%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT288^1 : 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 : n018.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 1.63s 1.39s
% Output : Refutation 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT288^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n018.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 06:14:01 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
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : DAT288^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.47 % Domain : Analysis
% 0.30/0.47 % Problem : list_CASES
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Kal16]
% 0.30/0.47 % Names : list_CASES_.p [Kal16]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.67 v8.1.0, 0.50 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.30/0.47 % Syntax : Number of formulae : 7 ( 2 unt; 3 typ; 0 def)
% 0.30/0.47 % Number of atoms : 7 ( 7 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 2 ( 1 avg)
% 0.30/0.47 % Number of connectives : 39 ( 1 ~; 1 |; 2 &; 33 @)
% 0.30/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 12 ( 7 avg)
% 0.30/0.47 % Number of types : 1 ( 0 usr)
% 0.30/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 4 ( 3 usr; 0 con; 1-3 aty)
% 0.30/0.47 % Number of variables : 19 ( 0 ^; 15 !; 2 ?; 19 :)
% 0.30/0.47 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.47 % SPC : TH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : Exported from core HOL Light.
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf('thf_type_type/ind_types/list',type,
% 0.30/0.47 'type/ind_types/list': $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf('thf_const_const/ind_types/NIL',type,
% 0.30/0.47 'const/ind_types/NIL':
% 0.30/0.47 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.30/0.47
% 0.30/0.47 thf('thf_const_const/ind_types/CONS',type,
% 0.30/0.47 'const/ind_types/CONS':
% 0.30/0.47 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf('thm/ind_types/list_INDUCT_',axiom,
% 0.30/0.47 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 0.30/0.47 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 0.30/0.47 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 0.30/0.47 ( ( P @ A1 )
% 0.30/0.47 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 0.30/0.47 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 0.30/0.47
% 0.30/0.47 thf('thm/lists/CONS_11_',axiom,
% 0.30/0.47 ! [A: $tType,A0: A,A1: A,A2: 'type/ind_types/list' @ A,A3: 'type/ind_types/list' @ A] :
% 0.30/0.47 ( ( ( 'const/ind_types/CONS' @ A @ A0 @ A2 )
% 0.30/0.47 = ( 'const/ind_types/CONS' @ A @ A1 @ A3 ) )
% 0.30/0.47 = ( ( A0 = A1 )
% 0.30/0.47 & ( A2 = A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf('thm/lists/NOT_CONS_NIL_',axiom,
% 0.30/0.47 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.30/0.47 ( ( 'const/ind_types/CONS' @ A @ A0 @ A1 )
% 0.30/0.47 != ( 'const/ind_types/NIL' @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf('thm/lists/list_CASES_',conjecture,
% 0.30/0.47 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 0.30/0.47 ( ( A0
% 0.30/0.47 = ( 'const/ind_types/NIL' @ A ) )
% 0.30/0.47 | ? [A1: A,A2: 'type/ind_types/list' @ A] :
% 0.30/0.47 ( A0
% 0.30/0.47 = ( 'const/ind_types/CONS' @ A @ A1 @ A2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.49/1.26 ---- Embedded in THF ---
% 1.49/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.26 %%% Generated on Tue Feb 24 06:14:02 EST 2026
% 1.49/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.26 %%% Logic specification used:
% 1.49/1.26 %%% thf(spec, logic, $$dhol).
% 1.49/1.26
% 1.49/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lvFiUfAEUJ/DTF2DTF21745.p
% 1.49/1.26 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.49/1.26 thf('thf_const_const/ind_types/NIL', type, 'const/ind_types/NIL': (!> [A:$tType]: (('type/ind_types/list' @ A)))).
% 1.49/1.26 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.49/1.26 thf('thm/ind_types/list_INDUCT_', axiom, (! [A:$tType,P:(('type/ind_types/list' @ A) > $o)]: ((((P @ ('const/ind_types/NIL' @ A)) & (! [A0:A,A1:('type/ind_types/list' @ A)]: (((P @ A1) => (P @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)))))) => (! [A0:('type/ind_types/list' @ A)]: ((P @ A0))))))).
% 1.49/1.26 thf('thm/lists/CONS_11_', axiom, (! [A:$tType,A0:A,A1:A,A2:('type/ind_types/list' @ A),A3:('type/ind_types/list' @ A)]: (((((('const/ind_types/CONS' @ A) @ A0) @ A2) = ((('const/ind_types/CONS' @ A) @ A1) @ A3)) = ((A0 = A1) & (A2 = A3)))))).
% 1.49/1.26 thf('thm/lists/NOT_CONS_NIL_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: ((((('const/ind_types/CONS' @ A) @ A0) @ A1) != ('const/ind_types/NIL' @ A))))).
% 1.49/1.26 thf('thm/lists/list_CASES_', conjecture, (! [A:$tType,A0:('type/ind_types/list' @ A)]: (((A0 = ('const/ind_types/NIL' @ A)) | (? [A1:A,A2:('type/ind_types/list' @ A)]: ((A0 = ((('const/ind_types/CONS' @ A) @ A1) @ A2)))))))).
% 1.49/1.26 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.lvFiUfAEUJ/DTF2DTF21745.p
% 1.49/1.26 ------------------------
% 1.49/1.27 ---- Cleaned THF ---
% 1.49/1.27 thf('thf_type_type/ind_types/list',type,
% 1.49/1.27 'type/ind_types/list': $tType > $tType ).
% 1.49/1.27
% 1.49/1.27 thf('thf_const_const/ind_types/NIL',type,
% 1.49/1.27 'const/ind_types/NIL':
% 1.49/1.27 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 1.49/1.27
% 1.49/1.27 thf('thf_const_const/ind_types/CONS',type,
% 1.49/1.27 'const/ind_types/CONS':
% 1.49/1.27 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.49/1.27
% 1.49/1.27 thf('thm/ind_types/list_INDUCT_',axiom,
% 1.49/1.27 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 1.49/1.27 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 1.49/1.27 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 1.49/1.27 ( ( P @ A1 )
% 1.49/1.27 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 1.49/1.27 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 1.49/1.27
% 1.49/1.27 thf('thm/lists/CONS_11_',axiom,
% 1.49/1.27 ! [A: $tType,A0: A,A1: A,A2: 'type/ind_types/list' @ A,A3: 'type/ind_types/list' @ A] :
% 1.49/1.27 ( ( ( 'const/ind_types/CONS' @ A @ A0 @ A2 )
% 1.49/1.27 = ( 'const/ind_types/CONS' @ A @ A1 @ A3 ) )
% 1.49/1.27 = ( ( A0 = A1 )
% 1.49/1.27 & ( A2 = A3 ) ) ) ).
% 1.49/1.27
% 1.49/1.27 thf('thm/lists/NOT_CONS_NIL_',axiom,
% 1.49/1.27 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.49/1.27 ( ( 'const/ind_types/CONS' @ A @ A0 @ A1 )
% 1.49/1.27 != ( 'const/ind_types/NIL' @ A ) ) ).
% 1.49/1.27
% 1.49/1.27 thf('thm/lists/list_CASES_',conjecture,
% 1.49/1.27 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 1.49/1.27 ( ( A0
% 1.49/1.27 = ( 'const/ind_types/NIL' @ A ) )
% 1.49/1.27 | ? [A1: A,A2: 'type/ind_types/list' @ A] :
% 1.49/1.27 ( A0
% 1.49/1.27 = ( 'const/ind_types/CONS' @ A @ A1 @ A2 ) ) ) ).
% 1.49/1.27 ------------------------
% 1.49/1.28 % (22074)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/2Mi)
% 1.49/1.29 % (22074)Instruction limit reached!
% 1.49/1.29 % (22074)------------------------------
% 1.49/1.29 % (22074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (22074)Termination reason: Unknown
% 1.49/1.29 % (22074)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (22074)Memory used [KB]: 5500
% 1.49/1.29 % (22074)Time elapsed: 0.002 s
% 1.49/1.29 % (22074)Instructions burned: 2 (million)
% 1.49/1.29 % (22074)------------------------------
% 1.49/1.29 % (22074)------------------------------
% 1.49/1.29 % (22072)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_21745 for (2999ds/4Mi)
% 1.49/1.29 % (22072)Instruction limit reached!
% 1.49/1.29 % (22072)------------------------------
% 1.49/1.29 % (22072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (22072)Termination reason: Unknown
% 1.49/1.29 % (22072)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (22072)Memory used [KB]: 5500
% 1.49/1.29 % (22072)Time elapsed: 0.003 s
% 1.49/1.29 % (22072)Instructions burned: 4 (million)
% 1.49/1.29 % (22072)------------------------------
% 1.49/1.29 % (22072)------------------------------
% 1.49/1.29 % (22071)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/183Mi)
% 1.49/1.29 % (22073)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_21745 for (2999ds/27Mi)
% 1.49/1.29 % (22075)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_21745 for (2999ds/2Mi)
% 1.49/1.29 % (22076)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_21745 for (2999ds/275Mi)
% 1.49/1.29 % (22077)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/18Mi)
% 1.49/1.29 % Exception at run slice level
% 1.49/1.29 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
% 1.49/1.29 % (22076)Refutation not found, incomplete strategy
% 1.49/1.29 % (22076)------------------------------
% 1.49/1.29 % (22076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (22076)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.29
% 1.49/1.29
% 1.49/1.29 % (22076)Memory used [KB]: 5500
% 1.49/1.29 % (22076)Time elapsed: 0.003 s
% 1.49/1.29 % (22076)Instructions burned: 2 (million)
% 1.49/1.29 % (22076)------------------------------
% 1.49/1.29 % (22076)------------------------------
% 1.63/1.30 % (22079)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_21745 for (2999ds/37Mi)
% 1.63/1.30 % Exception at run slice level
% 1.63/1.30 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
% 1.63/1.30 % (22078)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/3Mi)
% 1.63/1.30 % (22077)Instruction limit reached!
% 1.63/1.30 % (22077)------------------------------
% 1.63/1.30 % (22077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (22077)Termination reason: Unknown
% 1.63/1.30 % (22077)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (22077)Memory used [KB]: 5628
% 1.63/1.30 % (22077)Time elapsed: 0.014 s
% 1.63/1.30 % (22077)Instructions burned: 18 (million)
% 1.63/1.30 % (22077)------------------------------
% 1.63/1.30 % (22077)------------------------------
% 1.63/1.30 % (22078)Instruction limit reached!
% 1.63/1.30 % (22078)------------------------------
% 1.63/1.30 % (22078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (22078)Termination reason: Unknown
% 1.63/1.30 % (22078)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (22078)Memory used [KB]: 5500
% 1.63/1.30 % (22078)Time elapsed: 0.004 s
% 1.63/1.30 % (22078)Instructions burned: 3 (million)
% 1.63/1.30 % (22078)------------------------------
% 1.63/1.30 % (22078)------------------------------
% 1.63/1.31 % (22082)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_21745 for (2999ds/1041Mi)
% 1.63/1.31 % Exception at run slice level
% 1.63/1.31 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
% 1.63/1.31 % (22073)Instruction limit reached!
% 1.63/1.31 % (22073)------------------------------
% 1.63/1.31 % (22073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (22073)Termination reason: Unknown
% 1.63/1.31 % (22073)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (22073)Memory used [KB]: 5500
% 1.63/1.31 % (22073)Time elapsed: 0.019 s
% 1.63/1.31 % (22073)Instructions burned: 27 (million)
% 1.63/1.31 % (22073)------------------------------
% 1.63/1.31 % (22073)------------------------------
% 1.63/1.31 % (22080)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_21745 for (2999ds/15Mi)
% 1.63/1.31 % (22081)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_21745 for (2999ds/3Mi)
% 1.63/1.31 % (22080)Refutation not found, incomplete strategy
% 1.63/1.31 % (22080)------------------------------
% 1.63/1.31 % (22080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (22080)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.31
% 1.63/1.31
% 1.63/1.31 % (22080)Memory used [KB]: 5500
% 1.63/1.31 % (22080)Time elapsed: 0.003 s
% 1.63/1.31 % (22080)Instructions burned: 2 (million)
% 1.63/1.31 % (22080)------------------------------
% 1.63/1.31 % (22080)------------------------------
% 1.63/1.31 % (22081)Instruction limit reached!
% 1.63/1.31 % (22081)------------------------------
% 1.63/1.31 % (22081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (22081)Termination reason: Unknown
% 1.63/1.31 % (22081)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (22081)Memory used [KB]: 5500
% 1.63/1.31 % (22081)Time elapsed: 0.004 s
% 1.63/1.31 % (22081)Instructions burned: 3 (million)
% 1.63/1.31 % (22081)------------------------------
% 1.63/1.31 % (22081)------------------------------
% 1.63/1.32 % (22085)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_21745 for (2999ds/3Mi)
% 1.63/1.32 % (22085)Instruction limit reached!
% 1.63/1.32 % (22085)------------------------------
% 1.63/1.32 % (22085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (22085)Termination reason: Unknown
% 1.63/1.32 % (22085)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (22085)Memory used [KB]: 5500
% 1.63/1.32 % (22085)Time elapsed: 0.003 s
% 1.63/1.32 % (22085)Instructions burned: 4 (million)
% 1.63/1.32 % (22085)------------------------------
% 1.63/1.32 % (22085)------------------------------
% 1.63/1.32 % (22083)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/7Mi)
% 1.63/1.32 % (22084)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/16Mi)
% 1.63/1.33 % (22086)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_21745 for (2999ds/3Mi)
% 1.63/1.33 % (22083)Instruction limit reached!
% 1.63/1.33 % (22083)------------------------------
% 1.63/1.33 % (22083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (22083)Termination reason: Unknown
% 1.63/1.33 % (22083)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (22083)Memory used [KB]: 1023
% 1.63/1.33 % (22083)Time elapsed: 0.007 s
% 1.63/1.33 % (22083)Instructions burned: 8 (million)
% 1.63/1.33 % (22083)------------------------------
% 1.63/1.33 % (22083)------------------------------
% 1.63/1.33 % (22086)Instruction limit reached!
% 1.63/1.33 % (22086)------------------------------
% 1.63/1.33 % (22086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (22086)Termination reason: Unknown
% 1.63/1.33 % (22086)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (22086)Memory used [KB]: 1023
% 1.63/1.33 % (22086)Time elapsed: 0.004 s
% 1.63/1.33 % (22086)Instructions burned: 4 (million)
% 1.63/1.33 % (22086)------------------------------
% 1.63/1.33 % (22086)------------------------------
% 1.63/1.33 % (22089)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/4Mi)
% 1.63/1.33 % (22087)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/7Mi)
% 1.63/1.33 % (22088)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/3Mi)
% 1.63/1.33 % (22089)Instruction limit reached!
% 1.63/1.33 % (22089)------------------------------
% 1.63/1.33 % (22089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (22089)Termination reason: Unknown
% 1.63/1.33 % (22089)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (22089)Memory used [KB]: 5500
% 1.63/1.33 % (22089)Time elapsed: 0.004 s
% 1.63/1.33 % (22089)Instructions burned: 6 (million)
% 1.63/1.33 % (22089)------------------------------
% 1.63/1.33 % (22089)------------------------------
% 1.63/1.33 % (22084)Instruction limit reached!
% 1.63/1.33 % (22084)------------------------------
% 1.63/1.33 % (22084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (22084)Termination reason: Unknown
% 1.63/1.33 % Exception at run slice level% (22084)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33
% 1.63/1.33 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
% 1.63/1.33 % (22084)Memory used [KB]: 5628
% 1.63/1.33 % (22084)Time elapsed: 0.012 s
% 1.63/1.33 % (22084)Instructions burned: 16 (million)
% 1.63/1.33 % (22084)------------------------------
% 1.63/1.33 % (22084)------------------------------
% 1.63/1.33 % (22087)Instruction limit reached!
% 1.63/1.33 % (22087)------------------------------
% 1.63/1.33 % (22087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (22087)Termination reason: Unknown
% 1.63/1.33 % (22087)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (22087)Memory used [KB]: 5500
% 1.63/1.33 % (22087)Time elapsed: 0.006 s
% 1.63/1.33 % (22087)Instructions burned: 7 (million)
% 1.63/1.33 % (22087)------------------------------
% 1.63/1.33 % (22087)------------------------------
% 1.63/1.34 % (22092)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/6Mi)
% 1.63/1.34 % (22092)Instruction limit reached!
% 1.63/1.34 % (22092)------------------------------
% 1.63/1.34 % (22092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (22092)Termination reason: Unknown
% 1.63/1.34 % (22092)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (22092)Memory used [KB]: 5500
% 1.63/1.34 % (22092)Time elapsed: 0.003 s
% 1.63/1.34 % (22092)Instructions burned: 6 (million)
% 1.63/1.34 % (22092)------------------------------
% 1.63/1.34 % (22092)------------------------------
% 1.63/1.34 % (22090)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/18Mi)
% 1.63/1.35 % (22091)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/710Mi)
% 1.63/1.35 % (22093)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_21745 for (2999ds/902Mi)
% 1.63/1.35 % (22094)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_21745 for (2999ds/21Mi)
% 1.63/1.35 % (22093)Refutation not found, incomplete strategy
% 1.63/1.35 % (22093)------------------------------
% 1.63/1.35 % (22093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (22093)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (22093)Memory used [KB]: 5500
% 1.63/1.35 % (22093)Time elapsed: 0.003 s
% 1.63/1.35 % (22093)Instructions burned: 2 (million)
% 1.63/1.35 % (22093)------------------------------
% 1.63/1.35 % (22093)------------------------------
% 1.63/1.35 % (22095)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/5Mi)
% 1.63/1.35 % (22096)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_21745 for (2999ds/6Mi)
% 1.63/1.35 % Exception at run slice level
% 1.63/1.35 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
% 1.63/1.35 % Exception at run slice level
% 1.63/1.35 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
% 1.63/1.36 % (22090)Instruction limit reached!
% 1.63/1.36 % (22090)------------------------------
% 1.63/1.36 % (22090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (22090)Termination reason: Unknown
% 1.63/1.36 % (22090)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (22090)Memory used [KB]: 5500
% 1.63/1.36 % (22090)Time elapsed: 0.013 s
% 1.63/1.36 % (22090)Instructions burned: 18 (million)
% 1.63/1.36 % (22090)------------------------------
% 1.63/1.36 % (22090)------------------------------
% 1.63/1.36 % (22099)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_21745 for (2999ds/19Mi)
% 1.63/1.36 % Exception at run slice level
% 1.63/1.36 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
% 1.63/1.36 % (22094)Instruction limit reached!
% 1.63/1.36 % (22094)------------------------------
% 1.63/1.36 % (22094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (22094)Termination reason: Unknown
% 1.63/1.36 % (22094)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (22094)Memory used [KB]: 5628
% 1.63/1.36 % (22094)Time elapsed: 0.016 s
% 1.63/1.36 % (22094)Instructions burned: 21 (million)
% 1.63/1.36 % (22094)------------------------------
% 1.63/1.36 % (22094)------------------------------
% 1.63/1.37 % (22097)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/377Mi)
% 1.63/1.37 % (22098)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_21745 for (2999ds/779Mi)
% 1.63/1.37 % Exception at run slice level
% 1.63/1.37 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
% 1.63/1.37 % (22101)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/17Mi)
% 1.63/1.37 % (22100)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/879Mi)
% 1.63/1.38 % (22102)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/3Mi)
% 1.63/1.38 % (22101)Instruction limit reached!
% 1.63/1.38 % (22101)------------------------------
% 1.63/1.38 % (22101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (22101)Termination reason: Unknown
% 1.63/1.38 % (22101)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (22101)Memory used [KB]: 5500
% 1.63/1.38 % (22101)Time elapsed: 0.007 s
% 1.63/1.38 % (22101)Instructions burned: 17 (million)
% 1.63/1.38 % (22101)------------------------------
% 1.63/1.38 % (22101)------------------------------
% 1.63/1.38 % (22102)Instruction limit reached!
% 1.63/1.38 % (22102)------------------------------
% 1.63/1.38 % (22102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (22102)Termination reason: Unknown
% 1.63/1.38 % (22102)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (22102)Memory used [KB]: 1023
% 1.63/1.38 % (22102)Time elapsed: 0.002 s
% 1.63/1.38 % (22102)Instructions burned: 3 (million)
% 1.63/1.38 % (22102)------------------------------
% 1.63/1.38 % (22102)------------------------------
% 1.63/1.39 % (22104)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/127Mi)
% 1.63/1.39 % (22100)First to succeed.
% 1.63/1.39 % (22105)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/100Mi)
% 1.63/1.39 % (22103)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21745 for (2999ds/30Mi)
% 1.63/1.39 % (22091)Also succeeded, but the first one will report.
% 1.63/1.39 % (22100)Refutation found. Thanks to Tanya!
% 1.63/1.39 % SZS status Theorem for DTF2THF_21745
% 1.63/1.39 % SZS output start Proof for DTF2THF_21745
% 1.63/1.39 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 1.63/1.39 thf(type_def_7, type, sK0: $tType).
% 1.63/1.39 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 1.63/1.39 thf(func_def_1, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 1.63/1.39 thf(func_def_2, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.63/1.39 thf(func_def_8, type, sK1: 'type/ind_types/list' @ sK0).
% 1.63/1.39 thf(func_def_9, type, sK2: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > X0)).
% 1.63/1.39 thf(func_def_10, type, sK3: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0)).
% 1.63/1.39 thf(func_def_13, type, ph5: !>[X0: $tType]:(X0)).
% 1.63/1.39 thf(f182,plain,(
% 1.63/1.39 $false),
% 1.63/1.39 inference(subsumption_resolution,[status(thm)],[f181,f21])).
% 1.63/1.39 thf(f21,plain,(
% 1.63/1.39 (sK1 != 'const/ind_types/NIL' @ sK0)),
% 1.63/1.39 inference(cnf_transformation,[status(thm)],[f17])).
% 1.63/1.39 thf(f17,plain,(
% 1.63/1.39 (sK1 != 'const/ind_types/NIL' @ sK0) & ! [X2 : sK0,X3 : 'type/ind_types/list' @ sK0] : (sK1 != ('const/ind_types/CONS' @ sK0 @ X2 @ X3))),
% 1.63/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16])).
% 1.63/1.39 thf(f16,plain,(
% 1.63/1.39 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X1) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (('const/ind_types/CONS' @ X0 @ X2 @ X3) != X1)) => ((sK1 != 'const/ind_types/NIL' @ sK0) & ! [X3 : 'type/ind_types/list' @ sK0,X2 : sK0] : (sK1 != ('const/ind_types/CONS' @ sK0 @ X2 @ X3)))),
% 1.63/1.39 introduced(definition,[],[choice_axiom])).
% 1.63/1.39 thf(f15,plain,(
% 1.63/1.39 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 != X1) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (('const/ind_types/CONS' @ X0 @ X2 @ X3) != X1))),
% 1.63/1.39 inference(ennf_transformation,[status(thm)],[f11])).
% 1.63/1.39 thf(f11,plain,(
% 1.63/1.39 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (('const/ind_types/CONS' @ X0 @ X2 @ X3) = X1))),
% 1.63/1.39 inference(rectify,[status(thm)],[f5])).
% 1.63/1.39 thf(f5,negated_conjecture,(
% 1.63/1.39 ~! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (('const/ind_types/CONS' @ X0 @ X3 @ X4) = X2) | ('const/ind_types/NIL' @ X0 = X2))),
% 1.63/1.39 inference(negated_conjecture,[status(cth)],[f4])).
% 1.63/1.39 thf(f4,conjecture,(
% 1.63/1.39 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (('const/ind_types/CONS' @ X0 @ X3 @ X4) = X2) | ('const/ind_types/NIL' @ X0 = X2))),
% 1.63/1.39 file('/export/starexec/sandbox/tmp/tmp.lvFiUfAEUJ/DTF2THF_21745.p','thm/lists/list_CASES_')).
% 1.63/1.39 thf(f181,plain,(
% 1.63/1.39 (sK1 = 'const/ind_types/NIL' @ sK0)),
% 1.63/1.39 inference(equality_resolution,[status(thm)],[f166])).
% 1.63/1.39 thf(f166,plain,(
% 1.63/1.39 ( ! [X0 : 'type/ind_types/list' @ sK0] : ((sK1 != X0) | ('const/ind_types/NIL' @ sK0 = X0)) )),
% 1.63/1.39 inference(superposition,[status(thm)],[f20,f62])).
% 1.63/1.39 thf(f62,plain,(
% 1.63/1.39 ( ! [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)) )),
% 1.63/1.39 inference(equality_proxy_clausification,[status(thm)],[f61])).
% 1.63/1.39 thf(f61,plain,(
% 1.63/1.39 ( ! [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))) )),
% 1.63/1.39 inference(not_proxy_clausification,[status(thm)],[f60])).
% 1.63/1.39 thf(f60,plain,(
% 1.63/1.39 ( ! [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)))) )),
% 1.63/1.39 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.63/1.39 thf(f50,plain,(
% 1.63/1.39 ( ! [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)) )),
% 1.63/1.39 inference(leibniz_equality_elimination,[status(thm)],[f23])).
% 1.63/1.39 thf(f23,plain,(
% 1.63/1.39 ( ! [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 @ X4) = $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.63/1.39 inference(cnf_transformation,[status(thm)],[f19])).
% 1.63/1.39 thf(f19,plain,(
% 1.63/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | (((X1 @ (sK3 @ X0 @ X1)) = $true) & ($true != (X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))))) | ! [X4 : 'type/ind_types/list' @ X0] : ((X1 @ X4) = $true))),
% 1.63/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f14,f18])).
% 1.63/1.39 thf(f18,plain,(
% 1.63/1.39 ! [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 @ (sK3 @ X0 @ X1)) = $true) & ($true != (X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))))))),
% 1.63/1.39 introduced(definition,[],[choice_axiom])).
% 1.63/1.39 thf(f14,plain,(
% 1.63/1.39 ! [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))),
% 1.63/1.39 inference(flattening,[status(thm)],[f13])).
% 1.63/1.39 thf(f13,plain,(
% 1.63/1.39 ! [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 @ X3) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true))))),
% 1.63/1.39 inference(ennf_transformation,[status(thm)],[f10])).
% 1.63/1.39 thf(f10,plain,(
% 1.63/1.39 ! [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))),
% 1.63/1.39 inference(fool_elimination,[status(thm)],[f9])).
% 1.63/1.39 thf(f9,plain,(
% 1.63/1.39 ! [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))),
% 1.63/1.39 inference(rectify,[status(thm)],[f1])).
% 1.63/1.39 thf(f1,axiom,(
% 1.63/1.39 ! [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))),
% 1.63/1.39 file('/export/starexec/sandbox/tmp/tmp.lvFiUfAEUJ/DTF2THF_21745.p','thm/ind_types/list_INDUCT_')).
% 1.63/1.39 thf(f20,plain,(
% 1.63/1.39 ( ! [X2 : sK0,X3 : 'type/ind_types/list' @ sK0] : ((sK1 != ('const/ind_types/CONS' @ sK0 @ X2 @ X3))) )),
% 1.63/1.39 inference(cnf_transformation,[status(thm)],[f17])).
% 1.63/1.39 % SZS output end Proof for DTF2THF_21745
% 1.63/1.39 % (22100)------------------------------
% 1.63/1.39 % (22100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (22100)Termination reason: Refutation
% 1.63/1.39
% 1.63/1.39 % (22100)Memory used [KB]: 5628
% 1.63/1.39 % (22100)Time elapsed: 0.017 s
% 1.63/1.39 % (22100)Instructions burned: 23 (million)
% 1.63/1.39 % (22100)------------------------------
% 1.63/1.39 % (22100)------------------------------
% 1.63/1.39 % (22070)Success in time 0.101 s
%------------------------------------------------------------------------------