%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET623^5 : 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 : n027.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 09:31:57 AM UTC 2026
% Result : Theorem 1.55s 1.23s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 166 ( 10 unt; 0 typ; 6 def)
% Number of atoms : 2292 ( 541 equ; 0 cnn)
% Maximal formula atoms : 6 ( 13 avg)
% Number of connectives : 3087 ( 641 ~; 630 |; 527 &;1282 @)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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(f1907,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1633,f1658,f1749,f1843,f1867,f1870,f1881,f1886,f1894,f1900,f1906]) ).
thf(f1906,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f1905]) ).
thf(f1905,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f1901]) ).
thf(f1901,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f1607,f1615]) ).
thf(f1615,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f1613]) ).
thf(f1613,definition,
( spl3_3
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f1607,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f1605]) ).
thf(f1605,definition,
( spl3_1
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f1900,plain,
( ~ spl3_4
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f1899]) ).
thf(f1899,plain,
( $false
| ~ spl3_4
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1896]) ).
thf(f1896,plain,
( ( $true = $false )
| ~ spl3_4
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f1631,f1619]) ).
thf(f1619,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f1617]) ).
thf(f1617,definition,
( spl3_4
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f1631,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f1629]) ).
thf(f1629,definition,
( spl3_6
<=> ( ( sK0 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f1894,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f1893]) ).
thf(f1893,plain,
( $false
| ~ spl3_2
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f1889]) ).
thf(f1889,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f1624,f1611]) ).
thf(f1611,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f1609]) ).
thf(f1609,definition,
( spl3_2
<=> ( ( sK1 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f1624,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f1622]) ).
thf(f1622,definition,
( spl3_5
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f1886,plain,
( spl3_2
| spl3_4
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f45,f1613,f1617,f1609]) ).
thf(f45,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $false )
| ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) ) ) )
| ( $false
= ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) ) )
!= ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ( sK0 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ 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] :
( ( ~ ( X0 @ Y0 )
& ( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) )
| ( ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
& ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) )
| ( ~ ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
& ( X2 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ 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] :
( ( ~ ( X0 @ Y0 )
& ( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) )
| ( ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
& ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) )
| ( ~ ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ 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] :
( ( ~ ( X0 @ Y0 )
& ( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) )
| ( ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
& ( X0 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) )
| ( ~ ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ 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 ) )
| ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) ) )
| ( ~ ( X2 @ X3 )
& ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) ) ) ) ) )
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( ( ( X2 @ X4 )
& ~ ( X1 @ X4 ) )
| ( ~ ( X2 @ X4 )
& ( X1 @ X4 ) ) ) )
| ( ( ( ~ ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( X2 @ X4 ) ) )
& ~ ( X0 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( ( X0 @ X3 )
& ~ ( ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) ) ) )
| ( ~ ( X0 @ X3 )
& ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) ) ) ) )
= ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ~ ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) ) ) )
| ( ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
& ~ ( X2 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( ( X0 @ X3 )
& ~ ( ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) ) ) )
| ( ~ ( X0 @ X3 )
& ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) ) ) ) )
= ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ~ ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) ) ) )
| ( ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
& ~ ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5jXpNrjop5/DTF2THF_12233.p',cBOOL_PROP_99_pme) ).
thf(f1881,plain,
( spl3_1
| spl3_5
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f76,f1617,f1622,f1605]) ).
thf(f76,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
= ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $false
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $false
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $false
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f1870,plain,
( spl3_3
| spl3_5
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f135,f1629,f1622,f1613]) ).
thf(f135,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $false
= ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
( ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $false )
| ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) )
| ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f1867,plain,
( spl3_6
| spl3_2
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f157,f1605,f1609,f1629]) ).
thf(f157,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f152]) ).
thf(f152,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
( ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f149]) ).
thf(f149,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
( ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
( ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( $true
= ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
= $false )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $false
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f1843,plain,
( spl3_1
| spl3_6
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f268,f1622,f1629,f1605]) ).
thf(f268,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f267]) ).
thf(f267,plain,
( ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f266]) ).
thf(f266,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f249]) ).
thf(f249,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f248]) ).
thf(f248,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f247]) ).
thf(f247,plain,
( ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f246]) ).
thf(f246,plain,
( ( $false
= ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f245]) ).
thf(f245,plain,
( ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f220]) ).
thf(f220,plain,
( ( $false
= ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f219]) ).
thf(f219,plain,
( ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f216]) ).
thf(f216,plain,
( ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f215]) ).
thf(f215,plain,
( ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f213]) ).
thf(f213,plain,
( ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f211]) ).
thf(f211,plain,
( ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f210]) ).
thf(f210,plain,
( ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f208]) ).
thf(f208,plain,
( ( ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) )
= $true )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
( ( $true
= ( ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ~ ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f1749,plain,
( spl3_6
| spl3_3
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f928,f1609,f1613,f1629]) ).
thf(f928,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f927]) ).
thf(f927,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f925]) ).
thf(f925,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f924]) ).
thf(f924,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f923]) ).
thf(f923,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f917]) ).
thf(f917,plain,
( ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f916]) ).
thf(f916,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f915]) ).
thf(f915,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f914]) ).
thf(f914,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f913]) ).
thf(f913,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f912]) ).
thf(f912,plain,
( ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $true )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f910]) ).
thf(f910,plain,
( ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f909]) ).
thf(f909,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $false )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f907]) ).
thf(f907,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
( ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f211]) ).
thf(f1658,plain,
( spl3_3
| spl3_4
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f1472,f1622,f1617,f1613]) ).
thf(f1472,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f1471]) ).
thf(f1471,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1469]) ).
thf(f1469,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f1468]) ).
thf(f1468,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1466]) ).
thf(f1466,plain,
( ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f1465]) ).
thf(f1465,plain,
( ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1463]) ).
thf(f1463,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1461]) ).
thf(f1461,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1460]) ).
thf(f1460,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1233]) ).
thf(f1233,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $true )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1162]) ).
thf(f1162,plain,
( ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true )
| ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1161]) ).
thf(f1161,plain,
( ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) )
| ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f209]) ).
thf(f209,plain,
( ( ( ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f208]) ).
thf(f1633,plain,
( spl3_4
| spl3_2
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f1583,f1605,f1609,f1617]) ).
thf(f1583,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1582]) ).
thf(f1582,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1580]) ).
thf(f1580,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1579]) ).
thf(f1579,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f1578]) ).
thf(f1578,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1577]) ).
thf(f1577,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f1576]) ).
thf(f1576,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1568]) ).
thf(f1568,plain,
( ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1567]) ).
thf(f1567,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1566]) ).
thf(f1566,plain,
( ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1545]) ).
thf(f1545,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $false )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1533]) ).
thf(f1533,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1532]) ).
thf(f1532,plain,
( ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1531]) ).
thf(f1531,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1530]) ).
thf(f1530,plain,
( ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1160]) ).
thf(f1160,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET623^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:01:07 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SET623^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : TPS problem BOOL-PROP-99
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English : Trybulec's 99th Boolean property of sets
% 0.27/0.46
% 0.27/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.27/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Bro09]
% 0.27/0.46 % Names : tps_0485 [Bro09]
% 0.27/0.46 % : BOOL-PROP-99 [TPS]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 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
% 0.27/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.27/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.27/0.46 % Number of connectives : 50 ( 12 ~; 6 |; 12 &; 20 @)
% 0.27/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.27/0.46 % Number of types : 2 ( 1 usr)
% 0.27/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.27/0.46 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.46 % : Polymorphic definitions expanded.
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(a_type,type,
% 0.27/0.46 a: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(cBOOL_PROP_99_pme,conjecture,
% 0.27/0.46 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.27/0.46 ( ( ^ [Xz: a] :
% 0.27/0.46 ( ( ( X @ Xz )
% 0.27/0.46 & ~ ( ( ( Y @ Xz )
% 0.27/0.46 & ~ ( Z @ Xz ) )
% 0.27/0.46 | ( ( Z @ Xz )
% 0.27/0.46 & ~ ( Y @ Xz ) ) ) )
% 0.27/0.46 | ( ( ( ( Y @ Xz )
% 0.27/0.46 & ~ ( Z @ Xz ) )
% 0.27/0.46 | ( ( Z @ Xz )
% 0.27/0.46 & ~ ( Y @ Xz ) ) )
% 0.27/0.46 & ~ ( X @ Xz ) ) ) )
% 0.27/0.46 = ( ^ [Xz: a] :
% 0.27/0.46 ( ( ( ( ( X @ Xz )
% 0.27/0.46 & ~ ( Y @ Xz ) )
% 0.27/0.46 | ( ( Y @ Xz )
% 0.27/0.46 & ~ ( X @ Xz ) ) )
% 0.27/0.46 & ~ ( Z @ Xz ) )
% 0.27/0.46 | ( ( Z @ Xz )
% 0.27/0.46 & ~ ( ( ( X @ Xz )
% 0.27/0.46 & ~ ( Y @ Xz ) )
% 0.27/0.46 | ( ( Y @ Xz )
% 0.27/0.46 & ~ ( X @ Xz ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.46/1.18 ---- Embedded in THF ---
% 1.46/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.18 %%% Generated on Tue Feb 24 12:01:08 EST 2026
% 1.46/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.18 %%% Logic specification used:
% 1.46/1.18 %%% thf(spec, logic, $$dhol).
% 1.46/1.18
% 1.46/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5jXpNrjop5/DTF2DTF12233.p
% See solution above
% 1.46/1.18 ------------------------
% 1.46/1.19 ---- Cleaned THF ---
% 1.46/1.19 thf(a_type,type,
% 1.46/1.19 a: $tType ).
% 1.46/1.19
% 1.46/1.19 thf(cBOOL_PROP_99_pme,conjecture,
% 1.46/1.19 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.46/1.19 ( ( ^ [Xz: a] :
% 1.46/1.19 ( ( ( X @ Xz )
% 1.46/1.19 & ~ ( ( ( Y @ Xz )
% 1.46/1.19 & ~ ( Z @ Xz ) )
% 1.46/1.19 | ( ( Z @ Xz )
% 1.46/1.19 & ~ ( Y @ Xz ) ) ) )
% 1.46/1.19 | ( ( ( ( Y @ Xz )
% 1.46/1.19 & ~ ( Z @ Xz ) )
% 1.46/1.19 | ( ( Z @ Xz )
% 1.46/1.19 & ~ ( Y @ Xz ) ) )
% 1.46/1.19 & ~ ( X @ Xz ) ) ) )
% 1.46/1.19 = ( ^ [Xz: a] :
% 1.46/1.19 ( ( ( ( ( X @ Xz )
% 1.46/1.19 & ~ ( Y @ Xz ) )
% 1.46/1.19 | ( ( Y @ Xz )
% 1.46/1.19 & ~ ( X @ Xz ) ) )
% 1.46/1.19 & ~ ( Z @ Xz ) )
% 1.46/1.19 | ( ( Z @ Xz )
% 1.46/1.19 & ~ ( ( ( X @ Xz )
% 1.46/1.19 & ~ ( Y @ Xz ) )
% 1.46/1.19 | ( ( Y @ Xz )
% 1.46/1.19 & ~ ( X @ Xz ) ) ) ) ) ) ) ).
% 1.46/1.19 ------------------------
% 1.55/1.20 % (12341)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12233 for (2999ds/183Mi)
% 1.55/1.20 % (12346)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_12233 for (2999ds/275Mi)
% 1.55/1.20 % (12343)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_12233 for (2999ds/27Mi)
% 1.55/1.21 % (12342)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_12233 for (2999ds/4Mi)
% 1.55/1.21 % (12344)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12233 for (2999ds/2Mi)
% 1.55/1.21 % (12345)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_12233 for (2999ds/2Mi)
% 1.55/1.21 % (12347)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12233 for (2999ds/18Mi)
% 1.55/1.21 % (12344)Instruction limit reached!
% 1.55/1.21 % (12344)------------------------------
% 1.55/1.21 % (12344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.21 % (12344)Termination reason: Unknown
% 1.55/1.21 % (12345)Instruction limit reached!
% 1.55/1.21 % (12345)------------------------------
% 1.55/1.21 % (12345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.21 % (12344)Termination phase: Preprocessing 3
% 1.55/1.21
% 1.55/1.21 % (12344)Memory used [KB]: 895
% 1.55/1.21 % (12344)Time elapsed: 0.003 s
% 1.55/1.21 % (12344)Instructions burned: 2 (million)
% 1.55/1.21 % (12344)------------------------------
% 1.55/1.21 % (12344)------------------------------
% 1.55/1.21 % (12345)Termination reason: Unknown
% 1.55/1.21 % (12345)Termination phase: Property scanning
% 1.55/1.21
% 1.55/1.21 % (12345)Memory used [KB]: 895
% 1.55/1.21 % (12345)Time elapsed: 0.003 s
% 1.55/1.21 % (12345)Instructions burned: 2 (million)
% 1.55/1.21 % (12345)------------------------------
% 1.55/1.21 % (12345)------------------------------
% 1.55/1.21 % (12343)Instruction limit reached!
% 1.55/1.21 % (12343)------------------------------
% 1.55/1.21 % (12343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.21 % (12343)Termination reason: Unknown
% 1.55/1.21 % (12343)Termination phase: Saturation
% 1.55/1.21
% 1.55/1.21 % (12343)Memory used [KB]: 5628
% 1.55/1.21 % (12343)Time elapsed: 0.010 s
% 1.55/1.21 % (12343)Instructions burned: 30 (million)
% 1.55/1.21 % (12343)------------------------------
% 1.55/1.21 % (12343)------------------------------
% 1.55/1.21 % (12342)Instruction limit reached!
% 1.55/1.21 % (12342)------------------------------
% 1.55/1.21 % (12342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.21 % (12342)Termination reason: Unknown
% 1.55/1.21 % (12342)Termination phase: Saturation
% 1.55/1.21
% 1.55/1.21 % (12342)Memory used [KB]: 5500
% 1.55/1.21 % (12342)Time elapsed: 0.005 s
% 1.55/1.21 % (12342)Instructions burned: 5 (million)
% 1.55/1.21 % (12342)------------------------------
% 1.55/1.21 % (12342)------------------------------
% 1.55/1.22 % (12347)Instruction limit reached!
% 1.55/1.22 % (12347)------------------------------
% 1.55/1.22 % (12347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.22 % (12347)Termination reason: Unknown
% 1.55/1.22 % (12347)Termination phase: Saturation
% 1.55/1.22
% 1.55/1.22 % (12347)Memory used [KB]: 5500
% 1.55/1.22 % (12347)Time elapsed: 0.012 s
% 1.55/1.22 % (12347)Instructions burned: 19 (million)
% 1.55/1.22 % (12347)------------------------------
% 1.55/1.22 % (12347)------------------------------
% 1.55/1.22 % (12341)First to succeed.
% 1.55/1.22 % (12350)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_12233 for (2999ds/15Mi)
% 1.55/1.23 % (12346)Also succeeded, but the first one will report.
% 1.55/1.23 % (12341)Refutation found. Thanks to Tanya!
% 1.55/1.23 % SZS status Theorem for DTF2THF_12233
% 1.55/1.23 % SZS output start Proof for DTF2THF_12233
% 1.55/1.23 thf(type_def_5, type, a: $tType).
% 1.55/1.23 thf(func_def_0, type, a: $tType).
% 1.55/1.23 thf(func_def_9, type, sK0: a > $o).
% 1.55/1.23 thf(func_def_10, type, sK1: a > $o).
% 1.55/1.23 thf(func_def_11, type, sK2: a > $o).
% 1.55/1.23 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.55/1.23 thf(func_def_14, type, sK5: a).
% 1.55/1.23 thf(f1907,plain,(
% 1.55/1.23 $false),
% 1.55/1.23 inference(avatar_sat_refutation,[status(thm)],[f1633,f1658,f1749,f1843,f1867,f1870,f1881,f1886,f1894,f1900,f1906])).
% 1.55/1.23 thf(f1906,plain,(
% 1.55/1.23 ~spl3_1 | ~spl3_3),
% 1.55/1.23 inference(avatar_contradiction_clause,[status(thm)],[f1905])).
% 1.55/1.23 thf(f1905,plain,(
% 1.55/1.23 $false | (~spl3_1 | ~spl3_3)),
% 1.55/1.23 inference(trivial_inequality_removal,[status(thm)],[f1901])).
% 1.55/1.23 thf(f1901,plain,(
% 1.55/1.23 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 1.55/1.23 inference(superposition,[status(thm)],[f1607,f1615])).
% 1.55/1.23 thf(f1615,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ~spl3_3),
% 1.55/1.23 inference(avatar_component_clause,[status(thm)],[f1613])).
% 1.55/1.23 thf(f1613,definition,(
% 1.55/1.23 spl3_3 <=> ($true = (sK2 @ sK5))),
% 1.55/1.23 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.55/1.23 thf(f1607,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ~spl3_1),
% 1.55/1.23 inference(avatar_component_clause,[status(thm)],[f1605])).
% 1.55/1.23 thf(f1605,definition,(
% 1.55/1.23 spl3_1 <=> ($false = (sK2 @ sK5))),
% 1.55/1.23 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.55/1.23 thf(f1900,plain,(
% 1.55/1.23 ~spl3_4 | ~spl3_6),
% 1.55/1.23 inference(avatar_contradiction_clause,[status(thm)],[f1899])).
% 1.55/1.23 thf(f1899,plain,(
% 1.55/1.23 $false | (~spl3_4 | ~spl3_6)),
% 1.55/1.23 inference(trivial_inequality_removal,[status(thm)],[f1896])).
% 1.55/1.23 thf(f1896,plain,(
% 1.55/1.23 ($true = $false) | (~spl3_4 | ~spl3_6)),
% 1.55/1.23 inference(superposition,[status(thm)],[f1631,f1619])).
% 1.55/1.23 thf(f1619,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $true) | ~spl3_4),
% 1.55/1.23 inference(avatar_component_clause,[status(thm)],[f1617])).
% 1.55/1.23 thf(f1617,definition,(
% 1.55/1.23 spl3_4 <=> ((sK0 @ sK5) = $true)),
% 1.55/1.23 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.55/1.23 thf(f1631,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ~spl3_6),
% 1.55/1.23 inference(avatar_component_clause,[status(thm)],[f1629])).
% 1.55/1.23 thf(f1629,definition,(
% 1.55/1.23 spl3_6 <=> ((sK0 @ sK5) = $false)),
% 1.55/1.23 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.55/1.23 thf(f1894,plain,(
% 1.55/1.23 ~spl3_2 | ~spl3_5),
% 1.55/1.23 inference(avatar_contradiction_clause,[status(thm)],[f1893])).
% 1.55/1.23 thf(f1893,plain,(
% 1.55/1.23 $false | (~spl3_2 | ~spl3_5)),
% 1.55/1.23 inference(trivial_inequality_removal,[status(thm)],[f1889])).
% 1.55/1.23 thf(f1889,plain,(
% 1.55/1.23 ($true = $false) | (~spl3_2 | ~spl3_5)),
% 1.55/1.23 inference(superposition,[status(thm)],[f1624,f1611])).
% 1.55/1.23 thf(f1611,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ~spl3_2),
% 1.55/1.23 inference(avatar_component_clause,[status(thm)],[f1609])).
% 1.55/1.23 thf(f1609,definition,(
% 1.55/1.23 spl3_2 <=> ((sK1 @ sK5) = $false)),
% 1.55/1.23 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.55/1.23 thf(f1624,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $true) | ~spl3_5),
% 1.55/1.23 inference(avatar_component_clause,[status(thm)],[f1622])).
% 1.55/1.23 thf(f1622,definition,(
% 1.55/1.23 spl3_5 <=> ((sK1 @ sK5) = $true)),
% 1.55/1.23 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.55/1.23 thf(f1886,plain,(
% 1.55/1.23 spl3_2 | spl3_4 | spl3_3),
% 1.55/1.23 inference(avatar_split_clause,[status(thm)],[f45,f1613,f1617,f1609])).
% 1.55/1.23 thf(f45,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f44])).
% 1.55/1.23 thf(f44,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f43])).
% 1.55/1.23 thf(f43,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ($false = (~ (sK0 @ sK5))) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f42])).
% 1.55/1.23 thf(f42,plain,(
% 1.55/1.23 ($false = (~ (sK0 @ sK5))) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $false) | ($true = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.55/1.23 thf(f41,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ($false = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f40])).
% 1.55/1.23 thf(f40,plain,(
% 1.55/1.23 ($false = (~ (sK0 @ sK5))) | ($false = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | ((sK1 @ sK5) = $false) | ($true = (sK2 @ sK5))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f39])).
% 1.55/1.23 thf(f39,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ($false = (~ (sK0 @ sK5))) | ($true = (sK2 @ sK5)) | ($false = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f38])).
% 1.55/1.23 thf(f38,plain,(
% 1.55/1.23 ($false = (~ (sK2 @ sK5))) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ($false = (~ (sK0 @ sK5))) | ($false = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.55/1.23 thf(f37,plain,(
% 1.55/1.23 (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $false) | ($false = (~ (sK0 @ sK5))) | ($true = (sK2 @ sK5)) | ($false = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.55/1.23 thf(f35,plain,(
% 1.55/1.23 ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $false) | ($true = (sK2 @ sK5)) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $false) | ($false = (~ (sK0 @ sK5)))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f34])).
% 1.55/1.23 thf(f34,plain,(
% 1.55/1.23 ($false = (~ (sK2 @ sK5))) | ($false = (~ (sK0 @ sK5))) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $false) | ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.55/1.23 thf(f19,plain,(
% 1.55/1.23 (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $false) | ($false = (~ (sK0 @ sK5))) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.55/1.23 thf(f18,plain,(
% 1.55/1.23 ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $false) | ($false = (~ (sK0 @ sK5))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.55/1.23 thf(f17,plain,(
% 1.55/1.23 ($false = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.55/1.23 thf(f15,plain,(
% 1.55/1.23 ($false = (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) | ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5)))) | ($false = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.55/1.23 thf(f13,plain,(
% 1.55/1.23 ($false = (((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5)))) | ($false = (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) | ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.55/1.23 thf(f11,plain,(
% 1.55/1.23 ((((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5))) != (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) | ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5))))),
% 1.55/1.23 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.55/1.23 thf(f10,plain,(
% 1.55/1.23 (((^[Y0 : a]: (((~ (sK0 @ Y0)) & (((sK2 @ Y0) & (~ (sK1 @ Y0))) | ((sK1 @ Y0) & (~ (sK2 @ Y0))))) | ((~ (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) & (sK0 @ Y0)))) @ sK5) != ((^[Y0 : a]: (((((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))) & (~ (sK2 @ Y0))) | ((~ (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) & (sK2 @ Y0)))) @ sK5))),
% 1.55/1.23 inference(negative_extensionality,[status(thm)],[f9])).
% 1.55/1.23 thf(f9,plain,(
% 1.55/1.23 ((^[Y0 : a]: (((~ (sK0 @ Y0)) & (((sK2 @ Y0) & (~ (sK1 @ Y0))) | ((sK1 @ Y0) & (~ (sK2 @ Y0))))) | ((~ (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) & (sK0 @ Y0)))) != (^[Y0 : a]: (((((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))) & (~ (sK2 @ Y0))) | ((~ (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) & (sK2 @ Y0)))))),
% 1.55/1.23 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.23 thf(f8,plain,(
% 1.55/1.23 ((^[Y0 : a]: (((~ (sK0 @ Y0)) & (((sK2 @ Y0) & (~ (sK1 @ Y0))) | ((sK1 @ Y0) & (~ (sK2 @ Y0))))) | ((~ (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) & (sK0 @ Y0)))) != (^[Y0 : a]: (((((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))) & (~ (sK2 @ Y0))) | ((~ (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) & (sK2 @ Y0)))))),
% 1.55/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.55/1.23 thf(f7,plain,(
% 1.55/1.23 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ (X0 @ Y0)) & (((X2 @ Y0) & (~ (X1 @ Y0))) | ((X1 @ Y0) & (~ (X2 @ Y0))))) | ((~ (((X1 @ Y0) & (~ (X2 @ Y0))) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) & (X0 @ Y0)))) != (^[Y0 : a]: (((((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0)))) & (~ (X2 @ Y0))) | ((~ (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) & (X2 @ Y0))))) => ((^[Y0 : a]: (((~ (sK0 @ Y0)) & (((sK2 @ Y0) & (~ (sK1 @ Y0))) | ((sK1 @ Y0) & (~ (sK2 @ Y0))))) | ((~ (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) & (sK0 @ Y0)))) != (^[Y0 : a]: (((((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))) & (~ (sK2 @ Y0))) | ((~ (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) & (sK2 @ Y0)))))),
% 1.55/1.23 introduced(definition,[],[choice_axiom])).
% 1.55/1.23 thf(f6,plain,(
% 1.55/1.23 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ (X0 @ Y0)) & (((X2 @ Y0) & (~ (X1 @ Y0))) | ((X1 @ Y0) & (~ (X2 @ Y0))))) | ((~ (((X1 @ Y0) & (~ (X2 @ Y0))) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) & (X0 @ Y0)))) != (^[Y0 : a]: (((((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0)))) & (~ (X2 @ Y0))) | ((~ (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) & (X2 @ Y0)))))),
% 1.55/1.23 inference(ennf_transformation,[status(thm)],[f5])).
% 1.55/1.23 thf(f5,plain,(
% 1.55/1.23 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ (X0 @ Y0)) & (((X2 @ Y0) & (~ (X1 @ Y0))) | ((X1 @ Y0) & (~ (X2 @ Y0))))) | ((~ (((X1 @ Y0) & (~ (X2 @ Y0))) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) & (X0 @ Y0)))) = (^[Y0 : a]: (((((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0)))) & (~ (X2 @ Y0))) | ((~ (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) & (X2 @ Y0)))))),
% 1.55/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.23 thf(f4,plain,(
% 1.55/1.23 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((X2 @ X3) & ~(((X1 @ X3) & ~(X0 @ X3)) | ((X0 @ X3) & ~(X1 @ X3)))) | (~(X2 @ X3) & ((~(X1 @ X3) & (X0 @ X3)) | (~(X0 @ X3) & (X1 @ X3)))))) = (^[X4 : a] : (((X0 @ X4) & ~(((X2 @ X4) & ~(X1 @ X4)) | (~(X2 @ X4) & (X1 @ X4)))) | (((~(X2 @ X4) & (X1 @ X4)) | (~(X1 @ X4) & (X2 @ X4))) & ~(X0 @ X4)))))),
% 1.55/1.23 inference(rectify,[status(thm)],[f2])).
% 1.55/1.23 thf(f2,negated_conjecture,(
% 1.55/1.23 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((^[X3 : a] : (((X0 @ X3) & ~(((X1 @ X3) & ~(X2 @ X3)) | ((X2 @ X3) & ~(X1 @ X3)))) | (~(X0 @ X3) & ((~(X1 @ X3) & (X2 @ X3)) | (~(X2 @ X3) & (X1 @ X3)))))) = (^[X3 : a] : (((X2 @ X3) & ~(((X0 @ X3) & ~(X1 @ X3)) | (~(X0 @ X3) & (X1 @ X3)))) | (((~(X0 @ X3) & (X1 @ X3)) | (~(X1 @ X3) & (X0 @ X3))) & ~(X2 @ X3)))))),
% 1.55/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.23 thf(f1,conjecture,(
% 1.55/1.23 ! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((^[X3 : a] : (((X0 @ X3) & ~(((X1 @ X3) & ~(X2 @ X3)) | ((X2 @ X3) & ~(X1 @ X3)))) | (~(X0 @ X3) & ((~(X1 @ X3) & (X2 @ X3)) | (~(X2 @ X3) & (X1 @ X3)))))) = (^[X3 : a] : (((X2 @ X3) & ~(((X0 @ X3) & ~(X1 @ X3)) | (~(X0 @ X3) & (X1 @ X3)))) | (((~(X0 @ X3) & (X1 @ X3)) | (~(X1 @ X3) & (X0 @ X3))) & ~(X2 @ X3)))))),
% 1.55/1.23 file('/export/starexec/sandbox/tmp/tmp.5jXpNrjop5/DTF2THF_12233.p',cBOOL_PROP_99_pme)).
% 1.55/1.23 thf(f1881,plain,(
% 1.55/1.23 spl3_1 | spl3_5 | spl3_4),
% 1.55/1.23 inference(avatar_split_clause,[status(thm)],[f76,f1617,f1622,f1605])).
% 1.55/1.23 thf(f76,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f73])).
% 1.55/1.23 thf(f73,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.55/1.23 thf(f72,plain,(
% 1.55/1.23 (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true) | ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f71])).
% 1.55/1.23 thf(f71,plain,(
% 1.55/1.23 ($false = (~ (sK1 @ sK5))) | (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f61])).
% 1.55/1.23 thf(f61,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5)) | ($false = (~ (sK1 @ sK5))) | (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.55/1.23 thf(f60,plain,(
% 1.55/1.23 ($true = ((~ (sK1 @ sK5)) & (sK0 @ sK5))) | ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $true) | (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.55/1.23 thf(f59,plain,(
% 1.55/1.23 ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($false = (~ (sK1 @ sK5)))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f58])).
% 1.55/1.23 thf(f58,plain,(
% 1.55/1.23 ($false = (~ (sK0 @ sK5))) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) | ($false = (sK2 @ sK5)) | ($false = (~ (sK1 @ sK5)))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f57])).
% 1.55/1.23 thf(f57,plain,(
% 1.55/1.23 ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) | ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (~ (sK0 @ sK5))) | ($false = (~ (sK1 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.55/1.23 thf(f56,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | (((sK2 @ sK5) & (~ (sK1 @ sK5))) = $false) | ($false = (~ (sK0 @ sK5))) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.55/1.23 thf(f54,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $false) | ($false = (~ (sK0 @ sK5))) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f53])).
% 1.55/1.23 thf(f53,plain,(
% 1.55/1.23 ($false = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))) | ($false = (~ (sK0 @ sK5))) | ($false = (sK2 @ sK5)) | ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.55/1.23 thf(f52,plain,(
% 1.55/1.23 ($false = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | ($false = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.55/1.23 thf(f16,plain,(
% 1.55/1.23 ($false = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5))) | ($false = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.55/1.23 thf(f1870,plain,(
% 1.55/1.23 spl3_3 | spl3_5 | spl3_6),
% 1.55/1.23 inference(avatar_split_clause,[status(thm)],[f135,f1629,f1622,f1613])).
% 1.55/1.23 thf(f135,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f134])).
% 1.55/1.23 thf(f134,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.55/1.23 thf(f132,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true) | ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f125])).
% 1.55/1.23 thf(f125,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.55/1.23 thf(f124,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ($true = ((~ (sK1 @ sK5)) & (sK2 @ sK5))) | ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5)) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.55/1.23 thf(f123,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f122])).
% 1.55/1.23 thf(f122,plain,(
% 1.55/1.23 ($false = (~ (sK1 @ sK5))) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f121])).
% 1.55/1.23 thf(f121,plain,(
% 1.55/1.23 ($false = (~ (sK2 @ sK5))) | ((sK0 @ sK5) = $false) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ($false = (~ (sK1 @ sK5)))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f120])).
% 1.55/1.23 thf(f120,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ((sK0 @ sK5) = $false) | ($false = (~ (sK2 @ sK5))) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ($false = (~ (sK1 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.55/1.23 thf(f119,plain,(
% 1.55/1.23 ($false = ((sK0 @ sK5) & (~ (sK1 @ sK5)))) | ($false = (~ (sK2 @ sK5))) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f118])).
% 1.55/1.23 thf(f118,plain,(
% 1.55/1.23 ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) = $false) | ($false = ((sK0 @ sK5) & (~ (sK1 @ sK5)))) | ((sK0 @ sK5) = $false) | ($false = (~ (sK2 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.55/1.23 thf(f97,plain,(
% 1.55/1.23 (((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5)) = $false) | ($false = (~ (sK2 @ sK5))) | ($false = ((sK0 @ sK5) & (~ (sK1 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.55/1.23 thf(f96,plain,(
% 1.55/1.23 ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $false) | ($false = (~ (sK2 @ sK5))) | (((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5)) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.55/1.23 thf(f95,plain,(
% 1.55/1.23 (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $false) | (((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5)) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.55/1.23 thf(f14,plain,(
% 1.55/1.23 ($false = (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) | ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5)))) | (((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5)) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.55/1.23 thf(f1867,plain,(
% 1.55/1.23 spl3_6 | spl3_2 | spl3_1),
% 1.55/1.23 inference(avatar_split_clause,[status(thm)],[f157,f1605,f1609,f1629])).
% 1.55/1.23 thf(f157,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f156])).
% 1.55/1.23 thf(f156,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f154])).
% 1.55/1.23 thf(f154,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($true = (~ (sK2 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.55/1.23 thf(f153,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $false) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f152])).
% 1.55/1.23 thf(f152,plain,(
% 1.55/1.23 (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f151])).
% 1.55/1.23 thf(f151,plain,(
% 1.55/1.23 ($true = (~ (sK1 @ sK5))) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true) | ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f149])).
% 1.55/1.23 thf(f149,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ($true = ((~ (sK1 @ sK5)) & (sK2 @ sK5))) | ((sK0 @ sK5) = $false) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f148])).
% 1.55/1.23 thf(f148,plain,(
% 1.55/1.23 ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f147])).
% 1.55/1.23 thf(f147,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($true = (~ (sK1 @ sK5))) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5))))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f146])).
% 1.55/1.23 thf(f146,plain,(
% 1.55/1.23 ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ((sK0 @ sK5) = $false) | ($true = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f145])).
% 1.55/1.23 thf(f145,plain,(
% 1.55/1.23 ($true = (~ (sK0 @ sK5))) | ($false = (sK2 @ sK5)) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ($true = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.55/1.23 thf(f143,plain,(
% 1.55/1.23 (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true) | ((sK0 @ sK5) = $false) | ($true = (~ (sK1 @ sK5))) | ($false = (sK2 @ sK5)) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f141])).
% 1.55/1.23 thf(f141,plain,(
% 1.55/1.23 ($true = ((~ (sK1 @ sK5)) & (sK0 @ sK5))) | ((sK0 @ sK5) = $false) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.55/1.23 thf(f140,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) | ($false = (sK2 @ sK5)) | ($true = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f139])).
% 1.55/1.23 thf(f139,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) = $false) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f138])).
% 1.55/1.23 thf(f138,plain,(
% 1.55/1.23 ($false = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))) | ((sK0 @ sK5) = $false) | ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) = $false) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f137])).
% 1.55/1.23 thf(f137,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ($false = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5))) | ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.55/1.23 thf(f94,plain,(
% 1.55/1.23 (((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5)) = $false) | ($false = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.55/1.23 thf(f1843,plain,(
% 1.55/1.23 spl3_1 | spl3_6 | spl3_5),
% 1.55/1.23 inference(avatar_split_clause,[status(thm)],[f268,f1622,f1629,f1605])).
% 1.55/1.23 thf(f268,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f267])).
% 1.55/1.23 thf(f267,plain,(
% 1.55/1.23 ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f266])).
% 1.55/1.23 thf(f266,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($false = (~ (sK1 @ sK5))) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f249])).
% 1.55/1.23 thf(f249,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ($true = (~ (sK2 @ sK5))) | ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f248])).
% 1.55/1.23 thf(f248,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($false = (~ (sK1 @ sK5)))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f247])).
% 1.55/1.23 thf(f247,plain,(
% 1.55/1.23 (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ((sK0 @ sK5) = $false) | ($false = (~ (sK1 @ sK5))) | ($false = (~ (sK1 @ sK5))) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f246])).
% 1.55/1.23 thf(f246,plain,(
% 1.55/1.23 ($false = ((~ (sK1 @ sK5)) & (sK2 @ sK5))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f245])).
% 1.55/1.23 thf(f245,plain,(
% 1.55/1.23 (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ((sK0 @ sK5) = $false) | ((sK0 @ sK5) = $false) | ($false = ((~ (sK1 @ sK5)) & (sK2 @ sK5))) | ($false = (~ (sK1 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f220])).
% 1.55/1.23 thf(f220,plain,(
% 1.55/1.23 ($false = ((~ (sK1 @ sK5)) & (sK0 @ sK5))) | ($false = ((~ (sK1 @ sK5)) & (sK2 @ sK5))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f219])).
% 1.55/1.23 thf(f219,plain,(
% 1.55/1.23 ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($false = ((~ (sK1 @ sK5)) & (sK0 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f217])).
% 1.55/1.23 thf(f217,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f216])).
% 1.55/1.23 thf(f216,plain,(
% 1.55/1.23 ($true = (~ (sK0 @ sK5))) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f215])).
% 1.55/1.23 thf(f215,plain,(
% 1.55/1.23 ($true = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ($true = (~ (sK0 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f213])).
% 1.55/1.23 thf(f213,plain,(
% 1.55/1.23 ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($true = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f211])).
% 1.55/1.23 thf(f211,plain,(
% 1.55/1.23 ($true = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5))) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f210])).
% 1.55/1.23 thf(f210,plain,(
% 1.55/1.23 ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) = $true) | ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($true = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f208])).
% 1.55/1.23 thf(f208,plain,(
% 1.55/1.23 (((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5)) = $true) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | ($true = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f207])).
% 1.55/1.23 thf(f207,plain,(
% 1.55/1.23 ($true = (((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5)))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($true = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.55/1.23 thf(f12,plain,(
% 1.55/1.23 ($true = (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) | ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5)))) | ($true = (((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))) | ((~ (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) & (sK0 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.55/1.23 thf(f1749,plain,(
% 1.55/1.23 spl3_6 | spl3_3 | spl3_2),
% 1.55/1.23 inference(avatar_split_clause,[status(thm)],[f928,f1609,f1613,f1629])).
% 1.55/1.23 thf(f928,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f927])).
% 1.55/1.23 thf(f927,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f925])).
% 1.55/1.23 thf(f925,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $false) | ($true = (~ (sK0 @ sK5))) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f924])).
% 1.55/1.23 thf(f924,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f923])).
% 1.55/1.23 thf(f923,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f917])).
% 1.55/1.23 thf(f917,plain,(
% 1.55/1.23 ($true = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f916])).
% 1.55/1.23 thf(f916,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ($true = ((sK0 @ sK5) & (~ (sK1 @ sK5)))) | ($true = (sK2 @ sK5)) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | ((sK0 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f915])).
% 1.55/1.23 thf(f915,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $true) | ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f914])).
% 1.55/1.23 thf(f914,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $true)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f913])).
% 1.55/1.23 thf(f913,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ($false = (~ (sK2 @ sK5))) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $false) | ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $true)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f912])).
% 1.55/1.23 thf(f912,plain,(
% 1.55/1.23 ($true = (~ (sK0 @ sK5))) | ((sK1 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $true) | ($false = (~ (sK2 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f910])).
% 1.55/1.23 thf(f910,plain,(
% 1.55/1.23 (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($true = (sK2 @ sK5)) | ($false = (~ (sK2 @ sK5))) | ($true = (~ (sK0 @ sK5))) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f909])).
% 1.55/1.23 thf(f909,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $false) | ($true = (~ (sK0 @ sK5))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f907])).
% 1.55/1.23 thf(f907,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ($true = (~ (sK0 @ sK5))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f212])).
% 1.55/1.23 thf(f212,plain,(
% 1.55/1.23 ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK1 @ sK5)) & (sK2 @ sK5)))) | ($true = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f211])).
% 1.55/1.23 thf(f1658,plain,(
% 1.55/1.23 spl3_3 | spl3_4 | spl3_5),
% 1.55/1.23 inference(avatar_split_clause,[status(thm)],[f1472,f1622,f1617,f1613])).
% 1.55/1.23 thf(f1472,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f1471])).
% 1.55/1.23 thf(f1471,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1469])).
% 1.55/1.23 thf(f1469,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $true) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f1468])).
% 1.55/1.23 thf(f1468,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ($true = (sK2 @ sK5)) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1466])).
% 1.55/1.23 thf(f1466,plain,(
% 1.55/1.23 ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f1465])).
% 1.55/1.23 thf(f1465,plain,(
% 1.55/1.23 ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ((sK1 @ sK5) = $true) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1463])).
% 1.55/1.23 thf(f1463,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($true = ((sK0 @ sK5) & (~ (sK1 @ sK5)))) | ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1461])).
% 1.55/1.23 thf(f1461,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $true) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true) | ($true = (sK2 @ sK5)) | ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ($true = ((sK0 @ sK5) & (~ (sK1 @ sK5)))) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1460])).
% 1.55/1.23 thf(f1460,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $true) | ((sK0 @ sK5) = $true) | ($true = ((sK0 @ sK5) & (~ (sK1 @ sK5)))) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1233])).
% 1.55/1.23 thf(f1233,plain,(
% 1.55/1.23 ($true = (sK2 @ sK5)) | ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $true) | ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $true) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1162])).
% 1.55/1.23 thf(f1162,plain,(
% 1.55/1.23 ($true = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5))) | ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $true) | ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $true) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1161])).
% 1.55/1.23 thf(f1161,plain,(
% 1.55/1.23 ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | ((sK0 @ sK5) = $true) | ($true = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5))) | ((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f209])).
% 1.55/1.23 thf(f209,plain,(
% 1.55/1.23 (((((sK1 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) & (~ (sK2 @ sK5))) = $true) | ((sK0 @ sK5) = $true) | ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | ($true = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5)))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f208])).
% 1.55/1.23 thf(f1633,plain,(
% 1.55/1.23 spl3_4 | spl3_2 | spl3_1),
% 1.55/1.23 inference(avatar_split_clause,[status(thm)],[f1583,f1605,f1609,f1617])).
% 1.55/1.23 thf(f1583,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f1582])).
% 1.55/1.23 thf(f1582,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f1580])).
% 1.55/1.23 thf(f1580,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5)) | ($true = (~ (sK1 @ sK5))) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1579])).
% 1.55/1.23 thf(f1579,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f1578])).
% 1.55/1.23 thf(f1578,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5)) | ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $false)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f1577])).
% 1.55/1.23 thf(f1577,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ($true = (~ (sK2 @ sK5))) | ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(duplicate_literal_removal,[status(thm)],[f1576])).
% 1.55/1.23 thf(f1576,plain,(
% 1.55/1.23 ((sK1 @ sK5) = $false) | ($true = (~ (sK2 @ sK5))) | ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f1568])).
% 1.55/1.23 thf(f1568,plain,(
% 1.55/1.23 ($false = (~ (sK0 @ sK5))) | ((sK0 @ sK5) = $true) | ($true = (~ (sK2 @ sK5))) | ((sK1 @ sK5) = $false) | ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1567])).
% 1.55/1.23 thf(f1567,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true) | ($false = (~ (sK0 @ sK5))) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1566])).
% 1.55/1.23 thf(f1566,plain,(
% 1.55/1.23 ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $true) | ($false = (~ (sK0 @ sK5))) | ((sK1 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1545])).
% 1.55/1.23 thf(f1545,plain,(
% 1.55/1.23 (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $false) | ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $true) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1533])).
% 1.55/1.23 thf(f1533,plain,(
% 1.55/1.23 ($false = (sK2 @ sK5)) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) | ((sK0 @ sK5) = $true) | ((((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))) = $true)),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1532])).
% 1.55/1.23 thf(f1532,plain,(
% 1.55/1.23 ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f1531])).
% 1.55/1.23 thf(f1531,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $true) | ($true = (~ (sK2 @ sK5))) | ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5)))))) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))),
% 1.55/1.23 inference(not_proxy_clausification,[status(thm)],[f1530])).
% 1.55/1.23 thf(f1530,plain,(
% 1.55/1.23 ($true = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))) | ($true = (~ (sK2 @ sK5))) | ((sK0 @ sK5) = $true) | ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f1160])).
% 1.55/1.23 thf(f1160,plain,(
% 1.55/1.23 ((sK0 @ sK5) = $true) | ($true = ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) & (sK2 @ sK5))) | ($true = (~ (sK2 @ sK5))) | ($true = ((~ (sK0 @ sK5)) & (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((sK1 @ sK5) & (~ (sK2 @ sK5))))))),
% 1.55/1.23 inference(binary_proxy_clausification,[status(thm)],[f209])).
% 1.55/1.23 % SZS output end Proof for DTF2THF_12233
% 1.55/1.23 % (12341)------------------------------
% 1.55/1.23 % (12341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.23 % (12341)Termination reason: Refutation
% 1.55/1.23
% 1.55/1.23 % (12341)Memory used [KB]: 6140
% 1.55/1.23 % (12341)Time elapsed: 0.024 s
% 1.55/1.23 % (12341)Instructions burned: 65 (million)
% 1.55/1.23 % (12341)------------------------------
% 1.55/1.23 % (12341)------------------------------
% 1.55/1.23 % (12340)Success in time 0.021 s
%------------------------------------------------------------------------------