TSTP Solution File: SWV112+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV112+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 21:49:21 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV112+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n024.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 03:55:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.65 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.VJRzgYZjzh/cvc5---1.0.5_9981.p...
% 0.20/0.65 ------- get file name : TPTP file name is SWV112+1
% 0.20/0.65 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9981.smt2...
% 0.20/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.65 % SZS status Theorem for SWV112+1
% 0.20/0.65 % SZS output start Proof for SWV112+1
% 0.20/0.65 (
% 0.20/0.65 (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_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 (tptp.succ _let_8))) (let ((_let_10 (= _let_9 tptp.n6))) (let ((_let_11 (= _let_8 tptp.n5))) (let ((_let_12 (= _let_7 tptp.n4))) (let ((_let_13 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n3)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3)))))) (let ((_let_14 (forall ((X $$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 ((_let_15 (tptp.gt tptp.n4 tptp.n3))) (let ((_let_16 (tptp.gt tptp.n3 tptp.n2))) (let ((_let_17 (tptp.gt tptp.n3 tptp.n1))) (let ((_let_18 (tptp.gt tptp.n3 tptp.n0))) (let ((_let_19 (tptp.leq tptp.pv5 (tptp.minus tptp.n999 tptp.n1)))) (let ((_let_20 (tptp.leq tptp.n0 tptp.pv5))) (let ((_let_21 (tptp.minus tptp.n6 tptp.n1))) (let ((_let_22 (tptp.leq tptp.pv57 _let_21))) (let ((_let_23 (tptp.leq tptp.n0 tptp.pv57))) (let ((_let_24 (not (=> (and _let_20 _let_23 _let_19 _let_22 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A _let_1) (tptp.leq B _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter A B) (tptp.a_select3 tptp.q_ds1_filter B A))))) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (=> (and (tptp.leq tptp.n0 C) (tptp.leq tptp.n0 D) (tptp.leq C _let_1) (tptp.leq D _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter C D) (tptp.a_select3 tptp.r_ds1_filter D C))))) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 E) (tptp.leq tptp.n0 F) (tptp.leq E _let_1) (tptp.leq F _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter E F) (tptp.a_select3 tptp.pminus_ds1_filter F E))))) (forall ((G $$unsorted) (H $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq tptp.n0 H) (tptp.leq G tptp.pv57) (tptp.leq H (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter G H) (tptp.a_select3 tptp.id_ds1_filter H G)))) (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I (tptp.minus tptp.pv57 tptp.n1))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter I J) (tptp.a_select3 tptp.id_ds1_filter J I))))))) (and _let_20 _let_19 (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 K) (tptp.leq tptp.n0 L) (tptp.leq K _let_1) (tptp.leq L _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter K L) (tptp.a_select3 tptp.q_ds1_filter L K))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (=> (and (tptp.leq tptp.n0 M) (tptp.leq tptp.n0 N) (tptp.leq M _let_1) (tptp.leq N _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter M N) (tptp.a_select3 tptp.r_ds1_filter N M))))) (forall ((O $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 O) (tptp.leq tptp.n0 P) (tptp.leq O _let_1) (tptp.leq P _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter O P) (tptp.a_select3 tptp.pminus_ds1_filter P O))))) (forall ((Q $$unsorted)) (=> (and (tptp.leq tptp.n0 Q) (tptp.leq Q (tptp.minus (tptp.plus tptp.n1 tptp.pv57) tptp.n1))) (forall ((R $$unsorted)) (=> (and (tptp.leq tptp.n0 R) (tptp.leq R (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter Q R) (tptp.a_select3 tptp.id_ds1_filter R Q))))))))))) (let ((_let_25 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_26 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))) (let ((_let_27 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_28 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))) (let ((_let_29 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_30 (= tptp.n1 _let_1))) (let ((_let_31 (tptp.plus tptp.n1 tptp.pv57))) (let ((_let_32 (tptp.minus _let_31 tptp.n1))) (let ((_let_33 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_32))) (let ((_let_34 (= _let_31 (tptp.succ tptp.pv57)))) (let ((_let_35 (= _let_32 (tptp.pred _let_31)))) (let ((_let_36 (= tptp.n0 (tptp.pred _let_1)))) (let ((_let_37 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.pv57))) (let ((_let_38 (= tptp.n0 tptp.pv57))) (let ((_let_39 (SYMM (ASSUME :args (_let_6))))) (let ((_let_40 (= (tptp.a_select3 tptp.id_ds1_filter SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.a_select3 tptp.id_ds1_filter SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_41 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_21))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_44 (not _let_43))) (let ((_let_45 (not _let_33))) (let ((_let_46 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_44 _let_42 _let_40))) (let ((_let_49 (forall ((Q $$unsorted) (BOUND_VARIABLE_2295 $$unsorted)) (or (not (tptp.leq tptp.n0 Q)) (not (tptp.leq Q (tptp.minus (tptp.plus tptp.n1 tptp.pv57) tptp.n1))) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2295)) (not (tptp.leq BOUND_VARIABLE_2295 (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter Q BOUND_VARIABLE_2295) (tptp.a_select3 tptp.id_ds1_filter BOUND_VARIABLE_2295 Q)))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (forall ((O $$unsorted) (P $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 O)) (not (tptp.leq tptp.n0 P)) (not (tptp.leq O _let_1)) (not (tptp.leq P _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter O P) (tptp.a_select3 tptp.pminus_ds1_filter P O))))))) (let ((_let_52 (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (or (not (tptp.leq tptp.n0 M)) (not (tptp.leq tptp.n0 N)) (not (tptp.leq M _let_1)) (not (tptp.leq N _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter M N) (tptp.a_select3 tptp.r_ds1_filter N M))))))) (let ((_let_53 (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 K)) (not (tptp.leq tptp.n0 L)) (not (tptp.leq K _let_1)) (not (tptp.leq L _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter K L) (tptp.a_select3 tptp.q_ds1_filter L K))))))) (let ((_let_54 (not _let_49))) (let ((_let_55 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq tptp.n0 F)) (not (tptp.leq E _let_1)) (not (tptp.leq F _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter E F) (tptp.a_select3 tptp.pminus_ds1_filter F E))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (NOT_IMPLIES_ELIM1 _let_56))) (let ((_let_58 (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq tptp.n0 D)) (not (tptp.leq C _let_1)) (not (tptp.leq D _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter C D) (tptp.a_select3 tptp.r_ds1_filter D C))))))) (let ((_let_59 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq tptp.n0 B)) (not (tptp.leq A _let_1)) (not (tptp.leq B _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter A B) (tptp.a_select3 tptp.q_ds1_filter B A))))))) (let ((_let_60 (or))) (let ((_let_61 (_let_54))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_61)) :args _let_61)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_49))) (REFL :args (_let_50)) :args _let_60)) (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_IMPLIES_ELIM2 _let_56)) (AND_ELIM _let_57 :args (0)) (AND_ELIM _let_57 :args (2)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_59 (= A K) (= B L)))) :args ((or _let_53 (not _let_59)))) (AND_ELIM _let_57 :args (4)) :args (_let_53 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_58 (= C M) (= D N)))) :args ((or _let_52 (not _let_58)))) (AND_ELIM _let_57 :args (5)) :args (_let_52 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_55 (= E O) (= F P)))) :args ((or _let_51 (not _let_55)))) (AND_ELIM _let_57 :args (6)) :args (_let_51 false _let_55)) :args (_let_54 false _let_20 false _let_19 false _let_53 false _let_52 false _let_51)) :args (_let_50 true _let_49)))) (let ((_let_63 (REFL :args (_let_48)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_33))) :args _let_60)) :args ((or _let_33 _let_48))) _let_62 :args (_let_33 true _let_48)))) (let ((_let_65 (_let_27))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (tptp.pv57 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.plus tptp.n1 X)))) :args _let_65)) _let_66 :args (_let_34 false _let_27)))) (let ((_let_68 (_let_26))) (let ((_let_69 (ASSUME :args _let_68))) (let ((_let_70 ((tptp.minus X tptp.n1)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (_let_31 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_70)) :args _let_68)) _let_69 :args (_let_35 false _let_26)))) (let ((_let_72 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (_let_72))) (let ((_let_75 ((tptp.succ X)))) (let ((_let_76 (not _let_37))) (let ((_let_77 (or _let_47 _let_44 _let_76 _let_42 _let_40))) (let ((_let_78 (forall ((G $$unsorted) (H $$unsorted)) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq tptp.n0 H)) (not (tptp.leq G tptp.pv57)) (not (tptp.leq H (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter G H) (tptp.a_select3 tptp.id_ds1_filter H G)))))) (let ((_let_79 (_let_78))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_47 _let_44 _let_42 _let_40 _let_76 (not _let_77)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_60)) :args ((or _let_46 _let_48))) _let_62 :args (_let_46 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_60)) :args ((or _let_43 _let_48))) _let_62 :args (_let_43 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 3)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_60)) :args ((or _let_41 _let_48))) _let_62 :args (_let_41 true _let_48)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 4)) _let_62 :args ((not _let_40) true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_79) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.a_select3 tptp.id_ds1_filter G H)))) :args _let_79)) (AND_ELIM _let_57 :args (7)) :args (_let_77 false _let_78)) :args (_let_76 false _let_46 false _let_43 false _let_41 true _let_40 false _let_77)))) (let ((_let_81 (= tptp.n3 tptp.pv57))) (let ((_let_82 (= tptp.n2 tptp.pv57))) (let ((_let_83 (= tptp.n1 tptp.pv57))) (let ((_let_84 (tptp.leq tptp.pv57 tptp.n3))) (let ((_let_85 (not _let_84))) (let ((_let_86 (not _let_23))) (let ((_let_87 (or _let_86 _let_85 _let_38 _let_83 _let_82 _let_81))) (let ((_let_88 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n3)) (= tptp.n0 X) (= tptp.n1 X) (= tptp.n2 X) (= tptp.n3 X))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (tptp.leq tptp.n0 tptp.n3))) (let ((_let_91 (tptp.leq tptp.n1 tptp.n3))) (let ((_let_92 (tptp.leq tptp.n2 tptp.n3))) (let ((_let_93 (= tptp.n4 _let_7))) (let ((_let_94 (= tptp.n3 _let_3))) (let ((_let_95 (= _let_3 (tptp.pred _let_7)))) (let ((_let_96 (tptp.leq tptp.n3 (tptp.pred tptp.n4)))) (let ((_let_97 (= tptp.n5 tptp.pv57))) (let ((_let_98 (= tptp.n4 tptp.pv57))) (let ((_let_99 (tptp.leq tptp.pv57 tptp.n5))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_86 _let_100 _let_38 _let_83 _let_82 _let_81 _let_98 _let_97))) (let ((_let_102 (not _let_18))) (let ((_let_103 (or _let_102 _let_90))) (let ((_let_104 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (_let_104))) (let ((_let_107 ((not (= (tptp.gt Y X) false))))) (let ((_let_108 (not _let_38))) (let ((_let_109 (not _let_90))) (let ((_let_110 (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_84))))) (let ((_let_111 (REFL :args (_let_108)))) (let ((_let_112 (APPLY_UF tptp.leq))) (let ((_let_113 (REFL :args (tptp.n3)))) (let ((_let_114 (ASSUME :args (_let_38)))) (let ((_let_115 (SYMM _let_114))) (let ((_let_116 (ASSUME :args (_let_85)))) (let ((_let_117 (SYMM (FALSE_INTRO _let_116)))) (let ((_let_118 (not _let_17))) (let ((_let_119 (or _let_118 _let_91))) (let ((_let_120 (not _let_83))) (let ((_let_121 (not _let_91))) (let ((_let_122 (REFL :args (_let_120)))) (let ((_let_123 (ASSUME :args (_let_83)))) (let ((_let_124 (SYMM _let_123))) (let ((_let_125 (not _let_16))) (let ((_let_126 (or _let_125 _let_92))) (let 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(CNF_OR_POS :args (_let_126)) :args ((or _let_125 _let_92 (not _let_126)))) (ASSUME :args (_let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.n2 tptp.n3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_107)) :args _let_106)) _let_105 :args (_let_126 false _let_104)) :args (_let_92 false _let_16 false _let_126)) (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_117 (CONG _let_124 _let_113 :args _let_112) (TRUE_INTRO (ASSUME :args (_let_91))))) :args (_let_91 _let_83 _let_85))) (CONG (REFL :args (_let_121)) _let_122 _let_110 :args _let_60)) :args ((or _let_84 _let_121 _let_120))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_118 _let_91 (not _let_119)))) (ASSUME :args (_let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.n1 tptp.n3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_107)) :args _let_106)) _let_105 :args (_let_119 false _let_104)) :args (_let_91 false _let_17 false _let_119)) (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_117 (CONG _let_115 _let_113 :args _let_112) (TRUE_INTRO (ASSUME :args (_let_90))))) :args (_let_90 _let_38 _let_85))) (CONG (REFL :args (_let_109)) _let_111 _let_110 :args _let_60)) :args ((or _let_84 _let_109 _let_108))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_102 _let_90 (not _let_103)))) (ASSUME :args (_let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.n0 tptp.n3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_107)) :args _let_106)) _let_105 :args (_let_103 false _let_104)) :args (_let_90 false _let_18 false _let_103)) :args (_let_84 true _let_98 true _let_97 false _let_99 false _let_101 false _let_23 true _let_81 false _let_96 false _let_95 false _let_94 false _let_93 true _let_82 false _let_92 true _let_83 false _let_91 true _let_38 false _let_90)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.pv57 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_38 false _let_23 true _let_83 true _let_82 true _let_81 false _let_84 false _let_87)) _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_36 false _let_72)) _let_71 _let_67 _let_64 _let_39 :args (false false _let_38 true _let_37 false _let_36 false _let_35 false _let_34 false _let_33 false _let_30)) :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 $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))) _let_29 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))) _let_28 (forall ((X $$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 $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) _let_26 _let_25 (forall ((X $$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_24 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n6 tptp.n4) (tptp.gt tptp.n999 tptp.n4) (tptp.gt tptp.n6 tptp.n5) (tptp.gt tptp.n999 tptp.n5) (tptp.gt tptp.n999 tptp.n6) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n6 tptp.tptp_minus_1) (tptp.gt tptp.n999 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.n6 tptp.n0) (tptp.gt tptp.n999 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) _let_18 (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n6 tptp.n1) (tptp.gt tptp.n999 tptp.n1) (tptp.gt tptp.n2 tptp.n1) _let_17 (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n6 tptp.n2) (tptp.gt tptp.n999 tptp.n2) _let_16 _let_15 (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n6 tptp.n3) (tptp.gt tptp.n999 tptp.n3) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))) _let_14 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n6)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5) (= X tptp.n6)))) (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)))) _let_13 _let_12 _let_11 _let_10 _let_6 _let_5 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.39/0.65 )
% 0.39/0.65 % SZS output end Proof for SWV112+1
% 0.39/0.65 % cvc5---1.0.5 exiting
% 0.39/0.66 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------