%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT317^1 : 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 : n001.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 08:45:27 AM UTC 2026
% Result : Theorem 1.80s 1.47s
% Output : Refutation 1.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT317^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n001.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 06:14:20 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : DAT317^1 : TPTP v9.2.1. Released v7.0.0.
% 0.26/0.47 % Domain : Analysis
% 0.26/0.47 % Problem : CONS_HD_TL
% 0.26/0.47 % Version : Especial.
% 0.26/0.47 % English :
% 0.26/0.47
% 0.26/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.26/0.47 % Source : [Kal16]
% 0.26/0.47 % Names : CONS_HD_TL_.p [Kal16]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.26/0.47 % Syntax : Number of formulae : 10 ( 3 unt; 5 typ; 0 def)
% 0.26/0.47 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 2 ( 1 avg)
% 0.26/0.47 % Number of connectives : 49 ( 2 ~; 0 |; 1 &; 43 @)
% 0.26/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 12 ( 6 avg)
% 0.26/0.47 % Number of types : 1 ( 0 usr)
% 0.26/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 6 ( 5 usr; 0 con; 1-3 aty)
% 0.26/0.47 % Number of variables : 20 ( 0 ^; 16 !; 0 ?; 20 :)
% 0.26/0.47 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.47 % SPC : TH1_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : Exported from core HOL Light.
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf('thf_type_type/ind_types/list',type,
% 0.26/0.47 'type/ind_types/list': $tType > $tType ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/lists/TL',type,
% 0.26/0.47 'const/lists/TL':
% 0.26/0.47 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/lists/HD',type,
% 0.26/0.47 'const/lists/HD':
% 0.26/0.47 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A ) ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/ind_types/NIL',type,
% 0.26/0.47 'const/ind_types/NIL':
% 0.26/0.47 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/ind_types/CONS',type,
% 0.26/0.47 'const/ind_types/CONS':
% 0.26/0.47 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/ind_types/list_INDUCT_',axiom,
% 0.26/0.47 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 0.26/0.47 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 0.26/0.47 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 0.26/0.47 ( ( P @ A1 )
% 0.26/0.47 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 0.26/0.47 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/lists/TL_',axiom,
% 0.26/0.47 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.26/0.47 ( ( 'const/lists/TL' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.26/0.47 = A1 ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/lists/HD_',axiom,
% 0.26/0.47 ! [A: $tType,A0: 'type/ind_types/list' @ A,A1: A] :
% 0.26/0.47 ( ( 'const/lists/HD' @ A @ ( 'const/ind_types/CONS' @ A @ A1 @ A0 ) )
% 0.26/0.47 = A1 ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/lists/NOT_CONS_NIL_',axiom,
% 0.26/0.47 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.26/0.47 ( ( 'const/ind_types/CONS' @ A @ A0 @ A1 )
% 0.26/0.47 != ( 'const/ind_types/NIL' @ A ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/lists/CONS_HD_TL_',conjecture,
% 0.26/0.47 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 0.26/0.47 ( ( A0
% 0.26/0.47 != ( 'const/ind_types/NIL' @ A ) )
% 0.26/0.47 => ( A0
% 0.26/0.47 = ( 'const/ind_types/CONS' @ A @ ( 'const/lists/HD' @ A @ A0 ) @ ( 'const/lists/TL' @ A @ A0 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.73/1.33 ---- Embedded in THF ---
% 1.73/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.73/1.33 %%% Generated on Tue Feb 24 06:14:21 EST 2026
% 1.73/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.73/1.33 %%% Logic specification used:
% 1.73/1.33 %%% thf(spec, logic, $$dhol).
% 1.73/1.33
% 1.73/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8iLam6mXFV/DTF2DTF22928.p
% 1.73/1.33 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.73/1.33 thf('thf_const_const/lists/TL', type, 'const/lists/TL': (!> [A:$tType]: ((('type/ind_types/list' @ A) > ('type/ind_types/list' @ A))))).
% 1.73/1.33 thf('thf_const_const/lists/HD', type, 'const/lists/HD': (!> [A:$tType]: ((('type/ind_types/list' @ A) > A)))).
% 1.73/1.33 thf('thf_const_const/ind_types/NIL', type, 'const/ind_types/NIL': (!> [A:$tType]: (('type/ind_types/list' @ A)))).
% 1.73/1.33 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.73/1.33 thf('thm/ind_types/list_INDUCT_', axiom, (! [A:$tType,P:(('type/ind_types/list' @ A) > $o)]: ((((P @ ('const/ind_types/NIL' @ A)) & (! [A0:A,A1:('type/ind_types/list' @ A)]: (((P @ A1) => (P @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)))))) => (! [A0:('type/ind_types/list' @ A)]: ((P @ A0))))))).
% 1.73/1.33 thf('thm/lists/TL_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: (((('const/lists/TL' @ A) @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)) = A1)))).
% 1.73/1.33 thf('thm/lists/HD_', axiom, (! [A:$tType,A0:('type/ind_types/list' @ A),A1:A]: (((('const/lists/HD' @ A) @ ((('const/ind_types/CONS' @ A) @ A1) @ A0)) = A1)))).
% 1.73/1.33 thf('thm/lists/NOT_CONS_NIL_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: ((((('const/ind_types/CONS' @ A) @ A0) @ A1) != ('const/ind_types/NIL' @ A))))).
% 1.73/1.33 thf('thm/lists/CONS_HD_TL_', conjecture, (! [A:$tType,A0:('type/ind_types/list' @ A)]: (((A0 != ('const/ind_types/NIL' @ A)) => (A0 = ((('const/ind_types/CONS' @ A) @ (('const/lists/HD' @ A) @ A0)) @ (('const/lists/TL' @ A) @ A0))))))).
% 1.73/1.33 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.8iLam6mXFV/DTF2DTF22928.p
% 1.73/1.33 ------------------------
% 1.73/1.34 ---- Cleaned THF ---
% 1.73/1.34 thf('thf_type_type/ind_types/list',type,
% 1.73/1.34 'type/ind_types/list': $tType > $tType ).
% 1.73/1.34
% 1.73/1.34 thf('thf_const_const/lists/TL',type,
% 1.73/1.34 'const/lists/TL':
% 1.73/1.34 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.73/1.34
% 1.73/1.34 thf('thf_const_const/lists/HD',type,
% 1.73/1.34 'const/lists/HD':
% 1.73/1.34 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A ) ).
% 1.73/1.34
% 1.73/1.34 thf('thf_const_const/ind_types/NIL',type,
% 1.73/1.34 'const/ind_types/NIL':
% 1.73/1.34 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 1.73/1.34
% 1.73/1.34 thf('thf_const_const/ind_types/CONS',type,
% 1.73/1.34 'const/ind_types/CONS':
% 1.73/1.34 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.73/1.34
% 1.73/1.34 thf('thm/ind_types/list_INDUCT_',axiom,
% 1.73/1.34 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 1.73/1.34 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 1.73/1.34 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 1.73/1.34 ( ( P @ A1 )
% 1.73/1.34 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 1.73/1.34 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 1.73/1.34
% 1.73/1.34 thf('thm/lists/TL_',axiom,
% 1.73/1.34 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.73/1.34 ( ( 'const/lists/TL' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 1.73/1.34 = A1 ) ).
% 1.73/1.34
% 1.73/1.34 thf('thm/lists/HD_',axiom,
% 1.73/1.34 ! [A: $tType,A0: 'type/ind_types/list' @ A,A1: A] :
% 1.73/1.34 ( ( 'const/lists/HD' @ A @ ( 'const/ind_types/CONS' @ A @ A1 @ A0 ) )
% 1.73/1.34 = A1 ) ).
% 1.73/1.34
% 1.73/1.34 thf('thm/lists/NOT_CONS_NIL_',axiom,
% 1.73/1.34 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.73/1.34 ( ( 'const/ind_types/CONS' @ A @ A0 @ A1 )
% 1.73/1.34 != ( 'const/ind_types/NIL' @ A ) ) ).
% 1.73/1.34
% 1.73/1.34 thf('thm/lists/CONS_HD_TL_',conjecture,
% 1.73/1.34 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 1.73/1.34 ( ( A0
% 1.73/1.34 != ( 'const/ind_types/NIL' @ A ) )
% 1.73/1.34 => ( A0
% 1.73/1.34 = ( 'const/ind_types/CONS' @ A @ ( 'const/lists/HD' @ A @ A0 ) @ ( 'const/lists/TL' @ A @ A0 ) ) ) ) ).
% 1.73/1.34 ------------------------
% 1.73/1.36 % (23116)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/183Mi)
% 1.73/1.36 % (23122)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/18Mi)
% 1.73/1.36 % (23117)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_22928 for (2999ds/4Mi)
% 1.73/1.36 % (23118)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_22928 for (2999ds/27Mi)
% 1.73/1.36 % (23121)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_22928 for (2999ds/275Mi)
% 1.73/1.36 % (23120)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_22928 for (2999ds/2Mi)
% 1.73/1.37 % Exception at run slice level
% 1.73/1.37 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
% 1.73/1.37 % (23121)Refutation not found, incomplete strategy
% 1.73/1.37 % (23121)------------------------------
% 1.73/1.37 % (23121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.37 % (23121)Termination reason: Refutation not found, incomplete strategy
% 1.73/1.37
% 1.73/1.37
% 1.73/1.37 % (23121)Memory used [KB]: 5500
% 1.73/1.37 % (23121)Time elapsed: 0.003 s
% 1.73/1.37 % (23121)Instructions burned: 2 (million)
% 1.73/1.37 % (23121)------------------------------
% 1.73/1.37 % (23121)------------------------------
% 1.73/1.37 % (23117)Instruction limit reached!
% 1.73/1.37 % (23117)------------------------------
% 1.73/1.37 % (23117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.37 % (23117)Termination reason: Unknown
% 1.73/1.37 % (23117)Termination phase: Saturation
% 1.73/1.37
% 1.73/1.37 % (23119)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/2Mi)
% 1.73/1.37 % (23117)Memory used [KB]: 5500
% 1.73/1.37 % (23117)Time elapsed: 0.005 s
% 1.73/1.37 % (23117)Instructions burned: 5 (million)
% 1.73/1.37 % (23117)------------------------------
% 1.73/1.37 % (23117)------------------------------
% 1.73/1.37 % (23119)Instruction limit reached!
% 1.73/1.37 % (23119)------------------------------
% 1.73/1.37 % (23119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.37 % (23119)Termination reason: Unknown
% 1.73/1.37 % (23119)Termination phase: Saturation
% 1.73/1.37
% 1.73/1.37 % (23119)Memory used [KB]: 5500
% 1.73/1.37 % (23119)Time elapsed: 0.003 s
% 1.73/1.37 % (23119)Instructions burned: 2 (million)
% 1.73/1.37 % (23119)------------------------------
% 1.73/1.37 % (23119)------------------------------
% 1.73/1.37 % (23122)Instruction limit reached!
% 1.73/1.37 % (23122)------------------------------
% 1.73/1.37 % (23122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.37 % (23122)Termination reason: Unknown
% 1.73/1.37 % (23122)Termination phase: Saturation
% 1.73/1.37
% 1.73/1.37 % (23122)Memory used [KB]: 5628
% 1.73/1.37 % (23122)Time elapsed: 0.011 s
% 1.73/1.37 % (23122)Instructions burned: 18 (million)
% 1.73/1.37 % (23122)------------------------------
% 1.73/1.37 % (23122)------------------------------
% 1.73/1.38 % (23118)Instruction limit reached!
% 1.73/1.38 % (23118)------------------------------
% 1.73/1.38 % (23118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.38 % (23118)Termination reason: Unknown
% 1.73/1.38 % (23118)Termination phase: Saturation
% 1.73/1.38
% 1.73/1.38 % (23118)Memory used [KB]: 5628
% 1.73/1.38 % (23118)Time elapsed: 0.016 s
% 1.73/1.38 % (23118)Instructions burned: 29 (million)
% 1.73/1.38 % (23118)------------------------------
% 1.73/1.38 % (23118)------------------------------
% 1.73/1.38 % (23126)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_22928 for (2999ds/3Mi)
% 1.73/1.38 % (23126)Instruction limit reached!
% 1.73/1.38 % (23126)------------------------------
% 1.73/1.38 % (23126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.38 % (23126)Termination reason: Unknown
% 1.73/1.38 % (23126)Termination phase: Saturation
% 1.73/1.38
% 1.73/1.38 % (23126)Memory used [KB]: 5500
% 1.73/1.38 % (23126)Time elapsed: 0.003 s
% 1.73/1.38 % (23126)Instructions burned: 4 (million)
% 1.73/1.38 % (23126)------------------------------
% 1.73/1.38 % (23126)------------------------------
% 1.73/1.38 % (23127)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_22928 for (2999ds/1041Mi)
% 1.73/1.38 % (23123)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/3Mi)
% 1.73/1.38 % Exception at run slice level
% 1.73/1.38 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
% 1.73/1.38 % (23124)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_22928 for (2999ds/37Mi)
% 1.73/1.38 % (23125)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_22928 for (2999ds/15Mi)
% 1.73/1.39 % Exception at run slice level
% 1.73/1.39 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
% 1.73/1.39 % (23123)Instruction limit reached!
% 1.73/1.39 % (23123)------------------------------
% 1.73/1.39 % (23123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.39 % (23123)Termination reason: Unknown
% 1.73/1.39 % (23123)Termination phase: Saturation
% 1.73/1.39
% 1.73/1.39 % (23123)Memory used [KB]: 5500
% 1.73/1.39 % (23123)Time elapsed: 0.004 s
% 1.73/1.39 % (23123)Instructions burned: 3 (million)
% 1.73/1.39 % (23123)------------------------------
% 1.73/1.39 % (23123)------------------------------
% 1.73/1.39 % (23125)Refutation not found, incomplete strategy
% 1.73/1.39 % (23125)------------------------------
% 1.73/1.39 % (23125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.39 % (23125)Termination reason: Refutation not found, incomplete strategy
% 1.73/1.39
% 1.73/1.39
% 1.73/1.39 % (23125)Memory used [KB]: 5500
% 1.73/1.39 % (23125)Time elapsed: 0.004 s
% 1.73/1.39 % (23125)Instructions burned: 3 (million)
% 1.73/1.39 % (23125)------------------------------
% 1.73/1.39 % (23125)------------------------------
% 1.73/1.39 % (23128)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/7Mi)
% 1.73/1.39 % (23129)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/16Mi)
% 1.73/1.39 % (23128)Instruction limit reached!
% 1.73/1.39 % (23128)------------------------------
% 1.73/1.39 % (23128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.39 % (23128)Termination reason: Unknown
% 1.73/1.39 % (23128)Termination phase: Saturation
% 1.73/1.39
% 1.73/1.39 % (23128)Memory used [KB]: 1023
% 1.73/1.39 % (23128)Time elapsed: 0.005 s
% 1.73/1.39 % (23128)Instructions burned: 9 (million)
% 1.73/1.39 % (23128)------------------------------
% 1.73/1.39 % (23128)------------------------------
% 1.80/1.40 % (23130)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_22928 for (2999ds/3Mi)
% 1.80/1.40 % (23129)Instruction limit reached!
% 1.80/1.40 % (23129)------------------------------
% 1.80/1.40 % (23129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.40 % (23129)Termination reason: Unknown
% 1.80/1.40 % (23129)Termination phase: Saturation
% 1.80/1.40
% 1.80/1.40 % (23129)Memory used [KB]: 5628
% 1.80/1.40 % (23129)Time elapsed: 0.008 s
% 1.80/1.40 % (23129)Instructions burned: 16 (million)
% 1.80/1.40 % (23129)------------------------------
% 1.80/1.40 % (23129)------------------------------
% 1.80/1.40 % (23130)Instruction limit reached!
% 1.80/1.40 % (23130)------------------------------
% 1.80/1.40 % (23130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.40 % (23130)Termination reason: Unknown
% 1.80/1.40 % (23130)Termination phase: Saturation
% 1.80/1.40
% 1.80/1.40 % (23130)Memory used [KB]: 5500
% 1.80/1.40 % (23130)Time elapsed: 0.003 s
% 1.80/1.40 % (23130)Instructions burned: 4 (million)
% 1.80/1.40 % (23130)------------------------------
% 1.80/1.40 % (23130)------------------------------
% 1.80/1.40 % (23132)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/7Mi)
% 1.80/1.40 % (23134)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/4Mi)
% 1.80/1.40 % (23132)Instruction limit reached!
% 1.80/1.40 % (23132)------------------------------
% 1.80/1.40 % (23132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.40 % (23131)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_22928 for (2999ds/3Mi)
% 1.80/1.40 % (23132)Termination reason: Unknown
% 1.80/1.40 % (23132)Termination phase: Saturation
% 1.80/1.40
% 1.80/1.40 % (23132)Memory used [KB]: 5500
% 1.80/1.40 % (23132)Time elapsed: 0.026 s
% 1.80/1.40 % (23132)Instructions burned: 9 (million)
% 1.80/1.40 % (23132)------------------------------
% 1.80/1.40 % (23132)------------------------------
% 1.80/1.40 % (23134)Instruction limit reached!
% 1.80/1.40 % (23134)------------------------------
% 1.80/1.40 % (23134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.40 % (23134)Termination reason: Unknown
% 1.80/1.40 % (23134)Termination phase: Saturation
% 1.80/1.40
% 1.80/1.40 % (23134)Memory used [KB]: 5500
% 1.80/1.40 % (23134)Time elapsed: 0.004 s
% 1.80/1.40 % (23134)Instructions burned: 5 (million)
% 1.80/1.40 % (23134)------------------------------
% 1.80/1.40 % (23134)------------------------------
% 1.80/1.40 % (23131)Instruction limit reached!
% 1.80/1.40 % (23131)------------------------------
% 1.80/1.40 % (23131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.40 % (23131)Termination reason: Unknown
% 1.80/1.40 % (23131)Termination phase: Saturation
% 1.80/1.40
% 1.80/1.40 % (23131)Memory used [KB]: 1023
% 1.80/1.40 % (23131)Time elapsed: 0.004 s
% 1.80/1.40 % (23131)Instructions burned: 3 (million)
% 1.80/1.40 % (23131)------------------------------
% 1.80/1.40 % (23131)------------------------------
% 1.80/1.40 % (23133)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/3Mi)
% 1.80/1.41 % Exception at run slice level
% 1.80/1.41 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
% 1.80/1.41 % (23141)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/710Mi)
% 1.80/1.41 % (23140)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/18Mi)
% 1.80/1.41 % (23142)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/6Mi)
% 1.80/1.41 % (23116)Instruction limit reached!
% 1.80/1.41 % (23116)------------------------------
% 1.80/1.41 % (23116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.41 % (23116)Termination reason: Unknown
% 1.80/1.41 % (23116)Termination phase: Saturation
% 1.80/1.41
% 1.80/1.41 % (23116)Memory used [KB]: 6268
% 1.80/1.41 % (23116)Time elapsed: 0.059 s
% 1.80/1.41 % (23116)Instructions burned: 183 (million)
% 1.80/1.41 % (23116)------------------------------
% 1.80/1.41 % (23116)------------------------------
% 1.80/1.42 % (23142)Instruction limit reached!
% 1.80/1.42 % (23142)------------------------------
% 1.80/1.42 % (23142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.42 % (23142)Termination reason: Unknown
% 1.80/1.42 % (23142)Termination phase: Saturation
% 1.80/1.42
% 1.80/1.42 % (23142)Memory used [KB]: 5500
% 1.80/1.42 % (23142)Time elapsed: 0.005 s
% 1.80/1.42 % (23142)Instructions burned: 8 (million)
% 1.80/1.42 % (23142)------------------------------
% 1.80/1.42 % (23142)------------------------------
% 1.80/1.42 % (23144)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_22928 for (2999ds/902Mi)
% 1.80/1.42 % (23144)Refutation not found, incomplete strategy
% 1.80/1.42 % (23144)------------------------------
% 1.80/1.42 % (23144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.42 % (23144)Termination reason: Refutation not found, incomplete strategy
% 1.80/1.42
% 1.80/1.42
% 1.80/1.42 % (23144)Memory used [KB]: 5500
% 1.80/1.42 % (23144)Time elapsed: 0.003 s
% 1.80/1.42 % (23144)Instructions burned: 2 (million)
% 1.80/1.42 % (23144)------------------------------
% 1.80/1.42 % (23144)------------------------------
% 1.80/1.42 % (23140)Instruction limit reached!
% 1.80/1.42 % (23140)------------------------------
% 1.80/1.42 % (23140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.42 % (23140)Termination reason: Unknown
% 1.80/1.42 % (23140)Termination phase: Saturation
% 1.80/1.42
% 1.80/1.42 % (23140)Memory used [KB]: 5500
% 1.80/1.42 % (23140)Time elapsed: 0.035 s
% 1.80/1.42 % (23140)Instructions burned: 19 (million)
% 1.80/1.42 % (23140)------------------------------
% 1.80/1.42 % (23140)------------------------------
% 1.80/1.43 % (23156)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/377Mi)
% 1.80/1.43 % (23155)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_22928 for (2999ds/6Mi)
% 1.80/1.43 % Exception at run slice level
% 1.80/1.43 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
% 1.80/1.43 % (23145)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_22928 for (2999ds/21Mi)
% 1.80/1.43 % (23158)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_22928 for (2999ds/19Mi)
% 1.80/1.43 % Exception at run slice level
% 1.80/1.43 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
% 1.80/1.43 % (23147)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/5Mi)
% 1.80/1.44 % Exception at run slice level
% 1.80/1.44 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
% 1.80/1.44 % (23157)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_22928 for (2999ds/779Mi)
% 1.80/1.44 % Exception at run slice level
% 1.80/1.44 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
% 1.80/1.44 % (23164)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/17Mi)
% 1.80/1.45 % (23145)Instruction limit reached!
% 1.80/1.45 % (23145)------------------------------
% 1.80/1.45 % (23145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.45 % (23145)Termination reason: Unknown
% 1.80/1.45 % (23145)Termination phase: Saturation
% 1.80/1.45
% 1.80/1.45 % (23145)Memory used [KB]: 5628
% 1.80/1.45 % (23145)Time elapsed: 0.019 s
% 1.80/1.45 % (23145)Instructions burned: 21 (million)
% 1.80/1.45 % (23145)------------------------------
% 1.80/1.45 % (23145)------------------------------
% 1.80/1.45 % (23163)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/879Mi)
% 1.80/1.45 % (23164)Instruction limit reached!
% 1.80/1.45 % (23164)------------------------------
% 1.80/1.45 % (23164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.45 % (23164)Termination reason: Unknown
% 1.80/1.45 % (23164)Termination phase: Saturation
% 1.80/1.45
% 1.80/1.45 % (23164)Memory used [KB]: 5628
% 1.80/1.45 % (23164)Time elapsed: 0.008 s
% 1.80/1.45 % (23164)Instructions burned: 19 (million)
% 1.80/1.45 % (23164)------------------------------
% 1.80/1.45 % (23164)------------------------------
% 1.80/1.45 % (23167)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/30Mi)
% 1.80/1.45 % (23165)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/3Mi)
% 1.80/1.46 % (23165)Instruction limit reached!
% 1.80/1.46 % (23165)------------------------------
% 1.80/1.46 % (23165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.46 % (23165)Termination reason: Unknown
% 1.80/1.46 % (23165)Termination phase: Saturation
% 1.80/1.46
% 1.80/1.46 % (23165)Memory used [KB]: 1023
% 1.80/1.46 % (23165)Time elapsed: 0.003 s
% 1.80/1.46 % (23165)Instructions burned: 3 (million)
% 1.80/1.46 % (23165)------------------------------
% 1.80/1.46 % (23165)------------------------------
% 1.80/1.46 % (23174)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22928 for (2998ds/100Mi)
% 1.80/1.47 % (23167)Instruction limit reached!
% 1.80/1.47 % (23167)------------------------------
% 1.80/1.47 % (23167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.47 % (23167)Termination reason: Unknown
% 1.80/1.47 % (23167)Termination phase: Saturation
% 1.80/1.47
% 1.80/1.47 % (23167)Memory used [KB]: 5756
% 1.80/1.47 % (23167)Time elapsed: 0.016 s
% 1.80/1.47 % (23167)Instructions burned: 30 (million)
% 1.80/1.47 % (23167)------------------------------
% 1.80/1.47 % (23167)------------------------------
% 1.80/1.47 % (23172)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22928 for (2999ds/127Mi)
% 1.80/1.47 % (23156)First to succeed.
% 1.80/1.47 % (23176)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_22928 for (2998ds/3Mi)
% 1.80/1.47 % Exception at run slice level
% 1.80/1.47 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
% 1.80/1.47 % (23156)Refutation found. Thanks to Tanya!
% 1.80/1.47 % SZS status Theorem for DTF2THF_22928
% 1.80/1.47 % SZS output start Proof for DTF2THF_22928
% 1.80/1.47 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 1.80/1.47 thf(type_def_7, type, sK0: $tType).
% 1.80/1.47 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 1.80/1.47 thf(func_def_1, type, 'const/lists/TL': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.80/1.47 thf(func_def_2, type, 'const/lists/HD': !>[X0: $tType]:('type/ind_types/list' @ X0 > X0)).
% 1.80/1.47 thf(func_def_3, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 1.80/1.47 thf(func_def_4, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.80/1.47 thf(func_def_8, type, sK1: 'type/ind_types/list' @ sK0).
% 1.80/1.47 thf(func_def_9, type, sK2: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > X0)).
% 1.80/1.47 thf(func_def_10, type, sK3: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0)).
% 1.80/1.47 thf(func_def_13, type, ph5: !>[X0: $tType]:(X0)).
% 1.80/1.47 thf(f362,plain,(
% 1.80/1.47 $false),
% 1.80/1.47 inference(trivial_inequality_removal,[status(thm)],[f357])).
% 1.80/1.47 thf(f357,plain,(
% 1.80/1.47 (sK1 != sK1)),
% 1.80/1.47 inference(superposition,[status(thm)],[f22,f353])).
% 1.80/1.47 thf(f353,plain,(
% 1.80/1.47 ('const/ind_types/NIL' @ sK0 = sK1)),
% 1.80/1.47 inference(trivial_inequality_removal,[status(thm)],[f348])).
% 1.80/1.47 thf(f348,plain,(
% 1.80/1.47 ('const/ind_types/NIL' @ sK0 = sK1) | (sK1 != sK1)),
% 1.80/1.47 inference(superposition,[status(thm)],[f21,f332])).
% 1.80/1.47 thf(f332,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.80/1.47 inference(duplicate_literal_removal,[status(thm)],[f317])).
% 1.80/1.47 thf(f317,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.80/1.47 inference(superposition,[status(thm)],[f244,f214])).
% 1.80/1.47 thf(f214,plain,(
% 1.80/1.47 ( ! [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)) )),
% 1.80/1.47 inference(superposition,[status(thm)],[f23,f90])).
% 1.80/1.47 thf(f90,plain,(
% 1.80/1.47 ( ! [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)) )),
% 1.80/1.47 inference(equality_proxy_clausification,[status(thm)],[f89])).
% 1.80/1.47 thf(f89,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ($true = (X1 = 'const/ind_types/NIL' @ X0))) )),
% 1.80/1.47 inference(not_proxy_clausification,[status(thm)],[f88])).
% 1.80/1.47 thf(f88,plain,(
% 1.80/1.47 ( ! [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)) )),
% 1.80/1.47 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.80/1.47 thf(f74,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ($true != ((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))) @ 'const/ind_types/NIL' @ X0))) )),
% 1.80/1.47 inference(leibniz_equality_elimination,[status(thm)],[f26])).
% 1.80/1.47 thf(f26,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o,X4 : 'type/ind_types/list' @ X0] : (($true != (X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ((X1 @ X4) = $true)) )),
% 1.80/1.47 inference(cnf_transformation,[status(thm)],[f20])).
% 1.80/1.47 thf(f20,plain,(
% 1.80/1.47 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | (($true != (X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) & ($true = (X1 @ (sK3 @ X0 @ X1)))) | ! [X4 : 'type/ind_types/list' @ X0] : ((X1 @ X4) = $true))),
% 1.80/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f15,f19])).
% 1.80/1.47 thf(f19,plain,(
% 1.80/1.47 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true) & ((X1 @ X3) = $true)) => (($true != (X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) & ($true = (X1 @ (sK3 @ X0 @ X1)))))),
% 1.80/1.47 introduced(definition,[],[choice_axiom])).
% 1.80/1.47 thf(f15,plain,(
% 1.80/1.47 ! [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 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true) & ((X1 @ X3) = $true)) | ! [X4 : 'type/ind_types/list' @ X0] : ((X1 @ X4) = $true))),
% 1.80/1.47 inference(flattening,[status(thm)],[f14])).
% 1.80/1.47 thf(f14,plain,(
% 1.80/1.47 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (! [X4 : 'type/ind_types/list' @ X0] : ((X1 @ X4) = $true) | (((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))))),
% 1.80/1.47 inference(ennf_transformation,[status(thm)],[f9])).
% 1.80/1.47 thf(f9,plain,(
% 1.80/1.47 ! [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] : ((X1 @ X4) = $true))),
% 1.80/1.47 inference(fool_elimination,[status(thm)],[f8])).
% 1.80/1.47 thf(f8,plain,(
% 1.80/1.47 ! [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))),
% 1.80/1.47 inference(rectify,[status(thm)],[f1])).
% 1.80/1.47 thf(f1,axiom,(
% 1.80/1.47 ! [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))),
% 1.80/1.47 file('/export/starexec/sandbox/tmp/tmp.8iLam6mXFV/DTF2THF_22928.p','thm/ind_types/list_INDUCT_')).
% 1.80/1.47 thf(f23,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = X2)) )),
% 1.80/1.47 inference(cnf_transformation,[status(thm)],[f10])).
% 1.80/1.47 thf(f10,plain,(
% 1.80/1.47 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = X2)),
% 1.80/1.47 inference(rectify,[status(thm)],[f2])).
% 1.80/1.47 thf(f2,axiom,(
% 1.80/1.47 ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) = X3)),
% 1.80/1.47 file('/export/starexec/sandbox/tmp/tmp.8iLam6mXFV/DTF2THF_22928.p','thm/lists/TL_')).
% 1.80/1.47 thf(f244,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.80/1.47 inference(duplicate_literal_removal,[status(thm)],[f234])).
% 1.80/1.47 thf(f234,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.80/1.47 inference(superposition,[status(thm)],[f90,f215])).
% 1.80/1.47 thf(f215,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) = ('const/lists/HD' @ X0 @ X1)) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.80/1.47 inference(superposition,[status(thm)],[f27,f90])).
% 1.80/1.47 thf(f27,plain,(
% 1.80/1.47 ( ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1)) = X2)) )),
% 1.80/1.47 inference(cnf_transformation,[status(thm)],[f12])).
% 1.80/1.47 thf(f12,plain,(
% 1.80/1.47 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : (('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1)) = X2)),
% 1.80/1.47 inference(rectify,[status(thm)],[f3])).
% 1.80/1.47 thf(f3,axiom,(
% 1.80/1.47 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : X0] : (('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2)) = X3)),
% 1.80/1.47 file('/export/starexec/sandbox/tmp/tmp.8iLam6mXFV/DTF2THF_22928.p','thm/lists/HD_')).
% 1.80/1.47 thf(f21,plain,(
% 1.80/1.47 (('const/ind_types/CONS' @ sK0 @ ('const/lists/HD' @ sK0 @ sK1) @ ('const/lists/TL' @ sK0 @ sK1)) != sK1)),
% 1.80/1.47 inference(cnf_transformation,[status(thm)],[f18])).
% 1.80/1.47 thf(f18,plain,(
% 1.80/1.47 ('const/ind_types/NIL' @ sK0 != sK1) & (('const/ind_types/CONS' @ sK0 @ ('const/lists/HD' @ sK0 @ sK1) @ ('const/lists/TL' @ sK0 @ sK1)) != sK1)),
% 1.80/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17])).
% 1.80/1.47 thf(f17,plain,(
% 1.80/1.47 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X1) & (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)) != X1)) => (('const/ind_types/NIL' @ sK0 != sK1) & (('const/ind_types/CONS' @ sK0 @ ('const/lists/HD' @ sK0 @ sK1) @ ('const/lists/TL' @ sK0 @ sK1)) != sK1))),
% 1.80/1.47 introduced(definition,[],[choice_axiom])).
% 1.80/1.47 thf(f16,plain,(
% 1.80/1.47 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X1) & (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)) != X1))),
% 1.80/1.47 inference(ennf_transformation,[status(thm)],[f11])).
% 1.80/1.47 thf(f11,plain,(
% 1.80/1.47 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X1) => (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)) = X1))),
% 1.80/1.47 inference(rectify,[status(thm)],[f6])).
% 1.80/1.47 thf(f6,negated_conjecture,(
% 1.80/1.47 ~! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X2) => (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X2) @ ('const/lists/TL' @ X0 @ X2)) = X2))),
% 1.80/1.47 inference(negated_conjecture,[status(cth)],[f5])).
% 1.80/1.47 thf(f5,conjecture,(
% 1.80/1.47 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X2) => (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X2) @ ('const/lists/TL' @ X0 @ X2)) = X2))),
% 1.80/1.47 file('/export/starexec/sandbox/tmp/tmp.8iLam6mXFV/DTF2THF_22928.p','thm/lists/CONS_HD_TL_')).
% 1.80/1.47 thf(f22,plain,(
% 1.80/1.47 ('const/ind_types/NIL' @ sK0 != sK1)),
% 1.80/1.47 inference(cnf_transformation,[status(thm)],[f18])).
% 1.80/1.47 % SZS output end Proof for DTF2THF_22928
% 1.80/1.47 % (23156)------------------------------
% 1.80/1.47 % (23156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.47 % (23156)Termination reason: Refutation
% 1.80/1.47
% 1.80/1.47 % (23156)Memory used [KB]: 5756
% 1.80/1.47 % (23156)Time elapsed: 0.048 s
% 1.80/1.47 % (23156)Instructions burned: 93 (million)
% 1.80/1.47 % (23156)------------------------------
% 1.80/1.47 % (23156)------------------------------
% 1.80/1.47 % (23115)Success in time 0.122 s
%------------------------------------------------------------------------------