TSTP Solution File: NUM861_1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM861_1 : TPTP v8.1.2. Released v4.1.0.
% 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 10:48:35 EDT 2023
% Result : Theorem 45.52s 45.77s
% Output : Proof 45.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM861_1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 10:45:48 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_ARI
% 45.52/45.77 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.6Oo8DujWBN/cvc5---1.0.5_31386.p...
% 45.52/45.77 ------- get file name : TPTP file name is NUM861_1
% 45.52/45.77 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31386.smt2...
% 45.52/45.77 --- Run --finite-model-find --decision=internal at 15...
% 45.52/45.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 45.52/45.77 --- Run --no-e-matching --full-saturate-quant at 15...
% 45.52/45.77 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 45.52/45.77 --- Run --macros-quant --macros-quant-mode=all --nl-ext-tplanes --full-saturate-quant...
% 45.52/45.77 % SZS status Theorem for NUM861_1
% 45.52/45.77 % SZS output start Proof for NUM861_1
% 45.52/45.77 (
% 45.52/45.77 (let ((_let_1 (not (forall ((X Int) (Y Int) (Z Int)) (= (tptp.minsol_model_ub X Y Z) (tptp.minsol_model_max X Y Z)))))) (let ((_let_2 (forall ((X Int) (Y Int) (N Int)) (= (tptp.minsol_model_ub X Y N) (and (tptp.model_ub X Y N) (forall ((Z Int)) (=> (tptp.model_ub X Y Z) (<= N Z)))))))) (let ((_let_3 (forall ((X Int) (Y Int) (N Int)) (= (tptp.minsol_model_max X Y N) (and (tptp.model_max X Y N) (forall ((Z Int)) (=> (tptp.model_max X Y Z) (<= N Z)))))))) (let ((_let_4 (forall ((X Int) (Y Int) (N Int)) (= (tptp.model_ub X Y N) (exists ((Z Int)) (and (tptp.ub X Y Z) (<= (+ tptp.c Z) N))))))) (let ((_let_5 (forall ((X Int) (Y Int) (N Int)) (= (tptp.model_max X Y N) (<= (+ tptp.c (tptp.max X Y)) N))))) (let ((_let_6 (forall ((X Int) (Y Int) (Z Int)) (= (tptp.ub X Y Z) (and (<= X Z) (<= Y Z)))))) (let ((_let_7 (forall ((X Int) (Y Int)) (or (= (tptp.max X Y) Y) (not (<= X Y)))))) (let ((_let_8 (forall ((X Int) (Y Int)) (or (= (tptp.max X Y) X) (not (<= Y X)))))) (let ((_let_9 (tptp.max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (+ tptp.c _let_10 _let_9))) (let ((_let_12 (>= _let_11 1))) (let ((_let_13 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_14 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13))) (let ((_let_15 (>= _let_14 1))) (let ((_let_16 (+ tptp.c _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_17 (>= _let_16 1))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))) (let ((_let_19 (forall ((Z Int)) (or (>= (+ tptp.c (* (- 1) Z) (tptp.max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) 1) (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) 0))))) (let ((_let_20 (not _let_12))) (let ((_let_21 (and _let_20 _let_19))) (let ((_let_22 (+ tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_10))) (let ((_let_23 (>= _let_22 1))) (let ((_let_24 (forall ((Z Int) (BOUND_VARIABLE_989 Int)) (or (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) 0) (not (>= (+ BOUND_VARIABLE_989 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) 0)) (not (>= (+ BOUND_VARIABLE_989 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) 0)) (>= (+ tptp.c (* (- 1) Z) BOUND_VARIABLE_989) 1))))) (let ((_let_25 (forall ((Z Int)) (or (not (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) 0)) (not (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) 0)) (>= (+ tptp.c Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) 1))))) (let ((_let_26 (not _let_25))) (let ((_let_27 (and _let_26 _let_24))) (let ((_let_28 (= _let_21 _let_27))) (let ((_let_29 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_30 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_29))) (let ((_let_31 (>= _let_30 1))) (let ((_let_32 (or _let_18 _let_31))) (let ((_let_33 (+ tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10))) (let ((_let_34 (>= _let_33 1))) (let ((_let_35 (>= _let_30 0))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_34))) (let ((_let_38 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_39 (or _let_38 _let_36))) (let ((_let_40 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_41 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_40) 1))) (let ((_let_42 (not _let_41))) (let ((_let_43 (+ tptp.c _let_40 _let_9))) (let ((_let_44 (>= _let_43 1))) (let ((_let_45 (or _let_44 _let_42))) (let ((_let_46 (>= _let_22 0))) (let ((_let_47 (or _let_31 _let_46))) (let ((_let_48 (>= _let_33 0))) (let ((_let_49 (or _let_36 _let_48))) (let ((_let_50 (not _let_21))) (let ((_let_51 (or))) (let ((_let_52 (not _let_19))) (let ((_let_53 (_let_52))) (let ((_let_54 (forall ((X Int) (Y Int) (Z Int)) (= (and (not (>= (+ tptp.c (* (- 1) Z) (tptp.max X Y)) 1)) (forall ((Z Int)) (or (>= (+ tptp.c (* (- 1) Z) (tptp.max X Y)) 1) (>= (+ Z (* (- 1) Z)) 0)))) (and (not (forall ((Z Int)) (or (not (>= (+ Z (* (- 1) X)) 0)) (not (>= (+ Z (* (- 1) Y)) 0)) (>= (+ tptp.c Z (* (- 1) Z)) 1)))) (forall ((Z Int) (BOUND_VARIABLE_989 Int)) (let ((_let_1 (* (- 1) BOUND_VARIABLE_989))) (or (>= (+ Z (* (- 1) Z)) 0) (>= (+ X _let_1) 1) (>= (+ Y _let_1) 1) (>= (+ tptp.c (* (- 1) Z) BOUND_VARIABLE_989) 1))))))))) (let ((_let_55 (not _let_28))) (let ((_let_56 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.ub (lambda ((BOUND_VARIABLE_779 Int) (BOUND_VARIABLE_780 Int) (BOUND_VARIABLE_781 Int)) (let ((_let_1 (* (- 1) BOUND_VARIABLE_781))) (and (not (>= (+ BOUND_VARIABLE_779 _let_1) 1)) (not (>= (+ BOUND_VARIABLE_780 _let_1) 1)))))))))) (let ((_let_57 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.model_max (lambda ((BOUND_VARIABLE_795 Int) (BOUND_VARIABLE_796 Int) (BOUND_VARIABLE_797 Int)) (not (>= (+ tptp.c (* (- 1) BOUND_VARIABLE_797) (tptp.max BOUND_VARIABLE_795 BOUND_VARIABLE_796)) 1)))))))) (let ((_let_58 (TRUST_SUBS_EQ (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_57 _let_56) :args ((forall ((X Int) (Y Int) (N Int)) (= (tptp.model_ub X Y N) (not (forall ((Z Int)) (or (not (tptp.ub X Y Z)) (>= (+ tptp.c (* (- 1) N) Z) 1)))))) SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.model_ub (lambda ((BOUND_VARIABLE_835 Int) (BOUND_VARIABLE_836 Int) (BOUND_VARIABLE_837 Int)) (not (forall ((Z Int)) (let ((_let_1 (* (- 1) Z))) (or (>= (+ BOUND_VARIABLE_835 _let_1) 1) (>= (+ BOUND_VARIABLE_836 _let_1) 1) (>= (+ tptp.c (* (- 1) BOUND_VARIABLE_837) Z) 1))))))))))) (let ((_let_59 (TRUST_SUBS_EQ (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_58 _let_57 _let_56) :args ((forall ((X Int) (Y Int) (N Int)) (= (tptp.minsol_model_max X Y N) (and (tptp.model_max X Y N) (forall ((Z Int)) (or (not (tptp.model_max X Y Z)) (not (>= (+ N (* (- 1) Z)) 1))))))) SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.minsol_model_max (lambda ((BOUND_VARIABLE_900 Int) (BOUND_VARIABLE_901 Int) (BOUND_VARIABLE_902 Int)) (and (not (>= (+ tptp.c (* (- 1) BOUND_VARIABLE_902) (tptp.max BOUND_VARIABLE_900 BOUND_VARIABLE_901)) 1)) (forall ((Z Int)) (let ((_let_1 (* (- 1) Z))) (or (>= (+ tptp.c _let_1 (tptp.max BOUND_VARIABLE_900 BOUND_VARIABLE_901)) 1) (not (>= (+ BOUND_VARIABLE_902 _let_1) 1)))))))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO (AND_INTRO (TRUST_SUBS_EQ (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_59 _let_58 _let_57 _let_56) :args ((forall ((X Int) (Y Int) (N Int)) (= (tptp.minsol_model_ub X Y N) (and (tptp.model_ub X Y N) (forall ((Z Int)) (or (not (tptp.model_ub X Y Z)) (not (>= (+ N (* (- 1) Z)) 1))))))) SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.minsol_model_ub (lambda ((BOUND_VARIABLE_1027 Int) (BOUND_VARIABLE_1028 Int) (BOUND_VARIABLE_1029 Int)) (and (not (forall ((Z Int)) (or (not (>= (+ Z (* (- 1) BOUND_VARIABLE_1027)) 0)) (not (>= (+ Z (* (- 1) BOUND_VARIABLE_1028)) 0)) (>= (+ tptp.c Z (* (- 1) BOUND_VARIABLE_1029)) 1)))) (forall ((Z Int) (BOUND_VARIABLE_989 Int)) (let ((_let_1 (* (- 1) Z))) (let ((_let_2 (* (- 1) BOUND_VARIABLE_989))) (or (not (>= (+ BOUND_VARIABLE_1029 _let_1) 1)) (>= (+ BOUND_VARIABLE_1027 _let_2) 1) (>= (+ BOUND_VARIABLE_1028 _let_2) 1) (>= (+ tptp.c _let_1 BOUND_VARIABLE_989) 1)))))))))) _let_59 _let_58 _let_57 _let_56) :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (not _let_54))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_60) :args (_let_61)) (REWRITE :args ((=> _let_61 (not (= _let_21 (and _let_26 (forall ((Z Int) (BOUND_VARIABLE_989 Int)) (let ((_let_1 (* (- 1) BOUND_VARIABLE_989))) (or (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) 0) (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_1) 1) (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_1) 1) (>= (+ tptp.c (* (- 1) Z) BOUND_VARIABLE_989) 1)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_54))) (REFL :args (_let_55)) :args _let_51)) _let_60 :args (_let_55 true _let_54)))) (let ((_let_63 (_let_28))) (let ((_let_64 (REORDERING (CNF_EQUIV_NEG1 :args _let_63) :args ((or _let_21 _let_27 _let_28))))) (let ((_let_65 (not _let_27))) (let ((_let_66 (_let_24))) (let ((_let_67 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_68 (ASSUME :args _let_66))) (let ((_let_69 (* (- 1) _let_9))) (let ((_let_70 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_69))) (let ((_let_71 (>= _let_70 1))) (let ((_let_72 (not _let_49))) (let ((_let_73 (not _let_47))) (let ((_let_74 (not _let_38))) (let ((_let_75 (_let_38))) (let ((_let_76 (not _let_71))) (let ((_let_77 (_let_76))) (let ((_let_78 ((< _let_70 1)))) (let ((_let_79 (_let_71))) (let ((_let_80 (false))) (let ((_let_81 ((- 1.0) 1.0))) (let ((_let_82 (ASSUME :args _let_75))) (let ((_let_83 (MACRO_SR_PRED_TRANSFORM _let_82 :args ((= _let_70 0))))) (let ((_let_84 (not _let_18))) (let ((_let_85 (not _let_31))) (let ((_let_86 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_87 (< _let_30 1))) (let ((_let_88 (_let_31))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 (ASSUME :args (_let_18)))) (let ((_let_91 (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_31 _let_46 _let_73))))) (let ((_let_92 (not _let_46))) (let ((_let_93 (not _let_44))) (let ((_let_94 (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_44))))) (let ((_let_95 (REFL :args (_let_42)))) (let ((_let_96 (REFL :args (_let_84)))) (let ((_let_97 (= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_69) 0))) (let ((_let_98 ((not _let_97)))) (let ((_let_99 (_let_97))) (let ((_let_100 (1.0 1.0 (- 1.0) (- 1.0)))) (let ((_let_101 (ASSUME :args (_let_46)))) (let ((_let_102 (ASSUME :args (_let_41)))) (let ((_let_103 (ASSUME :args (_let_93)))) (let ((_let_104 (MACRO_SR_PRED_TRANSFORM _let_103 :args ((< _let_43 1))))) (let ((_let_105 (ASSUME :args _let_99))) (let ((_let_106 (MACRO_SR_PRED_TRANSFORM _let_90 :args _let_99))) (let ((_let_107 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_101 _let_102 _let_103 _let_90) :args (_let_18 _let_41 _let_93 _let_46)) (SCOPE (CONTRA _let_106 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_105 _let_104 _let_102 _let_101 :args _let_100) :args _let_80) :args _let_99) :args _let_98) :args _let_98)) :args (_let_46 _let_41 _let_93 _let_18)) :args ((not (and _let_18 _let_41 _let_93 _let_46)) SB_LITERAL))) (CONG _let_96 _let_95 _let_94 (REFL :args (_let_92)) :args _let_51)) :args ((or _let_84 _let_44 _let_42 _let_92))))) (let ((_let_108 (forall ((X Int) (Y Int)) (or (= Y (tptp.max X Y)) (>= (+ X (* (- 1) Y)) 1))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.max X Y)))) :args (_let_108))) _let_109 :args (_let_32 false _let_108)))) (let ((_let_111 (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_18 _let_31 (not _let_32)))))) (let ((_let_112 ((< _let_30 0)))) (let ((_let_113 (REORDERING (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_89 (SCOPE (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_112) _let_89 :args (1.0 (- 1.0))) :args _let_80) :args _let_112) :args (_let_35)) :args _let_88)) :args _let_88)) :args ((or _let_35 _let_85))))) (let ((_let_114 (not _let_48))) (let ((_let_115 (_let_114))) (let ((_let_116 (_let_48))) (let ((_let_117 (ASSUME :args _let_77))) (let ((_let_118 (ASSUME :args _let_116))) (let ((_let_119 (forall ((X Int) (Y Int)) (or (= X (tptp.max X Y)) (not (>= (+ X (* (- 1) Y)) 0)))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.max X Y)))) :args (_let_119))) _let_120 :args (_let_39 false _let_119)))) (let ((_let_122 (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_36 (not _let_39)))))) (let ((_let_123 (MACRO_RESOLUTION_TRUST _let_107 _let_91 _let_111 _let_110 _let_113 _let_122 _let_121 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_117 _let_103 _let_102 _let_118) :args (_let_41 _let_93 _let_48 _let_76)) (SCOPE (CONTRA _let_118 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_118 _let_102 (INT_TIGHT_UB _let_104) (MACRO_SR_PRED_TRANSFORM _let_117 :args _let_78) :args ((- 1.0) (- 1.0) 1.0 1.0)) :args _let_80) :args _let_116) :args ((< _let_33 0))) :args _let_115)) :args (_let_76 _let_93 _let_41 _let_48)) :args ((not (and _let_41 _let_93 _let_48 _let_76)) SB_LITERAL))) (CONG _let_95 _let_94 (REFL :args _let_115) (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_71))) :args _let_51)) :args ((or _let_44 _let_42 _let_114 _let_71))) (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_36 _let_48 _let_72))) _let_113 _let_111 _let_110 (MACRO_RESOLUTION_TRUST _let_107 _let_91 (REORDERING (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_89 (MODUS_PONENS (AND_INTRO _let_90 _let_82) (SCOPE (TRANS (SYMM (SYMM _let_82)) (SYMM _let_90)) :args (_let_18 _let_38)))) :args (_let_38 _let_18 _let_31)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_89 (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_86)) :args ((= _let_30 0))) :args _let_81) :args _let_80) :args _let_88) :args (_let_87)) (MACRO_SR_PRED_TRANSFORM _let_89 :args ((not _let_87)))) :args (_let_31 _let_86)) :args ((not (and _let_38 _let_18 _let_31)) SB_LITERAL))) :args ((or _let_85 _let_74 _let_84))) :args ((or _let_74 _let_84 _let_44 _let_42 _let_73) false _let_46 true _let_31)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_82 (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_79) _let_83 :args _let_81) :args _let_80) :args _let_79) :args _let_78) :args _let_77) :args _let_75)) :args _let_75)) :args ((or _let_74 _let_44 _let_42 _let_73 _let_72) false _let_48 false _let_35 false _let_31 false _let_32 true _let_18 true _let_71)) (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_67 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CEGQI)) :args _let_66))) (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_67 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 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(MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_12))))) (let ((_let_125 (_let_21))) (let ((_let_126 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_125) (CONG (REFL :args _let_125) _let_124 (REFL :args _let_53) :args _let_51)) :args ((or _let_12 _let_21 _let_52))))) (let ((_let_127 (or _let_31 _let_23))) (let ((_let_128 (_let_25))) (let ((_let_129 (ASSUME :args _let_128))) (let ((_let_130 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_129 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CEGQI)) :args _let_128))))) (let ((_let_131 (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_34 (not _let_37)))))) (let ((_let_132 ((not _let_34)))) (let ((_let_133 (REFL :args (_let_74)))) (let ((_let_134 (_let_34))) (let ((_let_135 (_let_20))) (let ((_let_136 (ASSUME :args _let_135))) (let ((_let_137 (MACRO_SR_PRED_TRANSFORM _let_136 :args ((< _let_11 1))))) (let ((_let_138 (ASSUME :args _let_134))) (let ((_let_139 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_82 _let_136 _let_138) :args (_let_20 _let_38 _let_34)) (SCOPE (CONTRA _let_138 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_138 _let_137 _let_83 :args ((- 1.0) 1.0 1.0)) :args _let_80) :args _let_134) :args ((< _let_33 1))) :args _let_132)) :args (_let_38 _let_20 _let_34)) :args ((not (and _let_20 _let_38 _let_34)) SB_LITERAL))) (CONG _let_124 _let_133 (REFL :args _let_132) :args _let_51)))) (let ((_let_140 (CNF_EQUIV_NEG2 :args _let_63))) (let ((_let_141 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_142 (+ tptp.c _let_141 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_143 (>= _let_142 1))) (let ((_let_144 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_145 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_144))) (let ((_let_146 (>= _let_145 1))) (let ((_let_147 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_144))) (let ((_let_148 (>= _let_147 1))) (let ((_let_149 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_141) 1))) (let ((_let_150 (not _let_149))) (let ((_let_151 (or _let_150 _let_148 _let_146 _let_143))) (let ((_let_152 (>= _let_11 0))) (let ((_let_153 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_151 0)) (CONG (REFL :args (_let_151)) (MACRO_SR_PRED_INTRO :args ((= (not _let_150) _let_149))) :args _let_51)) :args ((or _let_149 _let_151))))) (let ((_let_154 (not _let_146))) (let ((_let_155 (CNF_OR_NEG :args (_let_151 3)))) (let ((_let_156 (_let_19))) (let ((_let_157 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_156) :args (_let_67 QUANTIFIERS_INST_CEGQI)) :args _let_156))) _let_123 :args (_let_152 false _let_19)))) (let ((_let_158 (not _let_152))) (let ((_let_159 (not _let_148))) (let ((_let_160 (not _let_143))) (let ((_let_161 (MACRO_SR_PRED_INTRO :args ((= (not _let_160) _let_143))))) (let ((_let_162 (REFL :args (_let_150)))) (let ((_let_163 (REFL :args (_let_158)))) (let ((_let_164 (<= _let_142 0))) (let ((_let_165 (_let_164))) (let ((_let_166 (ASSUME :args (_let_159)))) (let ((_let_167 (ASSUME :args (_let_149)))) (let ((_let_168 (ASSUME :args (_let_152)))) (let ((_let_169 (ASSUME :args (_let_160)))) (let ((_let_170 (MACRO_SR_PRED_TRANSFORM _let_169 :args ((< _let_142 1))))) (let ((_let_171 (ASSUME :args (_let_154)))) (let ((_let_172 (not _let_24))) (let ((_let_173 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_174 (_let_172))) (let ((_let_175 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_174)) :args _let_174) (REWRITE :args ((=> _let_172 (not (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_10) 0) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_173) 0)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_29) 0)) _let_143))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_172) _let_24))) (REFL :args ((not _let_151))) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_169 _let_168 _let_171 _let_167 _let_90) :args (_let_18 _let_152 _let_149 _let_154 _let_160)) (SCOPE (CONTRA _let_106 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_105 _let_167 (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_171 :args ((< _let_145 1)))) _let_168 _let_170 :args ((- 1.0) (- 1.0) 1.0 (- 1.0) 1.0)) :args _let_80) :args _let_99) :args _let_98) :args _let_98)) :args (_let_160 _let_152 _let_154 _let_149 _let_18)) :args ((not (and _let_18 _let_152 _let_149 _let_154 _let_160)) SB_LITERAL))) (CONG _let_96 _let_163 _let_162 (MACRO_SR_PRED_INTRO :args ((= (not _let_154) _let_146))) _let_161 :args _let_51)) :args ((or _let_84 _let_158 _let_143 _let_150 _let_146))) _let_157 _let_111 _let_110 _let_113 _let_122 _let_121 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_166 _let_167 _let_168 _let_82 _let_169) :args (_let_38 _let_152 _let_149 _let_159 _let_160)) (SCOPE (CONTRA (INT_TIGHT_UB _let_170) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_165) _let_83 _let_168 _let_167 (MACRO_SR_PRED_TRANSFORM _let_166 :args ((< _let_147 1))) :args (1.0 (- 1.0) (- 1.0) (- 1.0) 1.0)) :args _let_80) :args _let_165) :args ((> _let_142 0))) :args ((not _let_164)))) :args (_let_159 _let_149 _let_152 _let_38 _let_160)) :args ((not (and _let_38 _let_152 _let_149 _let_159 _let_160)) SB_LITERAL))) (CONG _let_133 _let_163 _let_162 (MACRO_SR_PRED_INTRO :args ((= (not _let_159) _let_148))) _let_161 :args _let_51)) :args ((or _let_74 _let_158 _let_143 _let_150 _let_148))) _let_155 (REORDERING (CNF_OR_NEG :args (_let_151 1)) :args ((or _let_159 _let_151))) _let_153 :args ((or _let_74 _let_158 _let_151) true _let_143 true _let_148 false _let_149)) _let_157 _let_155 (REORDERING (CNF_OR_NEG :args (_let_151 2)) :args ((or _let_154 _let_151))) _let_153 :args (_let_151 false _let_152 false _let_18 false _let_32 true _let_31 true _let_35 false _let_39 true _let_38 false _let_152 true _let_143 true _let_146 false _let_149)) :args (_let_24 false _let_151)))) (let ((_let_176 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))))) (let ((_let_177 (_let_27))) (let ((_let_178 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_177) (CONG (REFL :args _let_177) _let_176 (REFL :args _let_174) :args _let_51)) :args ((or _let_25 _let_27 _let_172))))) (let ((_let_179 (ASSUME :args (_let_23)))) (let ((_let_180 (MACRO_RESOLUTION_TRUST _let_139 _let_131 _let_122 _let_121 _let_113 _let_130 _let_111 _let_110 _let_178 _let_175 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_179 _let_136 _let_90) :args (_let_20 _let_18 _let_23)) (SCOPE (CONTRA _let_106 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_105 _let_137 _let_179 :args (1.0 1.0 (- 1.0))) :args _let_80) :args _let_99) :args _let_98) :args _let_98)) :args (_let_23 _let_20 _let_18)) :args ((not (and _let_20 _let_18 _let_23)) SB_LITERAL))) (CONG _let_124 _let_96 (REFL :args ((not _let_23))) :args _let_51)) _let_140 _let_62 (MACRO_RESOLUTION_TRUST _let_178 _let_175 _let_140 _let_62 (MACRO_RESOLUTION_TRUST _let_139 _let_131 _let_130 _let_122 _let_121 _let_113 (REORDERING (CNF_OR_POS :args (_let_127)) :args ((or _let_31 _let_23 (not _let_127)))) (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_129 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CEGQI)) :args _let_128))) :args ((or _let_12 _let_26 _let_23) false _let_34 false _let_37 false _let_38 false _let_39 false _let_35 false _let_31 false _let_127)) _let_126 _let_123 :args ((or _let_12 _let_23) false _let_24 true _let_27 true _let_28 true _let_25 false _let_21 false _let_19)) _let_126 _let_123 :args (_let_12 false _let_34 false _let_38 false _let_39 false _let_35 false _let_37 false _let_31 false _let_32 false _let_25 false _let_24 true _let_18 true _let_27 true _let_28 false _let_23 false _let_21 false _let_19)))) (let ((_let_181 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13))) (let ((_let_182 (>= _let_181 1))) (let ((_let_183 (or _let_182 _let_15 _let_17))) (let ((_let_184 (not _let_15))) (let ((_let_185 (not _let_183))) (let ((_let_186 (_let_26))) (let ((_let_187 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_186)) :args _let_186) (REWRITE :args ((=> _let_26 (not (or (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_173) 0)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_29) 0)) (>= (+ tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_10) 1)))))))) (CONG _let_176 (REFL :args (_let_185)) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_27 0)) :args ((or _let_26 _let_65))) (MACRO_RESOLUTION_TRUST _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_20 _let_50))) _let_180 :args (_let_50 false _let_12)) _let_62 :args (_let_27 true _let_21 true _let_28)) :args (_let_26 false _let_27)) :args (_let_185 true _let_25)))) (let ((_let_188 (not _let_17))) (let ((_let_189 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_183 2)) _let_187 :args (_let_188 true _let_183)))) (let ((_let_190 (not _let_182))) (let ((_let_191 (MACRO_SR_PRED_INTRO :args ((= (not _let_188) _let_17))))) (let ((_let_192 (REFL :args _let_135))) (let ((_let_193 (<= _let_16 0))) (let ((_let_194 ((not _let_193)))) (let ((_let_195 ((> _let_16 0)))) (let ((_let_196 (_let_193))) (let ((_let_197 (ASSUME :args (_let_190)))) (let ((_let_198 (ASSUME :args (_let_12)))) (let ((_let_199 (ASSUME :args _let_196))) (let ((_let_200 (ASSUME :args (_let_188)))) (let ((_let_201 (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_200 :args ((< _let_16 1)))))) (let ((_let_202 (ASSUME :args (_let_184)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_90 _let_198 _let_202 _let_200) :args (_let_12 _let_18 _let_184 _let_188)) (SCOPE (CONTRA _let_201 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_199 (MACRO_SR_PRED_TRANSFORM _let_202 :args ((< _let_14 1))) _let_198 _let_106 :args _let_100) :args _let_80) :args _let_196) :args _let_195) :args _let_194)) :args (_let_18 _let_12 _let_184 _let_188)) :args ((not (and _let_12 _let_18 _let_184 _let_188)) SB_LITERAL))) (CONG _let_192 _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_184) _let_15))) _let_191 :args _let_51)) (MACRO_RESOLUTION_TRUST _let_111 (MACRO_RESOLUTION_TRUST _let_113 (MACRO_RESOLUTION_TRUST _let_122 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_197 _let_198 _let_82 _let_200) :args (_let_12 _let_38 _let_190 _let_188)) (SCOPE (CONTRA _let_201 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_199 _let_83 _let_198 (MACRO_SR_PRED_TRANSFORM _let_197 :args ((< _let_181 1))) :args (1.0 (- 1.0) (- 1.0) 1.0)) :args _let_80) :args _let_196) :args _let_195) :args _let_194)) :args (_let_190 _let_12 _let_38 _let_188)) :args ((not (and _let_12 _let_38 _let_190 _let_188)) SB_LITERAL))) (CONG _let_192 _let_133 (MACRO_SR_PRED_INTRO :args ((= (not _let_190) _let_182))) _let_191 :args _let_51)) _let_180 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_183 0)) :args ((or _let_190 _let_183))) _let_187 :args (_let_190 true _let_183)) _let_189 :args (_let_74 false _let_12 true _let_182 true _let_17)) _let_121 :args (_let_36 true _let_38 false _let_39)) :args (_let_85 true _let_35)) _let_110 :args (_let_18 true _let_31 false _let_32)) _let_189 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_183 1)) :args ((or _let_184 _let_183))) _let_187 :args (_let_184 true _let_183)) _let_180 :args (false false _let_18 true _let_17 true _let_15 false _let_12)) :args ((forall ((X Int) (Y Int)) (= (<= X Y) (<= (tptp.summation X) (tptp.summation Y)))) _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 45.52/45.77 )
% 45.52/45.77 % SZS output end Proof for NUM861_1
% 45.52/45.77 % cvc5---1.0.5 exiting
% 45.52/45.77 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------