%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET620^5 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:31:56 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 481 ( 123 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 589 ( 107 ~; 123 |; 91 &; 263 @)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 20 ^; 8 !; 4 ?; 32 :)
% 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_12,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK4: a ).
thf(f135,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f109,f110,f117,f118,f127,f134]) ).
thf(f134,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f133]) ).
thf(f133,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f105,f93]) ).
thf(f93,plain,
( ( ( sK1 @ sK4 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f91]) ).
thf(f91,definition,
( spl2_1
<=> ( ( sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f105,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f103,definition,
( spl2_4
<=> ( ( sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f127,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f126]) ).
thf(f126,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f97,f101]) ).
thf(f101,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl2_3
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f97,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f95,definition,
( spl2_2
<=> ( $false
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f118,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f35,f95,f91]) ).
thf(f35,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK4 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true )
| ( $false
= ( ~ ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $true
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| ( $false
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
| ( $true
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| ( $false
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ~ ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) ) )
| ( $false
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
| ( $false
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ~ ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) )
& ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) ) )
| ( $false
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
!= ( ~ ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) )
& ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK4 )
!= ( ^ [Y0: a] :
( ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
& ( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ~ ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
& ( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
& ( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
= ( ^ [X3: a] :
( ( ( X1 @ X3 )
| ( X0 @ X3 ) )
& ~ ( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) )
= ( ^ [X3: a] :
( ( ( X0 @ X3 )
| ( X1 @ X3 ) )
& ~ ( ( X0 @ X3 )
& ( X1 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) )
= ( ^ [X3: a] :
( ( ( X0 @ X3 )
| ( X1 @ X3 ) )
& ~ ( ( X0 @ X3 )
& ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fPSSCZyQuY/DTF2THF_17882.p',cBOOL_PROP_96_pme) ).
thf(f117,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f43,f103,f99]) ).
thf(f43,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $true
= ( sK0 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK4 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $true
= ( sK0 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK4 ) ) )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $false
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( $true
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) )
| ( $true
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f110,plain,
( spl2_2
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f74,f103,f95]) ).
thf(f74,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $false )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $true
= ( ~ ( sK0 @ sK4 ) ) )
| ( $false
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $true )
| ( $false
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true
= ( ~ ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) ) )
| ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $true )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $true )
| ( $true
= ( ~ ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( ~ ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) )
& ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) ) )
| ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f109,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f82,f99,f91]) ).
thf(f82,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( $true
= ( sK0 @ sK4 ) )
| ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( $true
= ( sK0 @ sK4 ) )
| ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $true )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $true )
| ( ( sK1 @ sK4 )
= $true )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $true )
| ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET620^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n009.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 12:00:25 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SET620^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : TPS problem BOOL-PROP-96
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : Trybulec's 96th Boolean property of sets
% 0.20/0.46
% 0.20/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_0354 [Bro09]
% 0.20/0.46 % : BOOL-PROP-96 [TPS]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.20/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.46 % Number of connectives : 17 ( 3 ~; 2 |; 4 &; 8 @)
% 0.20/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 3 ( 3 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.46 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 % : Polymorphic definitions expanded.
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(a_type,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(cBOOL_PROP_96_pme,conjecture,
% 0.20/0.46 ! [X: a > $o,Y: a > $o] :
% 0.20/0.46 ( ( ^ [Xz: a] :
% 0.20/0.46 ( ( ( X @ Xz )
% 0.20/0.46 & ~ ( Y @ Xz ) )
% 0.20/0.46 | ( ( Y @ Xz )
% 0.20/0.46 & ~ ( X @ Xz ) ) ) )
% 0.20/0.46 = ( ^ [Xx: a] :
% 0.20/0.46 ( ( ( X @ Xx )
% 0.20/0.46 | ( Y @ Xx ) )
% 0.20/0.46 & ~ ( ( X @ Xx )
% 0.20/0.46 & ( Y @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 12:00:26 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fPSSCZyQuY/DTF2DTF17882.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(a_type,type,
% 1.47/1.27 a: $tType ).
% 1.47/1.27
% 1.47/1.27 thf(cBOOL_PROP_96_pme,conjecture,
% 1.47/1.27 ! [X: a > $o,Y: a > $o] :
% 1.47/1.27 ( ( ^ [Xz: a] :
% 1.47/1.27 ( ( ( X @ Xz )
% 1.47/1.27 & ~ ( Y @ Xz ) )
% 1.47/1.27 | ( ( Y @ Xz )
% 1.47/1.27 & ~ ( X @ Xz ) ) ) )
% 1.47/1.27 = ( ^ [Xx: a] :
% 1.47/1.27 ( ( ( X @ Xx )
% 1.47/1.27 | ( Y @ Xx ) )
% 1.47/1.27 & ~ ( ( X @ Xx )
% 1.47/1.27 & ( Y @ Xx ) ) ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.29 % (18211)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_17882 for (2999ds/4Mi)
% 1.47/1.29 % (18210)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17882 for (2999ds/183Mi)
% 1.47/1.29 % (18211)Instruction limit reached!
% 1.47/1.29 % (18211)------------------------------
% 1.47/1.29 % (18211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (18211)Termination reason: Unknown
% 1.47/1.29 % (18211)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (18211)Memory used [KB]: 5500
% 1.47/1.29 % (18211)Time elapsed: 0.003 s
% 1.47/1.29 % (18211)Instructions burned: 4 (million)
% 1.47/1.29 % (18211)------------------------------
% 1.47/1.29 % (18211)------------------------------
% 1.47/1.29 % (18210)First to succeed.
% 1.47/1.29 % (18210)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_17882
% 1.47/1.29 % SZS output start Proof for DTF2THF_17882
% 1.47/1.29 thf(type_def_5, type, a: $tType).
% 1.47/1.29 thf(func_def_0, type, a: $tType).
% 1.47/1.29 thf(func_def_9, type, sK0: a > $o).
% 1.47/1.29 thf(func_def_10, type, sK1: a > $o).
% 1.47/1.29 thf(func_def_12, type, ph3: !>[X0: $tType]:(X0)).
% 1.47/1.29 thf(func_def_13, type, sK4: a).
% 1.47/1.29 thf(f135,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(avatar_sat_refutation,[status(thm)],[f109,f110,f117,f118,f127,f134])).
% 1.47/1.29 thf(f134,plain,(
% 1.47/1.29 ~spl2_1 | ~spl2_4),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f133])).
% 1.47/1.29 thf(f133,plain,(
% 1.47/1.29 $false | (~spl2_1 | ~spl2_4)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.47/1.29 thf(f129,plain,(
% 1.47/1.29 ($false = $true) | (~spl2_1 | ~spl2_4)),
% 1.47/1.29 inference(superposition,[status(thm)],[f105,f93])).
% 1.47/1.29 thf(f93,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $true) | ~spl2_1),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f91])).
% 1.47/1.29 thf(f91,definition,(
% 1.47/1.29 spl2_1 <=> ((sK1 @ sK4) = $true)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.47/1.29 thf(f105,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $false) | ~spl2_4),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.47/1.29 thf(f103,definition,(
% 1.47/1.29 spl2_4 <=> ((sK1 @ sK4) = $false)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.47/1.29 thf(f127,plain,(
% 1.47/1.29 ~spl2_2 | ~spl2_3),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f126])).
% 1.47/1.29 thf(f126,plain,(
% 1.47/1.29 $false | (~spl2_2 | ~spl2_3)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.47/1.29 thf(f123,plain,(
% 1.47/1.29 ($false = $true) | (~spl2_2 | ~spl2_3)),
% 1.47/1.29 inference(superposition,[status(thm)],[f97,f101])).
% 1.47/1.29 thf(f101,plain,(
% 1.47/1.29 ($true = (sK0 @ sK4)) | ~spl2_3),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.47/1.29 thf(f99,definition,(
% 1.47/1.29 spl2_3 <=> ($true = (sK0 @ sK4))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.47/1.29 thf(f97,plain,(
% 1.47/1.29 ($false = (sK0 @ sK4)) | ~spl2_2),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.47/1.29 thf(f95,definition,(
% 1.47/1.29 spl2_2 <=> ($false = (sK0 @ sK4))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.47/1.29 thf(f118,plain,(
% 1.47/1.29 spl2_1 | spl2_2),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f35,f95,f91])).
% 1.47/1.29 thf(f35,plain,(
% 1.47/1.29 ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $true)),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f34])).
% 1.47/1.29 thf(f34,plain,(
% 1.47/1.29 ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $true) | ((sK1 @ sK4) = $true)),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f33])).
% 1.47/1.29 thf(f33,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $true) | ($false = (sK0 @ sK4)) | ($false = (~ (sK1 @ sK4)))),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.47/1.29 thf(f32,plain,(
% 1.47/1.29 ($false = (sK0 @ sK4)) | ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $true) | ($false = (~ (sK1 @ sK4)))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.47/1.29 thf(f28,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $true) | ($false = (sK0 @ sK4)) | ($false = ((sK0 @ sK4) & (~ (sK1 @ sK4))))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ($false = (sK0 @ sK4)) | ($false = (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4))))) | ((sK1 @ sK4) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 ($true = ((sK0 @ sK4) & (sK1 @ sK4))) | ($false = (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4))))) | ($false = (sK0 @ sK4))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 ($false = ((sK0 @ sK4) | (sK1 @ sK4))) | ($true = ((sK0 @ sK4) & (sK1 @ sK4))) | ($false = (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4)))))),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f14])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 ($false = (~ ((sK0 @ sK4) & (sK1 @ sK4)))) | ($false = ((sK0 @ sK4) | (sK1 @ sK4))) | ($false = (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4)))))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ($false = ((~ ((sK0 @ sK4) & (sK1 @ sK4))) & ((sK0 @ sK4) | (sK1 @ sK4)))) | ($false = (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4)))))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4)))) != ((~ ((sK0 @ sK4) & (sK1 @ sK4))) & ((sK0 @ sK4) | (sK1 @ sK4))))),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 (((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))) @ sK4) != ((^[Y0 : a]: ((~ ((sK0 @ Y0) & (sK1 @ Y0))) & ((sK0 @ Y0) | (sK1 @ Y0)))) @ sK4))),
% 1.47/1.29 inference(negative_extensionality,[status(thm)],[f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ((^[Y0 : a]: ((~ ((sK0 @ Y0) & (sK1 @ Y0))) & ((sK0 @ Y0) | (sK1 @ Y0)))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ((^[Y0 : a]: ((~ ((sK0 @ Y0) & (sK1 @ Y0))) & ((sK0 @ Y0) | (sK1 @ Y0)))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((~ ((X0 @ Y0) & (X1 @ Y0))) & ((X0 @ Y0) | (X1 @ Y0)))) != (^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0)))))) => ((^[Y0 : a]: ((~ ((sK0 @ Y0) & (sK1 @ Y0))) & ((sK0 @ Y0) | (sK1 @ Y0)))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((~ ((X0 @ Y0) & (X1 @ Y0))) & ((X0 @ Y0) | (X1 @ Y0)))) != (^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0))))))),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((~ ((X0 @ Y0) & (X1 @ Y0))) & ((X0 @ Y0) | (X1 @ Y0)))) = (^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0))))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,plain,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((~(X1 @ X2) & (X0 @ X2)) | (~(X0 @ X2) & (X1 @ X2)))) = (^[X3 : a] : (((X1 @ X3) | (X0 @ X3)) & ~((X1 @ X3) & (X0 @ X3)))))),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,negated_conjecture,(
% 1.47/1.29 ~! [X1 : a > $o,X0 : a > $o] : ((^[X2 : a] : ((~(X0 @ X2) & (X1 @ X2)) | (~(X1 @ X2) & (X0 @ X2)))) = (^[X3 : a] : (((X0 @ X3) | (X1 @ X3)) & ~((X0 @ X3) & (X1 @ X3)))))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.29 thf(f1,conjecture,(
% 1.47/1.29 ! [X1 : a > $o,X0 : a > $o] : ((^[X2 : a] : ((~(X0 @ X2) & (X1 @ X2)) | (~(X1 @ X2) & (X0 @ X2)))) = (^[X3 : a] : (((X0 @ X3) | (X1 @ X3)) & ~((X0 @ X3) & (X1 @ X3)))))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.fPSSCZyQuY/DTF2THF_17882.p',cBOOL_PROP_96_pme)).
% 1.47/1.29 thf(f117,plain,(
% 1.47/1.29 spl2_3 | spl2_4),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f43,f103,f99])).
% 1.47/1.29 thf(f43,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $false) | ($true = (sK0 @ sK4))),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f42])).
% 1.47/1.29 thf(f42,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $false) | ($true = (sK0 @ sK4)) | ($true = (sK0 @ sK4))),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f41])).
% 1.47/1.29 thf(f41,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $false) | ($true = (sK0 @ sK4)) | ($false = (~ (sK0 @ sK4)))),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.47/1.29 thf(f40,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $false) | ($true = (sK0 @ sK4)) | ($false = (~ (sK0 @ sK4))) | ((sK1 @ sK4) = $false)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.47/1.29 thf(f39,plain,(
% 1.47/1.29 ($false = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | ($true = (sK0 @ sK4)) | ((sK1 @ sK4) = $false)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.47/1.29 thf(f37,plain,(
% 1.47/1.29 ($false = (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4))))) | ($true = (sK0 @ sK4)) | ((sK1 @ sK4) = $false)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 ($true = ((sK0 @ sK4) & (sK1 @ sK4))) | ((sK1 @ sK4) = $false) | ($false = (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4)))))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.47/1.29 thf(f110,plain,(
% 1.47/1.29 spl2_2 | spl2_4),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f74,f103,f95])).
% 1.47/1.29 thf(f74,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $false) | ($false = (sK0 @ sK4))),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f73])).
% 1.47/1.29 thf(f73,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $false) | ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $false)),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f72])).
% 1.47/1.29 thf(f72,plain,(
% 1.47/1.29 ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $false) | ($true = (~ (sK1 @ sK4)))),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f71])).
% 1.47/1.29 thf(f71,plain,(
% 1.47/1.29 ($true = (~ (sK1 @ sK4))) | ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $false) | ($false = (sK0 @ sK4))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.47/1.29 thf(f70,plain,(
% 1.47/1.29 ($false = (sK0 @ sK4)) | ($false = ((sK0 @ sK4) & (sK1 @ sK4))) | ($true = (~ (sK1 @ sK4)))),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f65])).
% 1.47/1.29 thf(f65,plain,(
% 1.47/1.29 ($true = (~ (sK0 @ sK4))) | ($false = ((sK0 @ sK4) & (sK1 @ sK4))) | ($true = (~ (sK1 @ sK4)))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.47/1.29 thf(f58,plain,(
% 1.47/1.29 ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | ($true = (~ (sK1 @ sK4))) | ($false = ((sK0 @ sK4) & (sK1 @ sK4)))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.47/1.29 thf(f57,plain,(
% 1.47/1.29 (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $true) | ($false = ((sK0 @ sK4) & (sK1 @ sK4))) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4))))),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f56])).
% 1.47/1.29 thf(f56,plain,(
% 1.47/1.29 ($true = (~ ((sK0 @ sK4) & (sK1 @ sK4)))) | (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $true) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4))))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.47/1.29 thf(f55,plain,(
% 1.47/1.29 ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4)))) = $true) | ($true = (~ ((sK0 @ sK4) & (sK1 @ sK4))))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 ($true = ((~ ((sK0 @ sK4) & (sK1 @ sK4))) & ((sK0 @ sK4) | (sK1 @ sK4)))) | ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4)))) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.47/1.29 thf(f109,plain,(
% 1.47/1.29 spl2_1 | spl2_3),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f82,f99,f91])).
% 1.47/1.29 thf(f82,plain,(
% 1.47/1.29 ($true = (sK0 @ sK4)) | ((sK1 @ sK4) = $true)),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f81])).
% 1.47/1.29 thf(f81,plain,(
% 1.47/1.29 ($true = (sK0 @ sK4)) | ($true = (sK0 @ sK4)) | ((sK1 @ sK4) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.47/1.29 thf(f79,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $true) | ($true = (sK0 @ sK4)) | (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $true)),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f78])).
% 1.47/1.29 thf(f78,plain,(
% 1.47/1.29 ((sK1 @ sK4) = $true) | ($true = (sK0 @ sK4)) | (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $true) | ((sK1 @ sK4) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.47/1.29 thf(f76,plain,(
% 1.47/1.29 ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $true) | ((sK1 @ sK4) = $true) | ($true = (sK0 @ sK4))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.47/1.29 thf(f75,plain,(
% 1.47/1.29 ($true = ((sK0 @ sK4) | (sK1 @ sK4))) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.47/1.29 thf(f54,plain,(
% 1.47/1.29 ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((sK0 @ sK4) & (~ (sK1 @ sK4)))) = $true) | ($true = ((sK0 @ sK4) | (sK1 @ sK4)))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_17882
% 1.47/1.29 % (18210)------------------------------
% 1.47/1.29 % (18210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (18210)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (18210)Memory used [KB]: 5500
% 1.47/1.29 % (18210)Time elapsed: 0.004 s
% 1.47/1.29 % (18210)Instructions burned: 5 (million)
% 1.47/1.29 % (18210)------------------------------
% 1.47/1.29 % (18210)------------------------------
% 1.47/1.29 % (18209)Success in time 0.013 s
%------------------------------------------------------------------------------