%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : DAT097_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n015.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 22:10:35 EDT 2023

% Result   : Theorem 0.21s 0.63s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : DAT097_1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.19/0.35  % Computer : n015.cluster.edu
% 0.19/0.35  % Model    : x86_64 x86_64
% 0.19/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35  % Memory   : 8042.1875MB
% 0.19/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35  % CPULimit   : 300
% 0.19/0.35  % WCLimit    : 300
% 0.19/0.35  % DateTime   : Thu Aug 24 14:50:51 EDT 2023
% 0.19/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_ARI
% 0.21/0.63  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.P3c7Dxghp6/cvc5---1.0.5_32340.p...
% 0.21/0.63  ------- get file name : TPTP file name is DAT097_1
% 0.21/0.63  ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32340.smt2...
% 0.21/0.63  --- Run --finite-model-find --decision=internal at 15...
% 0.21/0.63  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.21/0.63  % SZS status Theorem for DAT097_1
% 0.21/0.63  % SZS output start Proof for DAT097_1
% 0.21/0.63  (
% 0.21/0.63  (let ((_let_1 (not (not (forall ((M Int) (N Int) (K tptp.list) (L tptp.list) (L1 tptp.list)) (=> (and (tptp.in N L) (not (tptp.in M K)) (= L1 (tptp.append L (tptp.cons M K)))) (= (tptp.count N L1) (tptp.count N L)))))))) (let ((_let_2 (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (> (tptp.count N L) 0))))) (let ((_let_3 (forall ((I Int) (K tptp.list) (L tptp.list)) (= (tptp.append (tptp.cons I K) L) (tptp.cons I (tptp.append K L)))))) (let ((_let_4 (forall ((L tptp.list)) (= (tptp.append tptp.nil L) L)))) (let ((_let_5 (forall ((K Int) (H Int) (T tptp.list) (N Int)) (=> (= K H) (= (tptp.count K (tptp.cons H T)) (+ (tptp.count K T) 1)))))) (let ((_let_6 (forall ((K Int)) (= (tptp.count K tptp.nil) 0)))) (let ((_let_7 (tptp.cons 0 tptp.nil))) (let ((_let_8 (tptp.count 0 _let_7))) (let ((_let_9 (tptp.count 0 tptp.nil))) (let ((_let_10 (= _let_9 (+ (- 1) _let_8)))) (let ((_let_11 (tptp.append tptp.nil _let_7))) (let ((_let_12 (= _let_7 _let_11))) (let ((_let_13 (tptp.count 0 _let_11))) (let ((_let_14 (* (- 1) _let_13))) (let ((_let_15 (+ _let_9 _let_14))) (let ((_let_16 (>= _let_15 0))) (let ((_let_17 (forall ((H Int) (T tptp.list)) (= (tptp.count H (tptp.cons H T)) (+ 1 (tptp.count H T)))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_17))) (let ((_let_20 (0 tptp.nil QUANTIFIERS_INST_ENUM))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_18 :args _let_20) :args _let_19))) _let_18 :args (_let_10 false _let_17)))) (let ((_let_22 (forall ((L tptp.list)) (= L (tptp.append tptp.nil L))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.append tptp.nil L)))) :args (_let_22))) _let_23 :args (_let_12 false _let_22)))) (let ((_let_25 (>= _let_15 1))) (let ((_let_26 (>= _let_13 1))) (let ((_let_27 (= _let_9 0))) (let ((_let_28 (= _let_9 _let_13))) (let ((_let_29 (tptp.in 0 _let_11))) (let ((_let_30 (= _let_26 _let_29))) (let ((_let_31 (not _let_26))) (let ((_let_32 (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_32))) (let ((_let_35 (tptp.count 0 (tptp.append _let_11 _let_7)))) (let ((_let_36 (= _let_13 _let_35))) (let ((_let_37 (tptp.in 0 tptp.nil))) (let ((_let_38 (not _let_29))) (let ((_let_39 (or _let_38 _let_37 _let_36))) (let ((_let_40 (forall ((M Int) (N Int) (K tptp.list) (L tptp.list)) (or (not (tptp.in N L)) (tptp.in M K) (= (tptp.count N L) (tptp.count N (tptp.append L (tptp.cons M K)))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (tptp.cons 0 _let_11))) (let ((_let_43 (tptp.count 0 _let_42))) (let ((_let_44 (= _let_13 (+ (- 1) _let_43)))) (let ((_let_45 (= (tptp.append _let_7 _let_7) _let_42))) (let ((_let_46 (not _let_36))) (let ((_let_47 (_let_3))) (let ((_let_48 (ASSUME :args _let_47))) (let ((_let_49 (not _let_12))) (let ((_let_50 (and _let_12 _let_45 _let_44))) (let ((_let_51 (= _let_35 _let_43))) (let ((_let_52 (= _let_13 _let_8))) (let ((_let_53 (not (= _let_8 _let_43)))) (let ((_let_54 (=))) (let ((_let_55 (ASSUME :args (_let_52)))) (let ((_let_56 (SYMM _let_55))) (let ((_let_57 (SYMM _let_56))) (let ((_let_58 (APPLY_UF tptp.count))) (let ((_let_59 (ASSUME :args (_let_45)))) (let ((_let_60 (_let_12))) (let ((_let_61 (ASSUME :args _let_60))) (let ((_let_62 (SYMM _let_61))) (let ((_let_63 (REFL :args (0)))) (let ((_let_64 (MODUS_PONENS _let_61 (SCOPE (CONG _let_63 _let_62 :args _let_58) :args _let_60)))) (let ((_let_65 ((= _let_13 _let_43)))) (let ((_let_66 (false))) (let ((_let_67 ((- 1) 1))) (let ((_let_68 (ASSUME :args (_let_44)))) (let ((_let_69 (>= _let_9 1))) (let ((_let_70 (= _let_37 _let_69))) (let ((_let_71 (not _let_37))) (let ((_let_72 (not _let_69))) (let ((_let_73 (_let_6))) (let ((_let_74 (ASSUME :args _let_73))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (0 QUANTIFIERS_INST_ENUM)) :args _let_73)) _let_74 :args (_let_27 false _let_6)))) (let ((_let_76 (_let_27))) (let ((_let_77 (_let_69))) (let ((_let_78 (ASSUME :args _let_76))) (let ((_let_79 (not _let_28))) (let ((_let_80 (not _let_27))) (let ((_let_81 (and _let_27 _let_10 _let_12))) (let ((_let_82 (not (= 0 _let_8)))) (let ((_let_83 (SYMM _let_78))) (let ((_let_84 ((= _let_9 _let_8)))) (let ((_let_85 (ASSUME :args (_let_10)))) (let ((_let_86 (MACRO_SR_PRED_TRANSFORM _let_85 :args ((= (+ _let_9 (* (- 1) _let_8)) (- 1)))))) (let ((_let_87 (not _let_25))) (let ((_let_88 (1.0 1.0 (- 1.0)))) (let ((_let_89 (>= _let_9 _let_13))) (let ((_let_90 (<= _let_9 _let_13))) (let ((_let_91 ((or _let_90 _let_89)))) (let ((_let_92 (not _let_89))) (let ((_let_93 (not _let_90))) (let ((_let_94 (= (+ _let_8 _let_14) 0))) (let ((_let_95 ((not _let_94)))) (let ((_let_96 (_let_94))) (let ((_let_97 (ASSUME :args (_let_16)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_97 _let_85 _let_64) :args (_let_10 _let_16 _let_12)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM _let_55 :args _let_96) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_96) _let_86 _let_97 :args _let_88) :args _let_66) :args _let_96) :args _let_95) :args _let_95)) :args (_let_16 _let_10 _let_52)) :args ((not (and _let_10 _let_16 _let_12)) SB_LITERAL))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (NOT_AND (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_93)) :args ((> _let_9 _let_13))) (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_92)) :args ((< _let_9 _let_13))) :args _let_67) :args _let_66) :args (_let_93 _let_92))) :args _let_91) (REWRITE :args _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (MACRO_SR_PRED_TRANSFORM (NOT_AND (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_31)) :args ((< _let_13 1))) (INT_TIGHT_UB (ARITH_TRICHOTOMY (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_79)) :args ((not (= _let_15 0)))) (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_87)) :args ((< _let_15 1)))) :args ((< _let_15 0)))) _let_78 :args _let_88) :args _let_66) :args (_let_79 _let_87 _let_27 _let_31))) :args ((or _let_28 _let_25 _let_80 _let_26))) :args ((or _let_28 _let_80 _let_25 _let_26))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_81)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO (MODUS_PONENS (AND_INTRO _let_78 _let_85) (SCOPE (FALSE_ELIM (TRANS (CONG _let_83 (REFL :args (_let_8)) :args _let_54) (FALSE_INTRO (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_84) _let_86 :args _let_67) :args _let_66) :args _let_84)))) :args (_let_27 _let_10))) _let_78 _let_64) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_83) _let_57 :args _let_54) (FALSE_INTRO (ASSUME :args (_let_82))))) :args (_let_82 _let_27 _let_52))) :args (_let_27 _let_10 _let_12))) :args (true _let_81)) :args ((or _let_80 (not _let_10) _let_79 _let_49))) _let_75 _let_21 _let_24 :args (_let_79 false _let_27 false _let_10 false _let_12)) _let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or _let_31 _let_29 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_37 _let_38 _let_36 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_70)) :args ((or _let_69 _let_71 (not _let_70)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_78 (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_77) _let_78 :args ((- 1.0) 1.0)) :args _let_66) :args _let_77) :args ((< _let_9 1))) :args (_let_72)) :args _let_76)) :args _let_76)) _let_75 :args (_let_72 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args _let_20) :args _let_34)) _let_33 :args (_let_70 false _let_32)) :args (_let_71 true _let_69 false _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_50)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO (MODUS_PONENS (AND_INTRO _let_64 _let_68) (SCOPE (FALSE_ELIM (TRANS (CONG _let_56 (REFL :args (_let_43)) :args _let_54) (FALSE_INTRO (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_65) (MACRO_SR_PRED_TRANSFORM _let_68 :args ((= (+ _let_13 (* (- 1) _let_43)) (- 1)))) :args _let_67) :args _let_66) :args _let_65)))) :args (_let_52 _let_44))) _let_64 (MODUS_PONENS (AND_INTRO _let_59 _let_61) (SCOPE (CONG _let_63 (TRANS (CONG _let_62 (REFL :args (_let_7)) :args (APPLY_UF tptp.append)) (SYMM (SYMM _let_59))) :args _let_58) :args (_let_45 _let_12)))) (SCOPE (FALSE_ELIM (TRANS (CONG _let_57 (SYMM (SYMM (ASSUME :args (_let_51)))) :args _let_54) (FALSE_INTRO (ASSUME :args (_let_53))))) :args (_let_53 _let_52 _let_51))) :args (_let_12 _let_45 _let_44))) :args (true _let_50)) :args ((or _let_49 _let_46 (not _let_45) (not _let_44)))) _let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (0 tptp.nil _let_7 QUANTIFIERS_INST_E_MATCHING ((tptp.append (tptp.cons I K) L)))) :args _let_47)) _let_48 :args (_let_45 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_18 :args (0 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons H T)))) :args _let_19))) _let_18 :args (_let_44 false _let_17)) :args (_let_46 false _let_12 false _let_45 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (0 0 tptp.nil _let_11 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.in N L) false)) (tptp.cons M K)))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_38 true _let_37 true _let_36 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_33 :args (0 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.count N L)))) :args _let_34))) _let_33 :args (_let_30 false _let_32)) :args (_let_31 true _let_29 false _let_30)) :args (_let_25 true _let_28 false _let_27 true _let_26)) :args (_let_16 false _let_25)) _let_24 _let_21 :args (false false _let_16 false _let_12 false _let_10)) :args ((forall ((K Int) (L tptp.list)) (= (tptp.head (tptp.cons K L)) K)) (forall ((K Int) (L tptp.list)) (= (tptp.tail (tptp.cons K L)) L)) (forall ((L tptp.list)) (or (= L tptp.nil) (= L (tptp.cons (tptp.head L) (tptp.tail L))))) (forall ((K Int) (L tptp.list)) (not (= (tptp.cons K L) tptp.nil))) (forall ((X Int) (L tptp.list)) (= (tptp.in X L) (or (exists ((H Int) (T tptp.list)) (and (= L (tptp.cons H T)) (= X H))) (exists ((H Int) (T tptp.list)) (and (= L (tptp.cons H T)) (tptp.in X T)))))) (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)))))) (= (tptp.length tptp.nil) 0) (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) _let_6 (forall ((K Int) (H Int) (T tptp.list) (N Int)) (=> (not (= K H)) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) _let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.63  )
% 0.21/0.63  % SZS output end Proof for DAT097_1
% 0.21/0.63  % cvc5---1.0.5 exiting
% 0.21/0.64  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------