%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT314^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 Feb 25 08:45:26 AM UTC 2026
% Result : Theorem 1.72s 1.41s
% Output : Refutation 1.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT314^1 : TPTP v9.2.1. Released v7.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n003.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 06:13:25 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : DAT314^1 : TPTP v9.2.1. Released v7.0.0.
% 0.32/0.47 % Domain : Analysis
% 0.32/0.47 % Problem : LENGTH_TL
% 0.32/0.47 % Version : Especial.
% 0.32/0.47 % English :
% 0.32/0.47
% 0.32/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.32/0.47 % Source : [Kal16]
% 0.32/0.47 % Names : LENGTH_TL_.p [Kal16]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.32/0.47 % Syntax : Number of formulae : 19 ( 6 unt; 11 typ; 0 def)
% 0.32/0.47 % Number of atoms : 8 ( 8 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 2 ( 1 avg)
% 0.32/0.47 % Number of connectives : 68 ( 1 ~; 0 |; 1 &; 63 @)
% 0.32/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 12 ( 4 avg)
% 0.32/0.47 % Number of types : 2 ( 1 usr)
% 0.32/0.47 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 11 ( 10 usr; 1 con; 0-3 aty)
% 0.32/0.47 % Number of variables : 22 ( 0 ^; 18 !; 0 ?; 22 :)
% 0.32/0.47 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.47 % SPC : TH1_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments : Exported from core HOL Light.
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 thf('thf_type_type/nums/num',type,
% 0.32/0.47 'type/nums/num': $tType ).
% 0.32/0.47
% 0.32/0.47 thf('thf_type_type/ind_types/list',type,
% 0.32/0.47 'type/ind_types/list': $tType > $tType ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/nums/SUC',type,
% 0.32/0.47 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/nums/NUMERAL',type,
% 0.32/0.47 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/nums/BIT1',type,
% 0.32/0.47 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/nums/_0',type,
% 0.32/0.47 'const/nums/_0': 'type/nums/num' ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/lists/TL',type,
% 0.32/0.47 'const/lists/TL':
% 0.32/0.47 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/lists/LENGTH',type,
% 0.32/0.47 'const/lists/LENGTH':
% 0.32/0.47 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > 'type/nums/num' ) ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/ind_types/NIL',type,
% 0.32/0.47 'const/ind_types/NIL':
% 0.32/0.47 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/ind_types/CONS',type,
% 0.32/0.47 'const/ind_types/CONS':
% 0.32/0.47 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/arith/-',type,
% 0.32/0.47 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 0.32/0.47
% 0.32/0.47 thf('thm/ind_types/list_INDUCT_',axiom,
% 0.32/0.47 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 0.32/0.47 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 0.32/0.47 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 0.32/0.47 ( ( P @ A1 )
% 0.32/0.47 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 0.32/0.47 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/arith/SUC_SUB1_',axiom,
% 0.32/0.47 ! [A: 'type/nums/num'] :
% 0.32/0.47 ( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
% 0.32/0.47 = A ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/lists/LENGTH_1',axiom,
% 0.32/0.47 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.32/0.47 ( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.32/0.47 = ( 'const/nums/SUC' @ ( 'const/lists/LENGTH' @ A @ A1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/lists/TL_',axiom,
% 0.32/0.47 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.32/0.47 ( ( 'const/lists/TL' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.32/0.47 = A1 ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/calc_num/ARITH_101',axiom,
% 0.32/0.47 ! [A: 'type/nums/num'] :
% 0.32/0.47 ( ( 'const/arith/-' @ 'const/nums/_0' @ ( 'const/nums/BIT1' @ A ) )
% 0.32/0.47 = 'const/nums/_0' ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/calc_num/ARITH_98',axiom,
% 0.32/0.47 ! [A: 'type/nums/num',A0: 'type/nums/num'] :
% 0.32/0.47 ( ( 'const/arith/-' @ ( 'const/nums/NUMERAL' @ A ) @ ( 'const/nums/NUMERAL' @ A0 ) )
% 0.32/0.47 = ( 'const/nums/NUMERAL' @ ( 'const/arith/-' @ A @ A0 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/lists/LENGTH_0',axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/NIL' @ A ) )
% 0.32/0.47 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/lists/LENGTH_TL_',conjecture,
% 0.32/0.47 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 0.32/0.47 ( ( A0
% 0.32/0.47 != ( 'const/ind_types/NIL' @ A ) )
% 0.32/0.47 => ( ( 'const/lists/LENGTH' @ A @ ( 'const/lists/TL' @ A @ A0 ) )
% 0.32/0.47 = ( 'const/arith/-' @ ( 'const/lists/LENGTH' @ A @ A0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 0.33/1.30 ---- Embedded in THF ---
% 0.33/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.33/1.30 %%% Generated on Tue Feb 24 06:13:26 EST 2026
% 0.33/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.33/1.30 %%% Logic specification used:
% 0.33/1.30 %%% thf(spec, logic, $$dhol).
% 0.33/1.30
% 0.33/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.A2JJAwxmrA/DTF2DTF1838.p
% 0.33/1.30 thf('thf_type_type/nums/num', type, 'type/nums/num': $tType).
% 0.33/1.30 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 0.33/1.30 thf('thf_const_const/nums/SUC', type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 0.33/1.30 thf('thf_const_const/nums/NUMERAL', type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.33/1.30 thf('thf_const_const/nums/BIT1', type, 'const/nums/BIT1': ('type/nums/num' > 'type/nums/num')).
% 0.33/1.30 thf('thf_const_const/nums/_0', type, 'const/nums/_0': 'type/nums/num').
% 0.33/1.30 thf('thf_const_const/lists/TL', type, 'const/lists/TL': (!> [A:$tType]: ((('type/ind_types/list' @ A) > ('type/ind_types/list' @ A))))).
% 0.33/1.30 thf('thf_const_const/lists/LENGTH', type, 'const/lists/LENGTH': (!> [A:$tType]: ((('type/ind_types/list' @ A) > 'type/nums/num')))).
% 0.33/1.30 thf('thf_const_const/ind_types/NIL', type, 'const/ind_types/NIL': (!> [A:$tType]: (('type/ind_types/list' @ A)))).
% 0.33/1.30 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 0.33/1.30 thf('thf_const_const/arith/-', type, 'const/arith/-': ('type/nums/num' > ('type/nums/num' > 'type/nums/num'))).
% 0.33/1.30 thf('thm/ind_types/list_INDUCT_', axiom, (! [A:$tType,P:(('type/ind_types/list' @ A) > $o)]: ((((P @ ('const/ind_types/NIL' @ A)) & (! [A0:A,A1:('type/ind_types/list' @ A)]: (((P @ A1) => (P @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)))))) => (! [A0:('type/ind_types/list' @ A)]: ((P @ A0))))))).
% 0.33/1.30 thf('thm/arith/SUC_SUB1_', axiom, (! [A:'type/nums/num']: (((('const/arith/-' @ ('const/nums/SUC' @ A)) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = A)))).
% 0.33/1.30 thf('thm/lists/LENGTH_1', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: (((('const/lists/LENGTH' @ A) @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)) = ('const/nums/SUC' @ (('const/lists/LENGTH' @ A) @ A1)))))).
% 0.33/1.30 thf('thm/lists/TL_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: (((('const/lists/TL' @ A) @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)) = A1)))).
% 0.33/1.30 thf('thm/calc_num/ARITH_101', axiom, (! [A:'type/nums/num']: (((('const/arith/-' @ 'const/nums/_0') @ ('const/nums/BIT1' @ A)) = 'const/nums/_0')))).
% 0.33/1.30 thf('thm/calc_num/ARITH_98', axiom, (! [A:'type/nums/num',A0:'type/nums/num']: (((('const/arith/-' @ ('const/nums/NUMERAL' @ A)) @ ('const/nums/NUMERAL' @ A0)) = ('const/nums/NUMERAL' @ (('const/arith/-' @ A) @ A0)))))).
% 0.33/1.30 thf('thm/lists/LENGTH_0', axiom, (! [A:$tType]: (((('const/lists/LENGTH' @ A) @ ('const/ind_types/NIL' @ A)) = ('const/nums/NUMERAL' @ 'const/nums/_0'))))).
% 0.33/1.30 thf('thm/lists/LENGTH_TL_', conjecture, (! [A:$tType,A0:('type/ind_types/list' @ A)]: (((A0 != ('const/ind_types/NIL' @ A)) => ((('const/lists/LENGTH' @ A) @ (('const/lists/TL' @ A) @ A0)) = (('const/arith/-' @ (('const/lists/LENGTH' @ A) @ A0)) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))))).
% 0.33/1.30 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.A2JJAwxmrA/DTF2DTF1838.p
% 0.33/1.30 ------------------------
% 0.33/1.31 ---- Cleaned THF ---
% 0.33/1.31 thf('thf_type_type/nums/num',type,
% 0.33/1.31 'type/nums/num': $tType ).
% 0.33/1.31
% 0.33/1.31 thf('thf_type_type/ind_types/list',type,
% 0.33/1.31 'type/ind_types/list': $tType > $tType ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/nums/SUC',type,
% 0.33/1.31 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/nums/NUMERAL',type,
% 0.33/1.31 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/nums/BIT1',type,
% 0.33/1.31 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/nums/_0',type,
% 0.33/1.31 'const/nums/_0': 'type/nums/num' ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/lists/TL',type,
% 0.33/1.31 'const/lists/TL':
% 0.33/1.31 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/lists/LENGTH',type,
% 0.33/1.31 'const/lists/LENGTH':
% 0.33/1.31 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > 'type/nums/num' ) ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/ind_types/NIL',type,
% 0.33/1.31 'const/ind_types/NIL':
% 0.33/1.31 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/ind_types/CONS',type,
% 0.33/1.31 'const/ind_types/CONS':
% 0.33/1.31 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.33/1.31
% 0.33/1.31 thf('thf_const_const/arith/-',type,
% 0.33/1.31 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
% 0.33/1.31
% 0.33/1.31 thf('thm/ind_types/list_INDUCT_',axiom,
% 0.33/1.31 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 0.33/1.31 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 0.33/1.31 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 0.33/1.31 ( ( P @ A1 )
% 0.33/1.31 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 0.33/1.31 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 0.33/1.31
% 0.33/1.31 thf('thm/arith/SUC_SUB1_',axiom,
% 0.33/1.31 ! [A: 'type/nums/num'] :
% 0.33/1.31 ( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
% 0.33/1.31 = A ) ).
% 0.33/1.31
% 0.33/1.31 thf('thm/lists/LENGTH_1',axiom,
% 0.33/1.31 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.33/1.31 ( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.33/1.31 = ( 'const/nums/SUC' @ ( 'const/lists/LENGTH' @ A @ A1 ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf('thm/lists/TL_',axiom,
% 0.33/1.31 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.33/1.31 ( ( 'const/lists/TL' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.33/1.31 = A1 ) ).
% 0.33/1.31
% 0.33/1.31 thf('thm/calc_num/ARITH_101',axiom,
% 0.33/1.31 ! [A: 'type/nums/num'] :
% 0.33/1.31 ( ( 'const/arith/-' @ 'const/nums/_0' @ ( 'const/nums/BIT1' @ A ) )
% 0.33/1.31 = 'const/nums/_0' ) ).
% 0.33/1.31
% 0.33/1.31 thf('thm/calc_num/ARITH_98',axiom,
% 0.33/1.31 ! [A: 'type/nums/num',A0: 'type/nums/num'] :
% 0.33/1.31 ( ( 'const/arith/-' @ ( 'const/nums/NUMERAL' @ A ) @ ( 'const/nums/NUMERAL' @ A0 ) )
% 0.33/1.31 = ( 'const/nums/NUMERAL' @ ( 'const/arith/-' @ A @ A0 ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf('thm/lists/LENGTH_0',axiom,
% 0.33/1.31 ! [A: $tType] :
% 0.33/1.31 ( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/NIL' @ A ) )
% 0.33/1.31 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
% 0.33/1.31
% 0.33/1.31 thf('thm/lists/LENGTH_TL_',conjecture,
% 0.33/1.31 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 0.33/1.31 ( ( A0
% 0.33/1.31 != ( 'const/ind_types/NIL' @ A ) )
% 0.33/1.31 => ( ( 'const/lists/LENGTH' @ A @ ( 'const/lists/TL' @ A @ A0 ) )
% 0.33/1.31 = ( 'const/arith/-' @ ( 'const/lists/LENGTH' @ A @ A0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ).
% 0.33/1.31 ------------------------
% 0.33/1.33 % (2181)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/2Mi)
% 0.33/1.33 % Exception at run slice level
% 0.33/1.33 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.33/1.33 % (2179)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/27Mi)
% 0.33/1.33 % (2179)Refutation not found, incomplete strategy
% 0.33/1.33 % (2179)------------------------------
% 0.33/1.33 % (2179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.33 % (2179)Termination reason: Refutation not found, incomplete strategy
% 0.33/1.33
% 0.33/1.33
% 0.33/1.33 % (2179)Memory used [KB]: 5500
% 0.33/1.33 % (2179)Time elapsed: 0.004 s
% 0.33/1.33 % (2179)Instructions burned: 6 (million)
% 0.33/1.33 % (2179)------------------------------
% 0.33/1.33 % (2179)------------------------------
% 0.33/1.33 % (2177)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/183Mi)
% 0.33/1.33 % (2178)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/4Mi)
% 0.33/1.34 % (2180)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/2Mi)
% 0.33/1.34 % (2182)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/275Mi)
% 0.33/1.34 % (2183)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/18Mi)
% 0.33/1.34 % (2180)Instruction limit reached!
% 0.33/1.34 % (2180)------------------------------
% 0.33/1.34 % (2180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.34 % (2180)Termination reason: Unknown
% 0.33/1.34 % (2180)Termination phase: Preprocessing 3
% 0.33/1.34
% 0.33/1.34 % (2180)Memory used [KB]: 895
% 0.33/1.34 % (2180)Time elapsed: 0.003 s
% 0.33/1.34 % (2180)Instructions burned: 2 (million)
% 0.33/1.34 % (2180)------------------------------
% 0.33/1.34 % (2180)------------------------------
% 0.33/1.34 % (2182)Refutation not found, incomplete strategy
% 0.33/1.34 % (2182)------------------------------
% 0.33/1.34 % (2182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.34 % (2182)Termination reason: Refutation not found, incomplete strategy
% 0.33/1.34
% 0.33/1.34
% 0.33/1.34 % (2182)Memory used [KB]: 5500
% 0.33/1.34 % (2182)Time elapsed: 0.004 s
% 0.33/1.34 % (2182)Instructions burned: 2 (million)
% 0.33/1.34 % (2182)------------------------------
% 0.33/1.34 % (2182)------------------------------
% 0.33/1.34 % (2184)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/3Mi)
% 0.33/1.34 % (2178)Instruction limit reached!
% 0.33/1.34 % (2178)------------------------------
% 0.33/1.34 % (2178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.34 % (2178)Termination reason: Unknown
% 0.33/1.34 % (2178)Termination phase: Saturation
% 0.33/1.34
% 0.33/1.34 % (2178)Memory used [KB]: 5500
% 0.33/1.34 % (2178)Time elapsed: 0.005 s
% 0.33/1.34 % (2178)Instructions burned: 5 (million)
% 0.33/1.34 % (2178)------------------------------
% 0.33/1.34 % (2178)------------------------------
% 0.33/1.34 % (2184)Instruction limit reached!
% 0.33/1.34 % (2184)------------------------------
% 0.33/1.34 % (2184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.34 % (2184)Termination reason: Unknown
% 0.33/1.34 % (2184)Termination phase: Saturation
% 0.33/1.34
% 0.33/1.34 % (2184)Memory used [KB]: 5500
% 0.33/1.34 % (2184)Time elapsed: 0.002 s
% 0.33/1.34 % (2184)Instructions burned: 3 (million)
% 0.33/1.34 % (2184)------------------------------
% 0.33/1.34 % (2184)------------------------------
% 0.33/1.34 % (2185)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/37Mi)
% 0.33/1.34 % Exception at run slice level
% 0.33/1.34 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.33/1.35 % (2183)Instruction limit reached!
% 0.33/1.35 % (2183)------------------------------
% 0.33/1.35 % (2183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.35 % (2183)Termination reason: Unknown
% 0.33/1.35 % (2183)Termination phase: Saturation
% 0.33/1.35
% 0.33/1.35 % (2183)Memory used [KB]: 5628
% 0.33/1.35 % (2183)Time elapsed: 0.014 s
% 0.33/1.35 % (2183)Instructions burned: 18 (million)
% 0.33/1.35 % (2183)------------------------------
% 0.33/1.35 % (2183)------------------------------
% 0.33/1.35 % (2189)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/7Mi)
% 0.33/1.35 % (2189)Instruction limit reached!
% 0.33/1.35 % (2189)------------------------------
% 0.33/1.35 % (2189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.35 % (2189)Termination reason: Unknown
% 0.33/1.35 % (2189)Termination phase: Saturation
% 0.33/1.35
% 0.33/1.35 % (2189)Memory used [KB]: 1023
% 0.33/1.35 % (2189)Time elapsed: 0.004 s
% 0.33/1.35 % (2189)Instructions burned: 8 (million)
% 0.33/1.35 % (2189)------------------------------
% 0.33/1.35 % (2189)------------------------------
% 0.33/1.35 % (2190)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/16Mi)
% 0.33/1.35 % (2186)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/15Mi)
% 0.33/1.36 % (2187)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/3Mi)
% 0.33/1.36 % (2188)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/1041Mi)
% 0.33/1.36 % (2186)Refutation not found, incomplete strategy
% 0.33/1.36 % (2186)------------------------------
% 0.33/1.36 % (2186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.36 % (2186)Termination reason: Refutation not found, incomplete strategy
% 0.33/1.36
% 0.33/1.36
% 0.33/1.36 % (2186)Memory used [KB]: 5500
% 0.33/1.36 % (2186)Time elapsed: 0.004 s
% 0.33/1.36 % (2186)Instructions burned: 3 (million)
% 0.33/1.36 % (2186)------------------------------
% 0.33/1.36 % (2186)------------------------------
% 0.33/1.36 % Exception at run slice level
% 0.33/1.36 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.33/1.36 % (2187)Instruction limit reached!
% 0.33/1.36 % (2187)------------------------------
% 0.33/1.36 % (2187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.36 % (2187)Termination reason: Unknown
% 0.33/1.36 % (2187)Termination phase: Saturation
% 0.33/1.36
% 0.33/1.36 % (2187)Memory used [KB]: 5500
% 0.33/1.36 % (2187)Time elapsed: 0.004 s
% 0.33/1.36 % (2187)Instructions burned: 3 (million)
% 0.33/1.36 % (2187)------------------------------
% 0.33/1.36 % (2187)------------------------------
% 0.33/1.36 % (2190)Instruction limit reached!
% 0.33/1.36 % (2190)------------------------------
% 0.33/1.36 % (2190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.36 % (2190)Termination reason: Unknown
% 0.33/1.36 % (2190)Termination phase: Saturation
% 0.33/1.36
% 0.33/1.36 % (2190)Memory used [KB]: 5628
% 0.33/1.36 % (2190)Time elapsed: 0.008 s
% 0.33/1.36 % (2190)Instructions burned: 16 (million)
% 0.33/1.36 % (2190)------------------------------
% 0.33/1.36 % (2190)------------------------------
% 0.33/1.36 % (2192)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/3Mi)
% 0.33/1.36 % (2192)Instruction limit reached!
% 0.33/1.36 % (2192)------------------------------
% 0.33/1.36 % (2192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.36 % (2192)Termination reason: Unknown
% 0.33/1.36 % (2192)Termination phase: Property scanning
% 0.33/1.36
% 0.33/1.36 % (2192)Memory used [KB]: 1023
% 0.33/1.36 % (2192)Time elapsed: 0.002 s
% 0.33/1.36 % (2192)Instructions burned: 3 (million)
% 0.33/1.36 % (2192)------------------------------
% 0.33/1.36 % (2192)------------------------------
% 0.33/1.36 % (2191)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/3Mi)
% 0.33/1.37 % (2191)Instruction limit reached!
% 0.33/1.37 % (2191)------------------------------
% 0.33/1.37 % (2191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.37 % (2191)Termination reason: Unknown
% 0.33/1.37 % (2191)Termination phase: Saturation
% 0.33/1.37
% 0.33/1.37 % (2191)Memory used [KB]: 5500
% 0.33/1.37 % (2191)Time elapsed: 0.004 s
% 0.33/1.37 % (2191)Instructions burned: 3 (million)
% 0.33/1.37 % (2191)------------------------------
% 0.33/1.37 % (2191)------------------------------
% 0.33/1.37 % (2196)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/18Mi)
% 0.33/1.37 % (2197)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/710Mi)
% 0.33/1.37 % (2196)Refutation not found, incomplete strategy
% 0.33/1.37 % (2196)------------------------------
% 0.33/1.37 % (2196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.37 % (2196)Termination reason: Refutation not found, incomplete strategy
% 0.33/1.37
% 0.33/1.37
% 0.33/1.37 % (2196)Memory used [KB]: 5500
% 0.33/1.37 % (2196)Time elapsed: 0.004 s
% 0.33/1.37 % (2196)Instructions burned: 6 (million)
% 0.33/1.37 % (2196)------------------------------
% 0.33/1.37 % (2196)------------------------------
% 0.33/1.37 % (2193)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/7Mi)
% 0.33/1.37 % (2194)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/3Mi)
% 0.33/1.37 % (2195)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/4Mi)
% 0.33/1.37 % Exception at run slice level
% 0.33/1.37 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.33/1.38 % (2195)Instruction limit reached!
% 0.33/1.38 % (2195)------------------------------
% 0.33/1.38 % (2195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.38 % (2195)Termination reason: Unknown
% 0.33/1.38 % (2195)Termination phase: Saturation
% 0.33/1.38
% 0.33/1.38 % (2195)Memory used [KB]: 5500
% 0.33/1.38 % (2195)Time elapsed: 0.005 s
% 0.33/1.38 % (2195)Instructions burned: 4 (million)
% 0.33/1.38 % (2195)------------------------------
% 0.33/1.38 % (2195)------------------------------
% 0.33/1.38 % (2193)Instruction limit reached!
% 0.33/1.38 % (2193)------------------------------
% 0.33/1.38 % (2193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.38 % (2193)Termination reason: Unknown
% 0.33/1.38 % (2193)Termination phase: Saturation
% 0.33/1.38
% 0.33/1.38 % (2193)Memory used [KB]: 5500
% 0.33/1.38 % (2193)Time elapsed: 0.007 s
% 0.33/1.38 % (2193)Instructions burned: 8 (million)
% 0.33/1.38 % (2193)------------------------------
% 0.33/1.38 % (2193)------------------------------
% 0.33/1.38 % (2198)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/6Mi)
% 0.33/1.38 % (2199)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/902Mi)
% 0.33/1.38 % (2199)Refutation not found, incomplete strategy
% 0.33/1.38 % (2199)------------------------------
% 0.33/1.38 % (2199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.38 % (2199)Termination reason: Refutation not found, incomplete strategy
% 0.33/1.38
% 0.33/1.38
% 0.33/1.38 % (2199)Memory used [KB]: 5500
% 0.33/1.38 % (2199)Time elapsed: 0.002 s
% 0.33/1.38 % (2199)Instructions burned: 1 (million)
% 0.33/1.38 % (2199)------------------------------
% 0.33/1.38 % (2199)------------------------------
% 0.33/1.38 % (2198)Instruction limit reached!
% 0.33/1.38 % (2198)------------------------------
% 0.33/1.38 % (2198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.38 % (2198)Termination reason: Unknown
% 0.33/1.38 % (2198)Termination phase: Saturation
% 0.33/1.38
% 0.33/1.38 % (2198)Memory used [KB]: 5500
% 0.33/1.38 % (2198)Time elapsed: 0.004 s
% 0.33/1.38 % (2198)Instructions burned: 7 (million)
% 0.33/1.38 % (2198)------------------------------
% 0.33/1.38 % (2198)------------------------------
% 0.33/1.39 % (2200)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/21Mi)
% 0.33/1.39 % (2203)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/377Mi)
% 0.33/1.39 % (2204)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/779Mi)
% 0.33/1.39 % Exception at run slice level
% 0.33/1.39 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.33/1.39 % (2201)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/5Mi)
% 0.33/1.40 % Exception at run slice level
% 0.33/1.40 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.72/1.40 % (2202)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/6Mi)
% 1.72/1.40 % Exception at run slice level
% 1.72/1.40 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.72/1.40 % (2205)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_1838 for (2999ds/19Mi)
% 1.72/1.40 % Exception at run slice level
% 1.72/1.40 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.72/1.40 % (2203)First to succeed.
% 1.72/1.41 % (2200)Instruction limit reached!
% 1.72/1.41 % (2200)------------------------------
% 1.72/1.41 % (2200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (2200)Termination reason: Unknown
% 1.72/1.41 % (2200)Termination phase: Saturation
% 1.72/1.41
% 1.72/1.41 % (2200)Memory used [KB]: 5628
% 1.72/1.41 % (2200)Time elapsed: 0.016 s
% 1.72/1.41 % (2200)Instructions burned: 22 (million)
% 1.72/1.41 % (2200)------------------------------
% 1.72/1.41 % (2200)------------------------------
% 1.72/1.41 % (2203)Refutation found. Thanks to Tanya!
% 1.72/1.41 % SZS status Theorem for DTF2THF_1838
% 1.72/1.41 % SZS output start Proof for DTF2THF_1838
% 1.72/1.41 thf(type_def_5, type, 'type/nums/num': $tType).
% 1.72/1.41 thf(type_def_7, type, 'type/ind_types/list': ($tType) > $tType).
% 1.72/1.41 thf(type_def_8, type, sK0: $tType).
% 1.72/1.41 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.72/1.41 thf(func_def_1, type, 'type/ind_types/list': ($tType) > $tType).
% 1.72/1.41 thf(func_def_2, type, 'const/nums/SUC': 'type/nums/num' > 'type/nums/num').
% 1.72/1.41 thf(func_def_3, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.72/1.41 thf(func_def_4, type, 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num').
% 1.72/1.41 thf(func_def_5, type, 'const/nums/_0': 'type/nums/num').
% 1.72/1.41 thf(func_def_6, type, 'const/lists/TL': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.72/1.41 thf(func_def_7, type, 'const/lists/LENGTH': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/nums/num')).
% 1.72/1.41 thf(func_def_8, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 1.72/1.41 thf(func_def_9, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.72/1.41 thf(func_def_10, type, 'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num').
% 1.72/1.41 thf(func_def_14, type, sK1: 'type/ind_types/list' @ sK0).
% 1.72/1.41 thf(func_def_15, type, sK2: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > X0)).
% 1.72/1.41 thf(func_def_16, type, sK3: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0)).
% 1.72/1.41 thf(func_def_19, type, ph5: !>[X0: $tType]:(X0)).
% 1.72/1.41 thf(f212,plain,(
% 1.72/1.41 $false),
% 1.72/1.41 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.72/1.41 thf(f207,plain,(
% 1.72/1.41 (sK1 != sK1)),
% 1.72/1.41 inference(superposition,[status(thm)],[f28,f203])).
% 1.72/1.41 thf(f203,plain,(
% 1.72/1.41 (sK1 = 'const/ind_types/NIL' @ sK0)),
% 1.72/1.41 inference(trivial_inequality_removal,[status(thm)],[f201])).
% 1.72/1.41 thf(f201,plain,(
% 1.72/1.41 (('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1)) != ('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1))) | (sK1 = 'const/ind_types/NIL' @ sK0)),
% 1.72/1.41 inference(superposition,[status(thm)],[f29,f196])).
% 1.72/1.41 thf(f196,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = ('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.72/1.41 inference(superposition,[status(thm)],[f33,f194])).
% 1.72/1.41 thf(f194,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) = ('const/lists/LENGTH' @ X0 @ X1)) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.72/1.41 inference(duplicate_literal_removal,[status(thm)],[f192])).
% 1.72/1.41 thf(f192,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ('const/ind_types/NIL' @ X0 = X1) | (('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) = ('const/lists/LENGTH' @ X0 @ X1))) )),
% 1.72/1.41 inference(superposition,[status(thm)],[f124,f125])).
% 1.72/1.41 thf(f125,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/TL' @ X0 @ X1) = (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.72/1.41 inference(superposition,[status(thm)],[f27,f76])).
% 1.72/1.41 thf(f76,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.72/1.41 inference(equality_proxy_clausification,[status(thm)],[f75])).
% 1.72/1.41 thf(f75,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((X1 = 'const/ind_types/NIL' @ X0) = $true) | (('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1)) )),
% 1.72/1.41 inference(not_proxy_clausification,[status(thm)],[f74])).
% 1.72/1.41 thf(f74,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ((~ (X1 = 'const/ind_types/NIL' @ X0)) != $true)) )),
% 1.72/1.41 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.72/1.41 thf(f68,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (($true != ((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))) @ 'const/ind_types/NIL' @ X0)) | (('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1)) )),
% 1.72/1.41 inference(leibniz_equality_elimination,[status(thm)],[f31])).
% 1.72/1.41 thf(f31,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))) != $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ((X1 @ X2) = $true)) )),
% 1.72/1.41 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.41 thf(f24,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ! [X2 : 'type/ind_types/list' @ X0] : ((X1 @ X2) = $true) | (((X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))) != $true) & ((X1 @ (sK3 @ X0 @ X1)) = $true)))),
% 1.72/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f22,f23])).
% 1.72/1.41 thf(f23,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)) != $true) & ($true = (X1 @ X4))) => (((X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))) != $true) & ((X1 @ (sK3 @ X0 @ X1)) = $true)))),
% 1.72/1.41 introduced(definition,[],[choice_axiom])).
% 1.72/1.41 thf(f22,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ! [X2 : 'type/ind_types/list' @ X0] : ((X1 @ X2) = $true) | ? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)) != $true) & ($true = (X1 @ X4))))),
% 1.72/1.41 inference(rectify,[status(thm)],[f19])).
% 1.72/1.41 thf(f19,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true) & ((X1 @ X3) = $true)))),
% 1.72/1.41 inference(flattening,[status(thm)],[f18])).
% 1.72/1.41 thf(f18,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)) | (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true) & ((X1 @ X3) = $true))))),
% 1.72/1.41 inference(ennf_transformation,[status(thm)],[f12])).
% 1.72/1.41 thf(f12,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : ((((X1 @ 'const/ind_types/NIL' @ X0) = $true) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ X3) = $true) => ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) = $true))) => ! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)))),
% 1.72/1.41 inference(fool_elimination,[status(thm)],[f11])).
% 1.72/1.41 thf(f11,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 1.72/1.41 inference(rectify,[status(thm)],[f1])).
% 1.72/1.41 thf(f1,axiom,(
% 1.72/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 1.72/1.41 file('/export/starexec/sandbox/tmp/tmp.A2JJAwxmrA/DTF2THF_1838.p','thm/ind_types/list_INDUCT_')).
% 1.72/1.41 thf(f27,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = X2)) )),
% 1.72/1.41 inference(cnf_transformation,[status(thm)],[f16])).
% 1.72/1.41 thf(f16,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = X2)),
% 1.72/1.41 inference(rectify,[status(thm)],[f4])).
% 1.72/1.41 thf(f4,axiom,(
% 1.72/1.41 ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) = X3)),
% 1.72/1.41 file('/export/starexec/sandbox/tmp/tmp.A2JJAwxmrA/DTF2THF_1838.p','thm/lists/TL_')).
% 1.72/1.41 thf(f124,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))))) = ('const/lists/LENGTH' @ X0 @ X1)) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.72/1.41 inference(superposition,[status(thm)],[f32,f76])).
% 1.72/1.41 thf(f32,plain,(
% 1.72/1.41 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = ('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2)))) )),
% 1.72/1.41 inference(cnf_transformation,[status(thm)],[f14])).
% 1.72/1.41 thf(f14,plain,(
% 1.72/1.41 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = ('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2)))),
% 1.72/1.41 inference(rectify,[status(thm)],[f3])).
% 1.72/1.41 thf(f3,axiom,(
% 1.72/1.41 ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) = ('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X3)))),
% 1.72/1.41 file('/export/starexec/sandbox/tmp/tmp.A2JJAwxmrA/DTF2THF_1838.p','thm/lists/LENGTH_1')).
% 1.72/1.41 thf(f33,plain,(
% 1.72/1.41 ( ! [X0 : 'type/nums/num'] : ((('const/arith/-' @ ('const/nums/SUC' @ X0) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = X0)) )),
% 1.72/1.41 inference(cnf_transformation,[status(thm)],[f2])).
% 1.72/1.41 thf(f2,axiom,(
% 1.72/1.41 ! [X0 : 'type/nums/num'] : (('const/arith/-' @ ('const/nums/SUC' @ X0) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = X0)),
% 1.72/1.41 file('/export/starexec/sandbox/tmp/tmp.A2JJAwxmrA/DTF2THF_1838.p','thm/arith/SUC_SUB1_')).
% 1.72/1.41 thf(f29,plain,(
% 1.72/1.41 (('const/arith/-' @ ('const/lists/LENGTH' @ sK0 @ sK1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != ('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1)))),
% 1.72/1.41 inference(cnf_transformation,[status(thm)],[f21])).
% 1.72/1.41 thf(f21,plain,(
% 1.72/1.41 (('const/arith/-' @ ('const/lists/LENGTH' @ sK0 @ sK1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != ('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1))) & (sK1 != 'const/ind_types/NIL' @ sK0)),
% 1.72/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f20])).
% 1.72/1.41 thf(f20,plain,(
% 1.72/1.41 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != ('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) & ('const/ind_types/NIL' @ X0 != X1)) => ((('const/arith/-' @ ('const/lists/LENGTH' @ sK0 @ sK1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != ('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1))) & (sK1 != 'const/ind_types/NIL' @ sK0))),
% 1.72/1.41 introduced(definition,[],[choice_axiom])).
% 1.72/1.41 thf(f17,plain,(
% 1.72/1.41 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) != ('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) & ('const/ind_types/NIL' @ X0 != X1))),
% 1.72/1.41 inference(ennf_transformation,[status(thm)],[f13])).
% 1.72/1.41 thf(f13,plain,(
% 1.72/1.41 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X1) => (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) = ('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))))),
% 1.72/1.41 inference(rectify,[status(thm)],[f9])).
% 1.72/1.41 thf(f9,negated_conjecture,(
% 1.72/1.41 ~! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X2) => (('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X2)) = ('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X2) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),
% 1.72/1.41 inference(negated_conjecture,[status(cth)],[f8])).
% 1.72/1.41 thf(f8,conjecture,(
% 1.72/1.41 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X2) => (('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X2)) = ('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X2) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),
% 1.72/1.41 file('/export/starexec/sandbox/tmp/tmp.A2JJAwxmrA/DTF2THF_1838.p','thm/lists/LENGTH_TL_')).
% 1.72/1.41 thf(f28,plain,(
% 1.72/1.41 (sK1 != 'const/ind_types/NIL' @ sK0)),
% 1.72/1.41 inference(cnf_transformation,[status(thm)],[f21])).
% 1.72/1.41 % SZS output end Proof for DTF2THF_1838
% 1.72/1.41 % (2203)------------------------------
% 1.72/1.41 % (2203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (2203)Termination reason: Refutation
% 1.72/1.41
% 1.72/1.41 % (2203)Memory used [KB]: 5628
% 1.72/1.41 % (2203)Time elapsed: 0.014 s
% 1.72/1.41 % (2203)Instructions burned: 32 (million)
% 1.72/1.41 % (2203)------------------------------
% 1.72/1.41 % (2203)------------------------------
% 1.72/1.41 % (2176)Success in time 0.076 s
%------------------------------------------------------------------------------