%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV427^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:41:13 AM UTC 2026
% Result : Theorem 1.47s 1.20s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 131 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 103 ( 23 ~; 25 |; 1 &; 50 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
p: $i > $o ).
thf(func_def_3,type,
q: $i > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f49,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f40,f41,f47,f48]) ).
thf(f48,plain,
~ spl0_1,
inference(avatar_split_clause,[status(thm)],[f16,f20]) ).
thf(f20,definition,
( spl0_1
<=> ( ( q @ ( eps @ q ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f16,plain,
( ( q @ ( eps @ q ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( p @ ( eps @ p ) )
!= $true )
& ( ( q @ ( eps @ q ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( ( p @ ( eps @ p ) )
= $true )
| ( ( q @ ( eps @ q ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( p @ ( eps @ p ) )
| ( q @ ( eps @ q ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( ( p @ ( eps @ p ) )
| ( q @ ( eps @ q ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( ( p @ ( eps @ p ) )
| ( q @ ( eps @ q ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sb0lXmfxgi/DTF2THF_4217.p',conj) ).
thf(f47,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f44,f25]) ).
thf(f25,plain,
( ! [X1: $i] :
( ( q @ X1 )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl0_2
<=> ! [X1: $i] :
( ( q @ X1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f44,plain,
( ! [X0: $i] :
( $true
= ( q @ X0 ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ! [X0: $i] :
( ( $true
= ( q @ X0 ) )
| ( $true = $false ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f14,f35]) ).
thf(f35,plain,
( ! [X1: $i] :
( ( p @ X1 )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl0_4
<=> ! [X1: $i] :
( ( p @ X1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f14,plain,
! [X0: $i] :
( ( $true
= ( p @ X0 ) )
| ( $true
= ( q @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i] :
( ( $true
= ( p @ X0 ) )
| ( $true
= ( q @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i] :
( ( q @ X0 )
| ( p @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i] :
( ( q @ X1 )
| ( p @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.sb0lXmfxgi/DTF2THF_4217.p',pq) ).
thf(f41,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f37,f30,f34]) ).
thf(f30,definition,
( spl0_3
<=> ( ( p @ ( eps @ p ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f37,plain,
! [X1: $i] :
( ( ( p @ ( eps @ p ) )
= $true )
| ( ( p @ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f39]) ).
thf(f39,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true != $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f17,f32]) ).
thf(f32,plain,
( ( ( p @ ( eps @ p ) )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f17,plain,
( ( p @ ( eps @ p ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f26,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f24,f20]) ).
thf(f18,plain,
! [X1: $i] :
( ( ( q @ ( eps @ q ) )
= $true )
| ( ( q @ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV427^1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n019.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:46:39 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : SEV427^1 : TPTP v9.2.1. Released v5.2.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : If two sets cover a type, a choice function must give an element
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro11]
% 0.19/0.45 % Names : CHOICE33 [Bro11]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.2.0
% 0.19/0.45 % Syntax : Number of formulae : 6 ( 0 unt; 3 typ; 0 def)
% 0.19/0.45 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 4 ( 2 avg)
% 0.19/0.45 % Number of connectives : 12 ( 0 ~; 2 |; 0 &; 9 @)
% 0.19/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 5 ( 4 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.19/0.45 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : Assume eps is a choice function on $i and p and q are sets
% 0.19/0.45 % covering $i. Since $i is nonempty, either p or q is nonempty and
% 0.19/0.45 % so (eps @ p) is in p or (eps @ q) is in q.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(eps,type,
% 0.19/0.45 eps: ( $i > $o ) > $i ).
% 0.19/0.45
% 0.19/0.45 thf(choiceax,axiom,
% 0.19/0.45 ! [P: $i > $o] :
% 0.19/0.45 ( ? [X: $i] : ( P @ X )
% 0.19/0.45 => ( P @ ( eps @ P ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(p,type,
% 0.19/0.45 p: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(q,type,
% 0.19/0.45 q: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(pq,axiom,
% 0.19/0.45 ! [X: $i] :
% 0.19/0.45 ( ( p @ X )
% 0.19/0.45 | ( q @ X ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(conj,conjecture,
% 0.19/0.45 ( ( p @ ( eps @ p ) )
% 0.19/0.45 | ( q @ ( eps @ q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.38/1.17 ---- Embedded in THF ---
% 1.38/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.17 %%% Generated on Tue Feb 24 12:46:40 EST 2026
% 1.38/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.17 %%% Logic specification used:
% 1.38/1.17 %%% thf(spec, logic, $$dhol).
% 1.38/1.17
% 1.38/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.sb0lXmfxgi/DTF2DTF4217.p
% See solution above
% 1.38/1.17 ------------------------
% 1.38/1.18 ---- Cleaned THF ---
% 1.38/1.18 thf(eps,type,
% 1.38/1.18 eps: ( $i > $o ) > $i ).
% 1.38/1.18
% 1.38/1.18 thf(choiceax,axiom,
% 1.38/1.18 ! [P: $i > $o] :
% 1.38/1.18 ( ? [X: $i] : ( P @ X )
% 1.38/1.18 => ( P @ ( eps @ P ) ) ) ).
% 1.38/1.18
% 1.38/1.18 thf(p,type,
% 1.38/1.18 p: $i > $o ).
% 1.38/1.18
% 1.38/1.18 thf(q,type,
% 1.38/1.18 q: $i > $o ).
% 1.38/1.18
% 1.38/1.18 thf(pq,axiom,
% 1.38/1.18 ! [X: $i] :
% 1.38/1.18 ( ( p @ X )
% 1.38/1.18 | ( q @ X ) ) ).
% 1.38/1.18
% 1.38/1.18 thf(conj,conjecture,
% 1.38/1.18 ( ( p @ ( eps @ p ) )
% 1.38/1.18 | ( q @ ( eps @ q ) ) ) ).
% 1.38/1.18 ------------------------
% 1.38/1.19 % (4314)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4217 for (2999ds/183Mi)
% 1.38/1.20 % (4316)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_4217 for (2999ds/27Mi)
% 1.47/1.20 % (4316)First to succeed.
% 1.47/1.20 % (4314)Also succeeded, but the first one will report.
% 1.47/1.20 % (4316)Refutation found. Thanks to Tanya!
% 1.47/1.20 % SZS status Theorem for DTF2THF_4217
% 1.47/1.20 % SZS output start Proof for DTF2THF_4217
% 1.47/1.20 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.47/1.20 thf(func_def_2, type, p: $i > $o).
% 1.47/1.20 thf(func_def_3, type, q: $i > $o).
% 1.47/1.20 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.47/1.20 thf(func_def_8, type, ph1: !>[X0: $tType]:(X0)).
% 1.47/1.20 thf(f49,plain,(
% 1.47/1.20 $false),
% 1.47/1.20 inference(avatar_sat_refutation,[status(thm)],[f26,f40,f41,f47,f48])).
% 1.47/1.20 thf(f48,plain,(
% 1.47/1.20 ~spl0_1),
% 1.47/1.20 inference(avatar_split_clause,[status(thm)],[f16,f20])).
% 1.47/1.20 thf(f20,definition,(
% 1.47/1.20 spl0_1 <=> ((q @ (eps @ q)) = $true)),
% 1.47/1.20 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.47/1.20 thf(f16,plain,(
% 1.47/1.20 ((q @ (eps @ q)) != $true)),
% 1.47/1.20 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.20 thf(f13,plain,(
% 1.47/1.20 ((p @ (eps @ p)) != $true) & ((q @ (eps @ q)) != $true)),
% 1.47/1.20 inference(ennf_transformation,[status(thm)],[f11])).
% 1.47/1.20 thf(f11,plain,(
% 1.47/1.20 ~(((p @ (eps @ p)) = $true) | ((q @ (eps @ q)) = $true))),
% 1.47/1.20 inference(fool_elimination,[status(thm)],[f10])).
% 1.47/1.20 thf(f10,plain,(
% 1.47/1.20 ~((p @ (eps @ p)) | (q @ (eps @ q)))),
% 1.47/1.20 inference(rectify,[status(thm)],[f4])).
% 1.47/1.20 thf(f4,negated_conjecture,(
% 1.47/1.20 ~((p @ (eps @ p)) | (q @ (eps @ q)))),
% 1.47/1.20 inference(negated_conjecture,[status(cth)],[f3])).
% 1.47/1.20 thf(f3,conjecture,(
% 1.47/1.20 (p @ (eps @ p)) | (q @ (eps @ q))),
% 1.47/1.20 file('/export/starexec/sandbox/tmp/tmp.sb0lXmfxgi/DTF2THF_4217.p',conj)).
% 1.47/1.20 thf(f47,plain,(
% 1.47/1.20 ~spl0_2 | ~spl0_4),
% 1.47/1.20 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.47/1.20 thf(f46,plain,(
% 1.47/1.20 $false | (~spl0_2 | ~spl0_4)),
% 1.47/1.20 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.47/1.20 thf(f45,plain,(
% 1.47/1.20 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 1.47/1.20 inference(forward_demodulation,[status(thm)],[f44,f25])).
% 1.47/1.20 thf(f25,plain,(
% 1.47/1.20 ( ! [X1 : $i] : (((q @ X1) = $false)) ) | ~spl0_2),
% 1.47/1.20 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.47/1.20 thf(f24,definition,(
% 1.47/1.20 spl0_2 <=> ! [X1 : $i] : ((q @ X1) = $false)),
% 1.47/1.20 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.47/1.20 thf(f44,plain,(
% 1.47/1.20 ( ! [X0 : $i] : (($true = (q @ X0))) ) | ~spl0_4),
% 1.47/1.20 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.47/1.20 thf(f43,plain,(
% 1.47/1.20 ( ! [X0 : $i] : (($true = (q @ X0)) | ($true = $false)) ) | ~spl0_4),
% 1.47/1.20 inference(forward_demodulation,[status(thm)],[f14,f35])).
% 1.47/1.20 thf(f35,plain,(
% 1.47/1.20 ( ! [X1 : $i] : (((p @ X1) = $false)) ) | ~spl0_4),
% 1.47/1.20 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.47/1.20 thf(f34,definition,(
% 1.47/1.20 spl0_4 <=> ! [X1 : $i] : ((p @ X1) = $false)),
% 1.47/1.20 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.47/1.20 thf(f14,plain,(
% 1.47/1.20 ( ! [X0 : $i] : (($true = (p @ X0)) | ($true = (q @ X0))) )),
% 1.47/1.20 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.20 thf(f9,plain,(
% 1.47/1.20 ! [X0 : $i] : (($true = (p @ X0)) | ($true = (q @ X0)))),
% 1.47/1.20 inference(fool_elimination,[status(thm)],[f8])).
% 1.47/1.20 thf(f8,plain,(
% 1.47/1.20 ! [X0 : $i] : ((q @ X0) | (p @ X0))),
% 1.47/1.20 inference(rectify,[status(thm)],[f2])).
% 1.47/1.20 thf(f2,axiom,(
% 1.47/1.20 ! [X1 : $i] : ((q @ X1) | (p @ X1))),
% 1.47/1.20 file('/export/starexec/sandbox/tmp/tmp.sb0lXmfxgi/DTF2THF_4217.p',pq)).
% 1.47/1.20 thf(f41,plain,(
% 1.47/1.20 spl0_4 | spl0_3),
% 1.47/1.20 inference(avatar_split_clause,[status(thm)],[f37,f30,f34])).
% 1.47/1.20 thf(f30,definition,(
% 1.47/1.20 spl0_3 <=> ((p @ (eps @ p)) = $true)),
% 1.47/1.20 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.47/1.20 thf(f37,plain,(
% 1.47/1.20 ( ! [X1 : $i] : (((p @ (eps @ p)) = $true) | ((p @ X1) = $false)) )),
% 1.47/1.20 introduced(definition,[],[choice_axiom])).
% 1.47/1.20 thf(f40,plain,(
% 1.47/1.20 ~spl0_3),
% 1.47/1.20 inference(avatar_contradiction_clause,[status(thm)],[f39])).
% 1.47/1.20 thf(f39,plain,(
% 1.47/1.20 $false | ~spl0_3),
% 1.47/1.20 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.47/1.20 thf(f38,plain,(
% 1.47/1.20 ($true != $true) | ~spl0_3),
% 1.47/1.20 inference(superposition,[status(thm)],[f17,f32])).
% 1.47/1.20 thf(f32,plain,(
% 1.47/1.20 ((p @ (eps @ p)) = $true) | ~spl0_3),
% 1.47/1.20 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.47/1.20 thf(f17,plain,(
% 1.47/1.20 ((p @ (eps @ p)) != $true)),
% 1.47/1.20 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.20 thf(f26,plain,(
% 1.47/1.20 spl0_1 | spl0_2),
% 1.47/1.20 inference(avatar_split_clause,[status(thm)],[f18,f24,f20])).
% 1.47/1.20 thf(f18,plain,(
% 1.47/1.20 ( ! [X1 : $i] : (((q @ (eps @ q)) = $true) | ((q @ X1) = $false)) )),
% 1.47/1.20 introduced(definition,[],[choice_axiom])).
% 1.47/1.20 % SZS output end Proof for DTF2THF_4217
% 1.47/1.20 % (4316)------------------------------
% 1.47/1.20 % (4316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.20 % (4316)Termination reason: Refutation
% 1.47/1.20
% 1.47/1.20 % (4316)Memory used [KB]: 5500
% 1.47/1.20 % (4316)Time elapsed: 0.002 s
% 1.47/1.20 % (4316)Instructions burned: 2 (million)
% 1.47/1.20 % (4316)------------------------------
% 1.47/1.20 % (4316)------------------------------
% 1.47/1.20 % (4313)Success in time 0.013 s
%------------------------------------------------------------------------------