%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET612^5 : 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 : n012.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 0.99s 0.90s
% Output : Refutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 17 unt; 0 typ; 6 def)
% Number of atoms : 387 ( 100 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 470 ( 106 ~; 93 |; 64 &; 200 @)
% ( 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 : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 40 ( 22 ^; 12 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
sK0: a > $o ).
thf(func_def_11,type,
sK1: a > $o ).
thf(func_def_12,type,
sK2: a > $o ).
thf(func_def_14,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK5: a ).
thf(f95,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f60,f61,f71,f84,f87,f90,f94]) ).
thf(f94,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f93]) ).
thf(f93,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f75,f54]) ).
thf(f54,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl3_1
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f75,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl3_4
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f90,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
| ~ spl3_2
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_6 ),
inference(forward_demodulation,[status(thm)],[f83,f58]) ).
thf(f58,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl3_2
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f83,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl3_6
<=> ( $true
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f87,plain,
( ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f65,f79]) ).
thf(f79,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl3_5
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f65,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl3_3
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f84,plain,
( spl3_4
| spl3_5
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f24,f81,f77,f73]) ).
thf(f24,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $true
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
!= ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ 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 )
& ( X1 @ Y0 )
& ~ ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X1 @ Y0 )
& ~ ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X1 @ Y0 )
& ~ ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ 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] :
( ~ ( X0 @ X4 )
& ~ ( X2 @ X4 )
& ( X1 @ X4 )
& ( X1 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( X2 @ X3 )
| ( X1 @ X3 ) )
& ( X0 @ X3 ) ) )
= ( ^ [X3: a] :
( ~ ( X1 @ X3 )
& ~ ( X2 @ X3 )
& ( X0 @ X3 )
& ( X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( ( X2 @ X3 )
| ( X1 @ X3 ) )
& ( X0 @ X3 ) ) )
= ( ^ [X3: a] :
( ~ ( X1 @ X3 )
& ~ ( X2 @ X3 )
& ( X0 @ X3 )
& ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fIbdRCrrtI/DTF2THF_32645.p',cBOOL_PROP_85_pme) ).
thf(f71,plain,
spl3_3,
inference(avatar_split_clause,[status(thm)],[f31,f63]) ).
thf(f31,plain,
( $true
= ( sK1 @ sK5 ) ),
inference(duplicate_literal_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
= $true )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f61,plain,
spl3_1,
inference(avatar_split_clause,[status(thm)],[f45,f52]) ).
thf(f45,plain,
( $false
= ( sK2 @ sK5 ) ),
inference(duplicate_literal_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ( sK1 @ sK5 )
& ~ ( sK2 @ sK5 )
& ~ ( sK0 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f60,plain,
spl3_2,
inference(avatar_split_clause,[status(thm)],[f50,f56]) ).
thf(f50,plain,
( $false
= ( sK0 @ sK5 ) ),
inference(duplicate_literal_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( ~ ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SET612^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 12:00:15 EST 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.24 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SET612^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.31 % Domain : Set Theory
% 0.07/0.31 % Problem : TPS problem BOOL-PROP-85
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English : Trybulec's 85th Boolean property of sets
% 0.07/0.31
% 0.07/0.31 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.07/0.31 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Bro09]
% 0.07/0.31 % Names : tps_0309 [Bro09]
% 0.07/0.31 % : BOOL-PROP-85 [TPS]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.07/0.31 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.07/0.31 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 1 ( 1 avg)
% 0.07/0.31 % Number of connectives : 15 ( 3 ~; 1 |; 4 &; 7 @)
% 0.07/0.31 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 4 ( 4 avg)
% 0.07/0.31 % Number of types : 2 ( 1 usr)
% 0.07/0.31 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.07/0.31 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.31 % : Polymorphic definitions expanded.
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(a_type,type,
% 0.07/0.31 a: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(cBOOL_PROP_85_pme,conjecture,
% 0.07/0.31 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.07/0.31 ( ( ^ [Xx: a] :
% 0.07/0.31 ( ( X @ Xx )
% 0.07/0.31 & ~ ( ( Y @ Xx )
% 0.07/0.31 | ( Z @ Xx ) ) ) )
% 0.07/0.31 = ( ^ [Xx: a] :
% 0.07/0.31 ( ( X @ Xx )
% 0.07/0.31 & ~ ( Y @ Xx )
% 0.07/0.31 & ( X @ Xx )
% 0.07/0.31 & ~ ( Z @ Xx ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.83/0.87 ---- Embedded in THF ---
% 0.83/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.83/0.88 %%% Generated on Tue Feb 24 12:00:16 EST 2026
% 0.83/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.83/0.88 %%% Logic specification used:
% 0.83/0.88 %%% thf(spec, logic, $$dhol).
% 0.83/0.88
% 0.83/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.fIbdRCrrtI/DTF2DTF32645.p
% See solution above
% 0.83/0.88 ------------------------
% 0.83/0.88 ---- Cleaned THF ---
% 0.83/0.88 thf(a_type,type,
% 0.83/0.88 a: $tType ).
% 0.83/0.88
% 0.83/0.88 thf(cBOOL_PROP_85_pme,conjecture,
% 0.83/0.88 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.83/0.88 ( ( ^ [Xx: a] :
% 0.83/0.88 ( ( X @ Xx )
% 0.83/0.88 & ~ ( ( Y @ Xx )
% 0.83/0.88 | ( Z @ Xx ) ) ) )
% 0.83/0.88 = ( ^ [Xx: a] :
% 0.83/0.88 ( ( X @ Xx )
% 0.83/0.88 & ~ ( Y @ Xx )
% 0.83/0.88 & ( X @ Xx )
% 0.83/0.88 & ~ ( Z @ Xx ) ) ) ) ).
% 0.83/0.88 ------------------------
% 0.83/0.89 % (373)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32645 for (3000ds/183Mi)
% 0.83/0.89 % (375)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_32645 for (3000ds/27Mi)
% 0.83/0.89 % (374)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_32645 for (3000ds/4Mi)
% 0.83/0.89 % (376)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32645 for (3000ds/2Mi)
% 0.83/0.89 % (377)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_32645 for (3000ds/2Mi)
% 0.83/0.89 % (378)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_32645 for (3000ds/275Mi)
% 0.83/0.89 % (379)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32645 for (3000ds/18Mi)
% 0.83/0.89 % (376)Instruction limit reached!
% 0.83/0.89 % (376)------------------------------
% 0.83/0.89 % (376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (376)Termination reason: Unknown
% 0.83/0.89 % (376)Termination phase: Saturation
% 0.83/0.89
% 0.83/0.89 % (376)Memory used [KB]: 5500
% 0.83/0.89 % (376)Time elapsed: 0.002 s
% 0.83/0.89 % (376)Instructions burned: 2 (million)
% 0.83/0.89 % (376)------------------------------
% 0.83/0.89 % (376)------------------------------
% 0.83/0.89 % (377)Instruction limit reached!
% 0.83/0.89 % (377)------------------------------
% 0.83/0.89 % (377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (377)Termination reason: Unknown
% 0.83/0.89 % (377)Termination phase: Saturation
% 0.83/0.89
% 0.83/0.89 % (377)Memory used [KB]: 5500
% 0.83/0.89 % (377)Time elapsed: 0.002 s
% 0.83/0.89 % (377)Instructions burned: 2 (million)
% 0.83/0.89 % (377)------------------------------
% 0.83/0.89 % (377)------------------------------
% 0.83/0.89 % (375)First to succeed.
% 0.83/0.90 % (374)Instruction limit reached!
% 0.83/0.90 % (374)------------------------------
% 0.83/0.90 % (374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.90 % (374)Termination reason: Unknown
% 0.83/0.90 % (374)Termination phase: Saturation
% 0.83/0.90
% 0.83/0.90 % (374)Memory used [KB]: 5500
% 0.83/0.90 % (374)Time elapsed: 0.003 s
% 0.83/0.90 % (374)Instructions burned: 5 (million)
% 0.83/0.90 % (374)------------------------------
% 0.83/0.90 % (374)------------------------------
% 0.99/0.90 % (373)Also succeeded, but the first one will report.
% 0.99/0.90 % (378)Also succeeded, but the first one will report.
% 0.99/0.90 % (375)Refutation found. Thanks to Tanya!
% 0.99/0.90 % SZS status Theorem for DTF2THF_32645
% 0.99/0.90 % SZS output start Proof for DTF2THF_32645
% 0.99/0.90 thf(type_def_5, type, a: $tType).
% 0.99/0.90 thf(func_def_0, type, a: $tType).
% 0.99/0.90 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.99/0.90 thf(func_def_10, type, sK0: a > $o).
% 0.99/0.90 thf(func_def_11, type, sK1: a > $o).
% 0.99/0.90 thf(func_def_12, type, sK2: a > $o).
% 0.99/0.90 thf(func_def_14, type, ph4: !>[X0: $tType]:(X0)).
% 0.99/0.90 thf(func_def_15, type, sK5: a).
% 0.99/0.90 thf(f95,plain,(
% 0.99/0.90 $false),
% 0.99/0.90 inference(avatar_sat_refutation,[status(thm)],[f60,f61,f71,f84,f87,f90,f94])).
% 0.99/0.90 thf(f94,plain,(
% 0.99/0.90 ~spl3_1 | ~spl3_4),
% 0.99/0.90 inference(avatar_contradiction_clause,[status(thm)],[f93])).
% 0.99/0.90 thf(f93,plain,(
% 0.99/0.90 $false | (~spl3_1 | ~spl3_4)),
% 0.99/0.90 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 0.99/0.90 thf(f92,plain,(
% 0.99/0.90 ($false = $true) | (~spl3_1 | ~spl3_4)),
% 0.99/0.90 inference(forward_demodulation,[status(thm)],[f75,f54])).
% 0.99/0.90 thf(f54,plain,(
% 0.99/0.90 ($false = (sK2 @ sK5)) | ~spl3_1),
% 0.99/0.90 inference(avatar_component_clause,[status(thm)],[f52])).
% 0.99/0.90 thf(f52,definition,(
% 0.99/0.90 spl3_1 <=> ($false = (sK2 @ sK5))),
% 0.99/0.90 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 0.99/0.90 thf(f75,plain,(
% 0.99/0.90 ($true = (sK2 @ sK5)) | ~spl3_4),
% 0.99/0.90 inference(avatar_component_clause,[status(thm)],[f73])).
% 0.99/0.90 thf(f73,definition,(
% 0.99/0.90 spl3_4 <=> ($true = (sK2 @ sK5))),
% 0.99/0.90 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 0.99/0.90 thf(f90,plain,(
% 0.99/0.90 ~spl3_2 | ~spl3_6),
% 0.99/0.90 inference(avatar_contradiction_clause,[status(thm)],[f89])).
% 0.99/0.90 thf(f89,plain,(
% 0.99/0.90 $false | (~spl3_2 | ~spl3_6)),
% 0.99/0.90 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 0.99/0.90 thf(f88,plain,(
% 0.99/0.90 ($false = $true) | (~spl3_2 | ~spl3_6)),
% 0.99/0.90 inference(forward_demodulation,[status(thm)],[f83,f58])).
% 0.99/0.90 thf(f58,plain,(
% 0.99/0.90 ($false = (sK0 @ sK5)) | ~spl3_2),
% 0.99/0.90 inference(avatar_component_clause,[status(thm)],[f56])).
% 0.99/0.90 thf(f56,definition,(
% 0.99/0.90 spl3_2 <=> ($false = (sK0 @ sK5))),
% 0.99/0.90 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 0.99/0.90 thf(f83,plain,(
% 0.99/0.90 ($true = (sK0 @ sK5)) | ~spl3_6),
% 0.99/0.90 inference(avatar_component_clause,[status(thm)],[f81])).
% 0.99/0.90 thf(f81,definition,(
% 0.99/0.90 spl3_6 <=> ($true = (sK0 @ sK5))),
% 0.99/0.90 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 0.99/0.90 thf(f87,plain,(
% 0.99/0.90 ~spl3_3 | ~spl3_5),
% 0.99/0.90 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 0.99/0.90 thf(f86,plain,(
% 0.99/0.90 $false | (~spl3_3 | ~spl3_5)),
% 0.99/0.90 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 0.99/0.90 thf(f85,plain,(
% 0.99/0.90 ($false = $true) | (~spl3_3 | ~spl3_5)),
% 0.99/0.90 inference(forward_demodulation,[status(thm)],[f65,f79])).
% 0.99/0.90 thf(f79,plain,(
% 0.99/0.90 ($false = (sK1 @ sK5)) | ~spl3_5),
% 0.99/0.90 inference(avatar_component_clause,[status(thm)],[f77])).
% 0.99/0.90 thf(f77,definition,(
% 0.99/0.90 spl3_5 <=> ($false = (sK1 @ sK5))),
% 0.99/0.90 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 0.99/0.90 thf(f65,plain,(
% 0.99/0.90 ($true = (sK1 @ sK5)) | ~spl3_3),
% 0.99/0.90 inference(avatar_component_clause,[status(thm)],[f63])).
% 0.99/0.90 thf(f63,definition,(
% 0.99/0.90 spl3_3 <=> ($true = (sK1 @ sK5))),
% 0.99/0.90 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 0.99/0.90 thf(f84,plain,(
% 0.99/0.90 spl3_4 | spl3_5 | spl3_6),
% 0.99/0.90 inference(avatar_split_clause,[status(thm)],[f24,f81,f77,f73])).
% 0.99/0.90 thf(f24,plain,(
% 0.99/0.90 ($false = (sK1 @ sK5)) | ($true = (sK0 @ sK5)) | ($true = (sK2 @ sK5))),
% 0.99/0.90 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 0.99/0.90 thf(f23,plain,(
% 0.99/0.90 ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ($true = (sK0 @ sK5)) | ($true = (sK2 @ sK5))),
% 0.99/0.90 inference(not_proxy_clausification,[status(thm)],[f22])).
% 0.99/0.90 thf(f22,plain,(
% 0.99/0.90 ($false = (sK1 @ sK5)) | ($true = (sK0 @ sK5)) | ($false = (~ (sK2 @ sK5))) | ($true = (sK2 @ sK5))),
% 0.99/0.90 inference(duplicate_literal_removal,[status(thm)],[f21])).
% 0.99/0.90 thf(f21,plain,(
% 0.99/0.90 ($true = (sK0 @ sK5)) | ($false = (~ (sK2 @ sK5))) | ($true = (sK0 @ sK5)) | ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5))),
% 0.99/0.90 inference(not_proxy_clausification,[status(thm)],[f20])).
% 0.99/0.90 thf(f20,plain,(
% 0.99/0.90 ($true = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ($false = (~ (sK0 @ sK5))) | ($true = (sK0 @ sK5)) | ($false = (~ (sK2 @ sK5)))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 0.99/0.90 thf(f19,plain,(
% 0.99/0.90 ($true = ((sK0 @ sK5) | (sK2 @ sK5))) | ($false = (~ (sK0 @ sK5))) | ($false = (sK1 @ sK5)) | ($false = (~ (sK2 @ sK5)))),
% 0.99/0.90 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 0.99/0.90 thf(f18,plain,(
% 0.99/0.90 ($false = (~ (sK0 @ sK5))) | ($false = (sK1 @ sK5)) | ($true = ((sK0 @ sK5) | (sK2 @ sK5))) | ($false = (sK1 @ sK5)) | ($false = (~ (sK2 @ sK5)))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 0.99/0.90 thf(f17,plain,(
% 0.99/0.90 ($false = (sK1 @ sK5)) | ($false = ((sK1 @ sK5) & (~ (sK2 @ sK5)))) | ($false = (~ (sK0 @ sK5))) | ($true = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 0.99/0.90 thf(f16,plain,(
% 0.99/0.90 ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) & (~ (sK0 @ sK5)))) | ($false = (sK1 @ sK5)) | ($true = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 0.99/0.90 inference(not_proxy_clausification,[status(thm)],[f15])).
% 0.99/0.90 thf(f15,plain,(
% 0.99/0.90 ($false = (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) & (~ (sK0 @ sK5)))) | ($false = (sK1 @ sK5))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 0.99/0.90 thf(f14,plain,(
% 0.99/0.90 ($false = ((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5))))) | ($false = (((sK1 @ sK5) & (~ (sK2 @ sK5))) & (~ (sK0 @ sK5))))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 0.99/0.90 thf(f12,plain,(
% 0.99/0.90 (((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) != (((sK1 @ sK5) & (~ (sK2 @ sK5))) & (~ (sK0 @ sK5))))),
% 0.99/0.90 inference(beta_eta_normalization,[status(thm)],[f11])).
% 0.99/0.90 thf(f11,plain,(
% 0.99/0.90 (((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK2 @ Y0))) & (~ (sK0 @ Y0)))) @ sK5) != ((^[Y0 : a]: ((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0))))) @ sK5))),
% 0.99/0.90 inference(negative_extensionality,[status(thm)],[f10])).
% 0.99/0.90 thf(f10,plain,(
% 0.99/0.90 ((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK2 @ Y0))) & (~ (sK0 @ Y0)))) != (^[Y0 : a]: ((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0))))))),
% 0.99/0.90 inference(boolean_simplification,[status(thm)],[f9])).
% 0.99/0.90 thf(f9,plain,(
% 0.99/0.90 ((^[Y0 : a]: ((((sK1 @ Y0) & (sK1 @ Y0)) & (~ (sK2 @ Y0))) & (~ (sK0 @ Y0)))) != (^[Y0 : a]: ((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0))))))),
% 0.99/0.90 inference(cnf_transformation,[status(thm)],[f8])).
% 0.99/0.90 thf(f8,plain,(
% 0.99/0.90 ((^[Y0 : a]: ((((sK1 @ Y0) & (sK1 @ Y0)) & (~ (sK2 @ Y0))) & (~ (sK0 @ Y0)))) != (^[Y0 : a]: ((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0))))))),
% 0.99/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 0.99/0.90 thf(f7,plain,(
% 0.99/0.90 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X1 @ Y0) & (X1 @ Y0)) & (~ (X2 @ Y0))) & (~ (X0 @ Y0)))) != (^[Y0 : a]: ((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0)))))) => ((^[Y0 : a]: ((((sK1 @ Y0) & (sK1 @ Y0)) & (~ (sK2 @ Y0))) & (~ (sK0 @ Y0)))) != (^[Y0 : a]: ((sK1 @ Y0) & (~ ((sK0 @ Y0) | (sK2 @ Y0))))))),
% 0.99/0.90 introduced(definition,[],[choice_axiom])).
% 0.99/0.90 thf(f6,plain,(
% 0.99/0.90 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X1 @ Y0) & (X1 @ Y0)) & (~ (X2 @ Y0))) & (~ (X0 @ Y0)))) != (^[Y0 : a]: ((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0))))))),
% 0.99/0.90 inference(ennf_transformation,[status(thm)],[f5])).
% 0.99/0.90 thf(f5,plain,(
% 0.99/0.90 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X1 @ Y0) & (X1 @ Y0)) & (~ (X2 @ Y0))) & (~ (X0 @ Y0)))) = (^[Y0 : a]: ((X1 @ Y0) & (~ ((X0 @ Y0) | (X2 @ Y0))))))),
% 0.99/0.90 inference(fool_elimination,[status(thm)],[f4])).
% 0.99/0.90 thf(f4,plain,(
% 0.99/0.90 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (~((X2 @ X3) | (X0 @ X3)) & (X1 @ X3))) = (^[X4 : a] : (~(X0 @ X4) & ~(X2 @ X4) & (X1 @ X4) & (X1 @ X4))))),
% 0.99/0.90 inference(rectify,[status(thm)],[f2])).
% 0.99/0.90 thf(f2,negated_conjecture,(
% 0.99/0.90 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((^[X3 : a] : (~((X2 @ X3) | (X1 @ X3)) & (X0 @ X3))) = (^[X3 : a] : (~(X1 @ X3) & ~(X2 @ X3) & (X0 @ X3) & (X0 @ X3))))),
% 0.99/0.90 inference(negated_conjecture,[status(cth)],[f1])).
% 0.99/0.90 thf(f1,conjecture,(
% 0.99/0.90 ! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((^[X3 : a] : (~((X2 @ X3) | (X1 @ X3)) & (X0 @ X3))) = (^[X3 : a] : (~(X1 @ X3) & ~(X2 @ X3) & (X0 @ X3) & (X0 @ X3))))),
% 0.99/0.90 file('/export/starexec/sandbox2/tmp/tmp.fIbdRCrrtI/DTF2THF_32645.p',cBOOL_PROP_85_pme)).
% 0.99/0.90 thf(f71,plain,(
% 0.99/0.90 spl3_3),
% 0.99/0.90 inference(avatar_split_clause,[status(thm)],[f31,f63])).
% 0.99/0.90 thf(f31,plain,(
% 0.99/0.90 ($true = (sK1 @ sK5))),
% 0.99/0.90 inference(duplicate_literal_removal,[status(thm)],[f30])).
% 0.99/0.90 thf(f30,plain,(
% 0.99/0.90 ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK5))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 0.99/0.90 thf(f28,plain,(
% 0.99/0.90 ($true = (sK1 @ sK5)) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true)),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 0.99/0.90 thf(f26,plain,(
% 0.99/0.90 ((((sK1 @ sK5) & (~ (sK2 @ sK5))) & (~ (sK0 @ sK5))) = $true) | ($true = (sK1 @ sK5))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 0.99/0.90 thf(f13,plain,(
% 0.99/0.90 (((sK1 @ sK5) & (~ ((sK0 @ sK5) | (sK2 @ sK5)))) = $true) | ((((sK1 @ sK5) & (~ (sK2 @ sK5))) & (~ (sK0 @ sK5))) = $true)),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 0.99/0.90 thf(f61,plain,(
% 0.99/0.90 spl3_1),
% 0.99/0.90 inference(avatar_split_clause,[status(thm)],[f45,f52])).
% 0.99/0.90 thf(f45,plain,(
% 0.99/0.90 ($false = (sK2 @ sK5))),
% 0.99/0.90 inference(duplicate_literal_removal,[status(thm)],[f44])).
% 0.99/0.90 thf(f44,plain,(
% 0.99/0.90 ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5))),
% 0.99/0.90 inference(not_proxy_clausification,[status(thm)],[f42])).
% 0.99/0.90 thf(f42,plain,(
% 0.99/0.90 ((~ (sK2 @ sK5)) = $true) | ($false = (sK2 @ sK5))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 0.99/0.90 thf(f37,plain,(
% 0.99/0.90 ($false = (sK2 @ sK5)) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true)),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 0.99/0.90 thf(f36,plain,(
% 0.99/0.90 ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true)),
% 0.99/0.90 inference(not_proxy_clausification,[status(thm)],[f35])).
% 0.99/0.90 thf(f35,plain,(
% 0.99/0.90 ($true = (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | (((sK1 @ sK5) & (~ (sK2 @ sK5))) = $true)),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 0.99/0.90 thf(f25,plain,(
% 0.99/0.90 ((((sK1 @ sK5) & (~ (sK2 @ sK5))) & (~ (sK0 @ sK5))) = $true) | ($true = (~ ((sK0 @ sK5) | (sK2 @ sK5))))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 0.99/0.90 thf(f60,plain,(
% 0.99/0.90 spl3_2),
% 0.99/0.90 inference(avatar_split_clause,[status(thm)],[f50,f56])).
% 0.99/0.90 thf(f50,plain,(
% 0.99/0.90 ($false = (sK0 @ sK5))),
% 0.99/0.90 inference(duplicate_literal_removal,[status(thm)],[f49])).
% 0.99/0.90 thf(f49,plain,(
% 0.99/0.90 ($false = (sK0 @ sK5)) | ($false = (sK0 @ sK5))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 0.99/0.90 thf(f47,plain,(
% 0.99/0.90 ($false = (sK0 @ sK5)) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 0.99/0.90 inference(not_proxy_clausification,[status(thm)],[f46])).
% 0.99/0.90 thf(f46,plain,(
% 0.99/0.90 ($true = (~ (sK0 @ sK5))) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 0.99/0.90 inference(not_proxy_clausification,[status(thm)],[f34])).
% 0.99/0.90 thf(f34,plain,(
% 0.99/0.90 ($true = (~ ((sK0 @ sK5) | (sK2 @ sK5)))) | ($true = (~ (sK0 @ sK5)))),
% 0.99/0.90 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 0.99/0.90 % SZS output end Proof for DTF2THF_32645
% 0.99/0.90 % (375)------------------------------
% 0.99/0.90 % (375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.99/0.90 % (375)Termination reason: Refutation
% 0.99/0.90
% 0.99/0.90 % (375)Memory used [KB]: 5500
% 0.99/0.90 % (375)Time elapsed: 0.003 s
% 0.99/0.90 % (375)Instructions burned: 2 (million)
% 0.99/0.90 % (375)------------------------------
% 0.99/0.90 % (375)------------------------------
% 0.99/0.90 % (372)Success in time 0.011 s
%------------------------------------------------------------------------------