%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : DAT101_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 : Wed Aug 30 22:10:36 EDT 2023

% Result   : Theorem 0.21s 0.56s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : DAT101_1 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 13:51:08 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_ARI
% 0.21/0.56  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YPhuPqPq3P/cvc5---1.0.5_15869.p...
% 0.21/0.56  ------- get file name : TPTP file name is DAT101_1
% 0.21/0.56  ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15869.smt2...
% 0.21/0.56  --- Run --finite-model-find --decision=internal at 15...
% 0.21/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.21/0.56  % SZS status Theorem for DAT101_1
% 0.21/0.56  % SZS output start Proof for DAT101_1
% 0.21/0.56  (
% 0.21/0.56  (let ((_let_1 (not (not (forall ((N Int)) (=> (>= N 4) (tptp.inRange N (tptp.cons 1 (tptp.cons 5 (tptp.cons 2 tptp.nil)))))))))) (let ((_let_2 (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= L tptp.nil) (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T)))))))) (let ((_let_3 (forall ((K Int) (L tptp.list)) (not (= (tptp.cons K L) tptp.nil))))) (let ((_let_4 (forall ((K Int) (L tptp.list)) (= (tptp.tail (tptp.cons K L)) L)))) (let ((_let_5 (forall ((K Int) (L tptp.list)) (= (tptp.head (tptp.cons K L)) K)))) (let ((_let_6 (tptp.cons 2 tptp.nil))) (let ((_let_7 (tptp.cons 5 _let_6))) (let ((_let_8 (tptp.head _let_7))) (let ((_let_9 (= _let_8 5))) (let ((_let_10 (tptp.cons 1 _let_7))) (let ((_let_11 (= _let_7 (tptp.tail _let_10)))) (let ((_let_12 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_13 (= _let_10 _let_12))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 (tptp.tail _let_12)))) (let ((_let_15 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_15))) (let ((_let_17 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 4))) (let ((_let_18 (tptp.head _let_15))) (let ((_let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_18))) (let ((_let_20 (forall ((K Int) (L tptp.list)) (= K (tptp.head (tptp.cons K L)))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (_let_20))) (let ((_let_23 ((tptp.cons K L)))) (let ((_let_24 (forall ((K Int) (L tptp.list)) (= L (tptp.tail (tptp.cons K L)))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (_let_24))) (let ((_let_27 ((tptp.cons K L)))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (1 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_27)) :args _let_26)) _let_25 :args (_let_11 false _let_24)))) (let ((_let_29 (tptp.inRange 4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_30 (not _let_29))) (let ((_let_31 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 4))) (let ((_let_32 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 0)))) (let ((_let_33 (not _let_13))) (let ((_let_34 (or _let_33 _let_32 _let_31 _let_30))) (let ((_let_35 (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 5 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (not _let_35))) (let ((_let_38 (= tptp.nil _let_10))) (let ((_let_39 (or _let_38 _let_37))) (let ((_let_40 (tptp.inRange 4 _let_10))) (let ((_let_41 (= _let_40 _let_39))) (let ((_let_42 (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (_let_42))) (let ((_let_45 ((tptp.inRange N L)))) (let ((_let_46 (forall ((N Int)) (or (not (>= N 4)) (tptp.inRange N (tptp.cons 1 (tptp.cons 5 (tptp.cons 2 tptp.nil)))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (forall ((K Int) (L tptp.list)) (not (= tptp.nil (tptp.cons K L)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_48))) (let ((_let_51 ((tptp.cons K L)))) (let ((_let_52 (or))) (let ((_let_53 (_let_37))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_53)) :args _let_53) (REWRITE :args ((=> _let_37 (not (or (not (= _let_12 _let_10)) _let_32 _let_31 _let_30))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_35))) (REFL :args (_let_36)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_37 (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (1 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args ((not _let_38) false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_41)) :args ((or (not _let_40) _let_39 (not _let_41)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (4 QUANTIFIERS_INST_ENUM)) :args (_let_46)))) _let_47 :args (_let_40 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (4 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_44))) _let_43 :args (_let_41 false _let_42)) :args (_let_39 false _let_40 false _let_41)) :args (_let_37 true _let_38 false _let_39)) :args (_let_36 true _let_35)))) (let ((_let_55 (REFL :args (_let_34)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_13))) :args _let_52)) :args ((or _let_13 _let_34))) _let_54 :args (_let_13 true _let_34)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_27)) :args _let_26)) _let_25 :args (_let_14 false _let_24)))) (let ((_let_58 (not (tptp.inRange 4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_59 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 0)))) (let ((_let_60 (not _let_16))) (let ((_let_61 (or _let_60 _let_59 _let_17 _let_58))) (let ((_let_62 (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (not _let_62))) (let ((_let_65 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_66 (or _let_65 _let_64))) (let ((_let_67 (= _let_29 _let_66))) (let ((_let_68 (= tptp.nil _let_7))) (let ((_let_69 (not _let_65))) (let ((_let_70 (not _let_68))) (let ((_let_71 (not _let_14))) (let ((_let_72 (not _let_11))) (let ((_let_73 (REFL :args (_let_71)))) (let ((_let_74 (REFL :args (_let_33)))) (let ((_let_75 (REFL :args (_let_72)))) (let ((_let_76 (and _let_11 _let_70 _let_13 _let_14))) (let ((_let_77 (ASSUME :args (_let_70)))) (let ((_let_78 (ASSUME :args (_let_11)))) (let ((_let_79 (SYMM _let_78))) (let ((_let_80 (ASSUME :args (_let_13)))) (let ((_let_81 (CONG (SYMM _let_80) :args (APPLY_UF tptp.tail)))) (let ((_let_82 (ASSUME :args (_let_14)))) (let ((_let_83 (SYMM (SYMM _let_82)))) (let ((_let_84 (_let_64))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84) (REWRITE :args ((=> _let_64 (not (or (not (= _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) _let_59 _let_17 _let_58))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_62))) (REFL :args (_let_63)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_64 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_76)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_77 _let_78 _let_80 _let_82) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.nil)) (TRANS _let_83 _let_81 _let_79) :args (=)) (FALSE_INTRO _let_77))) :args (_let_70 _let_11 _let_13 _let_14))) :args (_let_11 _let_70 _let_13 _let_14))) :args (true _let_76)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_68))) _let_74 _let_73 (REFL :args (_let_69)) :args _let_52)) :args ((or _let_68 _let_72 _let_33 _let_71 _let_69))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (5 _let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_70 false _let_48)) _let_28 _let_56 _let_57 :args (_let_69 true _let_68 false _let_11 false _let_13 false _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_67)) :args ((or _let_30 _let_66 (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 3)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_52)) :args ((or _let_29 _let_34))) _let_54 :args (_let_29 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_44))) _let_43 :args (_let_67 false _let_42)) :args (_let_66 false _let_29 false _let_67)) :args (_let_64 true _let_65 false _let_66)) :args (_let_63 true _let_62)))) (let ((_let_86 (not _let_17))) (let ((_let_87 (not _let_19))) (let ((_let_88 (not _let_9))) (let ((_let_89 (= 5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_90 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 5))) (let ((_let_91 (_let_90))) (let ((_let_92 (ASSUME :args (_let_86)))) (let ((_let_93 (= _let_18 5))) (let ((_let_94 (ASSUME :args (_let_19)))) (let ((_let_95 (= 5 _let_8))) (let ((_let_96 (ASSUME :args (_let_16)))) (let ((_let_97 (_let_9))) (let ((_let_98 (ASSUME :args _let_97))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_94 (MODUS_PONENS (AND_INTRO (MODUS_PONENS _let_98 (SCOPE (SYMM _let_98) :args _let_97)) _let_78 _let_80 _let_82 _let_96) (SCOPE (TRANS (CONG (TRANS (SYMM _let_96) _let_83 _let_81 _let_79) :args (APPLY_UF tptp.head)) (SYMM (ASSUME :args (_let_95)))) :args (_let_95 _let_11 _let_13 _let_14 _let_16)))) (SCOPE (TRANS (SYMM (ASSUME :args (_let_93))) (SYMM _let_94)) :args (_let_19 _let_93))) _let_92) :args (_let_9 _let_11 _let_13 _let_14 _let_16 _let_86 _let_19)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_89)) :args _let_91) :args _let_91) (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_91) (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_92 :args ((< SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 4)))) :args ((- 1.0) 1.0)) :args (false)) :args _let_91) :args ((not _let_90)))) :args (_let_89 _let_86)) :args ((not (and _let_9 _let_11 _let_13 _let_14 _let_16 _let_86 _let_19)) SB_LITERAL))) (CONG (REFL :args (_let_88)) _let_75 _let_74 _let_73 (REFL :args (_let_60)) (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_17))) (REFL :args (_let_87)) :args _let_52)) :args ((or _let_88 _let_72 _let_33 _let_71 _let_17 _let_60 _let_87))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_23)) :args _let_22)) _let_21 :args (_let_19 false _let_20)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_61 2)) _let_85 :args (_let_86 true _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_16))) :args _let_52)) :args ((or _let_16 _let_61))) _let_85 :args (_let_16 true _let_61)) _let_57 _let_56 _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_21 :args (5 _let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_23)) :args _let_22))) _let_21 :args (_let_9 false _let_20)) :args (false false _let_19 true _let_17 false _let_16 false _let_14 false _let_13 false _let_11 false _let_9)) :args (_let_5 _let_4 (forall ((L tptp.list)) (or (= L tptp.nil) (= L (tptp.cons (tptp.head L) (tptp.tail L))))) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.56  )
% 0.21/0.56  % SZS output end Proof for DAT101_1
% 0.21/0.56  % cvc5---1.0.5 exiting
% 0.21/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------