%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV457^1 : 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 : n026.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 09:41:17 AM UTC 2026
% Result : Theorem 1.22s 1.03s
% Output : Refutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 88 ( 6 ~; 0 |; 0 &; 81 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 18 ( 0 ^; 12 !; 6 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_4,type,
sK1: sK0 ).
thf(func_def_5,type,
sK2: sK0 > $o ).
thf(f10,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f8,f9]) ).
thf(f9,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ X2 )
= ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ X2 )
= ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IxEhNEHUF3/DTF2THF_8486.p','thm/sets/INSERT_INSERT_') ).
thf(f8,plain,
( ( 'const/sets/INSERT' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) )
!= ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( 'const/sets/INSERT' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) )
!= ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f5,f6]) ).
thf(f6,plain,
( ? [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ X2 )
!= ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ) )
=> ( ( 'const/sets/INSERT' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) )
!= ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f5,plain,
? [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ X2 )
!= ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ X2 )
= ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ X2 )
= ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IxEhNEHUF3/DTF2THF_8486.p','thm/sets/INSERT_AC_1') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV457^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n026.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:47:25 EST 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEV457^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.38 % Domain : Analysis
% 0.18/0.38 % Problem : INSERT_AC_
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English :
% 0.18/0.38
% 0.18/0.38 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.38 % Source : [Kal16]
% 0.18/0.38 % Names : INSERT_AC_1.p [Kal16]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v7.1.0
% 0.18/0.38 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 0 def)
% 0.18/0.38 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 1 ( 4 avg)
% 0.18/0.38 % Number of connectives : 18 ( 0 ~; 0 |; 0 &; 18 @)
% 0.18/0.38 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 4 ( 4 avg)
% 0.18/0.38 % Number of types : 1 ( 0 usr)
% 0.18/0.38 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 2 ( 1 usr; 0 con; 2-4 aty)
% 0.18/0.38 % Number of variables : 7 ( 0 ^; 6 !; 0 ?; 7 :)
% 0.18/0.38 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.38 % SPC : TH1_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : Exported from core HOL Light.
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf('thf_const_const/sets/INSERT',type,
% 0.18/0.38 'const/sets/INSERT':
% 0.18/0.38 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/INSERT_INSERT_',axiom,
% 0.18/0.38 ! [A: $tType,A0: A,A1: A > $o] :
% 0.18/0.38 ( ( 'const/sets/INSERT' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A0 @ A1 ) )
% 0.18/0.38 = ( 'const/sets/INSERT' @ A @ A0 @ A1 ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/INSERT_AC_1',conjecture,
% 0.18/0.38 ! [A: $tType,A0: A,A1: A > $o] :
% 0.18/0.38 ( ( 'const/sets/INSERT' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A0 @ A1 ) )
% 0.18/0.38 = ( 'const/sets/INSERT' @ A @ A0 @ A1 ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.00/1.01 ---- Embedded in THF ---
% 1.00/1.01 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.00/1.01 %%% Generated on Tue Feb 24 12:47:25 EST 2026
% 1.00/1.01 %%% using '$$dhol' embedding, version 1.3.0.
% 1.00/1.01 %%% Logic specification used:
% 1.00/1.01 %%% thf(spec, logic, $$dhol).
% 1.00/1.01
% 1.00/1.01 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IxEhNEHUF3/DTF2DTF8486.p
% See solution above
% 1.00/1.01 ------------------------
% 1.00/1.01 ---- Cleaned THF ---
% 1.00/1.02 thf('thf_const_const/sets/INSERT',type,
% 1.00/1.02 'const/sets/INSERT':
% 1.00/1.02 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.00/1.02
% 1.00/1.02 thf('thm/sets/INSERT_INSERT_',axiom,
% 1.00/1.02 ! [A: $tType,A0: A,A1: A > $o] :
% 1.00/1.02 ( ( 'const/sets/INSERT' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A0 @ A1 ) )
% 1.00/1.02 = ( 'const/sets/INSERT' @ A @ A0 @ A1 ) ) ).
% 1.00/1.02
% 1.00/1.02 thf('thm/sets/INSERT_AC_1',conjecture,
% 1.00/1.02 ! [A: $tType,A0: A,A1: A > $o] :
% 1.00/1.02 ( ( 'const/sets/INSERT' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A0 @ A1 ) )
% 1.00/1.02 = ( 'const/sets/INSERT' @ A @ A0 @ A1 ) ) ).
% 1.00/1.02 ------------------------
% 1.22/1.03 % (8583)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8486 for (3000ds/183Mi)
% 1.22/1.03 % (8583)First to succeed.
% 1.22/1.03 % (8583)Refutation found. Thanks to Tanya!
% 1.22/1.03 % SZS status Theorem for DTF2THF_8486
% 1.22/1.03 % SZS output start Proof for DTF2THF_8486
% 1.22/1.03 thf(type_def_6, type, sK0: $tType).
% 1.22/1.03 thf(func_def_0, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.22/1.03 thf(func_def_4, type, sK1: sK0).
% 1.22/1.03 thf(func_def_5, type, sK2: sK0 > $o).
% 1.22/1.03 thf(f10,plain,(
% 1.22/1.03 $false),
% 1.22/1.03 inference(subsumption_resolution,[status(thm)],[f8,f9])).
% 1.22/1.03 thf(f9,plain,(
% 1.22/1.03 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ((('const/sets/INSERT' @ X0 @ X1 @ X2) = ('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)))) )),
% 1.22/1.03 inference(cnf_transformation,[status(thm)],[f1])).
% 1.22/1.03 thf(f1,axiom,(
% 1.22/1.03 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/INSERT' @ X0 @ X1 @ X2) = ('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)))),
% 1.22/1.03 file('/export/starexec/sandbox2/tmp/tmp.IxEhNEHUF3/DTF2THF_8486.p','thm/sets/INSERT_INSERT_')).
% 1.22/1.03 thf(f8,plain,(
% 1.22/1.03 (('const/sets/INSERT' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK1 @ sK2)) != ('const/sets/INSERT' @ sK0 @ sK1 @ sK2))),
% 1.22/1.03 inference(cnf_transformation,[status(thm)],[f7])).
% 1.22/1.03 thf(f7,plain,(
% 1.22/1.03 (('const/sets/INSERT' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK1 @ sK2)) != ('const/sets/INSERT' @ sK0 @ sK1 @ sK2))),
% 1.22/1.03 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f5,f6])).
% 1.22/1.03 thf(f6,plain,(
% 1.22/1.03 ? [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/INSERT' @ X0 @ X1 @ X2) != ('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X1 @ X2))) => (('const/sets/INSERT' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK1 @ sK2)) != ('const/sets/INSERT' @ sK0 @ sK1 @ sK2))),
% 1.22/1.03 introduced(definition,[],[choice_axiom])).
% 1.22/1.03 thf(f5,plain,(
% 1.22/1.03 ? [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/INSERT' @ X0 @ X1 @ X2) != ('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)))),
% 1.22/1.03 inference(ennf_transformation,[status(thm)],[f3])).
% 1.22/1.03 thf(f3,negated_conjecture,(
% 1.22/1.03 ~! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/INSERT' @ X0 @ X1 @ X2) = ('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)))),
% 1.22/1.03 inference(negated_conjecture,[status(cth)],[f2])).
% 1.22/1.03 thf(f2,conjecture,(
% 1.22/1.03 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/INSERT' @ X0 @ X1 @ X2) = ('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)))),
% 1.22/1.03 file('/export/starexec/sandbox2/tmp/tmp.IxEhNEHUF3/DTF2THF_8486.p','thm/sets/INSERT_AC_1')).
% 1.22/1.03 % SZS output end Proof for DTF2THF_8486
% 1.22/1.03 % (8583)------------------------------
% 1.22/1.03 % (8583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.22/1.03 % (8583)Termination reason: Refutation
% 1.22/1.03
% 1.22/1.03 % (8583)Memory used [KB]: 5373
% 1.22/1.03 % (8583)Time elapsed: 0.002 s
% 1.22/1.03 % (8583)Instructions burned: 1 (million)
% 1.22/1.03 % (8583)------------------------------
% 1.22/1.03 % (8583)------------------------------
% 1.22/1.03 % (8582)Success in time 0.011 s
%------------------------------------------------------------------------------