%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU857^5 : 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 : n028.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 09:37:36 AM UTC 2026
% Result : Theorem 1.34s 1.16s
% Output : Refutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 165 ( 10 unt; 0 typ; 6 def)
% Number of atoms : 2301 ( 537 equ; 0 cnn)
% Maximal formula atoms : 5 ( 13 avg)
% Number of connectives : 3128 ( 647 ~; 644 |; 531 &;1299 @)
% ( 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(f1913,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1632,f1661,f1708,f1857,f1861,f1865,f1874,f1882,f1899,f1906,f1912]) ).
thf(f1912,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f1911]) ).
thf(f1911,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f1907]) ).
thf(f1907,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f1620,f1612]) ).
thf(f1612,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f1610]) ).
thf(f1610,definition,
( spl3_1
<=> ( ( sK0 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f1620,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f1618]) ).
thf(f1618,definition,
( spl3_3
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f1906,plain,
( ~ spl3_5
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f1905]) ).
thf(f1905,plain,
( $false
| ~ spl3_5
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1902]) ).
thf(f1902,plain,
( ( $true = $false )
| ~ spl3_5
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f1636,f1628]) ).
thf(f1628,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f1626]) ).
thf(f1626,definition,
( spl3_5
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f1636,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f1634]) ).
thf(f1634,definition,
( spl3_6
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f1899,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f1898]) ).
thf(f1898,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1895]) ).
thf(f1895,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f1616,f1624]) ).
thf(f1624,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f1622]) ).
thf(f1622,definition,
( spl3_4
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f1616,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f1614]) ).
thf(f1614,definition,
( spl3_2
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f1882,plain,
( spl3_4
| spl3_6
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f81,f1610,f1634,f1622]) ).
thf(f81,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) ) ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
= $false )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
= $false )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) )
= $false )
| ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) )
!= ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( ~ ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK2 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( ~ ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK2 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ~ ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK2 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) )
| ( ( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
& ~ ( X1 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ( ~ ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ( sK2 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) )
| ( ( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
& ~ ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) ) ) )
| ( ( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
& ~ ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) )
| ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) )
& ~ ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ~ ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( X1 @ X4 )
& ( ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) )
| ( ( X0 @ X4 )
& ~ ( X2 @ X4 ) ) ) )
| ( ~ ( ( ~ ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( X0 @ X4 )
& ( X2 @ X4 ) ) )
& ( X1 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ~ ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ~ ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) ) ) ) )
= ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) ) ) )
| ( ~ ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) )
& ( X0 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ~ ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ~ ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) ) ) ) )
= ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( ( ( X2 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) ) ) )
| ( ~ ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) )
& ( X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.46jENlINrL/DTF2THF_4080.p',cGAZING_THM43_pme) ).
thf(f1874,plain,
( spl3_6
| spl3_2
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f122,f1618,f1614,f1634]) ).
thf(f122,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $false
= ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f103]) ).
thf(f103,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( $false
= ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) )
= $false )
| ( $true
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f1865,plain,
( spl3_4
| spl3_5
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f178,f1618,f1626,f1622]) ).
thf(f178,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( sK0 @ sK5 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
( ( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
= $false )
| ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
( ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $false )
| ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) ) ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f1861,plain,
( spl3_2
| spl3_1
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f204,f1626,f1610,f1614]) ).
thf(f204,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f203]) ).
thf(f203,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f202]) ).
thf(f202,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f201]) ).
thf(f201,plain,
( ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f200]) ).
thf(f200,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f199]) ).
thf(f199,plain,
( ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f198]) ).
thf(f198,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f195]) ).
thf(f195,plain,
( ( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
= $false )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f193]) ).
thf(f193,plain,
( ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
= $false )
| ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f192]) ).
thf(f192,plain,
( ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $false )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f190]) ).
thf(f190,plain,
( ( $false
= ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) )
= $false )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f1857,plain,
( spl3_2
| spl3_1
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f249,f1634,f1610,f1614]) ).
thf(f249,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f247]) ).
thf(f247,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f246]) ).
thf(f246,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f245]) ).
thf(f245,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f244]) ).
thf(f244,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f243]) ).
thf(f243,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f241]) ).
thf(f241,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f240]) ).
thf(f240,plain,
( ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f238]) ).
thf(f238,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f236,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f235]) ).
thf(f235,plain,
( ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f234]) ).
thf(f234,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
( ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f227]) ).
thf(f227,plain,
( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f226]) ).
thf(f226,plain,
( ( $true
= ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f224]) ).
thf(f224,plain,
( ( ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) )
| ( ( ( ~ ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ~ ( sK1 @ sK5 ) ) ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f1708,plain,
( spl3_3
| spl3_5
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f1140,f1614,f1626,f1618]) ).
thf(f1140,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f1137]) ).
thf(f1137,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1136]) ).
thf(f1136,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1128]) ).
thf(f1128,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1127]) ).
thf(f1127,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1124]) ).
thf(f1124,plain,
( ( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1123]) ).
thf(f1123,plain,
( ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1063]) ).
thf(f1063,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1062]) ).
thf(f1062,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
= $true )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1061]) ).
thf(f1061,plain,
( ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f804]) ).
thf(f804,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f228]) ).
thf(f228,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f227]) ).
thf(f1661,plain,
( spl3_3
| spl3_4
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f1439,f1634,f1622,f1618]) ).
thf(f1439,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1438]) ).
thf(f1438,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1437]) ).
thf(f1437,plain,
( ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f1436]) ).
thf(f1436,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1435]) ).
thf(f1435,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1434]) ).
thf(f1434,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1428]) ).
thf(f1428,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1427]) ).
thf(f1427,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1426]) ).
thf(f1426,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1425]) ).
thf(f1425,plain,
( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1423]) ).
thf(f1423,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1421]) ).
thf(f1421,plain,
( ( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1420]) ).
thf(f1420,plain,
( ( $true
= ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1419]) ).
thf(f1419,plain,
( ( $true
= ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( $true
= ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1332]) ).
thf(f1332,plain,
( ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
= $true )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1331]) ).
thf(f1331,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1330]) ).
thf(f1330,plain,
( ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
= $true )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f225]) ).
thf(f225,plain,
( ( $true
= ( ( ~ ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
& ( sK2 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f224]) ).
thf(f1632,plain,
( spl3_5
| spl3_4
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f1602,f1610,f1622,f1626]) ).
thf(f1602,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f1601]) ).
thf(f1601,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1600]) ).
thf(f1600,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1599]) ).
thf(f1599,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1598]) ).
thf(f1598,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1596]) ).
thf(f1596,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1594]) ).
thf(f1594,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1591]) ).
thf(f1591,plain,
( ( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1590]) ).
thf(f1590,plain,
( ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f1589]) ).
thf(f1589,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1588]) ).
thf(f1588,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1564]) ).
thf(f1564,plain,
( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $false )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1563]) ).
thf(f1563,plain,
( ( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
= $false )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1418]) ).
thf(f1418,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ~ ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) ) ) )
| ( ( ~ ( sK2 @ sK5 )
& ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU857^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:35:42 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEU857^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.42 % Domain : Set Theory
% 0.15/0.42 % Problem : TPS problem GAZING-THM43
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.15/0.42 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : tps_0497 [Bro09]
% 0.15/0.42 % : 43 [Bar92]
% 0.15/0.42 % : GAZING-THM43 [TPS]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % 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
% 0.15/0.42 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.15/0.42 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 1 ( 1 avg)
% 0.15/0.42 % Number of connectives : 50 ( 12 ~; 6 |; 12 &; 20 @)
% 0.15/0.42 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 4 ( 4 avg)
% 0.15/0.42 % Number of types : 2 ( 1 usr)
% 0.15/0.42 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.15/0.42 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.15/0.42 % SPC : TH0_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.42 % : Polymorphic definitions expanded.
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(a_type,type,
% 0.15/0.42 a: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(cGAZING_THM43_pme,conjecture,
% 0.15/0.42 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.15/0.42 ( ( ^ [Xz: a] :
% 0.15/0.42 ( ( ( ( ( S @ Xz )
% 0.15/0.42 & ~ ( T @ Xz ) )
% 0.15/0.42 | ( ( T @ Xz )
% 0.15/0.42 & ~ ( S @ Xz ) ) )
% 0.15/0.42 & ~ ( U @ Xz ) )
% 0.15/0.42 | ( ( U @ Xz )
% 0.15/0.42 & ~ ( ( ( S @ Xz )
% 0.15/0.42 & ~ ( T @ Xz ) )
% 0.15/0.42 | ( ( T @ Xz )
% 0.15/0.42 & ~ ( S @ Xz ) ) ) ) ) )
% 0.15/0.42 = ( ^ [Xz: a] :
% 0.15/0.42 ( ( ( S @ Xz )
% 0.15/0.42 & ~ ( ( ( T @ Xz )
% 0.15/0.42 & ~ ( U @ Xz ) )
% 0.15/0.42 | ( ( U @ Xz )
% 0.15/0.42 & ~ ( T @ Xz ) ) ) )
% 0.15/0.42 | ( ( ( ( T @ Xz )
% 0.15/0.42 & ~ ( U @ Xz ) )
% 0.15/0.42 | ( ( U @ Xz )
% 0.15/0.42 & ~ ( T @ Xz ) ) )
% 0.15/0.42 & ~ ( S @ Xz ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.12/1.11 ---- Embedded in THF ---
% 1.12/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.11 %%% Generated on Tue Feb 24 12:35:42 EST 2026
% 1.12/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.11 %%% Logic specification used:
% 1.12/1.11 %%% thf(spec, logic, $$dhol).
% 1.12/1.11
% 1.12/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.46jENlINrL/DTF2DTF4080.p
% See solution above
% 1.12/1.11 ------------------------
% 1.34/1.12 ---- Cleaned THF ---
% 1.34/1.12 thf(a_type,type,
% 1.34/1.12 a: $tType ).
% 1.34/1.12
% 1.34/1.12 thf(cGAZING_THM43_pme,conjecture,
% 1.34/1.12 ! [S: a > $o,T: a > $o,U: a > $o] :
% 1.34/1.12 ( ( ^ [Xz: a] :
% 1.34/1.12 ( ( ( ( ( S @ Xz )
% 1.34/1.12 & ~ ( T @ Xz ) )
% 1.34/1.12 | ( ( T @ Xz )
% 1.34/1.12 & ~ ( S @ Xz ) ) )
% 1.34/1.12 & ~ ( U @ Xz ) )
% 1.34/1.12 | ( ( U @ Xz )
% 1.34/1.12 & ~ ( ( ( S @ Xz )
% 1.34/1.12 & ~ ( T @ Xz ) )
% 1.34/1.12 | ( ( T @ Xz )
% 1.34/1.12 & ~ ( S @ Xz ) ) ) ) ) )
% 1.34/1.12 = ( ^ [Xz: a] :
% 1.34/1.12 ( ( ( S @ Xz )
% 1.34/1.12 & ~ ( ( ( T @ Xz )
% 1.34/1.12 & ~ ( U @ Xz ) )
% 1.34/1.12 | ( ( U @ Xz )
% 1.34/1.12 & ~ ( T @ Xz ) ) ) )
% 1.34/1.12 | ( ( ( ( T @ Xz )
% 1.34/1.12 & ~ ( U @ Xz ) )
% 1.34/1.12 | ( ( U @ Xz )
% 1.34/1.12 & ~ ( T @ Xz ) ) )
% 1.34/1.12 & ~ ( S @ Xz ) ) ) ) ) ).
% 1.34/1.12 ------------------------
% 1.34/1.13 % (4178)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4080 for (2999ds/183Mi)
% 1.34/1.14 % (4182)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_4080 for (2999ds/2Mi)
% 1.34/1.14 % (4180)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_4080 for (2999ds/27Mi)
% 1.34/1.14 % (4181)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4080 for (2999ds/2Mi)
% 1.34/1.14 % (4179)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_4080 for (2999ds/4Mi)
% 1.34/1.14 % (4183)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_4080 for (2999ds/275Mi)
% 1.34/1.14 % (4184)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4080 for (2999ds/18Mi)
% 1.34/1.14 % (4182)Instruction limit reached!
% 1.34/1.14 % (4182)------------------------------
% 1.34/1.14 % (4182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.14 % (4182)Termination reason: Unknown
% 1.34/1.14 % (4182)Termination phase: Property scanning
% 1.34/1.14
% 1.34/1.14 % (4182)Memory used [KB]: 895
% 1.34/1.14 % (4182)Time elapsed: 0.002 s
% 1.34/1.14 % (4182)Instructions burned: 2 (million)
% 1.34/1.14 % (4182)------------------------------
% 1.34/1.14 % (4182)------------------------------
% 1.34/1.14 % (4181)Instruction limit reached!
% 1.34/1.14 % (4181)------------------------------
% 1.34/1.14 % (4181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.14 % (4181)Termination reason: Unknown
% 1.34/1.14 % (4181)Termination phase: Saturation
% 1.34/1.14
% 1.34/1.14 % (4181)Memory used [KB]: 5500
% 1.34/1.14 % (4181)Time elapsed: 0.003 s
% 1.34/1.14 % (4181)Instructions burned: 3 (million)
% 1.34/1.14 % (4181)------------------------------
% 1.34/1.14 % (4181)------------------------------
% 1.34/1.14 % (4179)Instruction limit reached!
% 1.34/1.14 % (4179)------------------------------
% 1.34/1.14 % (4179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.14 % (4179)Termination reason: Unknown
% 1.34/1.14 % (4179)Termination phase: Saturation
% 1.34/1.14
% 1.34/1.14 % (4179)Memory used [KB]: 5500
% 1.34/1.14 % (4179)Time elapsed: 0.004 s
% 1.34/1.14 % (4179)Instructions burned: 5 (million)
% 1.34/1.14 % (4179)------------------------------
% 1.34/1.14 % (4179)------------------------------
% 1.34/1.15 % (4184)Instruction limit reached!
% 1.34/1.15 % (4184)------------------------------
% 1.34/1.15 % (4184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.15 % (4184)Termination reason: Unknown
% 1.34/1.15 % (4184)Termination phase: Saturation
% 1.34/1.15
% 1.34/1.15 % (4184)Memory used [KB]: 5500
% 1.34/1.15 % (4184)Time elapsed: 0.010 s
% 1.34/1.15 % (4184)Instructions burned: 19 (million)
% 1.34/1.15 % (4184)------------------------------
% 1.34/1.15 % (4184)------------------------------
% 1.34/1.15 % (4180)Instruction limit reached!
% 1.34/1.15 % (4180)------------------------------
% 1.34/1.15 % (4180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.15 % (4180)Termination reason: Unknown
% 1.34/1.15 % (4180)Termination phase: Saturation
% 1.34/1.15
% 1.34/1.15 % (4180)Memory used [KB]: 5628
% 1.34/1.15 % (4180)Time elapsed: 0.014 s
% 1.34/1.15 % (4180)Instructions burned: 28 (million)
% 1.34/1.15 % (4180)------------------------------
% 1.34/1.15 % (4180)------------------------------
% 1.34/1.15 % (4178)First to succeed.
% 1.34/1.16 % (4185)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4080 for (2999ds/3Mi)
% 1.34/1.16 % (4186)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_4080 for (2999ds/37Mi)
% 1.34/1.16 % (4178)Refutation found. Thanks to Tanya!
% 1.34/1.16 % SZS status Theorem for DTF2THF_4080
% 1.34/1.16 % SZS output start Proof for DTF2THF_4080
% 1.34/1.16 thf(type_def_5, type, a: $tType).
% 1.34/1.16 thf(func_def_0, type, a: $tType).
% 1.34/1.16 thf(func_def_9, type, sK0: a > $o).
% 1.34/1.16 thf(func_def_10, type, sK1: a > $o).
% 1.34/1.16 thf(func_def_11, type, sK2: a > $o).
% 1.34/1.16 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.34/1.16 thf(func_def_14, type, sK5: a).
% 1.34/1.16 thf(f1913,plain,(
% 1.34/1.16 $false),
% 1.34/1.16 inference(avatar_sat_refutation,[status(thm)],[f1632,f1661,f1708,f1857,f1861,f1865,f1874,f1882,f1899,f1906,f1912])).
% 1.34/1.16 thf(f1912,plain,(
% 1.34/1.16 ~spl3_1 | ~spl3_3),
% 1.34/1.16 inference(avatar_contradiction_clause,[status(thm)],[f1911])).
% 1.34/1.16 thf(f1911,plain,(
% 1.34/1.16 $false | (~spl3_1 | ~spl3_3)),
% 1.34/1.16 inference(trivial_inequality_removal,[status(thm)],[f1907])).
% 1.34/1.16 thf(f1907,plain,(
% 1.34/1.16 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 1.34/1.16 inference(superposition,[status(thm)],[f1620,f1612])).
% 1.34/1.16 thf(f1612,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | ~spl3_1),
% 1.34/1.16 inference(avatar_component_clause,[status(thm)],[f1610])).
% 1.34/1.16 thf(f1610,definition,(
% 1.34/1.16 spl3_1 <=> ((sK0 @ sK5) = $false)),
% 1.34/1.16 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.34/1.16 thf(f1620,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | ~spl3_3),
% 1.34/1.16 inference(avatar_component_clause,[status(thm)],[f1618])).
% 1.34/1.16 thf(f1618,definition,(
% 1.34/1.16 spl3_3 <=> ((sK0 @ sK5) = $true)),
% 1.34/1.16 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.34/1.16 thf(f1906,plain,(
% 1.34/1.16 ~spl3_5 | ~spl3_6),
% 1.34/1.16 inference(avatar_contradiction_clause,[status(thm)],[f1905])).
% 1.34/1.16 thf(f1905,plain,(
% 1.34/1.16 $false | (~spl3_5 | ~spl3_6)),
% 1.34/1.16 inference(trivial_inequality_removal,[status(thm)],[f1902])).
% 1.34/1.16 thf(f1902,plain,(
% 1.34/1.16 ($true = $false) | (~spl3_5 | ~spl3_6)),
% 1.34/1.16 inference(superposition,[status(thm)],[f1636,f1628])).
% 1.34/1.16 thf(f1628,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ~spl3_5),
% 1.34/1.16 inference(avatar_component_clause,[status(thm)],[f1626])).
% 1.34/1.16 thf(f1626,definition,(
% 1.34/1.16 spl3_5 <=> ($true = (sK2 @ sK5))),
% 1.34/1.16 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.34/1.16 thf(f1636,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ~spl3_6),
% 1.34/1.16 inference(avatar_component_clause,[status(thm)],[f1634])).
% 1.34/1.16 thf(f1634,definition,(
% 1.34/1.16 spl3_6 <=> ($false = (sK2 @ sK5))),
% 1.34/1.16 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.34/1.16 thf(f1899,plain,(
% 1.34/1.16 ~spl3_2 | ~spl3_4),
% 1.34/1.16 inference(avatar_contradiction_clause,[status(thm)],[f1898])).
% 1.34/1.16 thf(f1898,plain,(
% 1.34/1.16 $false | (~spl3_2 | ~spl3_4)),
% 1.34/1.16 inference(trivial_inequality_removal,[status(thm)],[f1895])).
% 1.34/1.16 thf(f1895,plain,(
% 1.34/1.16 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 1.34/1.16 inference(superposition,[status(thm)],[f1616,f1624])).
% 1.34/1.16 thf(f1624,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ~spl3_4),
% 1.34/1.16 inference(avatar_component_clause,[status(thm)],[f1622])).
% 1.34/1.16 thf(f1622,definition,(
% 1.34/1.16 spl3_4 <=> ($false = (sK1 @ sK5))),
% 1.34/1.16 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.34/1.16 thf(f1616,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ~spl3_2),
% 1.34/1.16 inference(avatar_component_clause,[status(thm)],[f1614])).
% 1.34/1.16 thf(f1614,definition,(
% 1.34/1.16 spl3_2 <=> ($true = (sK1 @ sK5))),
% 1.34/1.16 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.34/1.16 thf(f1882,plain,(
% 1.34/1.16 spl3_4 | spl3_6 | spl3_1),
% 1.34/1.16 inference(avatar_split_clause,[status(thm)],[f81,f1610,f1634,f1622])).
% 1.34/1.16 thf(f81,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f80])).
% 1.34/1.16 thf(f80,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $false) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f79])).
% 1.34/1.16 thf(f79,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | ($true = (~ (sK0 @ sK5))) | ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f78])).
% 1.34/1.16 thf(f78,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($true = (~ (sK0 @ sK5))) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f74])).
% 1.34/1.16 thf(f74,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | ($false = (sK1 @ sK5)) | ($true = (~ (sK2 @ sK5))) | ($false = (sK2 @ sK5)) | ($true = (~ (sK0 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.34/1.16 thf(f68,plain,(
% 1.34/1.16 (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $true) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($true = (~ (sK2 @ sK5))) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.34/1.16 thf(f67,plain,(
% 1.34/1.16 (((sK0 @ sK5) & (~ (sK2 @ sK5))) = $true) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $true) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.34/1.16 thf(f66,plain,(
% 1.34/1.16 ((((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))) = $true) | ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f65])).
% 1.34/1.16 thf(f65,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f64])).
% 1.34/1.16 thf(f64,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $false) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f63])).
% 1.34/1.16 thf(f63,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ($true = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f62])).
% 1.34/1.16 thf(f62,plain,(
% 1.34/1.16 ($true = (~ (sK0 @ sK5))) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false) | ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ($true = (~ (sK1 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.34/1.16 thf(f22,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($true = (~ (sK0 @ sK5))) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.34/1.16 thf(f21,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($false = (sK1 @ sK5)) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.34/1.16 thf(f20,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.34/1.16 thf(f19,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) = $false) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5)))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.34/1.16 thf(f17,plain,(
% 1.34/1.16 ($false = (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | ((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5))))) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.34/1.16 thf(f16,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) = $false) | ($false = (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | ((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5)))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.34/1.16 thf(f15,plain,(
% 1.34/1.16 (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) = $false) | ($false = (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | ((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5)))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.34/1.16 thf(f13,plain,(
% 1.34/1.16 ((((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))) = $false) | ($false = (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | ((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5)))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.34/1.16 thf(f11,plain,(
% 1.34/1.16 ((((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))) != (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | ((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5)))))),
% 1.34/1.16 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.34/1.16 thf(f10,plain,(
% 1.34/1.16 (((^[Y0 : a]: (((~ (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) & (sK2 @ Y0)) | ((~ (sK2 @ Y0)) & (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))))) @ sK5) != ((^[Y0 : a]: (((sK1 @ Y0) & (~ (((sK2 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK2 @ Y0)))))) | ((((~ (sK2 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (~ (sK1 @ Y0))))) @ sK5))),
% 1.34/1.16 inference(negative_extensionality,[status(thm)],[f9])).
% 1.34/1.16 thf(f9,plain,(
% 1.34/1.16 ((^[Y0 : a]: (((~ (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) & (sK2 @ Y0)) | ((~ (sK2 @ Y0)) & (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (((sK2 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK2 @ Y0)))))) | ((((~ (sK2 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (~ (sK1 @ Y0))))))),
% 1.34/1.16 inference(cnf_transformation,[status(thm)],[f8])).
% 1.34/1.16 thf(f8,plain,(
% 1.34/1.16 ((^[Y0 : a]: (((~ (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) & (sK2 @ Y0)) | ((~ (sK2 @ Y0)) & (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (((sK2 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK2 @ Y0)))))) | ((((~ (sK2 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (~ (sK1 @ Y0))))))),
% 1.34/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.34/1.16 thf(f7,plain,(
% 1.34/1.16 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((X1 @ Y0) & (~ (X0 @ Y0))))) & (X2 @ Y0)) | ((~ (X2 @ Y0)) & (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))))) != (^[Y0 : a]: (((X1 @ Y0) & (~ (((X2 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X2 @ Y0)))))) | ((((~ (X2 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X2 @ Y0))) & (~ (X1 @ Y0)))))) => ((^[Y0 : a]: (((~ (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) & (sK2 @ Y0)) | ((~ (sK2 @ Y0)) & (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (((sK2 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK2 @ Y0)))))) | ((((~ (sK2 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (~ (sK1 @ Y0))))))),
% 1.34/1.16 introduced(definition,[],[choice_axiom])).
% 1.34/1.16 thf(f6,plain,(
% 1.34/1.16 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((X1 @ Y0) & (~ (X0 @ Y0))))) & (X2 @ Y0)) | ((~ (X2 @ Y0)) & (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))))) != (^[Y0 : a]: (((X1 @ Y0) & (~ (((X2 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X2 @ Y0)))))) | ((((~ (X2 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X2 @ Y0))) & (~ (X1 @ Y0))))))),
% 1.34/1.16 inference(ennf_transformation,[status(thm)],[f5])).
% 1.34/1.16 thf(f5,plain,(
% 1.34/1.16 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((X1 @ Y0) & (~ (X0 @ Y0))))) & (X2 @ Y0)) | ((~ (X2 @ Y0)) & (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))))) = (^[Y0 : a]: (((X1 @ Y0) & (~ (((X2 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X2 @ Y0)))))) | ((((~ (X2 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X2 @ Y0))) & (~ (X1 @ Y0))))))),
% 1.34/1.16 inference(fool_elimination,[status(thm)],[f4])).
% 1.34/1.16 thf(f4,plain,(
% 1.34/1.16 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((((X1 @ X3) & ~(X0 @ X3)) | ((X0 @ X3) & ~(X1 @ X3))) & ~(X2 @ X3)) | ((X2 @ X3) & ~((~(X0 @ X3) & (X1 @ X3)) | ((X0 @ X3) & ~(X1 @ X3)))))) = (^[X4 : a] : ((~(X1 @ X4) & (((X2 @ X4) & ~(X0 @ X4)) | ((X0 @ X4) & ~(X2 @ X4)))) | (~((~(X2 @ X4) & (X0 @ X4)) | (~(X0 @ X4) & (X2 @ X4))) & (X1 @ X4)))))),
% 1.34/1.16 inference(rectify,[status(thm)],[f2])).
% 1.34/1.16 thf(f2,negated_conjecture,(
% 1.34/1.16 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((((X0 @ X3) & ~(X1 @ X3)) | ((X1 @ X3) & ~(X0 @ X3))) & ~(X2 @ X3)) | ((X2 @ X3) & ~((~(X1 @ X3) & (X0 @ X3)) | ((X1 @ X3) & ~(X0 @ X3)))))) = (^[X3 : a] : ((~(X0 @ X3) & (((X2 @ X3) & ~(X1 @ X3)) | ((X1 @ X3) & ~(X2 @ X3)))) | (~((~(X2 @ X3) & (X1 @ X3)) | (~(X1 @ X3) & (X2 @ X3))) & (X0 @ X3)))))),
% 1.34/1.16 inference(negated_conjecture,[status(cth)],[f1])).
% 1.34/1.16 thf(f1,conjecture,(
% 1.34/1.16 ! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((((X0 @ X3) & ~(X1 @ X3)) | ((X1 @ X3) & ~(X0 @ X3))) & ~(X2 @ X3)) | ((X2 @ X3) & ~((~(X1 @ X3) & (X0 @ X3)) | ((X1 @ X3) & ~(X0 @ X3)))))) = (^[X3 : a] : ((~(X0 @ X3) & (((X2 @ X3) & ~(X1 @ X3)) | ((X1 @ X3) & ~(X2 @ X3)))) | (~((~(X2 @ X3) & (X1 @ X3)) | (~(X1 @ X3) & (X2 @ X3))) & (X0 @ X3)))))),
% 1.34/1.16 file('/export/starexec/sandbox/tmp/tmp.46jENlINrL/DTF2THF_4080.p',cGAZING_THM43_pme)).
% 1.34/1.16 thf(f1874,plain,(
% 1.34/1.16 spl3_6 | spl3_2 | spl3_3),
% 1.34/1.16 inference(avatar_split_clause,[status(thm)],[f122,f1618,f1614,f1634])).
% 1.34/1.16 thf(f122,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | ($true = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f121])).
% 1.34/1.16 thf(f121,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f120])).
% 1.34/1.16 thf(f120,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ((~ (sK0 @ sK5)) = $false) | ((sK0 @ sK5) = $true) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f119])).
% 1.34/1.16 thf(f119,plain,(
% 1.34/1.16 ((~ (sK0 @ sK5)) = $false) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($true = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.34/1.16 thf(f115,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | ($true = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | (((~ (sK0 @ sK5)) & (sK2 @ sK5)) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.34/1.16 thf(f105,plain,(
% 1.34/1.16 ($false = (((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.34/1.16 thf(f104,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($false = (sK2 @ sK5)) | ($false = (((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f103])).
% 1.34/1.16 thf(f103,plain,(
% 1.34/1.16 (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($false = (sK2 @ sK5)) | ($true = (sK1 @ sK5)) | ($false = (((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.34/1.16 thf(f101,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($true = ((sK1 @ sK5) & (~ (sK0 @ sK5)))) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($false = (((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.34/1.16 thf(f100,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ($false = (sK2 @ sK5)) | ($false = (((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f99])).
% 1.34/1.16 thf(f99,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($false = (~ (sK1 @ sK5))) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ($false = (((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.34/1.16 thf(f18,plain,(
% 1.34/1.16 (((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5))) = $false) | ($true = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.34/1.16 thf(f1865,plain,(
% 1.34/1.16 spl3_4 | spl3_5 | spl3_3),
% 1.34/1.16 inference(avatar_split_clause,[status(thm)],[f178,f1618,f1626,f1622])).
% 1.34/1.16 thf(f178,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f177])).
% 1.34/1.16 thf(f177,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f176])).
% 1.34/1.16 thf(f176,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($false = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f175])).
% 1.34/1.16 thf(f175,plain,(
% 1.34/1.16 ($false = (~ (sK2 @ sK5))) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f173])).
% 1.34/1.16 thf(f173,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | (((sK0 @ sK5) & (~ (sK2 @ sK5))) = $true) | ($false = (sK1 @ sK5)) | ($false = (~ (sK2 @ sK5))) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f171])).
% 1.34/1.16 thf(f171,plain,(
% 1.34/1.16 (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $true) | ((sK0 @ sK5) = $true) | ($false = (sK1 @ sK5)) | ($false = (~ (sK2 @ sK5))) | (((sK0 @ sK5) & (~ (sK2 @ sK5))) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f170])).
% 1.34/1.16 thf(f170,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ((((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))) = $true) | ($false = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f169])).
% 1.34/1.16 thf(f169,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ((~ (sK0 @ sK5)) = $false) | ($false = (~ (sK2 @ sK5))) | ((((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))) = $true)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f168])).
% 1.34/1.16 thf(f168,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false) | ($false = (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) = $false)),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f167])).
% 1.34/1.16 thf(f167,plain,(
% 1.34/1.16 ((~ (sK0 @ sK5)) = $false) | ($false = (sK1 @ sK5)) | ($false = (~ (sK2 @ sK5))) | ($false = (sK1 @ sK5)) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 1.34/1.16 thf(f166,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ($false = ((~ (sK0 @ sK5)) & (sK1 @ sK5))) | ($false = (~ (sK2 @ sK5))) | ((~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.34/1.16 thf(f147,plain,(
% 1.34/1.16 (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) = $false) | ($false = ((~ (sK0 @ sK5)) & (sK1 @ sK5))) | ($false = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f146])).
% 1.34/1.16 thf(f146,plain,(
% 1.34/1.16 ((((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))) = $false) | (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) = $false) | ($false = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f145])).
% 1.34/1.16 thf(f145,plain,(
% 1.34/1.16 (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $false) | (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.34/1.16 thf(f14,plain,(
% 1.34/1.16 ($false = (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | ((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5))))) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.34/1.16 thf(f1861,plain,(
% 1.34/1.16 spl3_2 | spl3_1 | spl3_5),
% 1.34/1.16 inference(avatar_split_clause,[status(thm)],[f204,f1626,f1610,f1614])).
% 1.34/1.16 thf(f204,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f203])).
% 1.34/1.16 thf(f203,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f202])).
% 1.34/1.16 thf(f202,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f201])).
% 1.34/1.16 thf(f201,plain,(
% 1.34/1.16 ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ($true = (sK1 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f200])).
% 1.34/1.16 thf(f200,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false) | ($true = (sK2 @ sK5)) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f199])).
% 1.34/1.16 thf(f199,plain,(
% 1.34/1.16 ($false = (~ (sK1 @ sK5))) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false) | ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f198])).
% 1.34/1.16 thf(f198,plain,(
% 1.34/1.16 (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false) | ($true = (sK2 @ sK5)) | ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f197])).
% 1.34/1.16 thf(f197,plain,(
% 1.34/1.16 ($false = (~ (sK2 @ sK5))) | ($false = (~ (sK1 @ sK5))) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f195])).
% 1.34/1.16 thf(f195,plain,(
% 1.34/1.16 ((((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))) = $false) | ($false = (~ (sK2 @ sK5))) | ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f194])).
% 1.34/1.16 thf(f194,plain,(
% 1.34/1.16 (((~ (sK2 @ sK5)) & (sK0 @ sK5)) = $false) | ($true = (sK2 @ sK5)) | ($false = (~ (sK1 @ sK5))) | ((((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))) = $false)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f193])).
% 1.34/1.16 thf(f193,plain,(
% 1.34/1.16 ($false = (~ (sK2 @ sK5))) | ($false = (~ (sK1 @ sK5))) | ((((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))) = $false) | (((~ (sK2 @ sK5)) & (sK0 @ sK5)) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f192])).
% 1.34/1.16 thf(f192,plain,(
% 1.34/1.16 (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $false) | ($false = (~ (sK1 @ sK5))) | (((~ (sK2 @ sK5)) & (sK0 @ sK5)) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f190])).
% 1.34/1.16 thf(f190,plain,(
% 1.34/1.16 ($false = (((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($false = (~ (sK1 @ sK5))) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.34/1.16 thf(f144,plain,(
% 1.34/1.16 (((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5))) = $false) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.34/1.16 thf(f1857,plain,(
% 1.34/1.16 spl3_2 | spl3_1 | spl3_6),
% 1.34/1.16 inference(avatar_split_clause,[status(thm)],[f249,f1634,f1610,f1614])).
% 1.34/1.16 thf(f249,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f248])).
% 1.34/1.16 thf(f248,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f247])).
% 1.34/1.16 thf(f247,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($false = (~ (sK1 @ sK5)))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f246])).
% 1.34/1.16 thf(f246,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | ($true = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($false = (~ (sK1 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f245])).
% 1.34/1.16 thf(f245,plain,(
% 1.34/1.16 (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f244])).
% 1.34/1.16 thf(f244,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f243])).
% 1.34/1.16 thf(f243,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($true = (~ (sK2 @ sK5))) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f241])).
% 1.34/1.16 thf(f241,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ($true = (~ (sK2 @ sK5))) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f240])).
% 1.34/1.16 thf(f240,plain,(
% 1.34/1.16 ($true = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5)))))) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($true = (sK1 @ sK5)) | ($true = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f238])).
% 1.34/1.16 thf(f238,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($true = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ($true = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 1.34/1.16 thf(f236,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) = $true) | ($true = (sK1 @ sK5)) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f235])).
% 1.34/1.16 thf(f235,plain,(
% 1.34/1.16 ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ((sK0 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f234])).
% 1.34/1.16 thf(f234,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($true = (~ (sK0 @ sK5))) | ($false = (sK2 @ sK5)) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f233])).
% 1.34/1.16 thf(f233,plain,(
% 1.34/1.16 ($true = (~ (sK2 @ sK5))) | ($true = (~ (sK0 @ sK5))) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f231])).
% 1.34/1.16 thf(f231,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ($true = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f229])).
% 1.34/1.16 thf(f229,plain,(
% 1.34/1.16 ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))))) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f227])).
% 1.34/1.16 thf(f227,plain,(
% 1.34/1.16 (((~ (sK2 @ sK5)) & (sK0 @ sK5)) = $true) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f226])).
% 1.34/1.16 thf(f226,plain,(
% 1.34/1.16 ($true = (((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f224])).
% 1.34/1.16 thf(f224,plain,(
% 1.34/1.16 (((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5))) = $true) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.34/1.16 thf(f12,plain,(
% 1.34/1.16 ($true = (((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | ((((~ (sK2 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (~ (sK1 @ sK5))))) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.34/1.16 thf(f1708,plain,(
% 1.34/1.16 spl3_3 | spl3_5 | spl3_2),
% 1.34/1.16 inference(avatar_split_clause,[status(thm)],[f1140,f1614,f1626,f1618])).
% 1.34/1.16 thf(f1140,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1137])).
% 1.34/1.16 thf(f1137,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1136])).
% 1.34/1.16 thf(f1136,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($true = (sK2 @ sK5)) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1128])).
% 1.34/1.16 thf(f1128,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1127])).
% 1.34/1.16 thf(f1127,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | ($true = ((~ (sK0 @ sK5)) & (sK1 @ sK5))) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($true = (sK2 @ sK5)) | ($true = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1124])).
% 1.34/1.16 thf(f1124,plain,(
% 1.34/1.16 ((((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))) = $true) | ($true = (sK1 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1123])).
% 1.34/1.16 thf(f1123,plain,(
% 1.34/1.16 (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1063])).
% 1.34/1.16 thf(f1063,plain,(
% 1.34/1.16 ($true = (sK1 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1062])).
% 1.34/1.16 thf(f1062,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) = $true) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1061])).
% 1.34/1.16 thf(f1061,plain,(
% 1.34/1.16 ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f804])).
% 1.34/1.16 thf(f804,plain,(
% 1.34/1.16 ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))))) | ($true = (sK2 @ sK5)) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ((sK0 @ sK5) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f228])).
% 1.34/1.16 thf(f228,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))))) | ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f227])).
% 1.34/1.16 thf(f1661,plain,(
% 1.34/1.16 spl3_3 | spl3_4 | spl3_6),
% 1.34/1.16 inference(avatar_split_clause,[status(thm)],[f1439,f1634,f1622,f1618])).
% 1.34/1.16 thf(f1439,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1438])).
% 1.34/1.16 thf(f1438,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1437])).
% 1.34/1.16 thf(f1437,plain,(
% 1.34/1.16 ((~ (sK0 @ sK5)) = $false) | ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1436])).
% 1.34/1.16 thf(f1436,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($false = (sK1 @ sK5)) | ((~ (sK0 @ sK5)) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1435])).
% 1.34/1.16 thf(f1435,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $true) | (((sK1 @ sK5) & (~ (sK0 @ sK5))) = $false) | ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1434])).
% 1.34/1.16 thf(f1434,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | (((sK1 @ sK5) & (~ (sK0 @ sK5))) = $false) | ((sK0 @ sK5) = $true)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1428])).
% 1.34/1.16 thf(f1428,plain,(
% 1.34/1.16 ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ($true = (~ (sK2 @ sK5))) | ((sK0 @ sK5) = $true) | (((sK1 @ sK5) & (~ (sK0 @ sK5))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1427])).
% 1.34/1.16 thf(f1427,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5)) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ($true = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1426])).
% 1.34/1.16 thf(f1426,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ((~ (sK0 @ sK5)) = $false) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ($false = (sK2 @ sK5)) | ($true = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1425])).
% 1.34/1.16 thf(f1425,plain,(
% 1.34/1.16 (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $false) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | ($false = (sK1 @ sK5)) | ($true = (~ (sK2 @ sK5)))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1423])).
% 1.34/1.16 thf(f1423,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1421])).
% 1.34/1.16 thf(f1421,plain,(
% 1.34/1.16 ((((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))) = $false) | ($false = (sK1 @ sK5)) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1420])).
% 1.34/1.16 thf(f1420,plain,(
% 1.34/1.16 ($true = (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($false = (sK1 @ sK5)) | ($false = (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5)))))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1419])).
% 1.34/1.16 thf(f1419,plain,(
% 1.34/1.16 ($true = (~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5)))))) | ($true = (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | ($false = (sK1 @ sK5)) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1332])).
% 1.34/1.16 thf(f1332,plain,(
% 1.34/1.16 (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) = $true) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($false = (sK1 @ sK5)) | ($true = (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1331])).
% 1.34/1.16 thf(f1331,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))))) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) = $true)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1330])).
% 1.34/1.16 thf(f1330,plain,(
% 1.34/1.16 ($true = (~ (sK1 @ sK5))) | ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5))))))) | (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) = $true) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f225])).
% 1.34/1.16 thf(f225,plain,(
% 1.34/1.16 ($true = (((~ (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((sK1 @ sK5) & (~ (sK0 @ sK5))))) & (sK2 @ sK5)) | ((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))))) | ($true = (~ (sK1 @ sK5))) | ($true = ((sK1 @ sK5) & (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f224])).
% 1.34/1.16 thf(f1632,plain,(
% 1.34/1.16 spl3_5 | spl3_4 | spl3_1),
% 1.34/1.16 inference(avatar_split_clause,[status(thm)],[f1602,f1610,f1622,f1626])).
% 1.34/1.16 thf(f1602,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1601])).
% 1.34/1.16 thf(f1601,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $false) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1600])).
% 1.34/1.16 thf(f1600,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | ($true = (~ (sK1 @ sK5))) | ($false = (sK1 @ sK5)) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1599])).
% 1.34/1.16 thf(f1599,plain,(
% 1.34/1.16 ($false = (sK1 @ sK5)) | ($true = (~ (sK1 @ sK5))) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1598])).
% 1.34/1.16 thf(f1598,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($true = (~ (sK0 @ sK5))) | ($true = (~ (sK1 @ sK5))) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1596])).
% 1.34/1.16 thf(f1596,plain,(
% 1.34/1.16 (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($true = (sK2 @ sK5)) | ($true = (~ (sK0 @ sK5))) | ((sK0 @ sK5) = $false) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1594])).
% 1.34/1.16 thf(f1594,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($true = ((~ (sK0 @ sK5)) & (sK1 @ sK5))) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1591])).
% 1.34/1.16 thf(f1591,plain,(
% 1.34/1.16 ((((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))) = $true) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $false) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1590])).
% 1.34/1.16 thf(f1590,plain,(
% 1.34/1.16 (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $false)),
% 1.34/1.16 inference(duplicate_literal_removal,[status(thm)],[f1589])).
% 1.34/1.16 thf(f1589,plain,(
% 1.34/1.16 ((sK0 @ sK5) = $false) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($false = (sK1 @ sK5)) | ($true = (sK2 @ sK5)) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1588])).
% 1.34/1.16 thf(f1588,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $false) | ($false = (sK1 @ sK5)) | ($false = (~ (sK2 @ sK5))) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1564])).
% 1.34/1.16 thf(f1564,plain,(
% 1.34/1.16 (((sK0 @ sK5) & (~ (sK2 @ sK5))) = $false) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1563])).
% 1.34/1.16 thf(f1563,plain,(
% 1.34/1.16 ((((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))) = $false) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true) | ($false = (sK1 @ sK5)) | ($true = (sK2 @ sK5))),
% 1.34/1.16 inference(not_proxy_clausification,[status(thm)],[f1418])).
% 1.34/1.16 thf(f1418,plain,(
% 1.34/1.16 ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ($true = (~ (((sK2 @ sK5) & (~ (sK0 @ sK5))) | ((sK0 @ sK5) & (~ (sK2 @ sK5)))))) | (((~ (sK2 @ sK5)) & (((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5)))) = $true)),
% 1.34/1.16 inference(binary_proxy_clausification,[status(thm)],[f1332])).
% 1.34/1.16 % SZS output end Proof for DTF2THF_4080
% 1.34/1.16 % (4178)------------------------------
% 1.34/1.16 % (4178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.16 % (4178)Termination reason: Refutation
% 1.34/1.16
% 1.34/1.16 % (4178)Memory used [KB]: 6140
% 1.34/1.16 % (4178)Time elapsed: 0.024 s
% 1.34/1.16 % (4178)Instructions burned: 66 (million)
% 1.34/1.16 % (4178)------------------------------
% 1.34/1.16 % (4178)------------------------------
% 1.34/1.16 % (4177)Success in time 0.03 s
%------------------------------------------------------------------------------