%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET609^5 : 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 : n010.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 09:31:54 AM UTC 2026
% Result : Theorem 1.65s 1.32s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 450 ( 117 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 527 ( 111 ~; 98 |; 84 &; 227 @)
% ( 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 : 38 ( 20 ^; 12 !; 6 ?; 38 :)
% 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(f119,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f91,f105,f106,f108,f111,f115,f118]) ).
thf(f118,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f117]) ).
thf(f117,plain,
( $false
| ~ spl3_1
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_6 ),
inference(backward_demodulation,[status(thm)],[f76,f103]) ).
thf(f103,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl3_6
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f76,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f74,definition,
( spl3_1
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f115,plain,
( ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f114]) ).
thf(f114,plain,
( $false
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $true = $false )
| ~ spl3_3
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f85,f99]) ).
thf(f99,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f97]) ).
thf(f97,definition,
( spl3_5
<=> ( ( sK1 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f85,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl3_3
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[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,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f95,f80]) ).
thf(f80,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl3_2
<=> ( ( sK0 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f95,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl3_4
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f108,plain,
spl3_1,
inference(avatar_split_clause,[status(thm)],[f72,f74]) ).
thf(f72,plain,
( $true
= ( sK2 @ sK5 ) ),
inference(duplicate_literal_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 ) )
= $true )
| ( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ 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] :
( ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ~ ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ~ ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ 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 )
& ( X0 @ Y0 ) )
& ( X2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ~ ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ 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] :
( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ 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 )
& ( X0 @ Y0 ) )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ 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 )
& ( X1 @ X3 ) )
| ( ( X2 @ X3 )
& ~ ( X0 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( X2 @ X4 )
& ~ ( ( X0 @ X4 )
& ~ ( X1 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ( X2 @ X4 ) )
| ( ( X0 @ X4 )
& ~ ( X1 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ( X2 @ X4 ) )
| ( ( X0 @ X4 )
& ~ ( X1 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6yFZodBfZ7/DTF2THF_3603.p',cBOOL_PROP_81_pme) ).
thf(f106,plain,
( spl3_6
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f27,f93,f101]) ).
thf(f27,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK2 @ sK5 ) )
= $false )
| ( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f105,plain,
( spl3_6
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f34,f97,f101]) ).
thf(f34,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f91,plain,
( spl3_3
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f47,f78,f83]) ).
thf(f47,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true
= ( ~ ( sK0 @ sK5 ) ) )
| ( $true
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET609^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n010.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:59:33 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SET609^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : TPS problem BOOL-PROP-81
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : Trybulec's 81st Boolean property of sets
% 0.30/0.46
% 0.30/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0310 [Bro09]
% 0.30/0.46 % : BOOL-PROP-81 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.46 % Number of connectives : 15 ( 3 ~; 1 |; 4 &; 7 @)
% 0.30/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % : Polymorphic definitions expanded.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(cBOOL_PROP_81_pme,conjecture,
% 0.30/0.46 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.30/0.46 ( ( ^ [Xx: a] :
% 0.30/0.46 ( ( X @ Xx )
% 0.30/0.46 & ~ ( ( Y @ Xx )
% 0.30/0.46 & ~ ( Z @ Xx ) ) ) )
% 0.30/0.46 = ( ^ [Xz: a] :
% 0.30/0.46 ( ( ( X @ Xz )
% 0.30/0.46 & ~ ( Y @ Xz ) )
% 0.30/0.46 | ( ( X @ Xz )
% 0.30/0.46 & ( Z @ Xz ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.44/1.29 ---- Embedded in THF ---
% 1.44/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.29 %%% Generated on Tue Feb 24 11:59:34 EST 2026
% 1.44/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.29 %%% Logic specification used:
% 1.44/1.29 %%% thf(spec, logic, $$dhol).
% 1.44/1.29
% 1.44/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6yFZodBfZ7/DTF2DTF3603.p
% See solution above
% 1.44/1.29 ------------------------
% 1.65/1.30 ---- Cleaned THF ---
% 1.65/1.30 thf(a_type,type,
% 1.65/1.30 a: $tType ).
% 1.65/1.30
% 1.65/1.30 thf(cBOOL_PROP_81_pme,conjecture,
% 1.65/1.30 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.65/1.30 ( ( ^ [Xx: a] :
% 1.65/1.30 ( ( X @ Xx )
% 1.65/1.30 & ~ ( ( Y @ Xx )
% 1.65/1.30 & ~ ( Z @ Xx ) ) ) )
% 1.65/1.30 = ( ^ [Xz: a] :
% 1.65/1.30 ( ( ( X @ Xz )
% 1.65/1.30 & ~ ( Y @ Xz ) )
% 1.65/1.30 | ( ( X @ Xz )
% 1.65/1.30 & ( Z @ Xz ) ) ) ) ) ).
% 1.65/1.30 ------------------------
% 1.65/1.32 % (3715)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_3603 for (2999ds/2Mi)
% 1.65/1.32 % (3713)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_3603 for (2999ds/27Mi)
% 1.65/1.32 % (3715)Instruction limit reached!
% 1.65/1.32 % (3715)------------------------------
% 1.65/1.32 % (3715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (3715)Termination reason: Unknown
% 1.65/1.32 % (3715)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (3715)Memory used [KB]: 5500
% 1.65/1.32 % (3715)Time elapsed: 0.002 s
% 1.65/1.32 % (3715)Instructions burned: 2 (million)
% 1.65/1.32 % (3715)------------------------------
% 1.65/1.32 % (3715)------------------------------
% 1.65/1.32 % (3713)First to succeed.
% 1.65/1.32 % (3713)Refutation found. Thanks to Tanya!
% 1.65/1.32 % SZS status Theorem for DTF2THF_3603
% 1.65/1.32 % SZS output start Proof for DTF2THF_3603
% 1.65/1.32 thf(type_def_5, type, a: $tType).
% 1.65/1.32 thf(func_def_0, type, a: $tType).
% 1.65/1.32 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.65/1.32 thf(func_def_10, type, sK0: a > $o).
% 1.65/1.32 thf(func_def_11, type, sK1: a > $o).
% 1.65/1.32 thf(func_def_12, type, sK2: a > $o).
% 1.65/1.32 thf(func_def_14, type, ph4: !>[X0: $tType]:(X0)).
% 1.65/1.32 thf(func_def_15, type, sK5: a).
% 1.65/1.32 thf(f119,plain,(
% 1.65/1.32 $false),
% 1.65/1.32 inference(avatar_sat_refutation,[status(thm)],[f91,f105,f106,f108,f111,f115,f118])).
% 1.65/1.32 thf(f118,plain,(
% 1.65/1.32 ~spl3_1 | ~spl3_6),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f117])).
% 1.65/1.32 thf(f117,plain,(
% 1.65/1.32 $false | (~spl3_1 | ~spl3_6)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.65/1.32 thf(f116,plain,(
% 1.65/1.32 ($true = $false) | (~spl3_1 | ~spl3_6)),
% 1.65/1.32 inference(backward_demodulation,[status(thm)],[f76,f103])).
% 1.65/1.32 thf(f103,plain,(
% 1.65/1.32 ($false = (sK2 @ sK5)) | ~spl3_6),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.65/1.32 thf(f101,definition,(
% 1.65/1.32 spl3_6 <=> ($false = (sK2 @ sK5))),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.65/1.32 thf(f76,plain,(
% 1.65/1.32 ($true = (sK2 @ sK5)) | ~spl3_1),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.65/1.32 thf(f74,definition,(
% 1.65/1.32 spl3_1 <=> ($true = (sK2 @ sK5))),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.65/1.32 thf(f115,plain,(
% 1.65/1.32 ~spl3_3 | ~spl3_5),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f114])).
% 1.65/1.32 thf(f114,plain,(
% 1.65/1.32 $false | (~spl3_3 | ~spl3_5)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.65/1.32 thf(f113,plain,(
% 1.65/1.32 ($true = $false) | (~spl3_3 | ~spl3_5)),
% 1.65/1.32 inference(forward_demodulation,[status(thm)],[f85,f99])).
% 1.65/1.32 thf(f99,plain,(
% 1.65/1.32 ((sK1 @ sK5) = $false) | ~spl3_5),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f97])).
% 1.65/1.32 thf(f97,definition,(
% 1.65/1.32 spl3_5 <=> ((sK1 @ sK5) = $false)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.65/1.32 thf(f85,plain,(
% 1.65/1.32 ((sK1 @ sK5) = $true) | ~spl3_3),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.65/1.32 thf(f83,definition,(
% 1.65/1.32 spl3_3 <=> ((sK1 @ sK5) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.65/1.32 thf(f111,plain,(
% 1.65/1.32 ~spl3_2 | ~spl3_4),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.65/1.32 thf(f110,plain,(
% 1.65/1.32 $false | (~spl3_2 | ~spl3_4)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.65/1.32 thf(f109,plain,(
% 1.65/1.32 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 1.65/1.32 inference(backward_demodulation,[status(thm)],[f95,f80])).
% 1.65/1.32 thf(f80,plain,(
% 1.65/1.32 ((sK0 @ sK5) = $false) | ~spl3_2),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.65/1.32 thf(f78,definition,(
% 1.65/1.32 spl3_2 <=> ((sK0 @ sK5) = $false)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.65/1.32 thf(f95,plain,(
% 1.65/1.32 ((sK0 @ sK5) = $true) | ~spl3_4),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.65/1.32 thf(f93,definition,(
% 1.65/1.32 spl3_4 <=> ((sK0 @ sK5) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.65/1.32 thf(f108,plain,(
% 1.65/1.32 spl3_1),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f72,f74])).
% 1.65/1.32 thf(f72,plain,(
% 1.65/1.32 ($true = (sK2 @ sK5))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f69])).
% 1.65/1.32 thf(f69,plain,(
% 1.65/1.32 ($true = (sK2 @ sK5)) | ($true = (sK2 @ sK5))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.65/1.32 thf(f68,plain,(
% 1.65/1.32 (((~ (sK0 @ sK5)) & (sK2 @ sK5)) = $true) | ($true = (sK2 @ sK5))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f62])).
% 1.65/1.32 thf(f62,plain,(
% 1.65/1.32 (((~ (sK0 @ sK5)) & (sK2 @ sK5)) = $true) | ($true = (sK2 @ sK5)) | ($true = (sK2 @ sK5))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.65/1.32 thf(f61,plain,(
% 1.65/1.32 (((sK1 @ sK5) & (sK2 @ sK5)) = $true) | ($true = (sK2 @ sK5)) | (((~ (sK0 @ sK5)) & (sK2 @ sK5)) = $true)),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.65/1.32 thf(f35,plain,(
% 1.65/1.32 ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (sK2 @ sK5))) = $true) | ($true = (sK2 @ sK5))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.65/1.32 thf(f12,plain,(
% 1.65/1.32 (((~ ((~ (sK1 @ sK5)) & (sK0 @ sK5))) & (sK2 @ sK5)) = $true) | ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (sK2 @ sK5))) = $true)),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.65/1.32 thf(f11,plain,(
% 1.65/1.32 ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (sK2 @ sK5))) != ((~ ((~ (sK1 @ sK5)) & (sK0 @ sK5))) & (sK2 @ sK5)))),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.65/1.32 thf(f10,plain,(
% 1.65/1.32 (((^[Y0 : a]: ((~ ((~ (sK1 @ Y0)) & (sK0 @ Y0))) & (sK2 @ Y0))) @ sK5) != ((^[Y0 : a]: (((~ (sK0 @ Y0)) & (sK2 @ Y0)) | ((sK1 @ Y0) & (sK2 @ Y0)))) @ sK5))),
% 1.65/1.32 inference(negative_extensionality,[status(thm)],[f9])).
% 1.65/1.32 thf(f9,plain,(
% 1.65/1.32 ((^[Y0 : a]: ((~ ((~ (sK1 @ Y0)) & (sK0 @ Y0))) & (sK2 @ Y0))) != (^[Y0 : a]: (((~ (sK0 @ Y0)) & (sK2 @ Y0)) | ((sK1 @ Y0) & (sK2 @ Y0)))))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f8])).
% 1.65/1.32 thf(f8,plain,(
% 1.65/1.32 ((^[Y0 : a]: ((~ ((~ (sK1 @ Y0)) & (sK0 @ Y0))) & (sK2 @ Y0))) != (^[Y0 : a]: (((~ (sK0 @ Y0)) & (sK2 @ Y0)) | ((sK1 @ Y0) & (sK2 @ Y0)))))),
% 1.65/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.65/1.32 thf(f7,plain,(
% 1.65/1.32 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((~ ((~ (X1 @ Y0)) & (X0 @ Y0))) & (X2 @ Y0))) != (^[Y0 : a]: (((~ (X0 @ Y0)) & (X2 @ Y0)) | ((X1 @ Y0) & (X2 @ Y0))))) => ((^[Y0 : a]: ((~ ((~ (sK1 @ Y0)) & (sK0 @ Y0))) & (sK2 @ Y0))) != (^[Y0 : a]: (((~ (sK0 @ Y0)) & (sK2 @ Y0)) | ((sK1 @ Y0) & (sK2 @ Y0)))))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f6,plain,(
% 1.65/1.32 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((~ ((~ (X1 @ Y0)) & (X0 @ Y0))) & (X2 @ Y0))) != (^[Y0 : a]: (((~ (X0 @ Y0)) & (X2 @ Y0)) | ((X1 @ Y0) & (X2 @ Y0)))))),
% 1.65/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.32 thf(f5,plain,(
% 1.65/1.32 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((~ ((~ (X1 @ Y0)) & (X0 @ Y0))) & (X2 @ Y0))) = (^[Y0 : a]: (((~ (X0 @ Y0)) & (X2 @ Y0)) | ((X1 @ Y0) & (X2 @ Y0)))))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.32 thf(f4,plain,(
% 1.65/1.32 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((X2 @ X3) & (X1 @ X3)) | ((X2 @ X3) & ~(X0 @ X3)))) = (^[X4 : a] : ((X2 @ X4) & ~((X0 @ X4) & ~(X1 @ X4)))))),
% 1.65/1.32 inference(rectify,[status(thm)],[f2])).
% 1.65/1.32 thf(f2,negated_conjecture,(
% 1.65/1.32 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((^[X4 : a] : (((X0 @ X4) & (X2 @ X4)) | ((X0 @ X4) & ~(X1 @ X4)))) = (^[X3 : a] : ((X0 @ X3) & ~((X1 @ X3) & ~(X2 @ X3)))))),
% 1.65/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.32 thf(f1,conjecture,(
% 1.65/1.32 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((^[X4 : a] : (((X0 @ X4) & (X2 @ X4)) | ((X0 @ X4) & ~(X1 @ X4)))) = (^[X3 : a] : ((X0 @ X3) & ~((X1 @ X3) & ~(X2 @ X3)))))),
% 1.65/1.32 file('/export/starexec/sandbox/tmp/tmp.6yFZodBfZ7/DTF2THF_3603.p',cBOOL_PROP_81_pme)).
% 1.65/1.32 thf(f106,plain,(
% 1.65/1.32 spl3_6 | spl3_4),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f27,f93,f101])).
% 1.65/1.32 thf(f27,plain,(
% 1.65/1.32 ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.65/1.32 thf(f26,plain,(
% 1.65/1.32 ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.65/1.32 inference(not_proxy_clausification,[status(thm)],[f25])).
% 1.65/1.32 thf(f25,plain,(
% 1.65/1.32 ($false = (sK2 @ sK5)) | ((~ (sK0 @ sK5)) = $false) | ((sK0 @ sK5) = $true)),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.65/1.32 thf(f24,plain,(
% 1.65/1.32 ((~ (sK0 @ sK5)) = $false) | ($false = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($false = (sK2 @ sK5))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.65/1.32 thf(f18,plain,(
% 1.65/1.32 ((sK0 @ sK5) = $true) | (((~ (sK0 @ sK5)) & (sK2 @ sK5)) = $false) | ($false = (sK2 @ sK5))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.65/1.32 thf(f17,plain,(
% 1.65/1.32 ($false = (sK2 @ sK5)) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | (((~ (sK0 @ sK5)) & (sK2 @ sK5)) = $false)),
% 1.65/1.32 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.65/1.32 thf(f16,plain,(
% 1.65/1.32 ($false = (sK2 @ sK5)) | ($false = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5)))) | (((~ (sK0 @ sK5)) & (sK2 @ sK5)) = $false)),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.65/1.32 thf(f14,plain,(
% 1.65/1.32 ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (sK2 @ sK5))) = $false) | ($false = (sK2 @ sK5)) | ($false = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5))))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.65/1.32 thf(f13,plain,(
% 1.65/1.32 (((~ ((~ (sK1 @ sK5)) & (sK0 @ sK5))) & (sK2 @ sK5)) = $false) | ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (sK2 @ sK5))) = $false)),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.65/1.32 thf(f105,plain,(
% 1.65/1.32 spl3_6 | spl3_5),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f34,f97,f101])).
% 1.65/1.32 thf(f34,plain,(
% 1.65/1.32 ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false)),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f33])).
% 1.65/1.32 thf(f33,plain,(
% 1.65/1.32 ((sK1 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5))),
% 1.65/1.32 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.65/1.32 thf(f32,plain,(
% 1.65/1.32 ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($true = (~ (sK1 @ sK5)))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.65/1.32 thf(f30,plain,(
% 1.65/1.32 ($false = (sK2 @ sK5)) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | ((sK1 @ sK5) = $false)),
% 1.65/1.32 inference(not_proxy_clausification,[status(thm)],[f29])).
% 1.65/1.32 thf(f29,plain,(
% 1.65/1.32 ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($false = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5))))),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f28])).
% 1.65/1.32 thf(f28,plain,(
% 1.65/1.32 ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($false = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5)))) | ($false = (sK2 @ sK5))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.65/1.32 thf(f15,plain,(
% 1.65/1.32 (((sK1 @ sK5) & (sK2 @ sK5)) = $false) | ($false = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5)))) | ($false = (sK2 @ sK5))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.65/1.32 thf(f91,plain,(
% 1.65/1.32 spl3_3 | spl3_2),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f47,f78,f83])).
% 1.65/1.32 thf(f47,plain,(
% 1.65/1.32 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $false)),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f46])).
% 1.65/1.32 thf(f46,plain,(
% 1.65/1.32 ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.65/1.32 inference(not_proxy_clausification,[status(thm)],[f45])).
% 1.65/1.32 thf(f45,plain,(
% 1.65/1.32 ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $true)),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f44])).
% 1.65/1.32 thf(f44,plain,(
% 1.65/1.32 ((sK1 @ sK5) = $true) | ($false = (~ (sK1 @ sK5))) | ((sK0 @ sK5) = $false) | ((sK0 @ sK5) = $false)),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.65/1.32 thf(f43,plain,(
% 1.65/1.32 ((sK0 @ sK5) = $false) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false) | ((sK1 @ sK5) = $true)),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.65/1.32 thf(f41,plain,(
% 1.65/1.32 (((sK1 @ sK5) & (sK2 @ sK5)) = $true) | ((sK0 @ sK5) = $false) | (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $false)),
% 1.65/1.32 inference(not_proxy_clausification,[status(thm)],[f40])).
% 1.65/1.32 thf(f40,plain,(
% 1.65/1.32 ((sK0 @ sK5) = $false) | ($true = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5)))) | (((sK1 @ sK5) & (sK2 @ sK5)) = $true)),
% 1.65/1.32 inference(not_proxy_clausification,[status(thm)],[f39])).
% 1.65/1.32 thf(f39,plain,(
% 1.65/1.32 ($true = (~ (sK0 @ sK5))) | ($true = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5)))) | (((sK1 @ sK5) & (sK2 @ sK5)) = $true)),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.65/1.32 thf(f37,plain,(
% 1.65/1.32 (((~ (sK0 @ sK5)) & (sK2 @ sK5)) = $true) | ($true = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5)))) | (((sK1 @ sK5) & (sK2 @ sK5)) = $true)),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.65/1.32 thf(f36,plain,(
% 1.65/1.32 ((((~ (sK0 @ sK5)) & (sK2 @ sK5)) | ((sK1 @ sK5) & (sK2 @ sK5))) = $true) | ($true = (~ ((~ (sK1 @ sK5)) & (sK0 @ sK5))))),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.65/1.32 % SZS output end Proof for DTF2THF_3603
% 1.65/1.32 % (3713)------------------------------
% 1.65/1.32 % (3713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (3713)Termination reason: Refutation
% 1.65/1.32
% 1.65/1.32 % (3713)Memory used [KB]: 5500
% 1.65/1.32 % (3713)Time elapsed: 0.004 s
% 1.65/1.32 % (3713)Instructions burned: 4 (million)
% 1.65/1.32 % (3713)------------------------------
% 1.65/1.32 % (3713)------------------------------
% 1.65/1.32 % (3710)Success in time 0.012 s
%------------------------------------------------------------------------------