let ((_let_85 (= _let_79 (tptp.plus tptp.n3 tptp.tptp_minus_1)))) (let ((_let_86 (= _let_2 (tptp.plus tptp.n2 tptp.n0)))) (let ((_let_87 (= _let_78 (tptp.plus tptp.n2 tptp.tptp_minus_1)))) (let ((_let_88 (= tptp.n2 _let_2))) (let ((_let_89 (= tptp.n1 _let_1))) (let ((_let_90 (= tptp.n5 _let_7))) (let ((_let_91 (= tptp.n0 _let_19))) (let ((_let_92 (not _let_25))) (let ((_let_93 (tptp.leq tptp.n0 tptp.tptp_minus_1))) (let ((_let_94 (not _let_93))) (let ((_let_95 (or _let_94 _let_58 _let_76))) (let ((_let_96 (or _let_35 _let_33 _let_93))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_94 _let_58 _let_76 (not _let_95)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_35 _let_33 _let_93 (not _let_96)))) _let_70 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_63)) :args _let_62)) _let_61 :args (_let_96 false _let_60)) :args (_let_93 false _let_34 false _let_32 false _let_96)) _let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_95 false _let_53)) :args (_let_76 false _let_93 false _let_57 false _let_95)))) (let ((_let_98 (_let_14))) (let ((_let_99 (ASSUME :args _let_98))) (let ((_let_100 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_101 (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_77 false _let_14)))) (let ((_let_102 (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_81 false _let_14)))) (let ((_let_103 (_let_15))) (let ((_let_104 (ASSUME :args _let_103))) (let ((_let_105 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_104 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_105)) :args _let_103))) _let_104 :args (_let_82 false _let_15)))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_104 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_105)) :args _let_103))) _let_104 :args (_let_83 false _let_15)))) (let ((_let_108 (_let_16))) (let ((_let_109 (ASSUME :args _let_108))) (let ((_let_110 ((tptp.succ (tptp.succ (tptp.succ X)))))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_109 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_110)) :args _let_108))) _let_109 :args (_let_84 false _let_16)))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_109 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_110)) :args _let_108))) _let_109 :args (_let_85 false _let_16)))) (let ((_let_113 (_let_17))) (let ((_let_114 (ASSUME :args _let_113))) (let ((_let_115 ((tptp.succ (tptp.succ X))))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_115)) :args _let_113))) _let_114 :args (_let_86 false _let_17)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_115)) :args _let_113))) _let_114 :args (_let_87 false _let_17)))) (let ((_let_118 (SYMM (ASSUME :args (_let_4))))) (let ((_let_119 (SYMM (ASSUME :args (_let_5))))) (let ((_let_120 (SYMM (ASSUME :args (_let_8))))) (let ((_let_121 (SYMM (ASSUME :args (_let_20))))) (let ((_let_122 (not _let_76))) (let ((_let_123 (not _let_77))) (let ((_let_124 (not _let_81))) (let ((_let_125 (not _let_82))) (let ((_let_126 (not _let_83))) (let ((_let_127 (not _let_84))) (let ((_let_128 (not _let_85))) (let ((_let_129 (not _let_86))) (let ((_let_130 (not _let_87))) (let ((_let_131 (not _let_88))) (let ((_let_132 (not _let_89))) (let ((_let_133 (not _let_90))) (let ((_let_134 (not _let_91))) (let ((_let_135 (REFL :args (_let_122)))) (let ((_let_136 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_26))))) (let ((_let_137 (REFL :args (_let_123)))) (let ((_let_138 (REFL :args (_let_124)))) (let ((_let_139 (REFL :args (_let_125)))) (let ((_let_140 (REFL :args (_let_126)))) (let ((_let_141 (REFL :args (_let_127)))) (let ((_let_142 (REFL :args (_let_128)))) (let ((_let_143 (REFL :args (_let_129)))) (let ((_let_144 (REFL :args (_let_130)))) (let ((_let_145 (REFL :args (_let_132)))) (let ((_let_146 (REFL :args (_let_133)))) (let ((_let_147 (REFL :args (_let_134)))) (let ((_let_148 (and _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_77 _let_49 _let_76))) (let ((_let_149 (= tptp.n2 tptp.n5))) (let ((_let_150 (= tptp.n1 tptp.n5))) (let ((_let_151 (ASSUME :args (_let_49)))) (let ((_let_152 (FALSE_INTRO _let_151))) (let ((_let_153 (=))) (let ((_let_154 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_155 (ASSUME :args (_let_150)))) (let ((_let_156 (SYMM _let_120))) (let ((_let_157 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(=> (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_20 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) _let_18 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) _let_17 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) _let_16 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) _let_15 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) _let_14 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)) (forall ((X $$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_13 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) _let_11 (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)))) _let_10 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))) _let_9 (forall ((X $$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) _let_8 _let_5 _let_4 (= _let_3 tptp.n3) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.41/0.66 )
% 0.41/0.66 % SZS output end Proof for SWV190+1
% 0.41/0.66 % cvc5---1.0.5 exiting
% 0.41/0.66 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------