%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET621^5 : 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 : n002.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 09:31:56 AM UTC 2026
% Result : Theorem 1.31s 1.19s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 93 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 858 ( 210 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 1077 ( 197 ~; 276 |; 128 &; 469 @)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 20 ^; 12 !; 6 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK5: a ).
thf(f300,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f245,f259,f270,f279,f280,f287,f293,f299]) ).
thf(f299,plain,
( ~ spl3_3
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f298]) ).
thf(f298,plain,
( $false
| ~ spl3_3
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f294]) ).
thf(f294,plain,
( ( $true = $false )
| ~ spl3_3
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f277,f221]) ).
thf(f221,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f219]) ).
thf(f219,definition,
( spl3_3
<=> ( ( sK0 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f277,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f275]) ).
thf(f275,definition,
( spl3_6
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f293,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f292]) ).
thf(f292,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f288]) ).
thf(f288,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f212,f216]) ).
thf(f216,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f214]) ).
thf(f214,definition,
( spl3_2
<=> ( ( sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f212,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f210]) ).
thf(f210,definition,
( spl3_1
<=> ( ( sK2 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f287,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f286]) ).
thf(f286,plain,
( $false
| ~ spl3_4
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f283]) ).
thf(f283,plain,
( ( $true = $false )
| ~ spl3_4
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f226,f232]) ).
thf(f232,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f230]) ).
thf(f230,definition,
( spl3_5
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f226,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f224]) ).
thf(f224,definition,
( spl3_4
<=> ( ( sK1 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f280,plain,
( spl3_2
| spl3_6
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f29,f224,f275,f214]) ).
thf(f29,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $true
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $false )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
= $false )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
!= ( ~ ( sK0 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ~ ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ~ ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ~ ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( ~ ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ~ ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( ~ ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( ~ ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( X2 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ~ ( ( X1 @ X3 )
| ( X0 @ X3 ) ) )
| ( ~ ( ( X2 @ X3 )
| ( X0 @ X3 ) )
& ( X1 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( ~ ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( ( X2 @ X4 )
& ~ ( X1 @ X4 ) ) )
& ~ ( X0 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( ( X1 @ X4 )
| ( X2 @ X4 ) ) )
| ( ~ ( ( X0 @ X4 )
| ( X2 @ X4 ) )
& ( X1 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) )
& ~ ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( ( X1 @ X4 )
| ( X2 @ X4 ) ) )
| ( ~ ( ( X0 @ X4 )
| ( X2 @ X4 ) )
& ( X1 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) )
& ~ ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HypX1F3OuE/DTF2THF_32161.p',cBOOL_PROP_97_pme) ).
thf(f279,plain,
( spl3_6
| spl3_5
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f38,f210,f230,f275]) ).
thf(f38,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true
= ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $false )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $false
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f270,plain,
spl3_3,
inference(avatar_split_clause,[status(thm)],[f68,f219]) ).
thf(f68,plain,
( ( sK0 @ sK5 )
= $false ),
inference(duplicate_literal_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false
= ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f259,plain,
( spl3_2
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f97,f230,f214]) ).
thf(f97,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f245,plain,
( spl3_4
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f155,f210,f224]) ).
thf(f155,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
( ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK2 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
( ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET621^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n002.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 12:00:48 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.25/0.47 ---- Original DTF file ---
% 0.25/0.48 thf(spec,logic,$$dhol).
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 % File : SET621^5 : TPTP v9.2.1. Released v4.0.0.
% 0.25/0.48 % Domain : Set Theory
% 0.25/0.48 % Problem : TPS problem BOOL-PROP-97
% 0.25/0.48 % Version : Especial.
% 0.25/0.48 % English : Trybulec's 97th Boolean property of sets
% 0.25/0.48
% 0.25/0.48 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.25/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.25/0.48 % Source : [Bro09]
% 0.25/0.48 % Names : tps_0421 [Bro09]
% 0.25/0.48 % : BOOL-PROP-97 [TPS]
% 0.25/0.48
% 0.25/0.48 % Status : Theorem
% 0.25/0.48 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.25/0.48 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.25/0.48 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.25/0.48 % Maximal formula atoms : 1 ( 1 avg)
% 0.25/0.48 % Number of connectives : 25 ( 5 ~; 4 |; 5 &; 11 @)
% 0.25/0.48 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.25/0.48 % Maximal formula depth : 4 ( 4 avg)
% 0.25/0.48 % Number of types : 2 ( 1 usr)
% 0.25/0.48 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.25/0.48 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.25/0.48 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.25/0.48 % SPC : TH0_THM_EQU_NAR
% 0.25/0.48
% 0.25/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.25/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.25/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.25/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.25/0.48 % : Polymorphic definitions expanded.
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 thf(a_type,type,
% 0.25/0.48 a: $tType ).
% 0.25/0.48
% 0.25/0.48 thf(cBOOL_PROP_97_pme,conjecture,
% 0.25/0.48 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.25/0.48 ( ( ^ [Xx: a] :
% 0.25/0.48 ( ( ( ( X @ Xx )
% 0.25/0.48 & ~ ( Y @ Xx ) )
% 0.25/0.48 | ( ( Y @ Xx )
% 0.25/0.48 & ~ ( X @ Xx ) ) )
% 0.25/0.48 & ~ ( Z @ Xx ) ) )
% 0.25/0.48 = ( ^ [Xz: a] :
% 0.25/0.48 ( ( ( X @ Xz )
% 0.25/0.48 & ~ ( ( Y @ Xz )
% 0.25/0.48 | ( Z @ Xz ) ) )
% 0.25/0.48 | ( ( Y @ Xz )
% 0.25/0.48 & ~ ( ( X @ Xz )
% 0.25/0.48 | ( Z @ Xz ) ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 ------------------------
% 1.31/1.16 ---- Embedded in THF ---
% 1.31/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.31/1.16 %%% Generated on Tue Feb 24 12:00:49 EST 2026
% 1.31/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.31/1.16 %%% Logic specification used:
% 1.31/1.16 %%% thf(spec, logic, $$dhol).
% 1.31/1.16
% 1.31/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.HypX1F3OuE/DTF2DTF32161.p
% See solution above
% 1.31/1.16 ------------------------
% 1.31/1.17 ---- Cleaned THF ---
% 1.31/1.17 thf(a_type,type,
% 1.31/1.17 a: $tType ).
% 1.31/1.17
% 1.31/1.17 thf(cBOOL_PROP_97_pme,conjecture,
% 1.31/1.17 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.31/1.17 ( ( ^ [Xx: a] :
% 1.31/1.17 ( ( ( ( X @ Xx )
% 1.31/1.17 & ~ ( Y @ Xx ) )
% 1.31/1.17 | ( ( Y @ Xx )
% 1.31/1.17 & ~ ( X @ Xx ) ) )
% 1.31/1.17 & ~ ( Z @ Xx ) ) )
% 1.31/1.17 = ( ^ [Xz: a] :
% 1.31/1.17 ( ( ( X @ Xz )
% 1.31/1.17 & ~ ( ( Y @ Xz )
% 1.31/1.17 | ( Z @ Xz ) ) )
% 1.31/1.17 | ( ( Y @ Xz )
% 1.31/1.17 & ~ ( ( X @ Xz )
% 1.31/1.17 | ( Z @ Xz ) ) ) ) ) ) ).
% 1.31/1.17 ------------------------
% 1.31/1.18 % (32259)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32161 for (3000ds/183Mi)
% 1.31/1.18 % (32259)First to succeed.
% 1.31/1.18 % (32262)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32161 for (3000ds/2Mi)
% 1.31/1.19 % (32262)Instruction limit reached!
% 1.31/1.19 % (32262)------------------------------
% 1.31/1.19 % (32262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.19 % (32262)Termination reason: Unknown
% 1.31/1.19 % (32262)Termination phase: Saturation
% 1.31/1.19
% 1.31/1.19 % (32262)Memory used [KB]: 5500
% 1.31/1.19 % (32262)Time elapsed: 0.003 s
% 1.31/1.19 % (32262)Instructions burned: 2 (million)
% 1.31/1.19 % (32262)------------------------------
% 1.31/1.19 % (32262)------------------------------
% 1.31/1.19 % (32259)Refutation found. Thanks to Tanya!
% 1.31/1.19 % SZS status Theorem for DTF2THF_32161
% 1.31/1.19 % SZS output start Proof for DTF2THF_32161
% 1.31/1.19 thf(type_def_5, type, a: $tType).
% 1.31/1.19 thf(func_def_0, type, a: $tType).
% 1.31/1.19 thf(func_def_9, type, sK0: a > $o).
% 1.31/1.19 thf(func_def_10, type, sK1: a > $o).
% 1.31/1.19 thf(func_def_11, type, sK2: a > $o).
% 1.31/1.19 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.31/1.19 thf(func_def_14, type, sK5: a).
% 1.31/1.19 thf(f300,plain,(
% 1.31/1.19 $false),
% 1.31/1.19 inference(avatar_sat_refutation,[status(thm)],[f245,f259,f270,f279,f280,f287,f293,f299])).
% 1.31/1.19 thf(f299,plain,(
% 1.31/1.19 ~spl3_3 | ~spl3_6),
% 1.31/1.19 inference(avatar_contradiction_clause,[status(thm)],[f298])).
% 1.31/1.19 thf(f298,plain,(
% 1.31/1.19 $false | (~spl3_3 | ~spl3_6)),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f294])).
% 1.31/1.19 thf(f294,plain,(
% 1.31/1.19 ($true = $false) | (~spl3_3 | ~spl3_6)),
% 1.31/1.19 inference(superposition,[status(thm)],[f277,f221])).
% 1.31/1.19 thf(f221,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $false) | ~spl3_3),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f219])).
% 1.31/1.19 thf(f219,definition,(
% 1.31/1.19 spl3_3 <=> ((sK0 @ sK5) = $false)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.31/1.19 thf(f277,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $true) | ~spl3_6),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f275])).
% 1.31/1.19 thf(f275,definition,(
% 1.31/1.19 spl3_6 <=> ((sK0 @ sK5) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.31/1.19 thf(f293,plain,(
% 1.31/1.19 ~spl3_1 | ~spl3_2),
% 1.31/1.19 inference(avatar_contradiction_clause,[status(thm)],[f292])).
% 1.31/1.19 thf(f292,plain,(
% 1.31/1.19 $false | (~spl3_1 | ~spl3_2)),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f288])).
% 1.31/1.19 thf(f288,plain,(
% 1.31/1.19 ($true = $false) | (~spl3_1 | ~spl3_2)),
% 1.31/1.19 inference(superposition,[status(thm)],[f212,f216])).
% 1.31/1.19 thf(f216,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $true) | ~spl3_2),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f214])).
% 1.31/1.19 thf(f214,definition,(
% 1.31/1.19 spl3_2 <=> ((sK2 @ sK5) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.31/1.19 thf(f212,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $false) | ~spl3_1),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f210])).
% 1.31/1.19 thf(f210,definition,(
% 1.31/1.19 spl3_1 <=> ((sK2 @ sK5) = $false)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.31/1.19 thf(f287,plain,(
% 1.31/1.19 ~spl3_4 | ~spl3_5),
% 1.31/1.19 inference(avatar_contradiction_clause,[status(thm)],[f286])).
% 1.31/1.19 thf(f286,plain,(
% 1.31/1.19 $false | (~spl3_4 | ~spl3_5)),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f283])).
% 1.31/1.19 thf(f283,plain,(
% 1.31/1.19 ($true = $false) | (~spl3_4 | ~spl3_5)),
% 1.31/1.19 inference(superposition,[status(thm)],[f226,f232])).
% 1.31/1.19 thf(f232,plain,(
% 1.31/1.19 ($true = (sK1 @ sK5)) | ~spl3_5),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f230])).
% 1.31/1.19 thf(f230,definition,(
% 1.31/1.19 spl3_5 <=> ($true = (sK1 @ sK5))),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.31/1.19 thf(f226,plain,(
% 1.31/1.19 ((sK1 @ sK5) = $false) | ~spl3_4),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f224])).
% 1.31/1.19 thf(f224,definition,(
% 1.31/1.19 spl3_4 <=> ((sK1 @ sK5) = $false)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.31/1.19 thf(f280,plain,(
% 1.31/1.19 spl3_2 | spl3_6 | spl3_4),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f29,f224,f275,f214])).
% 1.31/1.19 thf(f29,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $false) | ((sK2 @ sK5) = $true)),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f28])).
% 1.31/1.19 thf(f28,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $true) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $true)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.31/1.19 thf(f27,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $false) | ($false = (~ (sK2 @ sK5)))),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.31/1.19 thf(f26,plain,(
% 1.31/1.19 ($false = (~ (sK2 @ sK5))) | ((sK2 @ sK5) = $true) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $false)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.31/1.19 thf(f22,plain,(
% 1.31/1.19 ($false = ((sK1 @ sK5) & (~ (sK2 @ sK5)))) | ((sK2 @ sK5) = $true) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.31/1.19 thf(f21,plain,(
% 1.31/1.19 ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ($false = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((sK2 @ sK5) = $true)),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.31/1.19 thf(f20,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $true) | ((sK1 @ sK5) = $false) | ($false = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.31/1.19 thf(f19,plain,(
% 1.31/1.19 ($true = ((sK0 @ sK5) | (sK2 @ sK5))) | ((sK0 @ sK5) = $true) | ($false = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((sK1 @ sK5) = $false)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f18])).
% 1.31/1.19 thf(f18,plain,(
% 1.31/1.19 ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $false) | ($false = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.31/1.19 thf(f17,plain,(
% 1.31/1.19 ($false = ((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5))))) | ((sK0 @ sK5) = $true) | ($false = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.31/1.19 thf(f15,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $true) | ((((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) = $false) | ($false = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f14])).
% 1.31/1.19 thf(f14,plain,(
% 1.31/1.19 ($false = (~ (sK0 @ sK5))) | ($false = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) = $false)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.31/1.19 thf(f13,plain,(
% 1.31/1.19 (((~ (sK0 @ sK5)) & (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) = $false) | ((((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) = $false)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.31/1.19 thf(f11,plain,(
% 1.31/1.19 ((((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) != ((~ (sK0 @ sK5)) & (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))))),
% 1.31/1.19 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.31/1.19 thf(f10,plain,(
% 1.31/1.19 (((^[Y0 : a]: (((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0)))) | ((~ ((sK0 @ Y0) | (sK1 @ Y0))) & (sK2 @ Y0)))) @ sK5) != ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (((~ (sK1 @ Y0)) & (sK2 @ Y0)) | ((sK1 @ Y0) & (~ (sK2 @ Y0)))))) @ sK5))),
% 1.31/1.19 inference(negative_extensionality,[status(thm)],[f9])).
% 1.31/1.19 thf(f9,plain,(
% 1.31/1.19 ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (((~ (sK1 @ Y0)) & (sK2 @ Y0)) | ((sK1 @ Y0) & (~ (sK2 @ Y0)))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0)))) | ((~ ((sK0 @ Y0) | (sK1 @ Y0))) & (sK2 @ Y0)))))),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f8])).
% 1.31/1.19 thf(f8,plain,(
% 1.31/1.19 ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (((~ (sK1 @ Y0)) & (sK2 @ Y0)) | ((sK1 @ Y0) & (~ (sK2 @ Y0)))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0)))) | ((~ ((sK0 @ Y0) | (sK1 @ Y0))) & (sK2 @ Y0)))))),
% 1.31/1.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.31/1.19 thf(f7,plain,(
% 1.31/1.19 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0)))) | ((~ ((X0 @ Y0) | (X1 @ Y0))) & (X2 @ Y0)))) != (^[Y0 : a]: ((~ (X0 @ Y0)) & (((~ (X1 @ Y0)) & (X2 @ Y0)) | ((X1 @ Y0) & (~ (X2 @ Y0))))))) => ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (((~ (sK1 @ Y0)) & (sK2 @ Y0)) | ((sK1 @ Y0) & (~ (sK2 @ Y0)))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0)))) | ((~ ((sK0 @ Y0) | (sK1 @ Y0))) & (sK2 @ Y0)))))),
% 1.31/1.19 introduced(definition,[],[choice_axiom])).
% 1.31/1.19 thf(f6,plain,(
% 1.31/1.19 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0)))) | ((~ ((X0 @ Y0) | (X1 @ Y0))) & (X2 @ Y0)))) != (^[Y0 : a]: ((~ (X0 @ Y0)) & (((~ (X1 @ Y0)) & (X2 @ Y0)) | ((X1 @ Y0) & (~ (X2 @ Y0)))))))),
% 1.31/1.19 inference(ennf_transformation,[status(thm)],[f5])).
% 1.31/1.19 thf(f5,plain,(
% 1.31/1.19 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0)))) | ((~ ((X0 @ Y0) | (X1 @ Y0))) & (X2 @ Y0)))) = (^[Y0 : a]: ((~ (X0 @ Y0)) & (((~ (X1 @ Y0)) & (X2 @ Y0)) | ((X1 @ Y0) & (~ (X2 @ Y0)))))))),
% 1.31/1.19 inference(fool_elimination,[status(thm)],[f4])).
% 1.31/1.19 thf(f4,plain,(
% 1.31/1.19 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((X2 @ X3) & ~((X1 @ X3) | (X0 @ X3))) | (~((X2 @ X3) | (X0 @ X3)) & (X1 @ X3)))) = (^[X4 : a] : (((~(X2 @ X4) & (X1 @ X4)) | ((X2 @ X4) & ~(X1 @ X4))) & ~(X0 @ X4))))),
% 1.31/1.19 inference(rectify,[status(thm)],[f2])).
% 1.31/1.19 thf(f2,negated_conjecture,(
% 1.31/1.19 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((^[X4 : a] : (((X0 @ X4) & ~((X1 @ X4) | (X2 @ X4))) | (~((X0 @ X4) | (X2 @ X4)) & (X1 @ X4)))) = (^[X3 : a] : (((~(X0 @ X3) & (X1 @ X3)) | ((X0 @ X3) & ~(X1 @ X3))) & ~(X2 @ X3))))),
% 1.31/1.19 inference(negated_conjecture,[status(cth)],[f1])).
% 1.31/1.19 thf(f1,conjecture,(
% 1.31/1.19 ! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((^[X4 : a] : (((X0 @ X4) & ~((X1 @ X4) | (X2 @ X4))) | (~((X0 @ X4) | (X2 @ X4)) & (X1 @ X4)))) = (^[X3 : a] : (((~(X0 @ X3) & (X1 @ X3)) | ((X0 @ X3) & ~(X1 @ X3))) & ~(X2 @ X3))))),
% 1.31/1.19 file('/export/starexec/sandbox/tmp/tmp.HypX1F3OuE/DTF2THF_32161.p',cBOOL_PROP_97_pme)).
% 1.31/1.19 thf(f279,plain,(
% 1.31/1.19 spl3_6 | spl3_5 | spl3_1),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f38,f210,f230,f275])).
% 1.31/1.19 thf(f38,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false) | ($true = (sK1 @ sK5))),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f37])).
% 1.31/1.19 thf(f37,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false) | ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.31/1.19 thf(f36,plain,(
% 1.31/1.19 ($true = ((sK0 @ sK5) | (sK1 @ sK5))) | ($true = (sK1 @ sK5)) | ((sK2 @ sK5) = $false) | ((sK0 @ sK5) = $true)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f35])).
% 1.31/1.19 thf(f35,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false) | ($true = (sK1 @ sK5)) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) = $false)),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f34])).
% 1.31/1.19 thf(f34,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $false) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) = $false) | ($true = (sK1 @ sK5)) | ((sK2 @ sK5) = $false) | ((sK0 @ sK5) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.31/1.19 thf(f33,plain,(
% 1.31/1.19 ($false = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false) | ($true = (sK1 @ sK5))),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.31/1.19 thf(f32,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $false) | ((~ (sK1 @ sK5)) = $false) | ($false = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ((sK0 @ sK5) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.31/1.19 thf(f31,plain,(
% 1.31/1.19 (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $false) | ((sK0 @ sK5) = $true) | ($false = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5)))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.31/1.19 thf(f16,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $true) | ($false = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ($false = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5)))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.31/1.19 thf(f270,plain,(
% 1.31/1.19 spl3_3),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f68,f219])).
% 1.31/1.19 thf(f68,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $false)),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f67])).
% 1.31/1.19 thf(f67,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $false) | ((sK0 @ sK5) = $false)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.31/1.19 thf(f65,plain,(
% 1.31/1.19 ($false = ((sK0 @ sK5) | (sK1 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f64])).
% 1.31/1.19 thf(f64,plain,(
% 1.31/1.19 ((~ ((sK0 @ sK5) | (sK1 @ sK5))) = $true) | ((sK0 @ sK5) = $false)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.31/1.19 thf(f62,plain,(
% 1.31/1.19 ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f61])).
% 1.31/1.19 thf(f61,plain,(
% 1.31/1.19 ((sK0 @ sK5) = $false) | ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.31/1.19 thf(f59,plain,(
% 1.31/1.19 ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f58])).
% 1.31/1.19 thf(f58,plain,(
% 1.31/1.19 ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true) | ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f48])).
% 1.31/1.19 thf(f48,plain,(
% 1.31/1.19 ($true = (~ (sK0 @ sK5))) | ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true) | ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5)))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.31/1.19 thf(f47,plain,(
% 1.31/1.19 ($true = ((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5))))) | ($true = (~ (sK0 @ sK5))) | ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5)))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.31/1.19 thf(f46,plain,(
% 1.31/1.19 ($true = (((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5)))) | ($true = (~ (sK0 @ sK5)))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.31/1.19 thf(f12,plain,(
% 1.31/1.19 ($true = ((~ (sK0 @ sK5)) & (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | ($true = (((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.31/1.19 thf(f259,plain,(
% 1.31/1.19 spl3_2 | spl3_5),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f97,f230,f214])).
% 1.31/1.19 thf(f97,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $true) | ($true = (sK1 @ sK5))),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f94])).
% 1.31/1.19 thf(f94,plain,(
% 1.31/1.19 ($true = (sK1 @ sK5)) | ((sK2 @ sK5) = $true) | ((sK2 @ sK5) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.31/1.19 thf(f82,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $true) | (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $true) | ($true = (sK1 @ sK5))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.31/1.19 thf(f81,plain,(
% 1.31/1.19 ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $true) | ($true = (sK1 @ sK5))),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f80])).
% 1.31/1.19 thf(f80,plain,(
% 1.31/1.19 ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ($true = (sK1 @ sK5)) | (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $true) | ($true = (sK1 @ sK5))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.31/1.19 thf(f78,plain,(
% 1.31/1.19 ($true = ((sK1 @ sK5) & (~ (sK2 @ sK5)))) | ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $true) | ($true = (sK1 @ sK5))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.31/1.19 thf(f77,plain,(
% 1.31/1.19 ($true = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ($true = (sK1 @ sK5)) | ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5)))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.31/1.19 thf(f75,plain,(
% 1.31/1.19 ($true = ((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5))))) | ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ($true = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.31/1.19 thf(f45,plain,(
% 1.31/1.19 ($true = (((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5)))) | ($true = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.31/1.19 thf(f245,plain,(
% 1.31/1.19 spl3_4 | spl3_1),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f155,f210,f224])).
% 1.31/1.19 thf(f155,plain,(
% 1.31/1.19 ((sK1 @ sK5) = $false) | ((sK2 @ sK5) = $false)),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f154])).
% 1.31/1.19 thf(f154,plain,(
% 1.31/1.19 ((sK1 @ sK5) = $false) | ((sK2 @ sK5) = $false) | ((sK1 @ sK5) = $false)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f153])).
% 1.31/1.19 thf(f153,plain,(
% 1.31/1.19 ((~ (sK1 @ sK5)) = $true) | ((sK2 @ sK5) = $false) | ((sK1 @ sK5) = $false)),
% 1.31/1.19 inference(duplicate_literal_removal,[status(thm)],[f149])).
% 1.31/1.19 thf(f149,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ((sK2 @ sK5) = $false) | ((~ (sK1 @ sK5)) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f148])).
% 1.31/1.19 thf(f148,plain,(
% 1.31/1.19 ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ((sK2 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ((~ (sK1 @ sK5)) = $true)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f139])).
% 1.31/1.19 thf(f139,plain,(
% 1.31/1.19 ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true) | ((sK2 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ((~ (sK1 @ sK5)) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f138])).
% 1.31/1.19 thf(f138,plain,(
% 1.31/1.19 ((sK2 @ sK5) = $false) | ($false = ((sK0 @ sK5) | (sK1 @ sK5))) | ((~ (sK1 @ sK5)) = $true) | ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f137])).
% 1.31/1.19 thf(f137,plain,(
% 1.31/1.19 ($true = (~ (sK2 @ sK5))) | ($false = ((sK0 @ sK5) | (sK1 @ sK5))) | ((~ (sK1 @ sK5)) = $true) | ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true)),
% 1.31/1.19 inference(not_proxy_clausification,[status(thm)],[f121])).
% 1.31/1.19 thf(f121,plain,(
% 1.31/1.19 ((~ ((sK0 @ sK5) | (sK1 @ sK5))) = $true) | ((~ (sK1 @ sK5)) = $true) | ($true = (~ (sK2 @ sK5))) | ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f120])).
% 1.31/1.19 thf(f120,plain,(
% 1.31/1.19 ($true = ((sK1 @ sK5) & (~ (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true) | ((~ (sK1 @ sK5)) = $true) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.31/1.19 thf(f118,plain,(
% 1.31/1.19 (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $true) | ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true) | ($true = ((sK1 @ sK5) & (~ (sK2 @ sK5)))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.31/1.19 thf(f117,plain,(
% 1.31/1.19 ($true = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((~ ((sK0 @ sK5) | (sK1 @ sK5))) = $true) | ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.31/1.19 thf(f76,plain,(
% 1.31/1.19 ($true = ((~ ((sK0 @ sK5) | (sK1 @ sK5))) & (sK2 @ sK5))) | ($true = (((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true)),
% 1.31/1.19 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.31/1.19 % SZS output end Proof for DTF2THF_32161
% 1.31/1.19 % (32259)------------------------------
% 1.31/1.19 % (32259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.19 % (32259)Termination reason: Refutation
% 1.31/1.19
% 1.31/1.19 % (32259)Memory used [KB]: 5628
% 1.31/1.19 % (32259)Time elapsed: 0.006 s
% 1.31/1.19 % (32259)Instructions burned: 10 (million)
% 1.31/1.19 % (32259)------------------------------
% 1.31/1.19 % (32259)------------------------------
% 1.31/1.19 % (32258)Success in time 0.015 s
%------------------------------------------------------------------------------