%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT290^1 : 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 08:45:23 AM UTC 2026
% Result : Theorem 1.62s 1.35s
% Output : Refutation 1.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT290^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % 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 06:13:55 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : DAT290^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.48 % Domain : Analysis
% 0.20/0.48 % Problem : LENGTH_EQ_NIL
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Kal16]
% 0.20/0.48 % Names : LENGTH_EQ_NIL_.p [Kal16]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.20/0.48 % Syntax : Number of formulae : 14 ( 5 unt; 8 typ; 0 def)
% 0.20/0.48 % Number of atoms : 7 ( 7 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.48 % Number of connectives : 45 ( 2 ~; 0 |; 1 &; 40 @)
% 0.20/0.48 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 12 ( 5 avg)
% 0.20/0.48 % Number of types : 2 ( 1 usr)
% 0.20/0.48 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 8 ( 7 usr; 1 con; 0-3 aty)
% 0.20/0.48 % Number of variables : 18 ( 0 ^; 15 !; 0 ?; 18 :)
% 0.20/0.48 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.48 % SPC : TH1_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : Exported from core HOL Light.
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf('thf_type_type/nums/num',type,
% 0.20/0.48 'type/nums/num': $tType ).
% 0.20/0.48
% 0.20/0.48 thf('thf_type_type/ind_types/list',type,
% 0.20/0.48 'type/ind_types/list': $tType > $tType ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/nums/SUC',type,
% 0.20/0.48 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/nums/NUMERAL',type,
% 0.20/0.48 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/nums/_0',type,
% 0.20/0.48 'const/nums/_0': 'type/nums/num' ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/lists/LENGTH',type,
% 0.20/0.48 'const/lists/LENGTH':
% 0.20/0.48 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > 'type/nums/num' ) ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/ind_types/NIL',type,
% 0.20/0.48 'const/ind_types/NIL':
% 0.20/0.48 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.20/0.48
% 0.20/0.48 thf('thf_const_const/ind_types/CONS',type,
% 0.20/0.48 'const/ind_types/CONS':
% 0.20/0.48 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/ind_types/list_INDUCT_',axiom,
% 0.20/0.48 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 0.20/0.48 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 0.20/0.48 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 0.20/0.48 ( ( P @ A1 )
% 0.20/0.48 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 0.20/0.48 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/lists/NOT_CONS_NIL_',axiom,
% 0.20/0.48 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.20/0.48 ( ( 'const/ind_types/CONS' @ A @ A0 @ A1 )
% 0.20/0.48 != ( 'const/ind_types/NIL' @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/nums/NOT_SUC_',axiom,
% 0.20/0.48 ! [A: 'type/nums/num'] :
% 0.20/0.48 ( ( 'const/nums/SUC' @ A )
% 0.20/0.48 != ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/lists/LENGTH_1',axiom,
% 0.20/0.48 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.20/0.48 ( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.20/0.48 = ( 'const/nums/SUC' @ ( 'const/lists/LENGTH' @ A @ A1 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/lists/LENGTH_0',axiom,
% 0.20/0.48 ! [A: $tType] :
% 0.20/0.48 ( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/NIL' @ A ) )
% 0.20/0.48 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
% 0.20/0.48
% 0.20/0.48 thf('thm/lists/LENGTH_EQ_NIL_',conjecture,
% 0.20/0.48 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 0.20/0.48 ( ( ( 'const/lists/LENGTH' @ A @ A0 )
% 0.20/0.48 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 0.20/0.48 = ( A0
% 0.20/0.48 = ( 'const/ind_types/NIL' @ A ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.53/1.24 ---- Embedded in THF ---
% 1.53/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.24 %%% Generated on Tue Feb 24 06:13:56 EST 2026
% 1.53/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.24 %%% Logic specification used:
% 1.53/1.24 %%% thf(spec, logic, $$dhol).
% 1.53/1.24
% 1.53/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.pyMgmxYXgP/DTF2DTF4381.p
% 1.53/1.24 thf('thf_type_type/nums/num', type, 'type/nums/num': $tType).
% 1.53/1.24 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.53/1.24 thf('thf_const_const/nums/SUC', type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 1.53/1.24 thf('thf_const_const/nums/NUMERAL', type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 1.53/1.24 thf('thf_const_const/nums/_0', type, 'const/nums/_0': 'type/nums/num').
% 1.53/1.24 thf('thf_const_const/lists/LENGTH', type, 'const/lists/LENGTH': (!> [A:$tType]: ((('type/ind_types/list' @ A) > 'type/nums/num')))).
% 1.53/1.24 thf('thf_const_const/ind_types/NIL', type, 'const/ind_types/NIL': (!> [A:$tType]: (('type/ind_types/list' @ A)))).
% 1.53/1.24 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.53/1.24 thf('thm/ind_types/list_INDUCT_', axiom, (! [A:$tType,P:(('type/ind_types/list' @ A) > $o)]: ((((P @ ('const/ind_types/NIL' @ A)) & (! [A0:A,A1:('type/ind_types/list' @ A)]: (((P @ A1) => (P @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)))))) => (! [A0:('type/ind_types/list' @ A)]: ((P @ A0))))))).
% 1.53/1.24 thf('thm/lists/NOT_CONS_NIL_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: ((((('const/ind_types/CONS' @ A) @ A0) @ A1) != ('const/ind_types/NIL' @ A))))).
% 1.53/1.24 thf('thm/nums/NOT_SUC_', axiom, (! [A:'type/nums/num']: ((('const/nums/SUC' @ A) != ('const/nums/NUMERAL' @ 'const/nums/_0'))))).
% 1.53/1.24 thf('thm/lists/LENGTH_1', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: (((('const/lists/LENGTH' @ A) @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)) = ('const/nums/SUC' @ (('const/lists/LENGTH' @ A) @ A1)))))).
% 1.53/1.24 thf('thm/lists/LENGTH_0', axiom, (! [A:$tType]: (((('const/lists/LENGTH' @ A) @ ('const/ind_types/NIL' @ A)) = ('const/nums/NUMERAL' @ 'const/nums/_0'))))).
% 1.53/1.24 thf('thm/lists/LENGTH_EQ_NIL_', conjecture, (! [A:$tType,A0:('type/ind_types/list' @ A)]: ((((('const/lists/LENGTH' @ A) @ A0) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (A0 = ('const/ind_types/NIL' @ A)))))).
% 1.53/1.24 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.pyMgmxYXgP/DTF2DTF4381.p
% 1.53/1.24 ------------------------
% 1.53/1.25 ---- Cleaned THF ---
% 1.53/1.25 thf('thf_type_type/nums/num',type,
% 1.53/1.25 'type/nums/num': $tType ).
% 1.53/1.25
% 1.53/1.25 thf('thf_type_type/ind_types/list',type,
% 1.53/1.25 'type/ind_types/list': $tType > $tType ).
% 1.53/1.25
% 1.53/1.25 thf('thf_const_const/nums/SUC',type,
% 1.53/1.25 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 1.53/1.25
% 1.53/1.25 thf('thf_const_const/nums/NUMERAL',type,
% 1.53/1.25 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.53/1.25
% 1.53/1.25 thf('thf_const_const/nums/_0',type,
% 1.53/1.25 'const/nums/_0': 'type/nums/num' ).
% 1.53/1.25
% 1.53/1.25 thf('thf_const_const/lists/LENGTH',type,
% 1.53/1.25 'const/lists/LENGTH':
% 1.53/1.25 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > 'type/nums/num' ) ).
% 1.53/1.25
% 1.53/1.25 thf('thf_const_const/ind_types/NIL',type,
% 1.53/1.25 'const/ind_types/NIL':
% 1.53/1.25 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 1.53/1.25
% 1.53/1.25 thf('thf_const_const/ind_types/CONS',type,
% 1.53/1.25 'const/ind_types/CONS':
% 1.53/1.25 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.53/1.25
% 1.53/1.25 thf('thm/ind_types/list_INDUCT_',axiom,
% 1.53/1.25 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 1.53/1.25 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 1.53/1.25 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 1.53/1.25 ( ( P @ A1 )
% 1.53/1.25 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 1.53/1.25 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 1.53/1.25
% 1.53/1.25 thf('thm/lists/NOT_CONS_NIL_',axiom,
% 1.53/1.25 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.53/1.25 ( ( 'const/ind_types/CONS' @ A @ A0 @ A1 )
% 1.53/1.25 != ( 'const/ind_types/NIL' @ A ) ) ).
% 1.53/1.25
% 1.53/1.25 thf('thm/nums/NOT_SUC_',axiom,
% 1.53/1.25 ! [A: 'type/nums/num'] :
% 1.53/1.25 ( ( 'const/nums/SUC' @ A )
% 1.53/1.25 != ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
% 1.53/1.25
% 1.53/1.25 thf('thm/lists/LENGTH_1',axiom,
% 1.53/1.25 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.53/1.25 ( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 1.53/1.25 = ( 'const/nums/SUC' @ ( 'const/lists/LENGTH' @ A @ A1 ) ) ) ).
% 1.53/1.25
% 1.53/1.25 thf('thm/lists/LENGTH_0',axiom,
% 1.53/1.25 ! [A: $tType] :
% 1.53/1.25 ( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/NIL' @ A ) )
% 1.53/1.25 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
% 1.53/1.25
% 1.53/1.25 thf('thm/lists/LENGTH_EQ_NIL_',conjecture,
% 1.53/1.25 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 1.53/1.25 ( ( ( 'const/lists/LENGTH' @ A @ A0 )
% 1.53/1.25 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 1.53/1.25 = ( A0
% 1.53/1.25 = ( 'const/ind_types/NIL' @ A ) ) ) ).
% 1.53/1.25 ------------------------
% 1.53/1.27 % (4712)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_4381 for (2999ds/275Mi)
% 1.53/1.27 % (4711)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_4381 for (2999ds/2Mi)
% 1.53/1.27 % (4712)Refutation not found, incomplete strategy
% 1.53/1.27 % (4712)------------------------------
% 1.53/1.27 % (4712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (4712)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.27
% 1.53/1.27
% 1.53/1.27 % (4712)Memory used [KB]: 5500
% 1.53/1.27 % (4712)Time elapsed: 0.002 s
% 1.53/1.27 % (4712)Instructions burned: 1 (million)
% 1.53/1.27 % (4712)------------------------------
% 1.53/1.27 % (4712)------------------------------
% 1.53/1.27 % Exception at run slice level
% 1.53/1.27 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
% 1.53/1.28 % (4707)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/183Mi)
% 1.53/1.28 % (4708)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_4381 for (2999ds/4Mi)
% 1.53/1.28 % (4710)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/2Mi)
% 1.53/1.28 % (4709)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_4381 for (2999ds/27Mi)
% 1.53/1.28 % (4713)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/18Mi)
% 1.53/1.28 % (4710)Instruction limit reached!
% 1.53/1.28 % (4710)------------------------------
% 1.53/1.28 % (4710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (4710)Termination reason: Unknown
% 1.53/1.28 % (4710)Termination phase: Property scanning
% 1.53/1.28
% 1.53/1.28 % (4710)Memory used [KB]: 895
% 1.53/1.28 % (4710)Time elapsed: 0.003 s
% 1.53/1.28 % (4710)Instructions burned: 2 (million)
% 1.53/1.28 % (4710)------------------------------
% 1.53/1.28 % (4710)------------------------------
% 1.53/1.28 % (4708)Instruction limit reached!
% 1.53/1.28 % (4708)------------------------------
% 1.53/1.28 % (4708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (4708)Termination reason: Unknown
% 1.53/1.28 % (4708)Termination phase: Saturation
% 1.53/1.28
% 1.53/1.28 % (4708)Memory used [KB]: 5500
% 1.53/1.28 % (4708)Time elapsed: 0.005 s
% 1.53/1.28 % (4708)Instructions burned: 5 (million)
% 1.53/1.28 % (4708)------------------------------
% 1.53/1.28 % (4708)------------------------------
% 1.53/1.28 % (4709)Refutation not found, incomplete strategy
% 1.53/1.28 % (4709)------------------------------
% 1.53/1.28 % (4709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (4709)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.28
% 1.53/1.28
% 1.53/1.28 % (4709)Memory used [KB]: 5500
% 1.53/1.28 % (4709)Time elapsed: 0.005 s
% 1.53/1.28 % (4709)Instructions burned: 3 (million)
% 1.53/1.28 % (4709)------------------------------
% 1.53/1.28 % (4709)------------------------------
% 1.53/1.28 % (4715)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_4381 for (2999ds/37Mi)
% 1.53/1.28 % (4714)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/3Mi)
% 1.53/1.28 % Exception at run slice level
% 1.53/1.28 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
% 1.53/1.28 % (4714)Instruction limit reached!
% 1.53/1.28 % (4714)------------------------------
% 1.53/1.28 % (4714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (4714)Termination reason: Unknown
% 1.53/1.28 % (4714)Termination phase: Saturation
% 1.53/1.28
% 1.53/1.28 % (4714)Memory used [KB]: 5500
% 1.53/1.28 % (4714)Time elapsed: 0.003 s
% 1.53/1.28 % (4714)Instructions burned: 3 (million)
% 1.53/1.28 % (4714)------------------------------
% 1.53/1.28 % (4714)------------------------------
% 1.53/1.29 % (4713)Instruction limit reached!
% 1.53/1.29 % (4713)------------------------------
% 1.53/1.29 % (4713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (4713)Termination reason: Unknown
% 1.53/1.29 % (4713)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (4713)Memory used [KB]: 5628
% 1.53/1.29 % (4713)Time elapsed: 0.014 s
% 1.53/1.29 % (4713)Instructions burned: 18 (million)
% 1.53/1.29 % (4713)------------------------------
% 1.53/1.29 % (4713)------------------------------
% 1.53/1.29 % (4719)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/7Mi)
% 1.53/1.29 % (4720)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/16Mi)
% 1.53/1.29 % (4719)Instruction limit reached!
% 1.53/1.29 % (4719)------------------------------
% 1.53/1.29 % (4719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (4719)Termination reason: Unknown
% 1.53/1.29 % (4719)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (4719)Memory used [KB]: 1023
% 1.53/1.29 % (4719)Time elapsed: 0.004 s
% 1.53/1.29 % (4719)Instructions burned: 7 (million)
% 1.53/1.29 % (4719)------------------------------
% 1.53/1.29 % (4719)------------------------------
% 1.53/1.29 % (4716)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_4381 for (2999ds/15Mi)
% 1.53/1.29 % (4717)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_4381 for (2999ds/3Mi)
% 1.62/1.30 % (4717)Instruction limit reached!
% 1.62/1.30 % (4717)------------------------------
% 1.62/1.30 % (4717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (4717)Termination reason: Unknown
% 1.62/1.30 % (4717)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (4717)Memory used [KB]: 5500
% 1.62/1.30 % (4717)Time elapsed: 0.003 s
% 1.62/1.30 % (4717)Instructions burned: 3 (million)
% 1.62/1.30 % (4717)------------------------------
% 1.62/1.30 % (4717)------------------------------
% 1.62/1.30 % (4716)Refutation not found, incomplete strategy
% 1.62/1.30 % (4716)------------------------------
% 1.62/1.30 % (4716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (4716)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.30
% 1.62/1.30
% 1.62/1.30 % (4716)Memory used [KB]: 5500
% 1.62/1.30 % (4716)Time elapsed: 0.005 s
% 1.62/1.30 % (4716)Instructions burned: 4 (million)
% 1.62/1.30 % (4716)------------------------------
% 1.62/1.30 % (4716)------------------------------
% 1.62/1.30 % (4720)Instruction limit reached!
% 1.62/1.30 % (4720)------------------------------
% 1.62/1.30 % (4720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (4720)Termination reason: Unknown
% 1.62/1.30 % (4720)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (4720)Memory used [KB]: 5628
% 1.62/1.30 % (4720)Time elapsed: 0.008 s
% 1.62/1.30 % (4720)Instructions burned: 16 (million)
% 1.62/1.30 % (4720)------------------------------
% 1.62/1.30 % (4720)------------------------------
% 1.62/1.30 % (4718)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_4381 for (2999ds/1041Mi)
% 1.62/1.30 % Exception at run slice level
% 1.62/1.30 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
% 1.62/1.30 % (4722)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_4381 for (2999ds/3Mi)
% 1.62/1.30 % (4722)Instruction limit reached!
% 1.62/1.30 % (4722)------------------------------
% 1.62/1.30 % (4722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (4722)Termination reason: Unknown
% 1.62/1.30 % (4722)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (4722)Memory used [KB]: 1023
% 1.62/1.30 % (4722)Time elapsed: 0.002 s
% 1.62/1.30 % (4722)Instructions burned: 3 (million)
% 1.62/1.30 % (4722)------------------------------
% 1.62/1.30 % (4722)------------------------------
% 1.62/1.31 % (4721)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_4381 for (2999ds/3Mi)
% 1.62/1.31 % (4723)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/7Mi)
% 1.62/1.31 % (4721)Instruction limit reached!
% 1.62/1.31 % (4721)------------------------------
% 1.62/1.31 % (4721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (4721)Termination reason: Unknown
% 1.62/1.31 % (4721)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (4721)Memory used [KB]: 5500
% 1.62/1.31 % (4721)Time elapsed: 0.004 s
% 1.62/1.31 % (4721)Instructions burned: 3 (million)
% 1.62/1.31 % (4721)------------------------------
% 1.62/1.31 % (4721)------------------------------
% 1.62/1.31 % (4724)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/3Mi)
% 1.62/1.31 % Exception at run slice level
% 1.62/1.31 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
% 1.62/1.31 % (4723)Instruction limit reached!
% 1.62/1.31 % (4723)------------------------------
% 1.62/1.31 % (4723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (4723)Termination reason: Unknown
% 1.62/1.31 % (4723)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (4723)Memory used [KB]: 5500
% 1.62/1.31 % (4723)Time elapsed: 0.004 s
% 1.62/1.31 % (4723)Instructions burned: 7 (million)
% 1.62/1.31 % (4723)------------------------------
% 1.62/1.31 % (4723)------------------------------
% 1.62/1.31 % (4727)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/710Mi)
% 1.62/1.32 % (4725)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/4Mi)
% 1.62/1.32 % (4726)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/18Mi)
% 1.62/1.32 % (4729)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_4381 for (2999ds/902Mi)
% 1.62/1.32 % (4725)Instruction limit reached!
% 1.62/1.32 % (4725)------------------------------
% 1.62/1.32 % (4725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (4725)Termination reason: Unknown
% 1.62/1.32 % (4725)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (4725)Memory used [KB]: 5500
% 1.62/1.32 % (4725)Time elapsed: 0.005 s
% 1.62/1.32 % (4725)Instructions burned: 4 (million)
% 1.62/1.32 % (4725)------------------------------
% 1.62/1.32 % (4725)------------------------------
% 1.62/1.32 % (4729)Refutation not found, incomplete strategy
% 1.62/1.32 % (4729)------------------------------
% 1.62/1.32 % (4729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (4729)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.32
% 1.62/1.32
% 1.62/1.32 % (4729)Memory used [KB]: 5500
% 1.62/1.32 % (4729)Time elapsed: 0.002 s
% 1.62/1.32 % (4729)Instructions burned: 1 (million)
% 1.62/1.32 % (4729)------------------------------
% 1.62/1.32 % (4729)------------------------------
% 1.62/1.32 % (4730)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_4381 for (2999ds/21Mi)
% 1.62/1.32 % (4726)Refutation not found, incomplete strategy
% 1.62/1.32 % (4726)------------------------------
% 1.62/1.32 % (4726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (4726)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.32
% 1.62/1.32
% 1.62/1.32 % (4726)Memory used [KB]: 5500
% 1.62/1.32 % (4726)Time elapsed: 0.005 s
% 1.62/1.32 % (4726)Instructions burned: 4 (million)
% 1.62/1.32 % (4726)------------------------------
% 1.62/1.32 % (4726)------------------------------
% 1.62/1.33 % (4728)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/6Mi)
% 1.62/1.33 % (4730)Instruction limit reached!
% 1.62/1.33 % (4730)------------------------------
% 1.62/1.33 % (4730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (4730)Termination reason: Unknown
% 1.62/1.33 % (4730)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (4730)Memory used [KB]: 5628
% 1.62/1.33 % (4730)Time elapsed: 0.011 s
% 1.62/1.33 % (4730)Instructions burned: 23 (million)
% 1.62/1.33 % (4730)------------------------------
% 1.62/1.33 % (4730)------------------------------
% 1.62/1.33 % (4728)Instruction limit reached!
% 1.62/1.33 % (4728)------------------------------
% 1.62/1.33 % (4728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (4728)Termination reason: Unknown
% 1.62/1.33 % (4728)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (4728)Memory used [KB]: 5500
% 1.62/1.33 % (4728)Time elapsed: 0.006 s
% 1.62/1.33 % (4728)Instructions burned: 6 (million)
% 1.62/1.33 % (4728)------------------------------
% 1.62/1.33 % (4728)------------------------------
% 1.62/1.33 % (4732)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_4381 for (2999ds/6Mi)
% 1.62/1.33 % Exception at run slice level
% 1.62/1.33 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
% 1.62/1.34 % (4731)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/5Mi)
% 1.62/1.34 % Exception at run slice level
% 1.62/1.34 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
% 1.62/1.34 % (4733)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/377Mi)
% 1.62/1.34 % (4736)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4381 for (2999ds/879Mi)
% 1.62/1.35 % (4734)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_4381 for (2999ds/779Mi)
% 1.62/1.35 % (4735)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_4381 for (2999ds/19Mi)
% 1.62/1.35 % Exception at run slice level
% 1.62/1.35 User error: % Exception at run slice levelVampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.35
% 1.62/1.35 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
% 1.62/1.35 % (4736)First to succeed.
% 1.62/1.35 % (4733)Also succeeded, but the first one will report.
% 1.62/1.35 % (4736)Refutation found. Thanks to Tanya!
% 1.62/1.35 % SZS status Theorem for DTF2THF_4381
% 1.62/1.35 % SZS output start Proof for DTF2THF_4381
% 1.62/1.35 thf(type_def_5, type, 'type/nums/num': $tType).
% 1.62/1.35 thf(type_def_7, type, 'type/ind_types/list': ($tType) > $tType).
% 1.62/1.35 thf(type_def_8, type, sK2: $tType).
% 1.62/1.35 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.62/1.35 thf(func_def_1, type, 'type/ind_types/list': ($tType) > $tType).
% 1.62/1.35 thf(func_def_2, type, 'const/nums/SUC': 'type/nums/num' > 'type/nums/num').
% 1.62/1.35 thf(func_def_3, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.62/1.35 thf(func_def_4, type, 'const/nums/_0': 'type/nums/num').
% 1.62/1.35 thf(func_def_5, type, 'const/lists/LENGTH': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/nums/num')).
% 1.62/1.35 thf(func_def_6, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 1.62/1.35 thf(func_def_7, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.62/1.35 thf(func_def_12, type, sK0: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > X0)).
% 1.62/1.35 thf(func_def_13, type, sK1: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0)).
% 1.62/1.35 thf(func_def_14, type, sK3: 'type/ind_types/list' @ sK2).
% 1.62/1.35 thf(func_def_17, type, ph5: !>[X0: $tType]:(X0)).
% 1.62/1.35 thf(f231,plain,(
% 1.62/1.35 $false),
% 1.62/1.35 inference(avatar_sat_refutation,[status(thm)],[f43,f44,f224,f230])).
% 1.62/1.35 thf(f230,plain,(
% 1.62/1.35 ~spl4_1 | spl4_2),
% 1.62/1.35 inference(avatar_contradiction_clause,[status(thm)],[f229])).
% 1.62/1.35 thf(f229,plain,(
% 1.62/1.35 $false | (~spl4_1 | spl4_2)),
% 1.62/1.35 inference(subsumption_resolution,[status(thm)],[f228,f41])).
% 1.62/1.35 thf(f41,plain,(
% 1.62/1.35 (('const/nums/NUMERAL' @ 'const/nums/_0') != ('const/lists/LENGTH' @ sK2 @ sK3)) | spl4_2),
% 1.62/1.35 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.62/1.35 thf(f40,definition,(
% 1.62/1.35 spl4_2 <=> (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3))),
% 1.62/1.35 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.62/1.35 thf(f228,plain,(
% 1.62/1.35 (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)) | ~spl4_1),
% 1.62/1.35 inference(superposition,[status(thm)],[f26,f38])).
% 1.62/1.35 thf(f38,plain,(
% 1.62/1.35 ('const/ind_types/NIL' @ sK2 = sK3) | ~spl4_1),
% 1.62/1.35 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.62/1.35 thf(f36,definition,(
% 1.62/1.35 spl4_1 <=> ('const/ind_types/NIL' @ sK2 = sK3)),
% 1.62/1.35 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.62/1.35 thf(f26,plain,(
% 1.62/1.35 ( ! [X0 : $tType] : ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ X0 @ 'const/ind_types/NIL' @ X0))) )),
% 1.62/1.35 inference(cnf_transformation,[status(thm)],[f5])).
% 1.62/1.35 thf(f5,axiom,(
% 1.62/1.35 ! [X0 : $tType] : (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ X0 @ 'const/ind_types/NIL' @ X0))),
% 1.62/1.35 file('/export/starexec/sandbox/tmp/tmp.pyMgmxYXgP/DTF2THF_4381.p','thm/lists/LENGTH_0')).
% 1.62/1.35 thf(f224,plain,(
% 1.62/1.35 spl4_1 | ~spl4_2),
% 1.62/1.35 inference(avatar_contradiction_clause,[status(thm)],[f223])).
% 1.62/1.35 thf(f223,plain,(
% 1.62/1.35 $false | (spl4_1 | ~spl4_2)),
% 1.62/1.35 inference(subsumption_resolution,[status(thm)],[f222,f37])).
% 1.62/1.35 thf(f37,plain,(
% 1.62/1.35 ('const/ind_types/NIL' @ sK2 != sK3) | spl4_1),
% 1.62/1.35 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.62/1.35 thf(f222,plain,(
% 1.62/1.35 ('const/ind_types/NIL' @ sK2 = sK3) | ~spl4_2),
% 1.62/1.35 inference(trivial_inequality_removal,[status(thm)],[f219])).
% 1.62/1.35 thf(f219,plain,(
% 1.62/1.35 (('const/nums/NUMERAL' @ 'const/nums/_0') != ('const/nums/NUMERAL' @ 'const/nums/_0')) | ('const/ind_types/NIL' @ sK2 = sK3) | ~spl4_2),
% 1.62/1.35 inference(superposition,[status(thm)],[f218,f42])).
% 1.62/1.35 thf(f42,plain,(
% 1.62/1.35 (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)) | ~spl4_2),
% 1.62/1.35 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.62/1.35 thf(f218,plain,(
% 1.62/1.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/NUMERAL' @ 'const/nums/_0') != ('const/lists/LENGTH' @ X0 @ X1)) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.62/1.35 inference(superposition,[status(thm)],[f25,f186])).
% 1.62/1.35 thf(f186,plain,(
% 1.62/1.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))))) = ('const/lists/LENGTH' @ X0 @ X1)) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.62/1.35 inference(superposition,[status(thm)],[f27,f68])).
% 1.62/1.35 thf(f68,plain,(
% 1.62/1.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f67])).
% 1.62/1.35 thf(f67,plain,(
% 1.62/1.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ($true = (X1 = 'const/ind_types/NIL' @ X0))) )),
% 1.62/1.35 inference(not_proxy_clausification,[status(thm)],[f66])).
% 1.62/1.35 thf(f66,plain,(
% 1.62/1.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ($true != (~ (X1 = 'const/ind_types/NIL' @ X0)))) )),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.62/1.35 thf(f58,plain,(
% 1.62/1.35 ( ! [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 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1)) )),
% 1.62/1.35 inference(leibniz_equality_elimination,[status(thm)],[f22])).
% 1.62/1.35 thf(f22,plain,(
% 1.62/1.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o,X4 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) != $true) | ($true = (X1 @ X4)) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.62/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.62/1.35 thf(f19,plain,(
% 1.62/1.35 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : ((($true = (X1 @ (sK1 @ X0 @ X1))) & ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) != $true)) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)))),
% 1.62/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18])).
% 1.62/1.35 thf(f18,plain,(
% 1.62/1.35 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ X3) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true)) => (($true = (X1 @ (sK1 @ X0 @ X1))) & ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) != $true)))),
% 1.62/1.35 introduced(definition,[],[choice_axiom])).
% 1.62/1.35 thf(f17,plain,(
% 1.62/1.35 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ X3) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true)) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)))),
% 1.62/1.35 inference(flattening,[status(thm)],[f16])).
% 1.62/1.35 thf(f16,plain,(
% 1.62/1.35 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)) | (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ X3) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true)) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)))),
% 1.62/1.35 inference(ennf_transformation,[status(thm)],[f12])).
% 1.62/1.35 thf(f12,plain,(
% 1.62/1.35 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ X3) = $true) => ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) = $true)) & ((X1 @ 'const/ind_types/NIL' @ X0) = $true)) => ! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)))),
% 1.62/1.35 inference(fool_elimination,[status(thm)],[f11])).
% 1.62/1.35 thf(f11,plain,(
% 1.62/1.35 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 1.62/1.35 inference(rectify,[status(thm)],[f1])).
% 1.62/1.35 thf(f1,axiom,(
% 1.62/1.35 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 1.62/1.35 file('/export/starexec/sandbox/tmp/tmp.pyMgmxYXgP/DTF2THF_4381.p','thm/ind_types/list_INDUCT_')).
% 1.62/1.35 thf(f27,plain,(
% 1.62/1.35 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2)) = ('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)))) )),
% 1.62/1.35 inference(cnf_transformation,[status(thm)],[f13])).
% 1.62/1.35 thf(f13,plain,(
% 1.62/1.35 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2)) = ('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)))),
% 1.62/1.35 inference(rectify,[status(thm)],[f4])).
% 1.62/1.35 thf(f4,axiom,(
% 1.62/1.35 ! [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)))),
% 1.62/1.35 file('/export/starexec/sandbox/tmp/tmp.pyMgmxYXgP/DTF2THF_4381.p','thm/lists/LENGTH_1')).
% 1.62/1.35 thf(f25,plain,(
% 1.62/1.35 ( ! [X0 : 'type/nums/num'] : ((('const/nums/SUC' @ X0) != ('const/nums/NUMERAL' @ 'const/nums/_0'))) )),
% 1.62/1.35 inference(cnf_transformation,[status(thm)],[f3])).
% 1.62/1.35 thf(f3,axiom,(
% 1.62/1.35 ! [X0 : 'type/nums/num'] : (('const/nums/SUC' @ X0) != ('const/nums/NUMERAL' @ 'const/nums/_0'))),
% 1.62/1.35 file('/export/starexec/sandbox/tmp/tmp.pyMgmxYXgP/DTF2THF_4381.p','thm/nums/NOT_SUC_')).
% 1.62/1.35 thf(f44,plain,(
% 1.62/1.35 ~spl4_2 | ~spl4_1),
% 1.62/1.35 inference(avatar_split_clause,[status(thm)],[f32,f36,f40])).
% 1.62/1.35 thf(f32,plain,(
% 1.62/1.35 (('const/nums/NUMERAL' @ 'const/nums/_0') != ('const/lists/LENGTH' @ sK2 @ sK3)) | ('const/ind_types/NIL' @ sK2 != sK3)),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.62/1.35 thf(f31,plain,(
% 1.62/1.35 ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)) = $false) | ('const/ind_types/NIL' @ sK2 != sK3)),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f30])).
% 1.62/1.35 thf(f30,plain,(
% 1.62/1.35 ($false = ('const/ind_types/NIL' @ sK2 = sK3)) | ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)) = $false)),
% 1.62/1.35 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.62/1.35 thf(f28,plain,(
% 1.62/1.35 ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)) != ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.35 inference(cnf_transformation,[status(thm)],[f21])).
% 1.62/1.35 thf(f21,plain,(
% 1.62/1.35 ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)) != ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f15,f20])).
% 1.62/1.35 thf(f20,plain,(
% 1.62/1.35 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ X0 @ X1)) != ('const/ind_types/NIL' @ X0 = X1)) => ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)) != ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.35 introduced(definition,[],[choice_axiom])).
% 1.62/1.35 thf(f15,plain,(
% 1.62/1.35 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ X0 @ X1)) != ('const/ind_types/NIL' @ X0 = X1))),
% 1.62/1.35 inference(ennf_transformation,[status(thm)],[f10])).
% 1.62/1.35 thf(f10,plain,(
% 1.62/1.35 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ X0 @ X1)) = ('const/ind_types/NIL' @ X0 = X1))),
% 1.62/1.35 inference(fool_elimination,[status(thm)],[f9])).
% 1.62/1.35 thf(f9,plain,(
% 1.62/1.35 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ X0 @ X1)) = ('const/ind_types/NIL' @ X0 = X1))),
% 1.62/1.35 inference(rectify,[status(thm)],[f7])).
% 1.62/1.35 thf(f7,negated_conjecture,(
% 1.62/1.35 ~! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ X0 @ X2)) = ('const/ind_types/NIL' @ X0 = X2))),
% 1.62/1.35 inference(negated_conjecture,[status(cth)],[f6])).
% 1.62/1.35 thf(f6,conjecture,(
% 1.62/1.35 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ X0 @ X2)) = ('const/ind_types/NIL' @ X0 = X2))),
% 1.62/1.35 file('/export/starexec/sandbox/tmp/tmp.pyMgmxYXgP/DTF2THF_4381.p','thm/lists/LENGTH_EQ_NIL_')).
% 1.62/1.35 thf(f43,plain,(
% 1.62/1.35 spl4_1 | spl4_2),
% 1.62/1.35 inference(avatar_split_clause,[status(thm)],[f34,f40,f36])).
% 1.62/1.35 thf(f34,plain,(
% 1.62/1.35 ('const/ind_types/NIL' @ sK2 = sK3) | (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3))),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.62/1.35 thf(f33,plain,(
% 1.62/1.35 (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)) | ($true = ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.62/1.35 thf(f29,plain,(
% 1.62/1.35 ($true = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3))) | ($true = ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.35 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.62/1.35 % SZS output end Proof for DTF2THF_4381
% 1.62/1.35 % (4736)------------------------------
% 1.62/1.35 % (4736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (4736)Termination reason: Refutation
% 1.62/1.35
% 1.62/1.35 % (4736)Memory used [KB]: 5628
% 1.62/1.35 % (4736)Time elapsed: 0.033 s
% 1.62/1.35 % (4736)Instructions burned: 23 (million)
% 1.62/1.35 % (4736)------------------------------
% 1.62/1.35 % (4736)------------------------------
% 1.62/1.35 % (4706)Success in time 0.079 s
%------------------------------------------------------------------------------