%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET635^5 : 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 : n013.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 09:32:00 AM UTC 2026
% Result : Theorem 1.48s 1.24s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 14 unt; 0 typ; 6 def)
% Number of atoms : 387 ( 97 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 459 ( 82 ~; 69 |; 97 &; 204 @)
% ( 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_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: a > $o ).
thf(func_def_12,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK5: a ).
thf(f97,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f42,f71,f78,f87,f90,f93,f96]) ).
thf(f96,plain,
( ~ spl3_1
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
| ~ spl3_1
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f52,f28]) ).
thf(f28,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl3_1
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl3_5
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f93,plain,
( ~ spl3_4
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f92]) ).
thf(f92,plain,
( $false
| ~ spl3_4
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $false = $true )
| ~ spl3_4
| ~ spl3_6 ),
inference(backward_demodulation,[status(thm)],[f40,f59]) ).
thf(f59,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl3_6
<=> ( ( sK0 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f40,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl3_4
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f90,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[status(thm)],[f32,f36]) ).
thf(f36,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl3_3
<=> ( ( sK2 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f32,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl3_2
<=> ( ( sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f87,plain,
spl3_5,
inference(avatar_split_clause,[status(thm)],[f81,f50]) ).
thf(f81,plain,
( $true
= ( sK1 @ sK5 ) ),
inference(duplicate_literal_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
!= ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ~ ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( ( 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] :
( ~ ( ( X2 @ Y0 )
& ( X0 @ Y0 ) )
& ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
=> ( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( ( 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] :
( ~ ( ( X2 @ Y0 )
& ( X0 @ Y0 ) )
& ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( 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] :
( ~ ( ( X2 @ Y0 )
& ( X0 @ Y0 ) )
& ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 )
& ~ ( ( X0 @ X3 )
& ( X2 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( X1 @ X4 )
& ( X2 @ X4 )
& ~ ( X0 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 )
& ~ ( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 )
& ~ ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 )
& ~ ( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 )
& ~ ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6TjujYeqhS/DTF2THF_4109.p',cBOOL_PROP_117_pme) ).
thf(f78,plain,
spl3_2,
inference(avatar_split_clause,[status(thm)],[f74,f30]) ).
thf(f74,plain,
( ( sK2 @ sK5 )
= $true ),
inference(duplicate_literal_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true
= ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f71,plain,
( spl3_3
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f70,f57,f34]) ).
thf(f70,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $false
= ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
= ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f42,plain,
( spl3_3
| spl3_1
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f24,f38,f26,f34]) ).
thf(f24,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false )
| ( $true
= ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( $true
= ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $false )
| ( $true
= ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ~ ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 )
& ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET635^5 : 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
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:00:53 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SET635^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPS problem BOOL-PROP-117
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : Trybulec's 117th Boolean property of sets
% 0.19/0.45
% 0.19/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0414 [Bro09]
% 0.19/0.45 % : BOOL-PROP-117 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % 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
% 0.19/0.45 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.45 % Number of connectives : 14 ( 2 ~; 0 |; 5 &; 7 @)
% 0.19/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 4 ( 4 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.45 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % : Polymorphic definitions expanded.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(cBOOL_PROP_117_pme,conjecture,
% 0.19/0.45 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.19/0.45 ( ( ^ [Xx: a] :
% 0.19/0.45 ( ( X @ Xx )
% 0.19/0.45 & ( Y @ Xx )
% 0.19/0.45 & ~ ( Z @ Xx ) ) )
% 0.19/0.45 = ( ^ [Xx: a] :
% 0.19/0.45 ( ( X @ Xx )
% 0.19/0.45 & ( Y @ Xx )
% 0.19/0.45 & ~ ( ( X @ Xx )
% 0.19/0.45 & ( Z @ Xx ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.48/1.21 ---- Embedded in THF ---
% 1.48/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.22 %%% Generated on Tue Feb 24 12:00:54 EST 2026
% 1.48/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.22 %%% Logic specification used:
% 1.48/1.22 %%% thf(spec, logic, $$dhol).
% 1.48/1.22
% 1.48/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6TjujYeqhS/DTF2DTF4109.p
% See solution above
% 1.48/1.22 ------------------------
% 1.48/1.22 ---- Cleaned THF ---
% 1.48/1.22 thf(a_type,type,
% 1.48/1.22 a: $tType ).
% 1.48/1.22
% 1.48/1.22 thf(cBOOL_PROP_117_pme,conjecture,
% 1.48/1.22 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.48/1.22 ( ( ^ [Xx: a] :
% 1.48/1.22 ( ( X @ Xx )
% 1.48/1.22 & ( Y @ Xx )
% 1.48/1.22 & ~ ( Z @ Xx ) ) )
% 1.48/1.22 = ( ^ [Xx: a] :
% 1.48/1.22 ( ( X @ Xx )
% 1.48/1.22 & ( Y @ Xx )
% 1.48/1.22 & ~ ( ( X @ Xx )
% 1.48/1.22 & ( Z @ Xx ) ) ) ) ) ).
% 1.48/1.22 ------------------------
% 1.48/1.24 % (4209)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_4109 for (3000ds/4Mi)
% 1.48/1.24 % (4214)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4109 for (3000ds/18Mi)
% 1.48/1.24 % (4209)First to succeed.
% 1.48/1.24 % (4214)Also succeeded, but the first one will report.
% 1.48/1.24 % (4209)Refutation found. Thanks to Tanya!
% 1.48/1.24 % SZS status Theorem for DTF2THF_4109
% 1.48/1.24 % SZS output start Proof for DTF2THF_4109
% 1.48/1.24 thf(type_def_5, type, a: $tType).
% 1.48/1.24 thf(func_def_0, type, a: $tType).
% 1.48/1.24 thf(func_def_8, type, sK0: a > $o).
% 1.48/1.24 thf(func_def_9, type, sK1: a > $o).
% 1.48/1.24 thf(func_def_10, type, sK2: a > $o).
% 1.48/1.24 thf(func_def_12, type, ph4: !>[X0: $tType]:(X0)).
% 1.48/1.24 thf(func_def_13, type, sK5: a).
% 1.48/1.24 thf(f97,plain,(
% 1.48/1.24 $false),
% 1.48/1.24 inference(avatar_sat_refutation,[status(thm)],[f42,f71,f78,f87,f90,f93,f96])).
% 1.48/1.24 thf(f96,plain,(
% 1.48/1.24 ~spl3_1 | ~spl3_5),
% 1.48/1.24 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.48/1.24 thf(f95,plain,(
% 1.48/1.24 $false | (~spl3_1 | ~spl3_5)),
% 1.48/1.24 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.48/1.24 thf(f94,plain,(
% 1.48/1.24 ($false = $true) | (~spl3_1 | ~spl3_5)),
% 1.48/1.24 inference(backward_demodulation,[status(thm)],[f52,f28])).
% 1.48/1.24 thf(f28,plain,(
% 1.48/1.24 ($false = (sK1 @ sK5)) | ~spl3_1),
% 1.48/1.24 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.48/1.24 thf(f26,definition,(
% 1.48/1.24 spl3_1 <=> ($false = (sK1 @ sK5))),
% 1.48/1.24 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.48/1.24 thf(f52,plain,(
% 1.48/1.24 ($true = (sK1 @ sK5)) | ~spl3_5),
% 1.48/1.24 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.48/1.24 thf(f50,definition,(
% 1.48/1.24 spl3_5 <=> ($true = (sK1 @ sK5))),
% 1.48/1.24 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.48/1.24 thf(f93,plain,(
% 1.48/1.24 ~spl3_4 | ~spl3_6),
% 1.48/1.24 inference(avatar_contradiction_clause,[status(thm)],[f92])).
% 1.48/1.24 thf(f92,plain,(
% 1.48/1.24 $false | (~spl3_4 | ~spl3_6)),
% 1.48/1.24 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.48/1.24 thf(f91,plain,(
% 1.48/1.24 ($false = $true) | (~spl3_4 | ~spl3_6)),
% 1.48/1.24 inference(backward_demodulation,[status(thm)],[f40,f59])).
% 1.48/1.24 thf(f59,plain,(
% 1.48/1.24 ((sK0 @ sK5) = $false) | ~spl3_6),
% 1.48/1.24 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.48/1.24 thf(f57,definition,(
% 1.48/1.24 spl3_6 <=> ((sK0 @ sK5) = $false)),
% 1.48/1.24 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.48/1.24 thf(f40,plain,(
% 1.48/1.24 ((sK0 @ sK5) = $true) | ~spl3_4),
% 1.48/1.24 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.48/1.24 thf(f38,definition,(
% 1.48/1.24 spl3_4 <=> ((sK0 @ sK5) = $true)),
% 1.48/1.24 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.48/1.24 thf(f90,plain,(
% 1.48/1.24 ~spl3_2 | ~spl3_3),
% 1.48/1.24 inference(avatar_contradiction_clause,[status(thm)],[f89])).
% 1.48/1.24 thf(f89,plain,(
% 1.48/1.24 $false | (~spl3_2 | ~spl3_3)),
% 1.48/1.24 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.48/1.24 thf(f88,plain,(
% 1.48/1.24 ($false = $true) | (~spl3_2 | ~spl3_3)),
% 1.48/1.24 inference(backward_demodulation,[status(thm)],[f32,f36])).
% 1.48/1.24 thf(f36,plain,(
% 1.48/1.24 ((sK2 @ sK5) = $false) | ~spl3_3),
% 1.48/1.24 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.48/1.24 thf(f34,definition,(
% 1.48/1.24 spl3_3 <=> ((sK2 @ sK5) = $false)),
% 1.48/1.24 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.48/1.24 thf(f32,plain,(
% 1.48/1.24 ((sK2 @ sK5) = $true) | ~spl3_2),
% 1.48/1.24 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.48/1.24 thf(f30,definition,(
% 1.48/1.24 spl3_2 <=> ((sK2 @ sK5) = $true)),
% 1.48/1.24 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.48/1.24 thf(f87,plain,(
% 1.48/1.24 spl3_5),
% 1.48/1.24 inference(avatar_split_clause,[status(thm)],[f81,f50])).
% 1.48/1.24 thf(f81,plain,(
% 1.48/1.24 ($true = (sK1 @ sK5))),
% 1.48/1.24 inference(duplicate_literal_removal,[status(thm)],[f79])).
% 1.48/1.24 thf(f79,plain,(
% 1.48/1.24 ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK5))),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.48/1.24 thf(f43,plain,(
% 1.48/1.24 ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true) | ($true = (sK1 @ sK5))),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.48/1.24 thf(f12,plain,(
% 1.48/1.24 ($true = (((~ ((sK2 @ sK5) & (sK0 @ sK5))) & (sK2 @ sK5)) & (sK1 @ sK5))) | ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true)),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.48/1.24 thf(f11,plain,(
% 1.48/1.24 ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) & (sK1 @ sK5)) != (((~ ((sK2 @ sK5) & (sK0 @ sK5))) & (sK2 @ sK5)) & (sK1 @ sK5)))),
% 1.48/1.24 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.48/1.24 thf(f10,plain,(
% 1.48/1.24 (((^[Y0 : a]: (((~ ((sK2 @ Y0) & (sK0 @ Y0))) & (sK2 @ Y0)) & (sK1 @ Y0))) @ sK5) != ((^[Y0 : a]: (((~ (sK0 @ Y0)) & (sK2 @ Y0)) & (sK1 @ Y0))) @ sK5))),
% 1.48/1.24 inference(negative_extensionality,[status(thm)],[f9])).
% 1.48/1.24 thf(f9,plain,(
% 1.48/1.24 ((^[Y0 : a]: (((~ (sK0 @ Y0)) & (sK2 @ Y0)) & (sK1 @ Y0))) != (^[Y0 : a]: (((~ ((sK2 @ Y0) & (sK0 @ Y0))) & (sK2 @ Y0)) & (sK1 @ Y0))))),
% 1.48/1.24 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.24 thf(f8,plain,(
% 1.48/1.24 ((^[Y0 : a]: (((~ (sK0 @ Y0)) & (sK2 @ Y0)) & (sK1 @ Y0))) != (^[Y0 : a]: (((~ ((sK2 @ Y0) & (sK0 @ Y0))) & (sK2 @ Y0)) & (sK1 @ Y0))))),
% 1.48/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.48/1.24 thf(f7,plain,(
% 1.48/1.24 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ ((X2 @ Y0) & (X0 @ Y0))) & (X2 @ Y0)) & (X1 @ Y0))) != (^[Y0 : a]: (((~ (X0 @ Y0)) & (X2 @ Y0)) & (X1 @ Y0)))) => ((^[Y0 : a]: (((~ (sK0 @ Y0)) & (sK2 @ Y0)) & (sK1 @ Y0))) != (^[Y0 : a]: (((~ ((sK2 @ Y0) & (sK0 @ Y0))) & (sK2 @ Y0)) & (sK1 @ Y0))))),
% 1.48/1.24 introduced(definition,[],[choice_axiom])).
% 1.48/1.24 thf(f6,plain,(
% 1.48/1.24 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ ((X2 @ Y0) & (X0 @ Y0))) & (X2 @ Y0)) & (X1 @ Y0))) != (^[Y0 : a]: (((~ (X0 @ Y0)) & (X2 @ Y0)) & (X1 @ Y0))))),
% 1.48/1.24 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.24 thf(f5,plain,(
% 1.48/1.24 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((~ ((X2 @ Y0) & (X0 @ Y0))) & (X2 @ Y0)) & (X1 @ Y0))) = (^[Y0 : a]: (((~ (X0 @ Y0)) & (X2 @ Y0)) & (X1 @ Y0))))),
% 1.48/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.24 thf(f4,plain,(
% 1.48/1.24 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : ((X1 @ X3) & (X2 @ X3) & ~((X0 @ X3) & (X2 @ X3)))) = (^[X4 : a] : ((X1 @ X4) & (X2 @ X4) & ~(X0 @ X4))))),
% 1.48/1.24 inference(rectify,[status(thm)],[f2])).
% 1.48/1.24 thf(f2,negated_conjecture,(
% 1.48/1.24 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((^[X3 : a] : ((X1 @ X3) & (X0 @ X3) & ~((X2 @ X3) & (X0 @ X3)))) = (^[X3 : a] : ((X1 @ X3) & (X0 @ X3) & ~(X2 @ X3))))),
% 1.48/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.24 thf(f1,conjecture,(
% 1.48/1.24 ! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((^[X3 : a] : ((X1 @ X3) & (X0 @ X3) & ~((X2 @ X3) & (X0 @ X3)))) = (^[X3 : a] : ((X1 @ X3) & (X0 @ X3) & ~(X2 @ X3))))),
% 1.48/1.24 file('/export/starexec/sandbox2/tmp/tmp.6TjujYeqhS/DTF2THF_4109.p',cBOOL_PROP_117_pme)).
% 1.48/1.24 thf(f78,plain,(
% 1.48/1.24 spl3_2),
% 1.48/1.24 inference(avatar_split_clause,[status(thm)],[f74,f30])).
% 1.48/1.24 thf(f74,plain,(
% 1.48/1.24 ((sK2 @ sK5) = $true)),
% 1.48/1.24 inference(duplicate_literal_removal,[status(thm)],[f72])).
% 1.48/1.24 thf(f72,plain,(
% 1.48/1.24 ((sK2 @ sK5) = $true) | ((sK2 @ sK5) = $true)),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.48/1.24 thf(f61,plain,(
% 1.48/1.24 ($true = ((~ ((sK2 @ sK5) & (sK0 @ sK5))) & (sK2 @ sK5))) | ((sK2 @ sK5) = $true)),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.48/1.24 thf(f46,plain,(
% 1.48/1.24 ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = ((~ ((sK2 @ sK5) & (sK0 @ sK5))) & (sK2 @ sK5)))),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.48/1.24 thf(f44,plain,(
% 1.48/1.24 ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) & (sK1 @ sK5)) = $true) | ($true = ((~ ((sK2 @ sK5) & (sK0 @ sK5))) & (sK2 @ sK5)))),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.48/1.24 thf(f71,plain,(
% 1.48/1.24 spl3_3 | spl3_6),
% 1.48/1.24 inference(avatar_split_clause,[status(thm)],[f70,f57,f34])).
% 1.48/1.24 thf(f70,plain,(
% 1.48/1.24 ((sK0 @ sK5) = $false) | ((sK2 @ sK5) = $false)),
% 1.48/1.24 inference(duplicate_literal_removal,[status(thm)],[f69])).
% 1.48/1.24 thf(f69,plain,(
% 1.48/1.24 ((sK0 @ sK5) = $false) | ((sK0 @ sK5) = $false) | ((sK2 @ sK5) = $false)),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.48/1.24 thf(f68,plain,(
% 1.48/1.24 ($false = ((sK2 @ sK5) & (sK0 @ sK5))) | ((sK0 @ sK5) = $false)),
% 1.48/1.24 inference(not_proxy_clausification,[status(thm)],[f67])).
% 1.48/1.24 thf(f67,plain,(
% 1.48/1.24 ($true = (~ (sK0 @ sK5))) | ($false = ((sK2 @ sK5) & (sK0 @ sK5)))),
% 1.48/1.24 inference(not_proxy_clausification,[status(thm)],[f64])).
% 1.48/1.24 thf(f64,plain,(
% 1.48/1.24 ((~ ((sK2 @ sK5) & (sK0 @ sK5))) = $true) | ($true = (~ (sK0 @ sK5)))),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.48/1.24 thf(f62,plain,(
% 1.48/1.24 ($true = ((~ ((sK2 @ sK5) & (sK0 @ sK5))) & (sK2 @ sK5))) | ($true = (~ (sK0 @ sK5)))),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.48/1.24 thf(f42,plain,(
% 1.48/1.24 spl3_3 | spl3_1 | spl3_4),
% 1.48/1.24 inference(avatar_split_clause,[status(thm)],[f24,f38,f26,f34])).
% 1.48/1.24 thf(f24,plain,(
% 1.48/1.24 ($false = (sK1 @ sK5)) | ((sK2 @ sK5) = $false) | ((sK0 @ sK5) = $true)),
% 1.48/1.24 inference(duplicate_literal_removal,[status(thm)],[f22])).
% 1.48/1.24 thf(f22,plain,(
% 1.48/1.24 ((sK2 @ sK5) = $false) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($false = (sK1 @ sK5))),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.48/1.24 thf(f21,plain,(
% 1.48/1.24 ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false) | ($true = ((sK2 @ sK5) & (sK0 @ sK5))) | ($false = (sK1 @ sK5))),
% 1.48/1.24 inference(not_proxy_clausification,[status(thm)],[f20])).
% 1.48/1.24 thf(f20,plain,(
% 1.48/1.24 ($false = (sK1 @ sK5)) | ((sK2 @ sK5) = $false) | ($false = (~ (sK0 @ sK5))) | ($true = ((sK2 @ sK5) & (sK0 @ sK5)))),
% 1.48/1.24 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 1.48/1.24 thf(f19,plain,(
% 1.48/1.24 ((sK2 @ sK5) = $false) | ($true = ((sK2 @ sK5) & (sK0 @ sK5))) | ($false = (~ (sK0 @ sK5))) | ((sK2 @ sK5) = $false) | ($false = (sK1 @ sK5))),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.48/1.24 thf(f18,plain,(
% 1.48/1.24 ($false = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ((sK2 @ sK5) = $false) | ($true = ((sK2 @ sK5) & (sK0 @ sK5))) | ($false = (sK1 @ sK5))),
% 1.48/1.24 inference(not_proxy_clausification,[status(thm)],[f17])).
% 1.48/1.24 thf(f17,plain,(
% 1.48/1.24 ((sK2 @ sK5) = $false) | ((~ ((sK2 @ sK5) & (sK0 @ sK5))) = $false) | ($false = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($false = (sK1 @ sK5))),
% 1.48/1.24 inference(duplicate_literal_removal,[status(thm)],[f16])).
% 1.48/1.24 thf(f16,plain,(
% 1.48/1.24 ($false = (sK1 @ sK5)) | ($false = (sK1 @ sK5)) | ((~ ((sK2 @ sK5) & (sK0 @ sK5))) = $false) | ($false = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ((sK2 @ sK5) = $false)),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.48/1.24 thf(f15,plain,(
% 1.48/1.24 ((sK2 @ sK5) = $false) | ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) & (sK1 @ sK5)) = $false) | ($false = (sK1 @ sK5)) | ((~ ((sK2 @ sK5) & (sK0 @ sK5))) = $false)),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.48/1.24 thf(f14,plain,(
% 1.48/1.24 ($false = ((~ ((sK2 @ sK5) & (sK0 @ sK5))) & (sK2 @ sK5))) | ($false = (sK1 @ sK5)) | ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) & (sK1 @ sK5)) = $false)),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.48/1.24 thf(f13,plain,(
% 1.48/1.24 ($false = (((~ ((sK2 @ sK5) & (sK0 @ sK5))) & (sK2 @ sK5)) & (sK1 @ sK5))) | ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) & (sK1 @ sK5)) = $false)),
% 1.48/1.24 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.48/1.24 % SZS output end Proof for DTF2THF_4109
% 1.48/1.24 % (4209)------------------------------
% 1.48/1.24 % (4209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.24 % (4209)Termination reason: Refutation
% 1.48/1.24
% 1.48/1.24 % (4209)Memory used [KB]: 5500
% 1.48/1.24 % (4209)Time elapsed: 0.003 s
% 1.48/1.24 % (4209)Instructions burned: 2 (million)
% 1.48/1.24 % (4209)------------------------------
% 1.48/1.24 % (4209)------------------------------
% 1.48/1.24 % (4207)Success in time 0.002 s
%------------------------------------------------------------------------------