%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT324^1 : 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 : n004.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 1.67s 1.30s
% Output : Refutation 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT324^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n004.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:14:11 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : DAT324^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Analysis
% 0.19/0.45 % Problem : LENGTH_LIST_OF_SET
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Kal16]
% 0.19/0.45 % Names : LENGTH_LIST_OF_SET_.p [Kal16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 9 ( 0 unt; 7 typ; 0 def)
% 0.19/0.45 % Number of atoms : 6 ( 3 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.45 % Number of connectives : 26 ( 0 ~; 0 |; 1 &; 23 @)
% 0.19/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 6 ( 6 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.19/0.45 % Number of variables : 9 ( 0 ^; 4 !; 0 ?; 9 :)
% 0.19/0.45 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : Exported from core HOL Light.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf('thf_type_type/nums/num',type,
% 0.19/0.45 'type/nums/num': $tType ).
% 0.19/0.45
% 0.19/0.45 thf('thf_type_type/ind_types/list',type,
% 0.19/0.45 'type/ind_types/list': $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/set_of_list',type,
% 0.19/0.45 'const/sets/set_of_list':
% 0.19/0.45 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/list_of_set',type,
% 0.19/0.45 'const/sets/list_of_set':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/FINITE',type,
% 0.19/0.45 'const/sets/FINITE':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/CARD',type,
% 0.19/0.45 'const/sets/CARD':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/lists/LENGTH',type,
% 0.19/0.45 'const/lists/LENGTH':
% 0.19/0.45 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > 'type/nums/num' ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/sets/LIST_OF_SET_PROPERTIES_',axiom,
% 0.19/0.45 ! [A: $tType,A0: A > $o] :
% 0.19/0.45 ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.19/0.45 => ( ( ( 'const/sets/set_of_list' @ A @ ( 'const/sets/list_of_set' @ A @ A0 ) )
% 0.19/0.45 = A0 )
% 0.19/0.45 & ( ( 'const/lists/LENGTH' @ A @ ( 'const/sets/list_of_set' @ A @ A0 ) )
% 0.19/0.45 = ( 'const/sets/CARD' @ A @ A0 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/sets/LENGTH_LIST_OF_SET_',conjecture,
% 0.19/0.45 ! [A: $tType,A0: A > $o] :
% 0.19/0.45 ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.19/0.45 => ( ( 'const/lists/LENGTH' @ A @ ( 'const/sets/list_of_set' @ A @ A0 ) )
% 0.19/0.45 = ( 'const/sets/CARD' @ A @ A0 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.50/1.27 ---- Embedded in THF ---
% 1.50/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.27 %%% Generated on Tue Feb 24 06:14:12 EST 2026
% 1.50/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.27 %%% Logic specification used:
% 1.50/1.27 %%% thf(spec, logic, $$dhol).
% 1.50/1.27
% 1.50/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.1ZsFGNEGVj/DTF2DTF16438.p
% 1.50/1.27 thf('thf_type_type/nums/num', type, 'type/nums/num': $tType).
% 1.50/1.27 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.50/1.27 thf('thf_const_const/sets/set_of_list', type, 'const/sets/set_of_list': (!> [A:$tType]: ((('type/ind_types/list' @ A) > (A > $o))))).
% 1.50/1.27 thf('thf_const_const/sets/list_of_set', type, 'const/sets/list_of_set': (!> [A:$tType]: (((A > $o) > ('type/ind_types/list' @ A))))).
% 1.50/1.27 thf('thf_const_const/sets/FINITE', type, 'const/sets/FINITE': (!> [A:$tType]: (((A > $o) > $o)))).
% 1.50/1.27 thf('thf_const_const/sets/CARD', type, 'const/sets/CARD': (!> [A:$tType]: (((A > $o) > 'type/nums/num')))).
% 1.50/1.27 thf('thf_const_const/lists/LENGTH', type, 'const/lists/LENGTH': (!> [A:$tType]: ((('type/ind_types/list' @ A) > 'type/nums/num')))).
% 1.50/1.27 thf('thm/sets/LIST_OF_SET_PROPERTIES_', axiom, (! [A:$tType,A0:(A > $o)]: (((('const/sets/FINITE' @ A) @ A0) => (((('const/sets/set_of_list' @ A) @ (('const/sets/list_of_set' @ A) @ A0)) = A0) & ((('const/lists/LENGTH' @ A) @ (('const/sets/list_of_set' @ A) @ A0)) = (('const/sets/CARD' @ A) @ A0))))))).
% 1.50/1.27 thf('thm/sets/LENGTH_LIST_OF_SET_', conjecture, (! [A:$tType,A0:(A > $o)]: (((('const/sets/FINITE' @ A) @ A0) => ((('const/lists/LENGTH' @ A) @ (('const/sets/list_of_set' @ A) @ A0)) = (('const/sets/CARD' @ A) @ A0)))))).
% 1.50/1.27 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.1ZsFGNEGVj/DTF2DTF16438.p
% 1.50/1.27 ------------------------
% 1.50/1.28 ---- Cleaned THF ---
% 1.50/1.28 thf('thf_type_type/nums/num',type,
% 1.50/1.28 'type/nums/num': $tType ).
% 1.50/1.28
% 1.50/1.28 thf('thf_type_type/ind_types/list',type,
% 1.50/1.28 'type/ind_types/list': $tType > $tType ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/set_of_list',type,
% 1.50/1.28 'const/sets/set_of_list':
% 1.50/1.28 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A > $o ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/list_of_set',type,
% 1.50/1.28 'const/sets/list_of_set':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/FINITE',type,
% 1.50/1.28 'const/sets/FINITE':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/CARD',type,
% 1.50/1.28 'const/sets/CARD':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/lists/LENGTH',type,
% 1.50/1.28 'const/lists/LENGTH':
% 1.50/1.28 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > 'type/nums/num' ) ).
% 1.50/1.28
% 1.50/1.28 thf('thm/sets/LIST_OF_SET_PROPERTIES_',axiom,
% 1.50/1.28 ! [A: $tType,A0: A > $o] :
% 1.50/1.28 ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.50/1.28 => ( ( ( 'const/sets/set_of_list' @ A @ ( 'const/sets/list_of_set' @ A @ A0 ) )
% 1.50/1.29 = A0 )
% 1.50/1.29 & ( ( 'const/lists/LENGTH' @ A @ ( 'const/sets/list_of_set' @ A @ A0 ) )
% 1.50/1.29 = ( 'const/sets/CARD' @ A @ A0 ) ) ) ) ).
% 1.50/1.29
% 1.50/1.29 thf('thm/sets/LENGTH_LIST_OF_SET_',conjecture,
% 1.50/1.29 ! [A: $tType,A0: A > $o] :
% 1.50/1.29 ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.50/1.29 => ( ( 'const/lists/LENGTH' @ A @ ( 'const/sets/list_of_set' @ A @ A0 ) )
% 1.50/1.29 = ( 'const/sets/CARD' @ A @ A0 ) ) ) ).
% 1.50/1.29 ------------------------
% 1.67/1.30 % (16593)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16438 for (2999ds/18Mi)
% 1.67/1.30 % (16593)First to succeed.
% 1.67/1.30 % (16593)Refutation found. Thanks to Tanya!
% 1.67/1.30 % SZS status Theorem for DTF2THF_16438
% 1.67/1.30 % SZS output start Proof for DTF2THF_16438
% 1.67/1.30 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 1.67/1.30 thf(type_def_7, type, 'type/nums/num': $tType).
% 1.67/1.30 thf(type_def_8, type, sK0: $tType).
% 1.67/1.30 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.67/1.30 thf(func_def_1, type, 'type/ind_types/list': ($tType) > $tType).
% 1.67/1.30 thf(func_def_2, type, 'const/sets/set_of_list': !>[X0: $tType]:('type/ind_types/list' @ X0 > X0 > $o)).
% 1.67/1.30 thf(func_def_3, type, 'const/sets/list_of_set': !>[X0: $tType]:((X0 > $o) > 'type/ind_types/list' @ X0)).
% 1.67/1.30 thf(func_def_4, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.67/1.30 thf(func_def_5, type, 'const/sets/CARD': !>[X0: $tType]:((X0 > $o) > 'type/nums/num')).
% 1.67/1.30 thf(func_def_6, type, 'const/lists/LENGTH': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/nums/num')).
% 1.67/1.30 thf(func_def_10, type, sK1: sK0 > $o).
% 1.67/1.30 thf(func_def_12, type, ph3: !>[X0: $tType]:(X0)).
% 1.67/1.30 thf(f29,plain,(
% 1.67/1.30 $false),
% 1.67/1.30 inference(subsumption_resolution,[status(thm)],[f28,f16])).
% 1.67/1.30 thf(f16,plain,(
% 1.67/1.30 (('const/sets/CARD' @ sK0 @ sK1) != ('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1)))),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.30 thf(f12,plain,(
% 1.67/1.30 (('const/sets/CARD' @ sK0 @ sK1) != ('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1))) & (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 1.67/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f11])).
% 1.67/1.30 thf(f11,plain,(
% 1.67/1.30 ? [X0 : $tType,X1 : X0 > $o] : ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) != ('const/sets/CARD' @ X0 @ X1)) & (('const/sets/FINITE' @ X0 @ X1) = $true)) => ((('const/sets/CARD' @ sK0 @ sK1) != ('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1))) & (('const/sets/FINITE' @ sK0 @ sK1) = $true))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f10,plain,(
% 1.67/1.30 ? [X0 : $tType,X1 : X0 > $o] : ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) != ('const/sets/CARD' @ X0 @ X1)) & (('const/sets/FINITE' @ X0 @ X1) = $true))),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.67/1.30 thf(f8,plain,(
% 1.67/1.30 ~! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) => (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1)))),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.67/1.30 thf(f7,plain,(
% 1.67/1.30 ~! [X0 : $tType,X1 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X1) => (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1)))),
% 1.67/1.30 inference(rectify,[status(thm)],[f3])).
% 1.67/1.30 thf(f3,negated_conjecture,(
% 1.67/1.30 ~! [X0 : $tType,X1 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X1) => (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1)))),
% 1.67/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.67/1.30 thf(f2,conjecture,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X1) => (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1)))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.1ZsFGNEGVj/DTF2THF_16438.p','thm/sets/LENGTH_LIST_OF_SET_')).
% 1.67/1.30 thf(f28,plain,(
% 1.67/1.30 (('const/sets/CARD' @ sK0 @ sK1) = ('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1)))),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.67/1.30 thf(f27,plain,(
% 1.67/1.30 (('const/sets/CARD' @ sK0 @ sK1) = ('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1))) | ($true != $true)),
% 1.67/1.30 inference(superposition,[status(thm)],[f13,f15])).
% 1.67/1.30 thf(f15,plain,(
% 1.67/1.30 (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.30 thf(f13,plain,(
% 1.67/1.30 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1))) )),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f9])).
% 1.67/1.30 thf(f9,plain,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > $o] : (((('const/sets/set_of_list' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = X1) & (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1))) | (('const/sets/FINITE' @ X0 @ X1) != $true))),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.67/1.30 thf(f6,plain,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) => ((('const/sets/set_of_list' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = X1) & (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1))))),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.67/1.30 thf(f5,plain,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X1) => ((('const/sets/set_of_list' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = X1) & (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1))))),
% 1.67/1.30 inference(rectify,[status(thm)],[f1])).
% 1.67/1.30 thf(f1,axiom,(
% 1.67/1.30 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X1) => ((('const/sets/set_of_list' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = X1) & (('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1)) = ('const/sets/CARD' @ X0 @ X1))))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.1ZsFGNEGVj/DTF2THF_16438.p','thm/sets/LIST_OF_SET_PROPERTIES_')).
% 1.67/1.30 % SZS output end Proof for DTF2THF_16438
% 1.67/1.30 % (16593)------------------------------
% 1.67/1.30 % (16593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.30 % (16593)Termination reason: Refutation
% 1.67/1.30
% 1.67/1.30 % (16593)Memory used [KB]: 5500
% 1.67/1.30 % (16593)Time elapsed: 0.003 s
% 1.67/1.30 % (16593)Instructions burned: 2 (million)
% 1.67/1.30 % (16593)------------------------------
% 1.67/1.30 % (16593)------------------------------
% 1.67/1.30 % (16586)Success in time 0.014 s
%------------------------------------------------------------------------------