%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV405^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 09:41:11 AM UTC 2026
% Result : Theorem 1.47s 1.30s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 92 ( 23 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 81 ( 26 ~; 19 |; 0 &; 28 @)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 4 ^; 14 !; 6 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_7,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f19,f27,f39,f42,f50]) ).
thf(f50,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( ^ [Y0: $i] : $false
@ ( sK0
@ ^ [Y0: $i] : $false ) )
= $true )
| ~ spl1_2 ),
inference(primitive_instantiation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl1_2
<=> ! [X0: $i > $o] :
( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f42,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_4 ),
inference(backward_demodulation,[status(thm)],[f15,f26]) ).
thf(f26,plain,
( ( cA = $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl1_4
<=> ( cA = $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f15,plain,
( ( cA = $true )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f13,definition,
( spl1_1
<=> ( cA = $true ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f39,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true = $false )
| ~ spl1_3 ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( ^ [Y0: $i] : $true
@ ( sK0
@ ^ [Y0: $i] : $true ) )
= $false )
| ~ spl1_3 ),
inference(primitive_instantiation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i > $o] :
( ( X0 @ ( sK0 @ X0 ) )
= $false )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl1_3
<=> ! [X0: $i > $o] :
( ( X0 @ ( sK0 @ X0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f27,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f11,f24,f21]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ( cA = $false )
| ( ( X0 @ ( sK0 @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( cA
!= ( X0 @ ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( cA
!= ( X0 @ ( sK0 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
!= cA )
=> ( cA
!= ( X0 @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
!= cA ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $o] :
! [X1: $i] :
( ( X0 @ X1 )
= cA ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $o] :
! [X1: $i] :
( ( X0 @ X1 )
<=> cA ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $o] :
! [X1: $i] :
( ( X0 @ X1 )
<=> cA ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $o] :
! [X1: $i] :
( ( X0 @ X1 )
<=> cA ),
file('/export/starexec/sandbox/tmp/tmp.kw4B86idVH/DTF2THF_14383.p',cCOMP1) ).
thf(f19,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f10,f17,f13]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ( cA = $true )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV405^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n021.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:46:09 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEV405^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : TPS problem from SETS-THMS
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0625 [Bro09]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.19/0.47 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.47 % Number of atoms : 1 ( 0 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.47 % Number of connectives : 2 ( 0 ~; 0 |; 0 &; 1 @)
% 0.19/0.47 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 5 ( 5 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 1 ( 1 usr; 1 con; 0-0 aty)
% 0.31/0.47 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.31/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(cA,type,
% 0.31/0.47 cA: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cCOMP1,conjecture,
% 0.31/0.47 ? [U: $i > $o] :
% 0.31/0.47 ! [V: $i] :
% 0.31/0.47 ( ( U @ V )
% 0.31/0.47 <=> cA ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 12:46:09 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kw4B86idVH/DTF2DTF14383.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(cA,type,
% 1.47/1.28 cA: $o ).
% 1.47/1.28
% 1.47/1.28 thf(cCOMP1,conjecture,
% 1.47/1.28 ? [U: $i > $o] :
% 1.47/1.28 ! [V: $i] :
% 1.47/1.28 ( ( U @ V )
% 1.47/1.28 <=> cA ) ).
% 1.47/1.28 ------------------------
% 1.47/1.29 % (14715)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14383 for (2999ds/2Mi)
% 1.47/1.29 % (14715)First to succeed.
% 1.47/1.30 % (14715)Refutation found. Thanks to Tanya!
% 1.47/1.30 % SZS status Theorem for DTF2THF_14383
% 1.47/1.30 % SZS output start Proof for DTF2THF_14383
% 1.47/1.30 thf(func_def_4, type, sK0: ($i > $o) > $i).
% 1.47/1.30 thf(func_def_7, type, ph2: !>[X0: $tType]:(X0)).
% 1.47/1.30 thf(f53,plain,(
% 1.47/1.30 $false),
% 1.47/1.30 inference(avatar_sat_refutation,[status(thm)],[f19,f27,f39,f42,f50])).
% 1.47/1.30 thf(f50,plain,(
% 1.47/1.30 ~spl1_2),
% 1.47/1.30 inference(avatar_contradiction_clause,[status(thm)],[f49])).
% 1.47/1.30 thf(f49,plain,(
% 1.47/1.30 $false | ~spl1_2),
% 1.47/1.30 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.47/1.30 thf(f48,plain,(
% 1.47/1.30 ($true = $false) | ~spl1_2),
% 1.47/1.30 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.47/1.30 thf(f45,plain,(
% 1.47/1.30 (((^[Y0 : $i]: ($false)) @ (sK0 @ (^[Y0 : $i]: ($false)))) = $true) | ~spl1_2),
% 1.47/1.30 inference(primitive_instantiation,[status(thm)],[f18])).
% 1.47/1.30 thf(f18,plain,(
% 1.47/1.30 ( ! [X0 : $i > $o] : (($true = (X0 @ (sK0 @ X0)))) ) | ~spl1_2),
% 1.47/1.30 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.47/1.30 thf(f17,definition,(
% 1.47/1.30 spl1_2 <=> ! [X0 : $i > $o] : ($true = (X0 @ (sK0 @ X0)))),
% 1.47/1.30 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.47/1.30 thf(f42,plain,(
% 1.47/1.30 ~spl1_1 | ~spl1_4),
% 1.47/1.30 inference(avatar_contradiction_clause,[status(thm)],[f41])).
% 1.47/1.30 thf(f41,plain,(
% 1.47/1.30 $false | (~spl1_1 | ~spl1_4)),
% 1.47/1.30 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.47/1.30 thf(f40,plain,(
% 1.47/1.30 ($true = $false) | (~spl1_1 | ~spl1_4)),
% 1.47/1.30 inference(backward_demodulation,[status(thm)],[f15,f26])).
% 1.47/1.30 thf(f26,plain,(
% 1.47/1.30 (cA = $false) | ~spl1_4),
% 1.47/1.30 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.47/1.30 thf(f24,definition,(
% 1.47/1.30 spl1_4 <=> (cA = $false)),
% 1.47/1.30 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.47/1.30 thf(f15,plain,(
% 1.47/1.30 (cA = $true) | ~spl1_1),
% 1.47/1.30 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.47/1.30 thf(f13,definition,(
% 1.47/1.30 spl1_1 <=> (cA = $true)),
% 1.47/1.30 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.47/1.30 thf(f39,plain,(
% 1.47/1.30 ~spl1_3),
% 1.47/1.30 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.47/1.30 thf(f38,plain,(
% 1.47/1.30 $false | ~spl1_3),
% 1.47/1.30 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.47/1.30 thf(f37,plain,(
% 1.47/1.30 ($true = $false) | ~spl1_3),
% 1.47/1.30 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.47/1.30 thf(f31,plain,(
% 1.47/1.30 (((^[Y0 : $i]: ($true)) @ (sK0 @ (^[Y0 : $i]: ($true)))) = $false) | ~spl1_3),
% 1.47/1.30 inference(primitive_instantiation,[status(thm)],[f22])).
% 1.47/1.30 thf(f22,plain,(
% 1.47/1.30 ( ! [X0 : $i > $o] : (((X0 @ (sK0 @ X0)) = $false)) ) | ~spl1_3),
% 1.47/1.30 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.47/1.30 thf(f21,definition,(
% 1.47/1.30 spl1_3 <=> ! [X0 : $i > $o] : ((X0 @ (sK0 @ X0)) = $false)),
% 1.47/1.30 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.47/1.30 thf(f27,plain,(
% 1.47/1.30 spl1_3 | spl1_4),
% 1.47/1.30 inference(avatar_split_clause,[status(thm)],[f11,f24,f21])).
% 1.47/1.30 thf(f11,plain,(
% 1.47/1.30 ( ! [X0 : $i > $o] : ((cA = $false) | ((X0 @ (sK0 @ X0)) = $false)) )),
% 1.47/1.30 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.47/1.30 thf(f9,plain,(
% 1.47/1.30 ( ! [X0 : $i > $o] : ((cA != (X0 @ (sK0 @ X0)))) )),
% 1.47/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.47/1.30 thf(f8,plain,(
% 1.47/1.30 ! [X0 : $i > $o] : (cA != (X0 @ (sK0 @ X0)))),
% 1.47/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.47/1.30 thf(f7,plain,(
% 1.47/1.30 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) != cA) => (cA != (X0 @ (sK0 @ X0))))),
% 1.47/1.30 introduced(definition,[],[choice_axiom])).
% 1.47/1.30 thf(f6,plain,(
% 1.47/1.30 ! [X0 : $i > $o] : ? [X1 : $i] : ((X0 @ X1) != cA)),
% 1.47/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.47/1.30 thf(f5,plain,(
% 1.47/1.30 ~? [X0 : $i > $o] : ! [X1 : $i] : ((X0 @ X1) = cA)),
% 1.47/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.30 thf(f4,plain,(
% 1.47/1.30 ~? [X0 : $i > $o] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 1.47/1.30 inference(rectify,[status(thm)],[f2])).
% 1.47/1.30 thf(f2,negated_conjecture,(
% 1.47/1.30 ~? [X0 : $i > $o] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 1.47/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.30 thf(f1,conjecture,(
% 1.47/1.30 ? [X0 : $i > $o] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 1.47/1.30 file('/export/starexec/sandbox/tmp/tmp.kw4B86idVH/DTF2THF_14383.p',cCOMP1)).
% 1.47/1.30 thf(f19,plain,(
% 1.47/1.30 spl1_1 | spl1_2),
% 1.47/1.30 inference(avatar_split_clause,[status(thm)],[f10,f17,f13])).
% 1.47/1.30 thf(f10,plain,(
% 1.47/1.30 ( ! [X0 : $i > $o] : ((cA = $true) | ($true = (X0 @ (sK0 @ X0)))) )),
% 1.47/1.30 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.47/1.30 % SZS output end Proof for DTF2THF_14383
% 1.47/1.30 % (14715)------------------------------
% 1.47/1.30 % (14715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.30 % (14715)Termination reason: Refutation
% 1.47/1.30
% 1.47/1.30 % (14715)Memory used [KB]: 5500
% 1.47/1.30 % (14715)Time elapsed: 0.003 s
% 1.47/1.30 % (14715)Instructions burned: 1 (million)
% 1.47/1.30 % (14715)------------------------------
% 1.47/1.30 % (14715)------------------------------
% 1.47/1.30 % (14711)Success in time 0.013 s
%------------------------------------------------------------------------------