%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET615^5 : 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 : n016.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 09:31:55 AM UTC 2026
% Result : Theorem 1.68s 1.45s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 13 unt; 0 typ; 6 def)
% Number of atoms : 399 ( 102 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 482 ( 103 ~; 109 |; 57 &; 206 @)
% ( 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(f116,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f83,f87,f102,f103,f107,f111,f115]) ).
thf(f115,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f114]) ).
thf(f114,plain,
( $false
| ~ spl3_1
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_6 ),
inference(forward_demodulation,[status(thm)],[f100,f72]) ).
thf(f72,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl3_1
<=> ( ( sK1 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f100,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f98]) ).
thf(f98,definition,
( spl3_6
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f111,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f76,f92]) ).
thf(f92,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl3_4
<=> ( ( sK0 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f76,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f74,definition,
( spl3_2
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f107,plain,
( ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f80,f96]) ).
thf(f96,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f94,definition,
( spl3_5
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl3_3
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f103,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f26,f98,f94]) ).
thf(f26,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $false )
| ( ( sK1 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) )
= $false )
| ( ( sK1 @ sK5 )
= $true )
| ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $false )
| ( ( sK1 @ sK5 )
= $true )
| ( ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ~ ( sK1 @ sK5 ) )
= $false )
| ( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $false )
| ( ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ~ ( sK1 @ sK5 )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
!= ( ~ ( sK1 @ sK5 )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK0 @ 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 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK0 @ 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 ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X0 @ 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 ) ) ) )
= ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( X2 @ X3 )
| ( X0 @ X3 ) )
& ~ ( X1 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ~ ( X1 @ X4 )
& ( X0 @ X4 ) )
| ( ( X2 @ X4 )
& ~ ( X1 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( ( X0 @ X3 )
| ( X1 @ X3 ) )
& ~ ( X2 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ~ ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( ( X0 @ X4 )
& ~ ( X2 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( ( X0 @ X3 )
| ( X1 @ X3 ) )
& ~ ( X2 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ~ ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( ( X0 @ X4 )
& ~ ( X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.usXDoU91cz/DTF2THF_30401.p',cBOOL_PROP_89_pme) ).
thf(f102,plain,
( spl3_6
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f32,f90,f98]) ).
thf(f32,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) )
= $false )
| ( ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f87,plain,
spl3_1,
inference(avatar_split_clause,[status(thm)],[f46,f70]) ).
thf(f46,plain,
( ( sK1 @ sK5 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ~ ( sK1 @ sK5 ) )
= $true ),
inference(duplicate_literal_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true
= ( ~ ( sK1 @ sK5 )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( sK1 @ sK5 )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( ~ ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
= $true )
| ( $true
= ( ~ ( sK1 @ sK5 )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f83,plain,
( spl3_3
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f61,f74,f78]) ).
thf(f61,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true
= ( ~ ( sK1 @ sK5 )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
& ~ ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( sK1 @ sK5 )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET615^5 : 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 : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:01:21 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
% 0.30/0.49 ---- Original DTF file ---
% 0.30/0.49 thf(spec,logic,$$dhol).
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 % File : SET615^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.49 % Domain : Set Theory
% 0.30/0.49 % Problem : TPS problem BOOL-PROP-89
% 0.30/0.49 % Version : Especial.
% 0.30/0.49 % English : Trybulec's 89th Boolean property of sets
% 0.30/0.49
% 0.30/0.49 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.30/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.49 % Source : [Bro09]
% 0.30/0.49 % Names : tps_0307 [Bro09]
% 0.30/0.49 % : BOOL-PROP-89 [TPS]
% 0.30/0.49
% 0.30/0.49 % Status : Theorem
% 0.30/0.49 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 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 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.30/0.49 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.49 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.30/0.49 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.49 % Number of connectives : 15 ( 3 ~; 2 |; 3 &; 7 @)
% 0.30/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.49 % Maximal formula depth : 4 ( 4 avg)
% 0.30/0.49 % Number of types : 2 ( 1 usr)
% 0.30/0.49 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.49 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.49 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.30/0.49 % SPC : TH0_THM_EQU_NAR
% 0.30/0.49
% 0.30/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.49 % : Polymorphic definitions expanded.
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 thf(a_type,type,
% 0.30/0.49 a: $tType ).
% 0.30/0.49
% 0.30/0.49 thf(cBOOL_PROP_89_pme,conjecture,
% 0.30/0.49 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.30/0.49 ( ( ^ [Xx: a] :
% 0.30/0.49 ( ( ( X @ Xx )
% 0.30/0.49 | ( Y @ Xx ) )
% 0.30/0.49 & ~ ( Z @ Xx ) ) )
% 0.30/0.49 = ( ^ [Xz: a] :
% 0.30/0.49 ( ( ( X @ Xz )
% 0.30/0.49 & ~ ( Z @ Xz ) )
% 0.30/0.49 | ( ( Y @ Xz )
% 0.30/0.49 & ~ ( Z @ Xz ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 ------------------------
% 1.68/1.41 ---- Embedded in THF ---
% 1.68/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.41 %%% Generated on Tue Feb 24 12:01:22 EST 2026
% 1.68/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.41 %%% Logic specification used:
% 1.68/1.41 %%% thf(spec, logic, $$dhol).
% 1.68/1.41
% 1.68/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.usXDoU91cz/DTF2DTF30401.p
% See solution above
% 1.68/1.41 ------------------------
% 1.68/1.42 ---- Cleaned THF ---
% 1.68/1.42 thf(a_type,type,
% 1.68/1.42 a: $tType ).
% 1.68/1.42
% 1.68/1.42 thf(cBOOL_PROP_89_pme,conjecture,
% 1.68/1.42 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.68/1.42 ( ( ^ [Xx: a] :
% 1.68/1.42 ( ( ( X @ Xx )
% 1.68/1.42 | ( Y @ Xx ) )
% 1.68/1.42 & ~ ( Z @ Xx ) ) )
% 1.68/1.42 = ( ^ [Xz: a] :
% 1.68/1.42 ( ( ( X @ Xz )
% 1.68/1.42 & ~ ( Z @ Xz ) )
% 1.68/1.42 | ( ( Y @ Xz )
% 1.68/1.42 & ~ ( Z @ Xz ) ) ) ) ) ).
% 1.68/1.42 ------------------------
% 1.68/1.44 % (30509)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30401 for (3000ds/2Mi)
% 1.68/1.44 % (30506)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30401 for (3000ds/183Mi)
% 1.68/1.44 % (30508)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_30401 for (3000ds/27Mi)
% 1.68/1.44 % (30507)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_30401 for (3000ds/4Mi)
% 1.68/1.44 % (30510)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_30401 for (3000ds/2Mi)
% 1.68/1.44 % (30511)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_30401 for (3000ds/275Mi)
% 1.68/1.44 % (30512)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30401 for (3000ds/18Mi)
% 1.68/1.44 % (30509)Instruction limit reached!
% 1.68/1.44 % (30509)------------------------------
% 1.68/1.44 % (30509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (30509)Termination reason: Unknown
% 1.68/1.44 % (30509)Termination phase: Saturation
% 1.68/1.44
% 1.68/1.44 % (30509)Memory used [KB]: 5500
% 1.68/1.44 % (30509)Time elapsed: 0.003 s
% 1.68/1.44 % (30509)Instructions burned: 2 (million)
% 1.68/1.44 % (30509)------------------------------
% 1.68/1.44 % (30509)------------------------------
% 1.68/1.44 % (30510)Instruction limit reached!
% 1.68/1.44 % (30510)------------------------------
% 1.68/1.44 % (30510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (30510)Termination reason: Unknown
% 1.68/1.44 % (30510)Termination phase: Saturation
% 1.68/1.44
% 1.68/1.44 % (30510)Memory used [KB]: 5500
% 1.68/1.44 % (30510)Time elapsed: 0.003 s
% 1.68/1.44 % (30510)Instructions burned: 2 (million)
% 1.68/1.44 % (30510)------------------------------
% 1.68/1.44 % (30510)------------------------------
% 1.68/1.44 % (30511)First to succeed.
% 1.68/1.44 % (30507)Instruction limit reached!
% 1.68/1.44 % (30507)------------------------------
% 1.68/1.44 % (30507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (30507)Termination reason: Unknown
% 1.68/1.44 % (30507)Termination phase: Saturation
% 1.68/1.44
% 1.68/1.44 % (30507)Memory used [KB]: 5500
% 1.68/1.44 % (30507)Time elapsed: 0.005 s
% 1.68/1.44 % (30507)Instructions burned: 4 (million)
% 1.68/1.44 % (30507)------------------------------
% 1.68/1.44 % (30507)------------------------------
% 1.68/1.45 % (30506)Also succeeded, but the first one will report.
% 1.68/1.45 % (30511)Refutation found. Thanks to Tanya!
% 1.68/1.45 % SZS status Theorem for DTF2THF_30401
% 1.68/1.45 % SZS output start Proof for DTF2THF_30401
% 1.68/1.45 thf(type_def_5, type, a: $tType).
% 1.68/1.45 thf(func_def_0, type, a: $tType).
% 1.68/1.45 thf(func_def_9, type, sK0: a > $o).
% 1.68/1.45 thf(func_def_10, type, sK1: a > $o).
% 1.68/1.45 thf(func_def_11, type, sK2: a > $o).
% 1.68/1.45 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.68/1.45 thf(func_def_14, type, sK5: a).
% 1.68/1.45 thf(f116,plain,(
% 1.68/1.45 $false),
% 1.68/1.45 inference(avatar_sat_refutation,[status(thm)],[f83,f87,f102,f103,f107,f111,f115])).
% 1.68/1.45 thf(f115,plain,(
% 1.68/1.45 ~spl3_1 | ~spl3_6),
% 1.68/1.45 inference(avatar_contradiction_clause,[status(thm)],[f114])).
% 1.68/1.45 thf(f114,plain,(
% 1.68/1.45 $false | (~spl3_1 | ~spl3_6)),
% 1.68/1.45 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.68/1.45 thf(f113,plain,(
% 1.68/1.45 ($false = $true) | (~spl3_1 | ~spl3_6)),
% 1.68/1.45 inference(forward_demodulation,[status(thm)],[f100,f72])).
% 1.68/1.45 thf(f72,plain,(
% 1.68/1.45 ((sK1 @ sK5) = $false) | ~spl3_1),
% 1.68/1.45 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.68/1.45 thf(f70,definition,(
% 1.68/1.45 spl3_1 <=> ((sK1 @ sK5) = $false)),
% 1.68/1.45 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.68/1.45 thf(f100,plain,(
% 1.68/1.45 ((sK1 @ sK5) = $true) | ~spl3_6),
% 1.68/1.45 inference(avatar_component_clause,[status(thm)],[f98])).
% 1.68/1.45 thf(f98,definition,(
% 1.68/1.45 spl3_6 <=> ((sK1 @ sK5) = $true)),
% 1.68/1.45 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.68/1.45 thf(f111,plain,(
% 1.68/1.45 ~spl3_2 | ~spl3_4),
% 1.68/1.45 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.68/1.45 thf(f110,plain,(
% 1.68/1.45 $false | (~spl3_2 | ~spl3_4)),
% 1.68/1.45 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.68/1.45 thf(f109,plain,(
% 1.68/1.45 ($false = $true) | (~spl3_2 | ~spl3_4)),
% 1.68/1.45 inference(forward_demodulation,[status(thm)],[f76,f92])).
% 1.68/1.45 thf(f92,plain,(
% 1.68/1.45 ((sK0 @ sK5) = $false) | ~spl3_4),
% 1.68/1.45 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.68/1.45 thf(f90,definition,(
% 1.68/1.45 spl3_4 <=> ((sK0 @ sK5) = $false)),
% 1.68/1.45 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.68/1.45 thf(f76,plain,(
% 1.68/1.45 ((sK0 @ sK5) = $true) | ~spl3_2),
% 1.68/1.45 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.68/1.45 thf(f74,definition,(
% 1.68/1.45 spl3_2 <=> ((sK0 @ sK5) = $true)),
% 1.68/1.45 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.68/1.45 thf(f107,plain,(
% 1.68/1.45 ~spl3_3 | ~spl3_5),
% 1.68/1.45 inference(avatar_contradiction_clause,[status(thm)],[f106])).
% 1.68/1.45 thf(f106,plain,(
% 1.68/1.45 $false | (~spl3_3 | ~spl3_5)),
% 1.68/1.45 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.68/1.45 thf(f105,plain,(
% 1.68/1.45 ($false = $true) | (~spl3_3 | ~spl3_5)),
% 1.68/1.45 inference(forward_demodulation,[status(thm)],[f80,f96])).
% 1.68/1.45 thf(f96,plain,(
% 1.68/1.45 ($false = (sK2 @ sK5)) | ~spl3_5),
% 1.68/1.45 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.68/1.45 thf(f94,definition,(
% 1.68/1.45 spl3_5 <=> ($false = (sK2 @ sK5))),
% 1.68/1.45 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.68/1.45 thf(f80,plain,(
% 1.68/1.45 ($true = (sK2 @ sK5)) | ~spl3_3),
% 1.68/1.45 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.68/1.45 thf(f78,definition,(
% 1.68/1.45 spl3_3 <=> ($true = (sK2 @ sK5))),
% 1.68/1.45 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.68/1.45 thf(f103,plain,(
% 1.68/1.45 spl3_5 | spl3_6),
% 1.68/1.45 inference(avatar_split_clause,[status(thm)],[f26,f98,f94])).
% 1.68/1.45 thf(f26,plain,(
% 1.68/1.45 ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $true)),
% 1.68/1.45 inference(duplicate_literal_removal,[status(thm)],[f25])).
% 1.68/1.45 thf(f25,plain,(
% 1.68/1.45 ((sK1 @ sK5) = $true) | ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $true)),
% 1.68/1.45 inference(not_proxy_clausification,[status(thm)],[f24])).
% 1.68/1.45 thf(f24,plain,(
% 1.68/1.45 ((sK1 @ sK5) = $true) | ((~ (sK1 @ sK5)) = $false) | ($false = (sK2 @ sK5))),
% 1.68/1.45 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 1.68/1.45 thf(f23,plain,(
% 1.68/1.45 ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $true) | ((~ (sK1 @ sK5)) = $false)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.68/1.45 thf(f18,plain,(
% 1.68/1.45 (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $false) | ((sK1 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.68/1.45 thf(f17,plain,(
% 1.68/1.45 (((sK0 @ sK5) | (sK2 @ sK5)) = $false) | ((sK1 @ sK5) = $true) | (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $false)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.68/1.45 thf(f15,plain,(
% 1.68/1.45 ((((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $false) | ((sK1 @ sK5) = $true) | (((sK0 @ sK5) | (sK2 @ sK5)) = $false)),
% 1.68/1.45 inference(not_proxy_clausification,[status(thm)],[f14])).
% 1.68/1.45 thf(f14,plain,(
% 1.68/1.45 ((~ (sK1 @ sK5)) = $false) | ((((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $false) | (((sK0 @ sK5) | (sK2 @ sK5)) = $false)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.68/1.45 thf(f13,plain,(
% 1.68/1.45 ($false = ((~ (sK1 @ sK5)) & ((sK0 @ sK5) | (sK2 @ sK5)))) | ((((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $false)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.68/1.45 thf(f11,plain,(
% 1.68/1.45 ((((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) != ((~ (sK1 @ sK5)) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.68/1.45 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.68/1.45 thf(f10,plain,(
% 1.68/1.45 (((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK0 @ Y0) | (sK2 @ Y0)))) @ sK5) != ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))) @ sK5))),
% 1.68/1.45 inference(negative_extensionality,[status(thm)],[f9])).
% 1.68/1.45 thf(f9,plain,(
% 1.68/1.45 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK0 @ Y0) | (sK2 @ Y0)))) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 1.68/1.45 inference(cnf_transformation,[status(thm)],[f8])).
% 1.68/1.45 thf(f8,plain,(
% 1.68/1.45 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK0 @ Y0) | (sK2 @ Y0)))) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 1.68/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.68/1.45 thf(f7,plain,(
% 1.68/1.45 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((~ (X1 @ Y0)) & ((X0 @ Y0) | (X2 @ Y0)))) != (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) | ((X0 @ Y0) & (~ (X1 @ Y0)))))) => ((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK0 @ Y0) | (sK2 @ Y0)))) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 1.68/1.45 introduced(definition,[],[choice_axiom])).
% 1.68/1.45 thf(f6,plain,(
% 1.68/1.45 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((~ (X1 @ Y0)) & ((X0 @ Y0) | (X2 @ Y0)))) != (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) | ((X0 @ Y0) & (~ (X1 @ Y0))))))),
% 1.68/1.45 inference(ennf_transformation,[status(thm)],[f5])).
% 1.68/1.45 thf(f5,plain,(
% 1.68/1.45 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((~ (X1 @ Y0)) & ((X0 @ Y0) | (X2 @ Y0)))) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) | ((X0 @ Y0) & (~ (X1 @ Y0))))))),
% 1.68/1.45 inference(fool_elimination,[status(thm)],[f4])).
% 1.68/1.45 thf(f4,plain,(
% 1.68/1.45 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((X2 @ X3) | (X0 @ X3)) & ~(X1 @ X3))) = (^[X4 : a] : ((~(X1 @ X4) & (X0 @ X4)) | ((X2 @ X4) & ~(X1 @ X4)))))),
% 1.68/1.45 inference(rectify,[status(thm)],[f2])).
% 1.68/1.45 thf(f2,negated_conjecture,(
% 1.68/1.45 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((^[X3 : a] : (((X0 @ X3) | (X1 @ X3)) & ~(X2 @ X3))) = (^[X4 : a] : ((~(X2 @ X4) & (X1 @ X4)) | ((X0 @ X4) & ~(X2 @ X4)))))),
% 1.68/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.68/1.45 thf(f1,conjecture,(
% 1.68/1.45 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((^[X3 : a] : (((X0 @ X3) | (X1 @ X3)) & ~(X2 @ X3))) = (^[X4 : a] : ((~(X2 @ X4) & (X1 @ X4)) | ((X0 @ X4) & ~(X2 @ X4)))))),
% 1.68/1.45 file('/export/starexec/sandbox/tmp/tmp.usXDoU91cz/DTF2THF_30401.p',cBOOL_PROP_89_pme)).
% 1.68/1.45 thf(f102,plain,(
% 1.68/1.45 spl3_6 | spl3_4),
% 1.68/1.45 inference(avatar_split_clause,[status(thm)],[f32,f90,f98])).
% 1.68/1.45 thf(f32,plain,(
% 1.68/1.45 ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true)),
% 1.68/1.45 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.68/1.45 thf(f31,plain,(
% 1.68/1.45 ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.68/1.45 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.68/1.45 thf(f30,plain,(
% 1.68/1.45 ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true) | ((~ (sK1 @ sK5)) = $false)),
% 1.68/1.45 inference(duplicate_literal_removal,[status(thm)],[f29])).
% 1.68/1.45 thf(f29,plain,(
% 1.68/1.45 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $false) | ((~ (sK1 @ sK5)) = $false) | ((sK0 @ sK5) = $false)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.68/1.45 thf(f28,plain,(
% 1.68/1.45 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $false) | (((sK0 @ sK5) & (~ (sK1 @ sK5))) = $false)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.68/1.45 thf(f16,plain,(
% 1.68/1.45 ((sK1 @ sK5) = $true) | (((sK0 @ sK5) | (sK2 @ sK5)) = $false) | (((sK0 @ sK5) & (~ (sK1 @ sK5))) = $false)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.68/1.45 thf(f87,plain,(
% 1.68/1.45 spl3_1),
% 1.68/1.45 inference(avatar_split_clause,[status(thm)],[f46,f70])).
% 1.68/1.45 thf(f46,plain,(
% 1.68/1.45 ((sK1 @ sK5) = $false)),
% 1.68/1.45 inference(not_proxy_clausification,[status(thm)],[f45])).
% 1.68/1.45 thf(f45,plain,(
% 1.68/1.45 ((~ (sK1 @ sK5)) = $true)),
% 1.68/1.45 inference(duplicate_literal_removal,[status(thm)],[f42])).
% 1.68/1.45 thf(f42,plain,(
% 1.68/1.45 ((~ (sK1 @ sK5)) = $true) | ((~ (sK1 @ sK5)) = $true)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.68/1.45 thf(f41,plain,(
% 1.68/1.45 (((sK0 @ sK5) & (~ (sK1 @ sK5))) = $true) | ((~ (sK1 @ sK5)) = $true)),
% 1.68/1.45 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.68/1.45 thf(f40,plain,(
% 1.68/1.45 ((~ (sK1 @ sK5)) = $true) | ((~ (sK1 @ sK5)) = $true) | (((sK0 @ sK5) & (~ (sK1 @ sK5))) = $true)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.68/1.45 thf(f38,plain,(
% 1.68/1.45 ($true = ((~ (sK1 @ sK5)) & ((sK0 @ sK5) | (sK2 @ sK5)))) | (((sK0 @ sK5) & (~ (sK1 @ sK5))) = $true) | ((~ (sK1 @ sK5)) = $true)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.68/1.45 thf(f36,plain,(
% 1.68/1.45 (((~ (sK1 @ sK5)) & (sK2 @ sK5)) = $true) | (((sK0 @ sK5) & (~ (sK1 @ sK5))) = $true) | ($true = ((~ (sK1 @ sK5)) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.68/1.45 thf(f12,plain,(
% 1.68/1.45 ((((~ (sK1 @ sK5)) & (sK2 @ sK5)) | ((sK0 @ sK5) & (~ (sK1 @ sK5)))) = $true) | ($true = ((~ (sK1 @ sK5)) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.68/1.45 thf(f83,plain,(
% 1.68/1.45 spl3_3 | spl3_2),
% 1.68/1.45 inference(avatar_split_clause,[status(thm)],[f61,f74,f78])).
% 1.68/1.45 thf(f61,plain,(
% 1.68/1.45 ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5))),
% 1.68/1.45 inference(duplicate_literal_removal,[status(thm)],[f60])).
% 1.68/1.45 thf(f60,plain,(
% 1.68/1.45 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5))),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.68/1.45 thf(f57,plain,(
% 1.68/1.45 ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | (((sK0 @ sK5) | (sK2 @ sK5)) = $true)),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.68/1.45 thf(f56,plain,(
% 1.68/1.45 ($true = ((~ (sK1 @ sK5)) & ((sK0 @ sK5) | (sK2 @ sK5)))) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5))),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.68/1.45 thf(f37,plain,(
% 1.68/1.45 ($true = (sK2 @ sK5)) | (((sK0 @ sK5) & (~ (sK1 @ sK5))) = $true) | ($true = ((~ (sK1 @ sK5)) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.68/1.45 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.68/1.45 % SZS output end Proof for DTF2THF_30401
% 1.68/1.45 % (30511)------------------------------
% 1.68/1.45 % (30511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (30511)Termination reason: Refutation
% 1.68/1.45
% 1.68/1.45 % (30511)Memory used [KB]: 5500
% 1.68/1.45 % (30511)Time elapsed: 0.005 s
% 1.68/1.45 % (30511)Instructions burned: 3 (million)
% 1.68/1.45 % (30511)------------------------------
% 1.68/1.45 % (30511)------------------------------
% 1.68/1.45 % (30505)Success in time 0.014 s
%------------------------------------------------------------------------------