%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV221^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 09:40:35 AM UTC 2026
% Result : Theorem 0.18s 1.06s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 1 unt; 0 typ; 9 def)
% Number of atoms : 677 ( 192 equ; 0 cnn)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 669 ( 159 ~; 169 |; 90 &; 233 @)
% ( 13 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 109 ( 29 ^; 40 !; 40 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cZ: a > $o ).
thf(func_def_2,type,
cW: ( a > $o ) > $o ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_12,type,
sK3: a > $o ).
thf(func_def_15,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK6: a ).
thf(f172,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f36,f41,f50,f55,f56,f67,f68,f70,f71,f100,f104,f113,f158,f165,f171]) ).
thf(f171,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f170]) ).
thf(f170,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_7 ),
inference(subsumption_resolution,[status(thm)],[f169,f49]) ).
thf(f49,plain,
( ( ( sK3 @ sK0 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl4_5
<=> ( ( sK3 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f169,plain,
( ( ( sK3 @ sK0 )
!= $true )
| ~ spl4_1
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( ( sK3 @ sK0 )
!= $true )
| ( $true != $true )
| ~ spl4_1
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f59,f31]) ).
thf(f31,plain,
( ( ( cW @ sK3 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl4_1
<=> ( ( cW @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f59,plain,
( ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( ( X3 @ sK0 )
!= $true ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl4_7
<=> ! [X3: a > $o] :
( ( ( X3 @ sK0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f165,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f164]) ).
thf(f164,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f49,f152]) ).
thf(f152,plain,
( ( $false
= ( sK3 @ sK0 ) )
| ~ spl4_1
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( $true != $true )
| ( $false
= ( sK3 @ sK0 ) )
| ~ spl4_1
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f66,f31]) ).
thf(f66,plain,
( ! [X2: a > $o] :
( ( ( cW @ X2 )
!= $true )
| ( ( X2 @ sK0 )
= $false ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl4_9
<=> ! [X2: a > $o] :
( ( ( X2 @ sK0 )
= $false )
| ( ( cW @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition]) ).
thf(f158,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f157]) ).
thf(f157,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f92,f151]) ).
thf(f151,plain,
( ( $false
= ( sK2 @ sK0 ) )
| ~ spl4_4
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( $true != $true )
| ( $false
= ( sK2 @ sK0 ) )
| ~ spl4_4
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f66,f45]) ).
thf(f45,plain,
( ( $true
= ( cW @ sK2 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl4_4
<=> ( $true
= ( cW @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f92,plain,
( ( ( sK2 @ sK0 )
= $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( sK2 @ sK0 )
= $true )
| ( $false = $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f77,f35]) ).
thf(f35,plain,
( ( ( sK1 @ sK0 )
= $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl4_2
<=> ( ( sK1 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f77,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( sK2 @ X1 )
= $true ) )
| ~ spl4_3 ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ! [X1: a] :
( ( $true
= ( ( cZ @ X1 )
& ( sK2 @ X1 ) ) )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl4_3 ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( ( cZ @ X1 )
& ( sK2 @ X1 ) ) )
| ~ spl4_3 ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 )
= ( sK1 @ X1 ) )
| ~ spl4_3 ),
inference(argument_congruence,[status(thm)],[f40]) ).
thf(f40,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl4_3
<=> ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f113,plain,
( ~ spl4_6
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $false = $true )
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[status(thm)],[f63,f54]) ).
thf(f54,plain,
( ( $true
= ( cZ @ sK0 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl4_6
<=> ( $true
= ( cZ @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f63,plain,
( ( $false
= ( cZ @ sK0 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl4_8
<=> ( $false
= ( cZ @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition]) ).
thf(f104,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_7 ),
inference(subsumption_resolution,[status(thm)],[f102,f92]) ).
thf(f102,plain,
( ( ( sK2 @ sK0 )
!= $true )
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $true != $true )
| ( ( sK2 @ sK0 )
!= $true )
| ~ spl4_4
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f59,f45]) ).
thf(f100,plain,
( ~ spl4_2
| ~ spl4_3
| spl4_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f99]) ).
thf(f99,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| spl4_6 ),
inference(superposition,[status(thm)],[f35,f94]) ).
thf(f94,plain,
( ( $false
= ( sK1 @ sK0 ) )
| ~ spl4_3
| spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $false
= ( sK1 @ sK0 ) )
| ( $true != $true )
| ~ spl4_3
| spl4_6 ),
inference(superposition,[status(thm)],[f53,f78]) ).
thf(f78,plain,
( ! [X1: a] :
( ( $true
= ( cZ @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl4_3 ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f53,plain,
( ( $true
!= ( cZ @ sK0 ) )
| spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f71,plain,
( spl4_1
| spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f43,f29]) ).
thf(f18,plain,
( ( $true
= ( cW @ sK2 ) )
| ( ( cW @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ! [X1: a > $o] :
( ( $true
!= ( X1 @ sK0 ) )
| ! [X2: a > $o] :
( ( ( cW @ X2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 ) ) )
| ( $true
!= ( cZ @ sK0 ) )
| ! [X3: a > $o] :
( ( ( X3 @ sK0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) ) )
& ( ( ( ( sK1 @ sK0 )
= $true )
& ( $true
= ( cW @ sK2 ) )
& ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) ) )
| ( ( $true
= ( cZ @ sK0 ) )
& ( ( sK3 @ sK0 )
= $true )
& ( ( cW @ sK3 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: a] :
( ( ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ! [X2: a > $o] :
( ( ( cW @ X2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 ) ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) ) )
& ( ? [X4: a > $o] :
( ( $true
= ( X4 @ X0 ) )
& ? [X5: a > $o] :
( ( $true
= ( cW @ X5 ) )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X5 @ Y0 ) ) )
= X4 ) ) )
| ( ( ( cZ @ X0 )
= $true )
& ? [X6: a > $o] :
( ( ( X6 @ X0 )
= $true )
& ( ( cW @ X6 )
= $true ) ) ) ) )
=> ( ( ! [X1: a > $o] :
( ( $true
!= ( X1 @ sK0 ) )
| ! [X2: a > $o] :
( ( ( cW @ X2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 ) ) )
| ( $true
!= ( cZ @ sK0 ) )
| ! [X3: a > $o] :
( ( ( X3 @ sK0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) ) )
& ( ? [X4: a > $o] :
( ( ( X4 @ sK0 )
= $true )
& ? [X5: a > $o] :
( ( $true
= ( cW @ X5 ) )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X5 @ Y0 ) ) )
= X4 ) ) )
| ( ( $true
= ( cZ @ sK0 ) )
& ? [X6: a > $o] :
( ( $true
= ( X6 @ sK0 ) )
& ( ( cW @ X6 )
= $true ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: a > $o] :
( ( ( X4 @ sK0 )
= $true )
& ? [X5: a > $o] :
( ( $true
= ( cW @ X5 ) )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X5 @ Y0 ) ) )
= X4 ) ) )
=> ( ( ( sK1 @ sK0 )
= $true )
& ? [X5: a > $o] :
( ( $true
= ( cW @ X5 ) )
& ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X5 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X5: a > $o] :
( ( $true
= ( cW @ X5 ) )
& ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X5 @ Y0 ) ) ) ) )
=> ( ( $true
= ( cW @ sK2 ) )
& ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X6: a > $o] :
( ( $true
= ( X6 @ sK0 ) )
& ( ( cW @ X6 )
= $true ) )
=> ( ( ( sK3 @ sK0 )
= $true )
& ( ( cW @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a] :
( ( ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ! [X2: a > $o] :
( ( ( cW @ X2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 ) ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) ) )
& ( ? [X4: a > $o] :
( ( $true
= ( X4 @ X0 ) )
& ? [X5: a > $o] :
( ( $true
= ( cW @ X5 ) )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X5 @ Y0 ) ) )
= X4 ) ) )
| ( ( ( cZ @ X0 )
= $true )
& ? [X6: a > $o] :
( ( ( X6 @ X0 )
= $true )
& ( ( cW @ X6 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a] :
( ( ! [X2: a > $o] :
( ( ( X2 @ X0 )
!= $true )
| ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 ) ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) ) )
& ( ? [X2: a > $o] :
( ( ( X2 @ X0 )
= $true )
& ? [X3: a > $o] :
( ( ( cW @ X3 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
= X2 ) ) )
| ( ( ( cZ @ X0 )
= $true )
& ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( cW @ X1 )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a] :
( ( ! [X2: a > $o] :
( ( ( X2 @ X0 )
!= $true )
| ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 ) ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) ) )
& ( ? [X2: a > $o] :
( ( ( X2 @ X0 )
= $true )
& ? [X3: a > $o] :
( ( ( cW @ X3 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
= X2 ) ) )
| ( ( ( cZ @ X0 )
= $true )
& ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( cW @ X1 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
& ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( cW @ X1 )
= $true ) ) )
<~> ? [X2: a > $o] :
( ( ( X2 @ X0 )
= $true )
& ? [X3: a > $o] :
( ( ( cW @ X3 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
= X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
& ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( cW @ X1 )
= $true ) ) )
<=> ? [X2: a > $o] :
( ( ( X2 @ X0 )
= $true )
& ? [X3: a > $o] :
( ( ( cW @ X3 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
= X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ( ? [X1: a > $o] :
( ( cW @ X1 )
& ( X1 @ X0 ) )
& ( cZ @ X0 ) )
<=> ? [X2: a > $o] :
( ? [X3: a > $o] :
( ( X2
= ( ^ [X4: a] :
( ( X3 @ X4 )
& ( cZ @ X4 ) ) ) )
& ( cW @ X3 ) )
& ( X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ( ? [X1: a > $o] :
( ( cW @ X1 )
& ( X1 @ X0 ) )
& ( cZ @ X0 ) )
<=> ? [X1: a > $o] :
( ? [X2: a > $o] :
( ( X1
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( cZ @ X3 ) ) ) )
& ( cW @ X2 ) )
& ( X1 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ( ? [X1: a > $o] :
( ( cW @ X1 )
& ( X1 @ X0 ) )
& ( cZ @ X0 ) )
<=> ? [X1: a > $o] :
( ? [X2: a > $o] :
( ( X1
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( cZ @ X3 ) ) ) )
& ( cW @ X2 ) )
& ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WJCDTLrTj4/DTF2THF_19462.p',cTHM61_pme) ).
thf(f70,plain,
( spl4_3
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f16,f47,f38]) ).
thf(f16,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ( sK3 @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f68,plain,
( spl4_6
| spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f17,f38,f52]) ).
thf(f17,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f67,plain,
( spl4_7
| spl4_8
| ~ spl4_6
| spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f27,f65,f52,f61,f58]) ).
thf(f27,plain,
! [X2: a > $o,X3: a > $o] :
( ( ( X3 @ sK0 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) )
| ( $false
= ( cZ @ sK0 ) )
| ( ( X2 @ sK0 )
= $false )
| ( ( cW @ X2 )
!= $true )
| ( ( cW @ X3 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: a > $o,X3: a > $o] :
( ( $true
!= ( cZ @ sK0 ) )
| ( ( ( cZ @ sK0 )
& ( X2 @ sK0 ) )
!= $true )
| ( ( cW @ X3 )
!= $true )
| ( ( cW @ X2 )
!= $true )
| ( ( X3 @ sK0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: a > $o,X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) )
@ sK0 )
!= $true )
| ( ( X3 @ sK0 )
!= $true )
| ( ( cW @ X2 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) ) ),
inference(equality_resolution,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: a > $o,X3: a > $o,X1: a > $o] :
( ( $true
!= ( X1 @ sK0 ) )
| ( ( cW @ X2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 )
| ( $true
!= ( cZ @ sK0 ) )
| ( ( X3 @ sK0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f56,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f22,f33,f47]) ).
thf(f22,plain,
( ( ( sK3 @ sK0 )
= $true )
| ( ( sK1 @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f55,plain,
( spl4_6
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f23,f33,f52]) ).
thf(f23,plain,
( ( $true
= ( cZ @ sK0 ) )
| ( ( sK1 @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f50,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f19,f47,f43]) ).
thf(f19,plain,
( ( ( sK3 @ sK0 )
= $true )
| ( $true
= ( cW @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f41,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f15,f29,f38]) ).
thf(f15,plain,
( ( ( cW @ sK3 )
= $true )
| ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f36,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f33,f29]) ).
thf(f21,plain,
( ( ( sK1 @ sK0 )
= $true )
| ( ( cW @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEV221^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.08 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.28 % Computer : n012.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue Feb 24 12:42:00 EST 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.28 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.35 ---- Original DTF file ---
% 0.17/0.35 thf(spec,logic,$$dhol).
% 0.17/0.35 %------------------------------------------------------------------------------
% 0.17/0.35 % File : SEV221^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.35 % Domain : Set Theory (Sets of sets)
% 0.17/0.35 % Problem : TPS problem THM61
% 0.17/0.35 % Version : Especial.
% 0.17/0.35 % English :
% 0.17/0.35
% 0.17/0.35 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.35 % Source : [Bro09]
% 0.17/0.35 % Names : tps_0386 [Bro09]
% 0.17/0.35 % : THM61 [TPS]
% 0.17/0.35
% 0.17/0.35 % Status : Theorem
% 0.17/0.35 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.17/0.35 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.17/0.35 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.17/0.35 % Maximal formula atoms : 4 ( 5 avg)
% 0.17/0.35 % Number of connectives : 13 ( 0 ~; 0 |; 5 &; 7 @)
% 0.17/0.35 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.35 % Maximal formula depth : 8 ( 8 avg)
% 0.17/0.35 % Number of types : 2 ( 1 usr)
% 0.17/0.35 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.17/0.35 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.17/0.35 % Number of variables : 5 ( 1 ^; 1 !; 3 ?; 5 :)
% 0.17/0.35 % SPC : TH0_THM_EQU_NAR
% 0.17/0.35
% 0.17/0.35 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.35 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.35 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.35 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.35 % : Polymorphic definitions expanded.
% 0.17/0.35 %------------------------------------------------------------------------------
% 0.17/0.35 thf(a_type,type,
% 0.17/0.35 a: $tType ).
% 0.17/0.35
% 0.17/0.35 thf(cZ,type,
% 0.17/0.35 cZ: a > $o ).
% 0.17/0.35
% 0.17/0.35 thf(cW,type,
% 0.17/0.35 cW: ( a > $o ) > $o ).
% 0.17/0.35
% 0.17/0.35 thf(cTHM61_pme,conjecture,
% 0.17/0.35 ! [Xx: a] :
% 0.17/0.35 ( ( ? [S: a > $o] :
% 0.17/0.35 ( ( cW @ S )
% 0.17/0.35 & ( S @ Xx ) )
% 0.17/0.35 & ( cZ @ Xx ) )
% 0.17/0.35 <=> ? [S: a > $o] :
% 0.17/0.35 ( ? [Xt: a > $o] :
% 0.17/0.35 ( ( cW @ Xt )
% 0.17/0.35 & ( S
% 0.17/0.35 = ( ^ [Xx0: a] :
% 0.17/0.35 ( ( cZ @ Xx0 )
% 0.17/0.35 & ( Xt @ Xx0 ) ) ) ) )
% 0.17/0.35 & ( S @ Xx ) ) ) ).
% 0.17/0.35
% 0.17/0.35 %------------------------------------------------------------------------------
% 0.17/0.35 ------------------------
% 0.18/1.03 ---- Embedded in THF ---
% 0.18/1.03 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.18/1.03 %%% Generated on Tue Feb 24 12:42:01 EST 2026
% 0.18/1.03 %%% using '$$dhol' embedding, version 1.3.0.
% 0.18/1.03 %%% Logic specification used:
% 0.18/1.03 %%% thf(spec, logic, $$dhol).
% 0.18/1.03
% 0.18/1.03 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.WJCDTLrTj4/DTF2DTF19462.p
% See solution above
% 0.18/1.03 ------------------------
% 0.18/1.04 ---- Cleaned THF ---
% 0.18/1.04 thf(a_type,type,
% 0.18/1.04 a: $tType ).
% 0.18/1.04
% 0.18/1.04 thf(cZ,type,
% 0.18/1.04 cZ: a > $o ).
% 0.18/1.04
% 0.18/1.04 thf(cW,type,
% 0.18/1.04 cW: ( a > $o ) > $o ).
% 0.18/1.04
% 0.18/1.04 thf(cTHM61_pme,conjecture,
% 0.18/1.04 ! [Xx: a] :
% 0.18/1.04 ( ( ? [S: a > $o] :
% 0.18/1.04 ( ( cW @ S )
% 0.18/1.04 & ( S @ Xx ) )
% 0.18/1.04 & ( cZ @ Xx ) )
% 0.18/1.04 <=> ? [S: a > $o] :
% 0.18/1.04 ( ? [Xt: a > $o] :
% 0.18/1.04 ( ( cW @ Xt )
% 0.18/1.04 & ( S
% 0.18/1.04 = ( ^ [Xx0: a] :
% 0.18/1.04 ( ( cZ @ Xx0 )
% 0.18/1.04 & ( Xt @ Xx0 ) ) ) ) )
% 0.18/1.04 & ( S @ Xx ) ) ) ).
% 0.18/1.04 ------------------------
% 0.18/1.05 % (19560)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19462 for (3000ds/183Mi)
% 0.18/1.06 % (19560)First to succeed.
% 0.18/1.06 % (19560)Refutation found. Thanks to Tanya!
% 0.18/1.06 % SZS status Theorem for DTF2THF_19462
% 0.18/1.06 % SZS output start Proof for DTF2THF_19462
% 0.18/1.06 thf(type_def_5, type, a: $tType).
% 0.18/1.06 thf(func_def_0, type, a: $tType).
% 0.18/1.06 thf(func_def_1, type, cZ: a > $o).
% 0.18/1.06 thf(func_def_2, type, cW: (a > $o) > $o).
% 0.18/1.06 thf(func_def_9, type, sK0: a).
% 0.18/1.06 thf(func_def_10, type, sK1: a > $o).
% 0.18/1.06 thf(func_def_11, type, sK2: a > $o).
% 0.18/1.06 thf(func_def_12, type, sK3: a > $o).
% 0.18/1.06 thf(func_def_15, type, ph5: !>[X0: $tType]:(X0)).
% 0.18/1.06 thf(func_def_16, type, sK6: a).
% 0.18/1.06 thf(f172,plain,(
% 0.18/1.06 $false),
% 0.18/1.06 inference(avatar_sat_refutation,[status(thm)],[f36,f41,f50,f55,f56,f67,f68,f70,f71,f100,f104,f113,f158,f165,f171])).
% 0.18/1.06 thf(f171,plain,(
% 0.18/1.06 ~spl4_1 | ~spl4_5 | ~spl4_7),
% 0.18/1.06 inference(avatar_contradiction_clause,[status(thm)],[f170])).
% 0.18/1.06 thf(f170,plain,(
% 0.18/1.06 $false | (~spl4_1 | ~spl4_5 | ~spl4_7)),
% 0.18/1.06 inference(subsumption_resolution,[status(thm)],[f169,f49])).
% 0.18/1.06 thf(f49,plain,(
% 0.18/1.06 ((sK3 @ sK0) = $true) | ~spl4_5),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f47])).
% 0.18/1.06 thf(f47,definition,(
% 0.18/1.06 spl4_5 <=> ((sK3 @ sK0) = $true)),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 0.18/1.06 thf(f169,plain,(
% 0.18/1.06 ((sK3 @ sK0) != $true) | (~spl4_1 | ~spl4_7)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 0.18/1.06 thf(f167,plain,(
% 0.18/1.06 ((sK3 @ sK0) != $true) | ($true != $true) | (~spl4_1 | ~spl4_7)),
% 0.18/1.06 inference(superposition,[status(thm)],[f59,f31])).
% 0.18/1.06 thf(f31,plain,(
% 0.18/1.06 ((cW @ sK3) = $true) | ~spl4_1),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f29])).
% 0.18/1.06 thf(f29,definition,(
% 0.18/1.06 spl4_1 <=> ((cW @ sK3) = $true)),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 0.18/1.06 thf(f59,plain,(
% 0.18/1.06 ( ! [X3 : a > $o] : (((cW @ X3) != $true) | ((X3 @ sK0) != $true)) ) | ~spl4_7),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f58])).
% 0.18/1.06 thf(f58,definition,(
% 0.18/1.06 spl4_7 <=> ! [X3 : a > $o] : (((X3 @ sK0) != $true) | ((cW @ X3) != $true))),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 0.18/1.06 thf(f165,plain,(
% 0.18/1.06 ~spl4_1 | ~spl4_5 | ~spl4_9),
% 0.18/1.06 inference(avatar_contradiction_clause,[status(thm)],[f164])).
% 0.18/1.06 thf(f164,plain,(
% 0.18/1.06 $false | (~spl4_1 | ~spl4_5 | ~spl4_9)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 0.18/1.06 thf(f161,plain,(
% 0.18/1.06 ($false = $true) | (~spl4_1 | ~spl4_5 | ~spl4_9)),
% 0.18/1.06 inference(superposition,[status(thm)],[f49,f152])).
% 0.18/1.06 thf(f152,plain,(
% 0.18/1.06 ($false = (sK3 @ sK0)) | (~spl4_1 | ~spl4_9)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 0.18/1.06 thf(f150,plain,(
% 0.18/1.06 ($true != $true) | ($false = (sK3 @ sK0)) | (~spl4_1 | ~spl4_9)),
% 0.18/1.06 inference(superposition,[status(thm)],[f66,f31])).
% 0.18/1.06 thf(f66,plain,(
% 0.18/1.06 ( ! [X2 : a > $o] : (((cW @ X2) != $true) | ((X2 @ sK0) = $false)) ) | ~spl4_9),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f65])).
% 0.18/1.06 thf(f65,definition,(
% 0.18/1.06 spl4_9 <=> ! [X2 : a > $o] : (((X2 @ sK0) = $false) | ((cW @ X2) != $true))),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 0.18/1.06 thf(f158,plain,(
% 0.18/1.06 ~spl4_2 | ~spl4_3 | ~spl4_4 | ~spl4_9),
% 0.18/1.06 inference(avatar_contradiction_clause,[status(thm)],[f157])).
% 0.18/1.06 thf(f157,plain,(
% 0.18/1.06 $false | (~spl4_2 | ~spl4_3 | ~spl4_4 | ~spl4_9)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 0.18/1.06 thf(f154,plain,(
% 0.18/1.06 ($false = $true) | (~spl4_2 | ~spl4_3 | ~spl4_4 | ~spl4_9)),
% 0.18/1.06 inference(superposition,[status(thm)],[f92,f151])).
% 0.18/1.06 thf(f151,plain,(
% 0.18/1.06 ($false = (sK2 @ sK0)) | (~spl4_4 | ~spl4_9)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 0.18/1.06 thf(f149,plain,(
% 0.18/1.06 ($true != $true) | ($false = (sK2 @ sK0)) | (~spl4_4 | ~spl4_9)),
% 0.18/1.06 inference(superposition,[status(thm)],[f66,f45])).
% 0.18/1.06 thf(f45,plain,(
% 0.18/1.06 ($true = (cW @ sK2)) | ~spl4_4),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f43])).
% 0.18/1.06 thf(f43,definition,(
% 0.18/1.06 spl4_4 <=> ($true = (cW @ sK2))),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 0.18/1.06 thf(f92,plain,(
% 0.18/1.06 ((sK2 @ sK0) = $true) | (~spl4_2 | ~spl4_3)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 0.18/1.06 thf(f89,plain,(
% 0.18/1.06 ((sK2 @ sK0) = $true) | ($false = $true) | (~spl4_2 | ~spl4_3)),
% 0.18/1.06 inference(superposition,[status(thm)],[f77,f35])).
% 0.18/1.06 thf(f35,plain,(
% 0.18/1.06 ((sK1 @ sK0) = $true) | ~spl4_2),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f33])).
% 0.18/1.06 thf(f33,definition,(
% 0.18/1.06 spl4_2 <=> ((sK1 @ sK0) = $true)),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 0.18/1.06 thf(f77,plain,(
% 0.18/1.06 ( ! [X1 : a] : (($false = (sK1 @ X1)) | ((sK2 @ X1) = $true)) ) | ~spl4_3),
% 0.18/1.06 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 0.18/1.06 thf(f76,plain,(
% 0.18/1.06 ( ! [X1 : a] : (($true = ((cZ @ X1) & (sK2 @ X1))) | ($false = (sK1 @ X1))) ) | ~spl4_3),
% 0.18/1.06 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 0.18/1.06 thf(f74,plain,(
% 0.18/1.06 ( ! [X1 : a] : (((sK1 @ X1) = ((cZ @ X1) & (sK2 @ X1)))) ) | ~spl4_3),
% 0.18/1.06 inference(beta_eta_normalization,[status(thm)],[f72])).
% 0.18/1.06 thf(f72,plain,(
% 0.18/1.06 ( ! [X1 : a] : ((((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) @ X1) = (sK1 @ X1))) ) | ~spl4_3),
% 0.18/1.06 inference(argument_congruence,[status(thm)],[f40])).
% 0.18/1.06 thf(f40,plain,(
% 0.18/1.06 (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0)))) | ~spl4_3),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f38])).
% 0.18/1.06 thf(f38,definition,(
% 0.18/1.06 spl4_3 <=> (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))))),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 0.18/1.06 thf(f113,plain,(
% 0.18/1.06 ~spl4_6 | ~spl4_8),
% 0.18/1.06 inference(avatar_contradiction_clause,[status(thm)],[f112])).
% 0.18/1.06 thf(f112,plain,(
% 0.18/1.06 $false | (~spl4_6 | ~spl4_8)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 0.18/1.06 thf(f105,plain,(
% 0.18/1.06 ($false = $true) | (~spl4_6 | ~spl4_8)),
% 0.18/1.06 inference(superposition,[status(thm)],[f63,f54])).
% 0.18/1.06 thf(f54,plain,(
% 0.18/1.06 ($true = (cZ @ sK0)) | ~spl4_6),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f52])).
% 0.18/1.06 thf(f52,definition,(
% 0.18/1.06 spl4_6 <=> ($true = (cZ @ sK0))),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 0.18/1.06 thf(f63,plain,(
% 0.18/1.06 ($false = (cZ @ sK0)) | ~spl4_8),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f61])).
% 0.18/1.06 thf(f61,definition,(
% 0.18/1.06 spl4_8 <=> ($false = (cZ @ sK0))),
% 0.18/1.06 introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition])).
% 0.18/1.06 thf(f104,plain,(
% 0.18/1.06 ~spl4_2 | ~spl4_3 | ~spl4_4 | ~spl4_7),
% 0.18/1.06 inference(avatar_contradiction_clause,[status(thm)],[f103])).
% 0.18/1.06 thf(f103,plain,(
% 0.18/1.06 $false | (~spl4_2 | ~spl4_3 | ~spl4_4 | ~spl4_7)),
% 0.18/1.06 inference(subsumption_resolution,[status(thm)],[f102,f92])).
% 0.18/1.06 thf(f102,plain,(
% 0.18/1.06 ((sK2 @ sK0) != $true) | (~spl4_4 | ~spl4_7)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 0.18/1.06 thf(f101,plain,(
% 0.18/1.06 ($true != $true) | ((sK2 @ sK0) != $true) | (~spl4_4 | ~spl4_7)),
% 0.18/1.06 inference(superposition,[status(thm)],[f59,f45])).
% 0.18/1.06 thf(f100,plain,(
% 0.18/1.06 ~spl4_2 | ~spl4_3 | spl4_6),
% 0.18/1.06 inference(avatar_contradiction_clause,[status(thm)],[f99])).
% 0.18/1.06 thf(f99,plain,(
% 0.18/1.06 $false | (~spl4_2 | ~spl4_3 | spl4_6)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 0.18/1.06 thf(f96,plain,(
% 0.18/1.06 ($false = $true) | (~spl4_2 | ~spl4_3 | spl4_6)),
% 0.18/1.06 inference(superposition,[status(thm)],[f35,f94])).
% 0.18/1.06 thf(f94,plain,(
% 0.18/1.06 ($false = (sK1 @ sK0)) | (~spl4_3 | spl4_6)),
% 0.18/1.06 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 0.18/1.06 thf(f93,plain,(
% 0.18/1.06 ($false = (sK1 @ sK0)) | ($true != $true) | (~spl4_3 | spl4_6)),
% 0.18/1.06 inference(superposition,[status(thm)],[f53,f78])).
% 0.18/1.06 thf(f78,plain,(
% 0.18/1.06 ( ! [X1 : a] : (($true = (cZ @ X1)) | ($false = (sK1 @ X1))) ) | ~spl4_3),
% 0.18/1.06 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 0.18/1.06 thf(f53,plain,(
% 0.18/1.06 ($true != (cZ @ sK0)) | spl4_6),
% 0.18/1.06 inference(avatar_component_clause,[status(thm)],[f52])).
% 0.18/1.06 thf(f71,plain,(
% 0.18/1.06 spl4_1 | spl4_4),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f18,f43,f29])).
% 0.18/1.06 thf(f18,plain,(
% 0.18/1.06 ($true = (cW @ sK2)) | ((cW @ sK3) = $true)),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 thf(f14,plain,(
% 0.18/1.06 (! [X1 : a > $o] : (($true != (X1 @ sK0)) | ! [X2 : a > $o] : (((cW @ X2) != $true) | ((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) != X1))) | ($true != (cZ @ sK0)) | ! [X3 : a > $o] : (((X3 @ sK0) != $true) | ((cW @ X3) != $true))) & ((((sK1 @ sK0) = $true) & (($true = (cW @ sK2)) & (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0)))))) | (($true = (cZ @ sK0)) & (((sK3 @ sK0) = $true) & ((cW @ sK3) = $true))))),
% 0.18/1.06 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f13,f12,f11,f10])).
% 0.18/1.06 thf(f10,plain,(
% 0.18/1.06 ? [X0 : a] : ((! [X1 : a > $o] : (((X1 @ X0) != $true) | ! [X2 : a > $o] : (((cW @ X2) != $true) | ((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) != X1))) | ((cZ @ X0) != $true) | ! [X3 : a > $o] : (((X3 @ X0) != $true) | ((cW @ X3) != $true))) & (? [X4 : a > $o] : (($true = (X4 @ X0)) & ? [X5 : a > $o] : (($true = (cW @ X5)) & ((^[Y0 : a]: ((cZ @ Y0) & (X5 @ Y0))) = X4))) | (((cZ @ X0) = $true) & ? [X6 : a > $o] : (((X6 @ X0) = $true) & ((cW @ X6) = $true))))) => ((! [X1 : a > $o] : (($true != (X1 @ sK0)) | ! [X2 : a > $o] : (((cW @ X2) != $true) | ((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) != X1))) | ($true != (cZ @ sK0)) | ! [X3 : a > $o] : (((X3 @ sK0) != $true) | ((cW @ X3) != $true))) & (? [X4 : a > $o] : (((X4 @ sK0) = $true) & ? [X5 : a > $o] : (($true = (cW @ X5)) & ((^[Y0 : a]: ((cZ @ Y0) & (X5 @ Y0))) = X4))) | (($true = (cZ @ sK0)) & ? [X6 : a > $o] : (($true = (X6 @ sK0)) & ((cW @ X6) = $true)))))),
% 0.18/1.06 introduced(definition,[],[choice_axiom])).
% 0.18/1.06 thf(f11,plain,(
% 0.18/1.06 ? [X4 : a > $o] : (((X4 @ sK0) = $true) & ? [X5 : a > $o] : (($true = (cW @ X5)) & ((^[Y0 : a]: ((cZ @ Y0) & (X5 @ Y0))) = X4))) => (((sK1 @ sK0) = $true) & ? [X5 : a > $o] : (($true = (cW @ X5)) & (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (X5 @ Y0))))))),
% 0.18/1.06 introduced(definition,[],[choice_axiom])).
% 0.18/1.06 thf(f12,plain,(
% 0.18/1.06 ? [X5 : a > $o] : (($true = (cW @ X5)) & (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (X5 @ Y0))))) => (($true = (cW @ sK2)) & (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0)))))),
% 0.18/1.06 introduced(definition,[],[choice_axiom])).
% 0.18/1.06 thf(f13,plain,(
% 0.18/1.06 ? [X6 : a > $o] : (($true = (X6 @ sK0)) & ((cW @ X6) = $true)) => (((sK3 @ sK0) = $true) & ((cW @ sK3) = $true))),
% 0.18/1.06 introduced(definition,[],[choice_axiom])).
% 0.18/1.06 thf(f9,plain,(
% 0.18/1.06 ? [X0 : a] : ((! [X1 : a > $o] : (((X1 @ X0) != $true) | ! [X2 : a > $o] : (((cW @ X2) != $true) | ((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) != X1))) | ((cZ @ X0) != $true) | ! [X3 : a > $o] : (((X3 @ X0) != $true) | ((cW @ X3) != $true))) & (? [X4 : a > $o] : (($true = (X4 @ X0)) & ? [X5 : a > $o] : (($true = (cW @ X5)) & ((^[Y0 : a]: ((cZ @ Y0) & (X5 @ Y0))) = X4))) | (((cZ @ X0) = $true) & ? [X6 : a > $o] : (((X6 @ X0) = $true) & ((cW @ X6) = $true)))))),
% 0.18/1.06 inference(rectify,[status(thm)],[f8])).
% 0.18/1.06 thf(f8,plain,(
% 0.18/1.06 ? [X0 : a] : ((! [X2 : a > $o] : (((X2 @ X0) != $true) | ! [X3 : a > $o] : (((cW @ X3) != $true) | ((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) != X2))) | ((cZ @ X0) != $true) | ! [X1 : a > $o] : (((X1 @ X0) != $true) | ((cW @ X1) != $true))) & (? [X2 : a > $o] : (((X2 @ X0) = $true) & ? [X3 : a > $o] : (((cW @ X3) = $true) & ((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) = X2))) | (((cZ @ X0) = $true) & ? [X1 : a > $o] : (((X1 @ X0) = $true) & ((cW @ X1) = $true)))))),
% 0.18/1.06 inference(flattening,[status(thm)],[f7])).
% 0.18/1.06 thf(f7,plain,(
% 0.18/1.06 ? [X0 : a] : ((! [X2 : a > $o] : (((X2 @ X0) != $true) | ! [X3 : a > $o] : (((cW @ X3) != $true) | ((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) != X2))) | (((cZ @ X0) != $true) | ! [X1 : a > $o] : (((X1 @ X0) != $true) | ((cW @ X1) != $true)))) & (? [X2 : a > $o] : (((X2 @ X0) = $true) & ? [X3 : a > $o] : (((cW @ X3) = $true) & ((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) = X2))) | (((cZ @ X0) = $true) & ? [X1 : a > $o] : (((X1 @ X0) = $true) & ((cW @ X1) = $true)))))),
% 0.18/1.06 inference(nnf_transformation,[status(thm)],[f6])).
% 0.18/1.06 thf(f6,plain,(
% 0.18/1.06 ? [X0 : a] : ((((cZ @ X0) = $true) & ? [X1 : a > $o] : (((X1 @ X0) = $true) & ((cW @ X1) = $true))) <~> ? [X2 : a > $o] : (((X2 @ X0) = $true) & ? [X3 : a > $o] : (((cW @ X3) = $true) & ((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) = X2))))),
% 0.18/1.06 inference(ennf_transformation,[status(thm)],[f5])).
% 0.18/1.06 thf(f5,plain,(
% 0.18/1.06 ~! [X0 : a] : ((((cZ @ X0) = $true) & ? [X1 : a > $o] : (((X1 @ X0) = $true) & ((cW @ X1) = $true))) <=> ? [X2 : a > $o] : (((X2 @ X0) = $true) & ? [X3 : a > $o] : (((cW @ X3) = $true) & ((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) = X2))))),
% 0.18/1.06 inference(fool_elimination,[status(thm)],[f4])).
% 0.18/1.06 thf(f4,plain,(
% 0.18/1.06 ~! [X0 : a] : ((? [X1 : a > $o] : ((cW @ X1) & (X1 @ X0)) & (cZ @ X0)) <=> ? [X2 : a > $o] : (? [X3 : a > $o] : ((X2 = (^[X4 : a] : ((X3 @ X4) & (cZ @ X4)))) & (cW @ X3)) & (X2 @ X0)))),
% 0.18/1.06 inference(rectify,[status(thm)],[f2])).
% 0.18/1.06 thf(f2,negated_conjecture,(
% 0.18/1.06 ~! [X0 : a] : ((? [X1 : a > $o] : ((cW @ X1) & (X1 @ X0)) & (cZ @ X0)) <=> ? [X1 : a > $o] : (? [X2 : a > $o] : ((X1 = (^[X3 : a] : ((X2 @ X3) & (cZ @ X3)))) & (cW @ X2)) & (X1 @ X0)))),
% 0.18/1.06 inference(negated_conjecture,[status(cth)],[f1])).
% 0.18/1.06 thf(f1,conjecture,(
% 0.18/1.06 ! [X0 : a] : ((? [X1 : a > $o] : ((cW @ X1) & (X1 @ X0)) & (cZ @ X0)) <=> ? [X1 : a > $o] : (? [X2 : a > $o] : ((X1 = (^[X3 : a] : ((X2 @ X3) & (cZ @ X3)))) & (cW @ X2)) & (X1 @ X0)))),
% 0.18/1.06 file('/export/starexec/sandbox2/tmp/tmp.WJCDTLrTj4/DTF2THF_19462.p',cTHM61_pme)).
% 0.18/1.06 thf(f70,plain,(
% 0.18/1.06 spl4_3 | spl4_5),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f16,f47,f38])).
% 0.18/1.06 thf(f16,plain,(
% 0.18/1.06 (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0)))) | ((sK3 @ sK0) = $true)),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 thf(f68,plain,(
% 0.18/1.06 spl4_6 | spl4_3),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f17,f38,f52])).
% 0.18/1.06 thf(f17,plain,(
% 0.18/1.06 (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0)))) | ($true = (cZ @ sK0))),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 thf(f67,plain,(
% 0.18/1.06 spl4_7 | spl4_8 | ~spl4_6 | spl4_9),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f27,f65,f52,f61,f58])).
% 0.18/1.06 thf(f27,plain,(
% 0.18/1.06 ( ! [X2 : a > $o,X3 : a > $o] : (((X3 @ sK0) != $true) | ($true != (cZ @ sK0)) | ($false = (cZ @ sK0)) | ((X2 @ sK0) = $false) | ((cW @ X2) != $true) | ((cW @ X3) != $true)) )),
% 0.18/1.06 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 0.18/1.06 thf(f26,plain,(
% 0.18/1.06 ( ! [X2 : a > $o,X3 : a > $o] : (($true != (cZ @ sK0)) | (((cZ @ sK0) & (X2 @ sK0)) != $true) | ((cW @ X3) != $true) | ((cW @ X2) != $true) | ((X3 @ sK0) != $true)) )),
% 0.18/1.06 inference(beta_eta_normalization,[status(thm)],[f25])).
% 0.18/1.06 thf(f25,plain,(
% 0.18/1.06 ( ! [X2 : a > $o,X3 : a > $o] : (((cW @ X3) != $true) | (((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) @ sK0) != $true) | ((X3 @ sK0) != $true) | ((cW @ X2) != $true) | ($true != (cZ @ sK0))) )),
% 0.18/1.06 inference(equality_resolution,[status(thm)],[f24])).
% 0.18/1.06 thf(f24,plain,(
% 0.18/1.06 ( ! [X2 : a > $o,X3 : a > $o,X1 : a > $o] : (($true != (X1 @ sK0)) | ((cW @ X2) != $true) | ((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) != X1) | ($true != (cZ @ sK0)) | ((X3 @ sK0) != $true) | ((cW @ X3) != $true)) )),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 thf(f56,plain,(
% 0.18/1.06 spl4_5 | spl4_2),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f22,f33,f47])).
% 0.18/1.06 thf(f22,plain,(
% 0.18/1.06 ((sK3 @ sK0) = $true) | ((sK1 @ sK0) = $true)),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 thf(f55,plain,(
% 0.18/1.06 spl4_6 | spl4_2),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f23,f33,f52])).
% 0.18/1.06 thf(f23,plain,(
% 0.18/1.06 ($true = (cZ @ sK0)) | ((sK1 @ sK0) = $true)),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 thf(f50,plain,(
% 0.18/1.06 spl4_4 | spl4_5),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f19,f47,f43])).
% 0.18/1.06 thf(f19,plain,(
% 0.18/1.06 ((sK3 @ sK0) = $true) | ($true = (cW @ sK2))),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 thf(f41,plain,(
% 0.18/1.06 spl4_3 | spl4_1),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f15,f29,f38])).
% 0.18/1.06 thf(f15,plain,(
% 0.18/1.06 ((cW @ sK3) = $true) | (sK1 = (^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))))),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 thf(f36,plain,(
% 0.18/1.06 spl4_1 | spl4_2),
% 0.18/1.06 inference(avatar_split_clause,[status(thm)],[f21,f33,f29])).
% 0.18/1.06 thf(f21,plain,(
% 0.18/1.06 ((sK1 @ sK0) = $true) | ((cW @ sK3) = $true)),
% 0.18/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 0.18/1.06 % SZS output end Proof for DTF2THF_19462
% 0.18/1.06 % (19560)------------------------------
% 0.18/1.06 % (19560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.18/1.06 % (19560)Termination reason: Refutation
% 0.18/1.06
% 0.18/1.06 % (19560)Memory used [KB]: 5628
% 0.18/1.06 % (19560)Time elapsed: 0.007 s
% 0.18/1.06 % (19560)Instructions burned: 7 (million)
% 0.18/1.06 % (19560)------------------------------
% 0.18/1.06 % (19560)------------------------------
% 0.18/1.06 % (19559)Success in time 0.016 s
%------------------------------------------------------------------------------