%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT280^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 08:45:22 AM UTC 2026
% Result : Theorem 1.24s 1.13s
% Output : Refutation 1.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT280^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 06:13:16 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : DAT280^1 : TPTP v9.2.1. Released v7.0.0.
% 0.15/0.42 % Domain : Analysis
% 0.15/0.42 % Problem : ITLIST2_
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Kal16]
% 0.15/0.42 % Names : ITLIST2_0.p [Kal16]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.00 v7.1.0
% 0.15/0.42 % Syntax : Number of formulae : 5 ( 2 unt; 3 typ; 0 def)
% 0.15/0.42 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 1 ( 1 avg)
% 0.15/0.42 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 21 @)
% 0.15/0.42 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 7 ( 7 avg)
% 0.15/0.42 % Number of types : 0 ( 0 usr)
% 0.15/0.42 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 4 ( 3 usr; 0 con; 1-7 aty)
% 0.15/0.42 % Number of variables : 15 ( 0 ^; 11 !; 0 ?; 15 :)
% 0.15/0.42 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.42 % SPC : TH1_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : Exported from core HOL Light.
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf('thf_type_type/ind_types/list',type,
% 0.15/0.42 'type/ind_types/list': $tType > $tType ).
% 0.15/0.42
% 0.15/0.42 thf('thf_const_const/lists/ITLIST2',type,
% 0.15/0.42 'const/lists/ITLIST2':
% 0.15/0.42 !>[A: $tType,A0: $tType,A1: $tType] : ( ( A > A0 > A1 > A1 ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A0 ) > A1 > A1 ) ).
% 0.15/0.42
% 0.15/0.42 thf('thf_const_const/ind_types/NIL',type,
% 0.15/0.42 'const/ind_types/NIL':
% 0.15/0.42 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.15/0.42
% 0.15/0.42 thf('thm/lists/ITLIST2_DEF_0',axiom,
% 0.15/0.42 ! [A: $tType,A0: $tType,A1: $tType,A2: A > A0 > A1 > A1,A3: 'type/ind_types/list' @ A0,A4: A1] :
% 0.15/0.42 ( ( 'const/lists/ITLIST2' @ A @ A0 @ A1 @ A2 @ ( 'const/ind_types/NIL' @ A ) @ A3 @ A4 )
% 0.15/0.42 = A4 ) ).
% 0.15/0.42
% 0.15/0.42 thf('thm/lists/ITLIST2_0',conjecture,
% 0.15/0.42 ! [A: $tType,A0: $tType,A1: $tType,A2: A > A0 > A1 > A1,A3: A1] :
% 0.15/0.42 ( ( 'const/lists/ITLIST2' @ A @ A0 @ A1 @ A2 @ ( 'const/ind_types/NIL' @ A ) @ ( 'const/ind_types/NIL' @ A0 ) @ A3 )
% 0.15/0.42 = A3 ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.07/1.10 ---- Embedded in THF ---
% 1.07/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.07/1.10 %%% Generated on Tue Feb 24 06:13:16 EST 2026
% 1.07/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.07/1.10 %%% Logic specification used:
% 1.07/1.10 %%% thf(spec, logic, $$dhol).
% 1.07/1.10
% 1.07/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YUYRAag2E4/DTF2DTF18034.p
% 1.07/1.10 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.07/1.10 thf('thf_const_const/lists/ITLIST2', type, 'const/lists/ITLIST2': (!> [A:$tType,A0:$tType,A1:$tType]: (((A > (A0 > (A1 > A1))) > (('type/ind_types/list' @ A) > (('type/ind_types/list' @ A0) > (A1 > A1))))))).
% 1.07/1.10 thf('thf_const_const/ind_types/NIL', type, 'const/ind_types/NIL': (!> [A:$tType]: (('type/ind_types/list' @ A)))).
% 1.07/1.10 thf('thm/lists/ITLIST2_DEF_0', axiom, (! [A:$tType,A0:$tType,A1:$tType,A2:(A > (A0 > (A1 > A1))),A3:('type/ind_types/list' @ A0),A4:A1]: ((((((((('const/lists/ITLIST2' @ A) @ A0) @ A1) @ A2) @ ('const/ind_types/NIL' @ A)) @ A3) @ A4) = A4)))).
% 1.07/1.10 thf('thm/lists/ITLIST2_0', conjecture, (! [A:$tType,A0:$tType,A1:$tType,A2:(A > (A0 > (A1 > A1))),A3:A1]: ((((((((('const/lists/ITLIST2' @ A) @ A0) @ A1) @ A2) @ ('const/ind_types/NIL' @ A)) @ ('const/ind_types/NIL' @ A0)) @ A3) = A3)))).
% 1.07/1.10 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YUYRAag2E4/DTF2DTF18034.p
% 1.07/1.10 ------------------------
% 1.24/1.11 ---- Cleaned THF ---
% 1.24/1.11 thf('thf_type_type/ind_types/list',type,
% 1.24/1.11 'type/ind_types/list': $tType > $tType ).
% 1.24/1.11
% 1.24/1.11 thf('thf_const_const/lists/ITLIST2',type,
% 1.24/1.11 'const/lists/ITLIST2':
% 1.24/1.11 !>[A: $tType,A0: $tType,A1: $tType] : ( ( A > A0 > A1 > A1 ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A0 ) > A1 > A1 ) ).
% 1.24/1.11
% 1.24/1.11 thf('thf_const_const/ind_types/NIL',type,
% 1.24/1.11 'const/ind_types/NIL':
% 1.24/1.11 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 1.24/1.11
% 1.24/1.11 thf('thm/lists/ITLIST2_DEF_0',axiom,
% 1.24/1.11 ! [A: $tType,A0: $tType,A1: $tType,A2: A > A0 > A1 > A1,A3: 'type/ind_types/list' @ A0,A4: A1] :
% 1.24/1.11 ( ( 'const/lists/ITLIST2' @ A @ A0 @ A1 @ A2 @ ( 'const/ind_types/NIL' @ A ) @ A3 @ A4 )
% 1.24/1.11 = A4 ) ).
% 1.24/1.11
% 1.24/1.11 thf('thm/lists/ITLIST2_0',conjecture,
% 1.24/1.11 ! [A: $tType,A0: $tType,A1: $tType,A2: A > A0 > A1 > A1,A3: A1] :
% 1.24/1.11 ( ( 'const/lists/ITLIST2' @ A @ A0 @ A1 @ A2 @ ( 'const/ind_types/NIL' @ A ) @ ( 'const/ind_types/NIL' @ A0 ) @ A3 )
% 1.24/1.11 = A3 ) ).
% 1.24/1.11 ------------------------
% 1.24/1.12 % (18200)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_18034 for (3000ds/275Mi)
% 1.24/1.12 % (18197)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_18034 for (3000ds/27Mi)
% 1.24/1.12 % (18195)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18034 for (3000ds/183Mi)
% 1.24/1.12 % (18199)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_18034 for (3000ds/2Mi)
% 1.24/1.12 % (18196)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_18034 for (3000ds/4Mi)
% 1.24/1.12 % (18198)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18034 for (3000ds/2Mi)
% 1.24/1.12 % (18201)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18034 for (3000ds/18Mi)
% 1.24/1.12 % (18199)Instruction limit reached!
% 1.24/1.12 % (18199)------------------------------
% 1.24/1.12 % (18199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.24/1.12 % (18199)Termination reason: Unknown
% 1.24/1.12 % (18199)Termination phase: shuffling
% 1.24/1.12
% 1.24/1.12 % (18199)Memory used [KB]: 895
% 1.24/1.12 % (18199)Time elapsed: 0.002 s
% 1.24/1.12 % (18199)Instructions burned: 2 (million)
% 1.24/1.12 % (18199)------------------------------
% 1.24/1.12 % (18199)------------------------------
% 1.24/1.12 % (18200)First to succeed.
% 1.24/1.13 % (18198)Also succeeded, but the first one will report.
% 1.24/1.13 % (18200)Refutation found. Thanks to Tanya!
% 1.24/1.13 % SZS status Theorem for DTF2THF_18034
% 1.24/1.13 % SZS output start Proof for DTF2THF_18034
% 1.24/1.13 thf(type_def_6, type, 'type/ind_types/list': ($tType) > $tType).
% 1.24/1.13 thf(type_def_7, type, sK0: $tType).
% 1.24/1.13 thf(type_def_8, type, sK1: $tType).
% 1.24/1.13 thf(type_def_9, type, sK2: $tType).
% 1.24/1.13 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 1.24/1.13 thf(func_def_1, type, 'const/lists/ITLIST2': !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2 > X2) > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X1 > X2 > X2)).
% 1.24/1.13 thf(func_def_2, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 1.24/1.13 thf(func_def_6, type, sK3: sK0 > sK1 > sK2 > sK2).
% 1.24/1.13 thf(func_def_7, type, sK4: sK2).
% 1.24/1.13 thf(func_def_9, type, ph6: !>[X0: $tType]:(X0)).
% 1.24/1.13 thf(f10,plain,(
% 1.24/1.13 $false),
% 1.24/1.13 inference(subsumption_resolution,[status(thm)],[f8,f9])).
% 1.24/1.13 thf(f9,plain,(
% 1.24/1.13 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X1 > X2 > X2,X4 : 'type/ind_types/list' @ X1,X5 : X2] : ((('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ X4 @ X5) = X5)) )),
% 1.24/1.13 inference(cnf_transformation,[status(thm)],[f1])).
% 1.24/1.13 thf(f1,axiom,(
% 1.24/1.13 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X1 > X2 > X2,X4 : 'type/ind_types/list' @ X1,X5 : X2] : (('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ X4 @ X5) = X5)),
% 1.24/1.13 file('/export/starexec/sandbox2/tmp/tmp.YUYRAag2E4/DTF2THF_18034.p','thm/lists/ITLIST2_DEF_0')).
% 1.24/1.13 thf(f8,plain,(
% 1.24/1.13 (sK4 != ('const/lists/ITLIST2' @ sK0 @ sK1 @ sK2 @ sK3 @ 'const/ind_types/NIL' @ sK0 @ 'const/ind_types/NIL' @ sK1 @ sK4))),
% 1.24/1.13 inference(cnf_transformation,[status(thm)],[f7])).
% 1.24/1.13 thf(f7,plain,(
% 1.24/1.13 (sK4 != ('const/lists/ITLIST2' @ sK0 @ sK1 @ sK2 @ sK3 @ 'const/ind_types/NIL' @ sK0 @ 'const/ind_types/NIL' @ sK1 @ sK4))),
% 1.24/1.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f5,f6])).
% 1.24/1.13 thf(f6,plain,(
% 1.24/1.13 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X1 > X2 > X2,X4 : X2] : (('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ 'const/ind_types/NIL' @ X1 @ X4) != X4) => (sK4 != ('const/lists/ITLIST2' @ sK0 @ sK1 @ sK2 @ sK3 @ 'const/ind_types/NIL' @ sK0 @ 'const/ind_types/NIL' @ sK1 @ sK4))),
% 1.24/1.13 introduced(definition,[],[choice_axiom])).
% 1.24/1.13 thf(f5,plain,(
% 1.24/1.13 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X1 > X2 > X2,X4 : X2] : (('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ 'const/ind_types/NIL' @ X1 @ X4) != X4)),
% 1.24/1.13 inference(ennf_transformation,[status(thm)],[f3])).
% 1.24/1.13 thf(f3,negated_conjecture,(
% 1.24/1.13 ~! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X1 > X2 > X2,X4 : X2] : (('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ 'const/ind_types/NIL' @ X1 @ X4) = X4)),
% 1.24/1.13 inference(negated_conjecture,[status(cth)],[f2])).
% 1.24/1.13 thf(f2,conjecture,(
% 1.24/1.13 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X1 > X2 > X2,X4 : X2] : (('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ 'const/ind_types/NIL' @ X1 @ X4) = X4)),
% 1.24/1.13 file('/export/starexec/sandbox2/tmp/tmp.YUYRAag2E4/DTF2THF_18034.p','thm/lists/ITLIST2_0')).
% 1.24/1.13 % SZS output end Proof for DTF2THF_18034
% 1.24/1.13 % (18200)------------------------------
% 1.24/1.13 % (18200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.24/1.13 % (18200)Termination reason: Refutation
% 1.24/1.13
% 1.24/1.13 % (18200)Memory used [KB]: 5500
% 1.24/1.13 % (18200)Time elapsed: 0.002 s
% 1.24/1.13 % (18200)Instructions burned: 1 (million)
% 1.24/1.13 % (18200)------------------------------
% 1.24/1.13 % (18200)------------------------------
% 1.24/1.13 % (18194)Success in time 0.011 s
%------------------------------------------------------------------------------