%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET622^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:31:57 AM UTC 2026
% Result : Theorem 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 90 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 819 ( 198 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 1030 ( 177 ~; 223 |; 169 &; 454 @)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 20 ^; 12 !; 6 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK5: a ).
thf(f239,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f191,f192,f208,f215,f222,f225,f231,f238]) ).
thf(f238,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f237]) ).
thf(f237,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f234]) ).
thf(f234,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f167,f180]) ).
thf(f180,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f178]) ).
thf(f178,definition,
( spl3_4
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f167,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f165]) ).
thf(f165,definition,
( spl3_1
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f231,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f230]) ).
thf(f230,plain,
( $false
| ~ spl3_2
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f227]) ).
thf(f227,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f214,f171]) ).
thf(f171,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f169]) ).
thf(f169,definition,
( spl3_2
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f214,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f212]) ).
thf(f212,definition,
( spl3_6
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f225,plain,
( ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f224]) ).
thf(f224,plain,
( $false
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f223]) ).
thf(f223,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f185,f175]) ).
thf(f175,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f173]) ).
thf(f173,definition,
( spl3_3
<=> ( ( sK2 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f185,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f183]) ).
thf(f183,definition,
( spl3_5
<=> ( ( sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f222,plain,
( spl3_6
| spl3_5
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f28,f165,f183,f212]) ).
thf(f28,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) )
!= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ 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 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ 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 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ 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 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) )
= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ 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] :
( ~ ( ( ~ ( X0 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X0 @ X3 ) ) )
& ( X1 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
| ( X0 @ X4 ) )
& ( X1 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ( X1 @ X4 )
& ( X2 @ X4 ) )
| ( ~ ( ( X1 @ X4 )
| ( X2 @ X4 ) )
& ( X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ( X1 @ X4 )
& ( X2 @ X4 ) )
| ( ~ ( ( X1 @ X4 )
| ( X2 @ X4 ) )
& ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CI0VBkQZcM/DTF2THF_22382.p',cBOOL_PROP_98_pme) ).
thf(f215,plain,
( spl3_4
| spl3_6
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f54,f173,f212,f178]) ).
thf(f54,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( ( ~ ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( ( ~ ( sK0 @ sK5 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true )
| ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false
= ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f208,plain,
spl3_2,
inference(avatar_split_clause,[status(thm)],[f65,f169]) ).
thf(f65,plain,
( ( sK1 @ sK5 )
= $true ),
inference(duplicate_literal_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f192,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f129,f173,f165]) ).
thf(f129,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
( ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
( ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
= $true )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true )
| ( $true
= ( ( sK1 @ sK5 )
& ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) )
| ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f191,plain,
( spl3_5
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f138,f178,f183]) ).
thf(f138,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f137]) ).
thf(f137,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( ~ ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET622^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n006.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:00:30 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SET622^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : TPS problem BOOL-PROP-98
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : Trybulec's 98th Boolean property of sets
% 0.30/0.46
% 0.30/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0434 [Bro09]
% 0.30/0.46 % : BOOL-PROP-98 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.46 % Number of connectives : 24 ( 4 ~; 3 |; 6 &; 11 @)
% 0.30/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % : Polymorphic definitions expanded.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(cBOOL_PROP_98_pme,conjecture,
% 0.30/0.46 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.30/0.46 ( ( ^ [Xx: a] :
% 0.30/0.46 ( ( X @ Xx )
% 0.30/0.46 & ~ ( ( ( Y @ Xx )
% 0.30/0.46 & ~ ( Z @ Xx ) )
% 0.30/0.46 | ( ( Z @ Xx )
% 0.30/0.46 & ~ ( Y @ Xx ) ) ) ) )
% 0.30/0.46 = ( ^ [Xz: a] :
% 0.30/0.46 ( ( ( X @ Xz )
% 0.30/0.46 & ~ ( ( Y @ Xz )
% 0.30/0.46 | ( Z @ Xz ) ) )
% 0.30/0.46 | ( ( X @ Xz )
% 0.30/0.46 & ( Y @ Xz )
% 0.30/0.46 & ( Z @ Xz ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 12:00:31 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.CI0VBkQZcM/DTF2DTF22382.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(a_type,type,
% 1.49/1.26 a: $tType ).
% 1.49/1.26
% 1.49/1.26 thf(cBOOL_PROP_98_pme,conjecture,
% 1.49/1.26 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.49/1.26 ( ( ^ [Xx: a] :
% 1.49/1.26 ( ( X @ Xx )
% 1.49/1.26 & ~ ( ( ( Y @ Xx )
% 1.49/1.26 & ~ ( Z @ Xx ) )
% 1.49/1.26 | ( ( Z @ Xx )
% 1.49/1.26 & ~ ( Y @ Xx ) ) ) ) )
% 1.49/1.26 = ( ^ [Xz: a] :
% 1.49/1.26 ( ( ( X @ Xz )
% 1.49/1.26 & ~ ( ( Y @ Xz )
% 1.49/1.26 | ( Z @ Xz ) ) )
% 1.49/1.26 | ( ( X @ Xz )
% 1.49/1.26 & ( Y @ Xz )
% 1.49/1.26 & ( Z @ Xz ) ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.28 % (22659)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_22382 for (2999ds/275Mi)
% 1.49/1.28 % (22656)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_22382 for (2999ds/27Mi)
% 1.49/1.28 % (22659)First to succeed.
% 1.49/1.28 % (22656)Also succeeded, but the first one will report.
% 1.49/1.28 % (22659)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_22382
% 1.49/1.28 % SZS output start Proof for DTF2THF_22382
% 1.49/1.28 thf(type_def_5, type, a: $tType).
% 1.49/1.28 thf(func_def_0, type, a: $tType).
% 1.49/1.28 thf(func_def_9, type, sK0: a > $o).
% 1.49/1.28 thf(func_def_10, type, sK1: a > $o).
% 1.49/1.28 thf(func_def_11, type, sK2: a > $o).
% 1.49/1.28 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.49/1.28 thf(func_def_14, type, sK5: a).
% 1.49/1.28 thf(f239,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(avatar_sat_refutation,[status(thm)],[f191,f192,f208,f215,f222,f225,f231,f238])).
% 1.49/1.28 thf(f238,plain,(
% 1.49/1.28 ~spl3_1 | ~spl3_4),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f237])).
% 1.49/1.28 thf(f237,plain,(
% 1.49/1.28 $false | (~spl3_1 | ~spl3_4)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f234])).
% 1.49/1.28 thf(f234,plain,(
% 1.49/1.28 ($false = $true) | (~spl3_1 | ~spl3_4)),
% 1.49/1.28 inference(superposition,[status(thm)],[f167,f180])).
% 1.49/1.28 thf(f180,plain,(
% 1.49/1.28 ($false = (sK0 @ sK5)) | ~spl3_4),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f178])).
% 1.49/1.28 thf(f178,definition,(
% 1.49/1.28 spl3_4 <=> ($false = (sK0 @ sK5))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.49/1.28 thf(f167,plain,(
% 1.49/1.28 ((sK0 @ sK5) = $true) | ~spl3_1),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f165])).
% 1.49/1.28 thf(f165,definition,(
% 1.49/1.28 spl3_1 <=> ((sK0 @ sK5) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.49/1.28 thf(f231,plain,(
% 1.49/1.28 ~spl3_2 | ~spl3_6),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f230])).
% 1.49/1.28 thf(f230,plain,(
% 1.49/1.28 $false | (~spl3_2 | ~spl3_6)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f227])).
% 1.49/1.28 thf(f227,plain,(
% 1.49/1.28 ($false = $true) | (~spl3_2 | ~spl3_6)),
% 1.49/1.28 inference(superposition,[status(thm)],[f214,f171])).
% 1.49/1.28 thf(f171,plain,(
% 1.49/1.28 ((sK1 @ sK5) = $true) | ~spl3_2),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f169])).
% 1.49/1.28 thf(f169,definition,(
% 1.49/1.28 spl3_2 <=> ((sK1 @ sK5) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.49/1.28 thf(f214,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ~spl3_6),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f212])).
% 1.49/1.28 thf(f212,definition,(
% 1.49/1.28 spl3_6 <=> ($false = (sK1 @ sK5))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.49/1.28 thf(f225,plain,(
% 1.49/1.28 ~spl3_3 | ~spl3_5),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f224])).
% 1.49/1.28 thf(f224,plain,(
% 1.49/1.28 $false | (~spl3_3 | ~spl3_5)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f223])).
% 1.49/1.28 thf(f223,plain,(
% 1.49/1.28 ($false = $true) | (~spl3_3 | ~spl3_5)),
% 1.49/1.28 inference(forward_demodulation,[status(thm)],[f185,f175])).
% 1.49/1.28 thf(f175,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $false) | ~spl3_3),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f173])).
% 1.49/1.28 thf(f173,definition,(
% 1.49/1.28 spl3_3 <=> ((sK2 @ sK5) = $false)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.49/1.28 thf(f185,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $true) | ~spl3_5),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f183])).
% 1.49/1.28 thf(f183,definition,(
% 1.49/1.28 spl3_5 <=> ((sK2 @ sK5) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.49/1.28 thf(f222,plain,(
% 1.49/1.28 spl3_6 | spl3_5 | spl3_1),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f28,f165,f183,f212])).
% 1.49/1.28 thf(f28,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $true) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f27])).
% 1.49/1.28 thf(f27,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ((sK2 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.49/1.28 thf(f25,plain,(
% 1.49/1.28 (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $true) | ($false = (sK1 @ sK5)) | ((sK2 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.49/1.28 thf(f24,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $true) | (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $true) | ((sK0 @ sK5) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.49/1.28 thf(f22,plain,(
% 1.49/1.28 (((sK0 @ sK5) & (~ (sK2 @ sK5))) = $true) | ((sK0 @ sK5) = $true) | (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $true) | ($false = (sK1 @ sK5)) | ((sK2 @ sK5) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.49/1.28 thf(f21,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ((((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))) = $true) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $true)),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f20])).
% 1.49/1.28 thf(f20,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $true) | ($false = (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.49/1.28 thf(f19,plain,(
% 1.49/1.28 (((sK0 @ sK5) | (sK2 @ sK5)) = $true) | ($false = (sK1 @ sK5)) | ($false = (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.49/1.28 thf(f18,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ($false = (sK1 @ sK5)) | (((sK0 @ sK5) | (sK2 @ sK5)) = $true) | ($false = (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.49/1.28 thf(f17,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ($false = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))) | (((sK0 @ sK5) | (sK2 @ sK5)) = $true)),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.49/1.28 thf(f16,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ($false = (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ($false = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.49/1.28 thf(f15,plain,(
% 1.49/1.28 ($false = ((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5))))) | ($false = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.49/1.28 thf(f13,plain,(
% 1.49/1.28 ($false = (((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | (((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)))) | ($false = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 ((((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | (((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5))) != ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))))),
% 1.49/1.28 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 (((^[Y0 : a]: ((sK1 @ Y0) & (~ (((sK0 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK0 @ Y0))))))) @ sK5) != ((^[Y0 : a]: (((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0)))) | (((sK0 @ Y0) & (sK2 @ Y0)) & (sK1 @ Y0)))) @ sK5))),
% 1.49/1.28 inference(negative_extensionality,[status(thm)],[f9])).
% 1.49/1.28 thf(f9,plain,(
% 1.49/1.28 ((^[Y0 : a]: ((sK1 @ Y0) & (~ (((sK0 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK0 @ Y0))))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0)))) | (((sK0 @ Y0) & (sK2 @ Y0)) & (sK1 @ Y0)))))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.28 thf(f8,plain,(
% 1.49/1.28 ((^[Y0 : a]: ((sK1 @ Y0) & (~ (((sK0 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK0 @ Y0))))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0)))) | (((sK0 @ Y0) & (sK2 @ Y0)) & (sK1 @ Y0)))))),
% 1.49/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.49/1.28 thf(f7,plain,(
% 1.49/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((X1 @ Y0) & (~ (((X0 @ Y0) & (~ (X2 @ Y0))) | ((X2 @ Y0) & (~ (X0 @ Y0))))))) != (^[Y0 : a]: (((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0)))) | (((X0 @ Y0) & (X2 @ Y0)) & (X1 @ Y0))))) => ((^[Y0 : a]: ((sK1 @ Y0) & (~ (((sK0 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK0 @ Y0))))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0)))) | (((sK0 @ Y0) & (sK2 @ Y0)) & (sK1 @ Y0)))))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f6,plain,(
% 1.49/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((X1 @ Y0) & (~ (((X0 @ Y0) & (~ (X2 @ Y0))) | ((X2 @ Y0) & (~ (X0 @ Y0))))))) != (^[Y0 : a]: (((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0)))) | (((X0 @ Y0) & (X2 @ Y0)) & (X1 @ Y0)))))),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.28 thf(f5,plain,(
% 1.49/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((X1 @ Y0) & (~ (((X0 @ Y0) & (~ (X2 @ Y0))) | ((X2 @ Y0) & (~ (X0 @ Y0))))))) = (^[Y0 : a]: (((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0)))) | (((X0 @ Y0) & (X2 @ Y0)) & (X1 @ Y0)))))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.28 thf(f4,plain,(
% 1.49/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (~((~(X0 @ X3) & (X2 @ X3)) | (~(X2 @ X3) & (X0 @ X3))) & (X1 @ X3))) = (^[X4 : a] : (((X1 @ X4) & (X2 @ X4) & (X0 @ X4)) | (~((X2 @ X4) | (X0 @ X4)) & (X1 @ X4)))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f2])).
% 1.49/1.28 thf(f2,negated_conjecture,(
% 1.49/1.28 ~! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : ((^[X3 : a] : (~((~(X2 @ X3) & (X1 @ X3)) | (~(X1 @ X3) & (X2 @ X3))) & (X0 @ X3))) = (^[X4 : a] : (((X0 @ X4) & (X1 @ X4) & (X2 @ X4)) | (~((X1 @ X4) | (X2 @ X4)) & (X0 @ X4)))))),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.28 thf(f1,conjecture,(
% 1.49/1.28 ! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : ((^[X3 : a] : (~((~(X2 @ X3) & (X1 @ X3)) | (~(X1 @ X3) & (X2 @ X3))) & (X0 @ X3))) = (^[X4 : a] : (((X0 @ X4) & (X1 @ X4) & (X2 @ X4)) | (~((X1 @ X4) | (X2 @ X4)) & (X0 @ X4)))))),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.CI0VBkQZcM/DTF2THF_22382.p',cBOOL_PROP_98_pme)).
% 1.49/1.28 thf(f215,plain,(
% 1.49/1.28 spl3_4 | spl3_6 | spl3_3),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f54,f173,f212,f178])).
% 1.49/1.28 thf(f54,plain,(
% 1.49/1.28 ($false = (sK0 @ sK5)) | ((sK2 @ sK5) = $false) | ($false = (sK1 @ sK5))),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f53])).
% 1.49/1.28 thf(f53,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ((sK2 @ sK5) = $false) | ($false = (sK0 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f52])).
% 1.49/1.28 thf(f52,plain,(
% 1.49/1.28 ($false = (sK0 @ sK5)) | ((sK2 @ sK5) = $false) | ((~ (sK0 @ sK5)) = $true) | ($false = (sK1 @ sK5))),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f51])).
% 1.49/1.28 thf(f51,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $false) | ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5)) | ((sK2 @ sK5) = $false) | ((~ (sK0 @ sK5)) = $true)),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f47])).
% 1.49/1.28 thf(f47,plain,(
% 1.49/1.28 ($false = (sK0 @ sK5)) | ($true = (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) = $true) | ($false = (sK1 @ sK5)) | ((sK2 @ sK5) = $false)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.49/1.28 thf(f41,plain,(
% 1.49/1.28 (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $true) | ($true = (~ (sK2 @ sK5))) | ($false = (sK0 @ sK5)) | ((sK2 @ sK5) = $false) | ($false = (sK1 @ sK5))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.49/1.28 thf(f40,plain,(
% 1.49/1.28 (((sK0 @ sK5) & (~ (sK2 @ sK5))) = $true) | (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $true) | ($false = (sK0 @ sK5)) | ((sK2 @ sK5) = $false) | ($false = (sK1 @ sK5))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.49/1.28 thf(f39,plain,(
% 1.49/1.28 ($false = (sK1 @ sK5)) | ((((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))) = $true) | ((sK2 @ sK5) = $false) | ($false = (sK0 @ sK5))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.49/1.28 thf(f38,plain,(
% 1.49/1.28 ($false = ((sK0 @ sK5) & (sK2 @ sK5))) | ($false = (sK1 @ sK5)) | ((((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))) = $true)),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f37])).
% 1.49/1.28 thf(f37,plain,(
% 1.49/1.28 ($false = (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))) | ($false = (sK1 @ sK5)) | ($false = ((sK0 @ sK5) & (sK2 @ sK5)))),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f36])).
% 1.49/1.28 thf(f36,plain,(
% 1.49/1.28 ($false = ((sK0 @ sK5) & (sK2 @ sK5))) | ($false = (sK1 @ sK5)) | ($false = (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))) | ($false = (sK1 @ sK5))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.49/1.28 thf(f35,plain,(
% 1.49/1.28 ($false = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))) | ($false = ((sK0 @ sK5) & (sK2 @ sK5))) | ($false = (sK1 @ sK5))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.49/1.28 thf(f14,plain,(
% 1.49/1.28 ((((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)) = $false) | ($false = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.49/1.28 thf(f208,plain,(
% 1.49/1.28 spl3_2),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f65,f169])).
% 1.49/1.28 thf(f65,plain,(
% 1.49/1.28 ((sK1 @ sK5) = $true)),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f61])).
% 1.49/1.28 thf(f61,plain,(
% 1.49/1.28 ((sK1 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.49/1.28 thf(f60,plain,(
% 1.49/1.28 ((sK1 @ sK5) = $true) | ((((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true)),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f59])).
% 1.49/1.28 thf(f59,plain,(
% 1.49/1.28 ((sK1 @ sK5) = $true) | ((((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true) | ((sK1 @ sK5) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.49/1.28 thf(f57,plain,(
% 1.49/1.28 ($true = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))) | ((((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true) | ((sK1 @ sK5) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.49/1.28 thf(f55,plain,(
% 1.49/1.28 (((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) = $true) | ($true = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))) | ((((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.49/1.28 thf(f12,plain,(
% 1.49/1.28 ($true = (((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | (((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)))) | ($true = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.49/1.28 thf(f192,plain,(
% 1.49/1.28 spl3_1 | spl3_3),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f129,f173,f165])).
% 1.49/1.28 thf(f129,plain,(
% 1.49/1.28 ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false)),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f128])).
% 1.49/1.28 thf(f128,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f127])).
% 1.49/1.28 thf(f127,plain,(
% 1.49/1.28 ((~ (sK0 @ sK5)) = $false) | ((sK2 @ sK5) = $false) | ((sK0 @ sK5) = $true)),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f126])).
% 1.49/1.28 thf(f126,plain,(
% 1.49/1.28 ((~ (sK0 @ sK5)) = $false) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false) | ((sK2 @ sK5) = $false)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.49/1.28 thf(f122,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $false) | ((sK0 @ sK5) = $true) | (((sK2 @ sK5) & (~ (sK0 @ sK5))) = $false)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.49/1.28 thf(f121,plain,(
% 1.49/1.28 ($false = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false)),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f110])).
% 1.49/1.28 thf(f110,plain,(
% 1.49/1.28 ((~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))) = $true) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.49/1.28 thf(f109,plain,(
% 1.49/1.28 ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ((~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))) = $true) | ((sK0 @ sK5) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.49/1.28 thf(f107,plain,(
% 1.49/1.28 ($true = ((sK0 @ sK5) & (sK2 @ sK5))) | ((~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))) = $true) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.49/1.28 thf(f93,plain,(
% 1.49/1.28 ((((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true) | ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ((~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.49/1.28 thf(f92,plain,(
% 1.49/1.28 ($true = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))) | ((((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f56])).
% 1.49/1.28 thf(f56,plain,(
% 1.49/1.28 ((~ ((sK0 @ sK5) | (sK2 @ sK5))) = $true) | ($true = ((sK1 @ sK5) & (~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))))) | ((((sK0 @ sK5) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.49/1.28 thf(f191,plain,(
% 1.49/1.28 spl3_5 | spl3_4),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f138,f178,f183])).
% 1.49/1.28 thf(f138,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $true) | ($false = (sK0 @ sK5))),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f137])).
% 1.49/1.28 thf(f137,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $true) | ($false = (sK0 @ sK5)) | ((sK2 @ sK5) = $true)),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f136])).
% 1.49/1.28 thf(f136,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $true) | ($false = (~ (sK2 @ sK5))) | ($false = (sK0 @ sK5))),
% 1.49/1.28 inference(duplicate_literal_removal,[status(thm)],[f135])).
% 1.49/1.28 thf(f135,plain,(
% 1.49/1.28 ($false = (~ (sK2 @ sK5))) | ((sK2 @ sK5) = $true) | ($false = (sK0 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.49/1.28 thf(f134,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $true) | ($false = (sK0 @ sK5)) | (((sK0 @ sK5) & (~ (sK2 @ sK5))) = $false)),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.49/1.28 thf(f132,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $true) | ($false = (sK0 @ sK5)) | ($false = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.49/1.28 thf(f130,plain,(
% 1.49/1.28 ((sK2 @ sK5) = $true) | ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ($false = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5)))))),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f108])).
% 1.49/1.28 thf(f108,plain,(
% 1.49/1.28 ((~ (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((sK2 @ sK5) & (~ (sK0 @ sK5))))) = $true) | ((sK2 @ sK5) = $true) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.49/1.28 % SZS output end Proof for DTF2THF_22382
% 1.49/1.28 % (22659)------------------------------
% 1.49/1.28 % (22659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (22659)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (22659)Memory used [KB]: 5500
% 1.49/1.28 % (22659)Time elapsed: 0.005 s
% 1.49/1.28 % (22659)Instructions burned: 8 (million)
% 1.49/1.28 % (22659)------------------------------
% 1.49/1.28 % (22659)------------------------------
% 1.49/1.28 % (22653)Success in time 0.015 s
%------------------------------------------------------------------------------