%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU851^5 : 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 : n026.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 09:37:35 AM UTC 2026
% Result : Theorem 1.38s 1.30s
% Output : Refutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 467 ( 118 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 608 ( 133 ~; 117 |; 94 &; 259 @)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 20 ^; 8 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_12,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK4: a ).
thf(f122,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f96,f108,f112,f113,f117,f120]) ).
thf(f120,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f119]) ).
thf(f119,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_demodulation,[status(thm)],[f86,f94]) ).
thf(f94,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl2_3
<=> ( $false
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f86,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl2_1
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f117,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f116]) ).
thf(f116,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[status(thm)],[f100,f90]) ).
thf(f90,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f88,definition,
( spl2_2
<=> ( ( sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f100,plain,
( ( ( sK1 @ sK4 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f98]) ).
thf(f98,definition,
( spl2_4
<=> ( ( sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f113,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f88,f84]) ).
thf(f25,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK1 @ sK4 )
= $false )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $false
= ( ~ ( sK0 @ sK4 ) ) )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( ~ ( sK0 @ sK4 ) ) )
| ( ( sK1 @ sK4 )
= $false )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK1 @ sK4 )
= $false )
| ( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
| ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( ~ ( sK0 @ sK4 ) ) )
| ( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
| ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
| ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ) )
| ( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
| ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
| ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
!= ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK4 )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) )
= ( ^ [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
| ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
= ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
= ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rjNW2Hzxn8/DTF2THF_32590.p',cGAZING_THM42_pme) ).
thf(f112,plain,
( spl2_4
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f31,f92,f98]) ).
thf(f31,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $false
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $false
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $false )
| ( $false
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $false
= ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
| ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
| ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
= $false )
| ( $false
= ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f108,plain,
( spl2_4
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f50,f84,f98]) ).
thf(f50,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK0 @ sK4 )
= $true )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) )
= $true )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) )
= $true )
| ( ( sK0 @ sK4 )
= $true )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $true )
| ( ( sK0 @ sK4 )
= $true )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $true )
| ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $true )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
| ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
= $true )
| ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f96,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f82,f92,f88]) ).
thf(f82,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( ~ ( sK1 @ sK4 ) )
= $true )
| ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) )
= $true )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) )
= $true )
| ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $false
= ( sK0 @ sK4 ) )
| ( ( ~ ( sK0 @ sK4 ) )
= $true )
| ( ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $true )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( ~ ( sK0 @ sK4 ) )
= $true )
| ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ~ ( sK1 @ sK4 ) )
= $true )
| ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $true )
| ( ( ~ ( sK0 @ sK4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true
= ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) ) )
| ( ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
| ( ~ ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU851^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n026.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:35:55 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.38 ---- Original DTF file ---
% 0.19/0.38 thf(spec,logic,$$dhol).
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 % File : SEU851^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.38 % Domain : Set Theory
% 0.19/0.38 % Problem : TPS problem GAZING-THM42
% 0.19/0.38 % Version : Especial.
% 0.19/0.38 % English :
% 0.19/0.38
% 0.19/0.38 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.19/0.38 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.38 % Source : [Bro09]
% 0.19/0.38 % Names : tps_0390 [Bro09]
% 0.19/0.38 % : 42 [Bar92]
% 0.19/0.38 % : GAZING-THM42 [TPS]
% 0.19/0.38
% 0.19/0.38 % Status : Theorem
% 0.19/0.38 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.19/0.38 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.38 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.19/0.38 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.38 % Number of connectives : 18 ( 4 ~; 2 |; 4 &; 8 @)
% 0.19/0.38 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.38 % Maximal formula depth : 3 ( 3 avg)
% 0.19/0.38 % Number of types : 2 ( 1 usr)
% 0.19/0.38 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.38 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.38 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.19/0.38 % SPC : TH0_THM_EQU_NAR
% 0.19/0.38
% 0.19/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.38 % : Polymorphic definitions expanded.
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 thf(a_type,type,
% 0.19/0.38 a: $tType ).
% 0.19/0.38
% 0.19/0.38 thf(cGAZING_THM42_pme,conjecture,
% 0.19/0.38 ! [S: a > $o,T: a > $o] :
% 0.19/0.38 ( ( ^ [Xz: a] :
% 0.19/0.38 ( ( ( S @ Xz )
% 0.19/0.38 & ~ ( T @ Xz ) )
% 0.19/0.38 | ( ( T @ Xz )
% 0.19/0.38 & ~ ( S @ Xz ) ) ) )
% 0.19/0.38 = ( ^ [Xz: a] :
% 0.19/0.38 ( ( ( T @ Xz )
% 0.19/0.38 & ~ ( S @ Xz ) )
% 0.19/0.38 | ( ( S @ Xz )
% 0.19/0.38 & ~ ( T @ Xz ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 ------------------------
% 1.38/1.26 ---- Embedded in THF ---
% 1.38/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.26 %%% Generated on Tue Feb 24 12:35:56 EST 2026
% 1.38/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.26 %%% Logic specification used:
% 1.38/1.26 %%% thf(spec, logic, $$dhol).
% 1.38/1.26
% 1.38/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rjNW2Hzxn8/DTF2DTF32590.p
% See solution above
% 1.38/1.26 ------------------------
% 1.38/1.27 ---- Cleaned THF ---
% 1.38/1.27 thf(a_type,type,
% 1.38/1.27 a: $tType ).
% 1.38/1.27
% 1.38/1.27 thf(cGAZING_THM42_pme,conjecture,
% 1.38/1.27 ! [S: a > $o,T: a > $o] :
% 1.38/1.27 ( ( ^ [Xz: a] :
% 1.38/1.27 ( ( ( S @ Xz )
% 1.38/1.27 & ~ ( T @ Xz ) )
% 1.38/1.27 | ( ( T @ Xz )
% 1.38/1.27 & ~ ( S @ Xz ) ) ) )
% 1.38/1.27 = ( ^ [Xz: a] :
% 1.38/1.27 ( ( ( T @ Xz )
% 1.38/1.27 & ~ ( S @ Xz ) )
% 1.38/1.27 | ( ( S @ Xz )
% 1.38/1.27 & ~ ( T @ Xz ) ) ) ) ) ).
% 1.38/1.27 ------------------------
% 1.38/1.29 % (32693)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32590 for (3000ds/18Mi)
% 1.38/1.29 % (32687)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32590 for (3000ds/183Mi)
% 1.38/1.29 % (32689)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_32590 for (3000ds/27Mi)
% 1.38/1.29 % (32688)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_32590 for (3000ds/4Mi)
% 1.38/1.29 % (32691)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_32590 for (3000ds/2Mi)
% 1.38/1.29 % (32690)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32590 for (3000ds/2Mi)
% 1.38/1.29 % (32692)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_32590 for (3000ds/275Mi)
% 1.38/1.29 % (32690)Instruction limit reached!
% 1.38/1.29 % (32690)------------------------------
% 1.38/1.29 % (32690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.29 % (32690)Termination reason: Unknown
% 1.38/1.29 % (32691)Instruction limit reached!
% 1.38/1.29 % (32691)------------------------------
% 1.38/1.29 % (32691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.29 % (32690)Termination phase: Saturation
% 1.38/1.29
% 1.38/1.29 % (32690)Memory used [KB]: 5500
% 1.38/1.29 % (32690)Time elapsed: 0.003 s
% 1.38/1.29 % (32690)Instructions burned: 2 (million)
% 1.38/1.29 % (32690)------------------------------
% 1.38/1.29 % (32690)------------------------------
% 1.38/1.29 % (32691)Termination reason: Unknown
% 1.38/1.29 % (32691)Termination phase: Saturation
% 1.38/1.29
% 1.38/1.29 % (32691)Memory used [KB]: 5500
% 1.38/1.29 % (32691)Time elapsed: 0.003 s
% 1.38/1.29 % (32691)Instructions burned: 2 (million)
% 1.38/1.29 % (32691)------------------------------
% 1.38/1.29 % (32691)------------------------------
% 1.38/1.29 % (32688)Instruction limit reached!
% 1.38/1.29 % (32688)------------------------------
% 1.38/1.29 % (32688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.29 % (32688)Termination reason: Unknown
% 1.38/1.29 % (32688)Termination phase: Saturation
% 1.38/1.29
% 1.38/1.29 % (32688)Memory used [KB]: 5500
% 1.38/1.29 % (32688)Time elapsed: 0.004 s
% 1.38/1.29 % (32688)Instructions burned: 4 (million)
% 1.38/1.29 % (32688)------------------------------
% 1.38/1.29 % (32688)------------------------------
% 1.38/1.29 % (32692)First to succeed.
% 1.38/1.29 % (32693)Also succeeded, but the first one will report.
% 1.38/1.30 % (32692)Refutation found. Thanks to Tanya!
% 1.38/1.30 % SZS status Theorem for DTF2THF_32590
% 1.38/1.30 % SZS output start Proof for DTF2THF_32590
% 1.38/1.30 thf(type_def_5, type, a: $tType).
% 1.38/1.30 thf(func_def_0, type, a: $tType).
% 1.38/1.30 thf(func_def_9, type, sK0: a > $o).
% 1.38/1.30 thf(func_def_10, type, sK1: a > $o).
% 1.38/1.30 thf(func_def_12, type, ph3: !>[X0: $tType]:(X0)).
% 1.38/1.30 thf(func_def_13, type, sK4: a).
% 1.38/1.30 thf(f122,plain,(
% 1.38/1.30 $false),
% 1.38/1.30 inference(avatar_sat_refutation,[status(thm)],[f96,f108,f112,f113,f117,f120])).
% 1.38/1.30 thf(f120,plain,(
% 1.38/1.30 ~spl2_1 | ~spl2_3),
% 1.38/1.30 inference(avatar_contradiction_clause,[status(thm)],[f119])).
% 1.38/1.30 thf(f119,plain,(
% 1.38/1.30 $false | (~spl2_1 | ~spl2_3)),
% 1.38/1.30 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.38/1.30 thf(f118,plain,(
% 1.38/1.30 ($false = $true) | (~spl2_1 | ~spl2_3)),
% 1.38/1.30 inference(forward_demodulation,[status(thm)],[f86,f94])).
% 1.38/1.30 thf(f94,plain,(
% 1.38/1.30 ($false = (sK0 @ sK4)) | ~spl2_3),
% 1.38/1.30 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.38/1.30 thf(f92,definition,(
% 1.38/1.30 spl2_3 <=> ($false = (sK0 @ sK4))),
% 1.38/1.30 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.38/1.30 thf(f86,plain,(
% 1.38/1.30 ((sK0 @ sK4) = $true) | ~spl2_1),
% 1.38/1.30 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.38/1.30 thf(f84,definition,(
% 1.38/1.30 spl2_1 <=> ((sK0 @ sK4) = $true)),
% 1.38/1.30 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.38/1.30 thf(f117,plain,(
% 1.38/1.30 ~spl2_2 | ~spl2_4),
% 1.38/1.30 inference(avatar_contradiction_clause,[status(thm)],[f116])).
% 1.38/1.30 thf(f116,plain,(
% 1.38/1.30 $false | (~spl2_2 | ~spl2_4)),
% 1.38/1.30 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.38/1.30 thf(f115,plain,(
% 1.38/1.30 ($false = $true) | (~spl2_2 | ~spl2_4)),
% 1.38/1.30 inference(forward_demodulation,[status(thm)],[f100,f90])).
% 1.38/1.30 thf(f90,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ~spl2_2),
% 1.38/1.30 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.38/1.30 thf(f88,definition,(
% 1.38/1.30 spl2_2 <=> ((sK1 @ sK4) = $false)),
% 1.38/1.30 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.38/1.30 thf(f100,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $true) | ~spl2_4),
% 1.38/1.30 inference(avatar_component_clause,[status(thm)],[f98])).
% 1.38/1.30 thf(f98,definition,(
% 1.38/1.30 spl2_4 <=> ((sK1 @ sK4) = $true)),
% 1.38/1.30 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.38/1.30 thf(f113,plain,(
% 1.38/1.30 spl2_1 | spl2_2),
% 1.38/1.30 inference(avatar_split_clause,[status(thm)],[f25,f88,f84])).
% 1.38/1.30 thf(f25,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ((sK0 @ sK4) = $true)),
% 1.38/1.30 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.38/1.30 thf(f24,plain,(
% 1.38/1.30 ((sK0 @ sK4) = $true) | ((sK1 @ sK4) = $false) | ((sK0 @ sK4) = $true)),
% 1.38/1.30 inference(not_proxy_clausification,[status(thm)],[f23])).
% 1.38/1.30 thf(f23,plain,(
% 1.38/1.30 ((sK0 @ sK4) = $true) | ($false = (~ (sK0 @ sK4))) | ((sK1 @ sK4) = $false)),
% 1.38/1.30 inference(duplicate_literal_removal,[status(thm)],[f22])).
% 1.38/1.30 thf(f22,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ($false = (~ (sK0 @ sK4))) | ((sK1 @ sK4) = $false) | ((sK0 @ sK4) = $true)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.38/1.30 thf(f18,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ($false = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | ((sK0 @ sK4) = $true)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.38/1.30 thf(f17,plain,(
% 1.38/1.30 ((sK0 @ sK4) = $true) | ((sK1 @ sK4) = $false) | ((((sK0 @ sK4) & (~ (sK1 @ sK4))) | ((sK1 @ sK4) & (~ (sK0 @ sK4)))) = $false)),
% 1.38/1.30 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.38/1.30 thf(f16,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ($false = (~ (sK0 @ sK4))) | ((((sK0 @ sK4) & (~ (sK1 @ sK4))) | ((sK1 @ sK4) & (~ (sK0 @ sK4)))) = $false)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.38/1.30 thf(f15,plain,(
% 1.38/1.30 ($false = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | ((((sK0 @ sK4) & (~ (sK1 @ sK4))) | ((sK1 @ sK4) & (~ (sK0 @ sK4)))) = $false)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.38/1.30 thf(f13,plain,(
% 1.38/1.30 ($false = (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4)))) | ((((sK0 @ sK4) & (~ (sK1 @ sK4))) | ((sK1 @ sK4) & (~ (sK0 @ sK4)))) = $false)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.38/1.30 thf(f11,plain,(
% 1.38/1.30 ((((sK0 @ sK4) & (~ (sK1 @ sK4))) | ((sK1 @ sK4) & (~ (sK0 @ sK4)))) != (((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4))))),
% 1.38/1.30 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.38/1.30 thf(f10,plain,(
% 1.38/1.30 (((^[Y0 : a]: (((sK0 @ Y0) & (~ (sK1 @ Y0))) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) @ sK4) != ((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((~ (sK1 @ Y0)) & (sK0 @ Y0)))) @ sK4))),
% 1.38/1.30 inference(negative_extensionality,[status(thm)],[f9])).
% 1.38/1.30 thf(f9,plain,(
% 1.38/1.30 ((^[Y0 : a]: (((sK0 @ Y0) & (~ (sK1 @ Y0))) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((~ (sK1 @ Y0)) & (sK0 @ Y0)))))),
% 1.38/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.38/1.30 thf(f8,plain,(
% 1.38/1.30 ((^[Y0 : a]: (((sK0 @ Y0) & (~ (sK1 @ Y0))) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((~ (sK1 @ Y0)) & (sK0 @ Y0)))))),
% 1.38/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.38/1.30 thf(f7,plain,(
% 1.38/1.30 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((~ (X1 @ Y0)) & (X0 @ Y0)))) != (^[Y0 : a]: (((X0 @ Y0) & (~ (X1 @ Y0))) | ((X1 @ Y0) & (~ (X0 @ Y0)))))) => ((^[Y0 : a]: (((sK0 @ Y0) & (~ (sK1 @ Y0))) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((~ (sK1 @ Y0)) & (sK0 @ Y0)))))),
% 1.38/1.30 introduced(definition,[],[choice_axiom])).
% 1.38/1.30 thf(f6,plain,(
% 1.38/1.30 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((~ (X1 @ Y0)) & (X0 @ Y0)))) != (^[Y0 : a]: (((X0 @ Y0) & (~ (X1 @ Y0))) | ((X1 @ Y0) & (~ (X0 @ Y0))))))),
% 1.38/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.38/1.30 thf(f5,plain,(
% 1.38/1.30 ~! [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((~ (X1 @ Y0)) & (X0 @ Y0)))) = (^[Y0 : a]: (((X0 @ Y0) & (~ (X1 @ Y0))) | ((X1 @ Y0) & (~ (X0 @ Y0))))))),
% 1.38/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.38/1.30 thf(f4,plain,(
% 1.38/1.30 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((~(X0 @ X2) & (X1 @ X2)) | (~(X1 @ X2) & (X0 @ X2)))) = (^[X3 : a] : (((X0 @ X3) & ~(X1 @ X3)) | (~(X0 @ X3) & (X1 @ X3)))))),
% 1.38/1.30 inference(rectify,[status(thm)],[f2])).
% 1.38/1.30 thf(f2,negated_conjecture,(
% 1.38/1.30 ~! [X1 : a > $o,X0 : a > $o] : ((^[X2 : a] : ((~(X1 @ X2) & (X0 @ X2)) | (~(X0 @ X2) & (X1 @ X2)))) = (^[X2 : a] : (((X1 @ X2) & ~(X0 @ X2)) | (~(X1 @ X2) & (X0 @ X2)))))),
% 1.38/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.38/1.30 thf(f1,conjecture,(
% 1.38/1.30 ! [X1 : a > $o,X0 : a > $o] : ((^[X2 : a] : ((~(X1 @ X2) & (X0 @ X2)) | (~(X0 @ X2) & (X1 @ X2)))) = (^[X2 : a] : (((X1 @ X2) & ~(X0 @ X2)) | (~(X1 @ X2) & (X0 @ X2)))))),
% 1.38/1.30 file('/export/starexec/sandbox/tmp/tmp.rjNW2Hzxn8/DTF2THF_32590.p',cGAZING_THM42_pme)).
% 1.38/1.30 thf(f112,plain,(
% 1.38/1.30 spl2_4 | spl2_3),
% 1.38/1.30 inference(avatar_split_clause,[status(thm)],[f31,f92,f98])).
% 1.38/1.30 thf(f31,plain,(
% 1.38/1.30 ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $true)),
% 1.38/1.30 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.38/1.30 thf(f30,plain,(
% 1.38/1.30 ($false = (~ (sK1 @ sK4))) | ($false = (sK0 @ sK4))),
% 1.38/1.30 inference(duplicate_literal_removal,[status(thm)],[f29])).
% 1.38/1.30 thf(f29,plain,(
% 1.38/1.30 ($false = (~ (sK1 @ sK4))) | ($false = (sK0 @ sK4)) | ($false = (sK0 @ sK4)) | ($false = (~ (sK1 @ sK4)))),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.38/1.30 thf(f28,plain,(
% 1.38/1.30 (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $false) | ($false = (~ (sK1 @ sK4))) | ($false = (sK0 @ sK4))),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.38/1.30 thf(f27,plain,(
% 1.38/1.30 ($false = ((~ (sK1 @ sK4)) & (sK0 @ sK4))) | (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $false)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.38/1.30 thf(f14,plain,(
% 1.38/1.30 ((((sK0 @ sK4) & (~ (sK1 @ sK4))) | ((sK1 @ sK4) & (~ (sK0 @ sK4)))) = $false) | ($false = ((~ (sK1 @ sK4)) & (sK0 @ sK4)))),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.38/1.30 thf(f108,plain,(
% 1.38/1.30 spl2_4 | spl2_1),
% 1.38/1.30 inference(avatar_split_clause,[status(thm)],[f50,f84,f98])).
% 1.38/1.30 thf(f50,plain,(
% 1.38/1.30 ((sK0 @ sK4) = $true) | ((sK1 @ sK4) = $true)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.38/1.30 thf(f48,plain,(
% 1.38/1.30 ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | ((sK0 @ sK4) = $true)),
% 1.38/1.30 inference(duplicate_literal_removal,[status(thm)],[f41])).
% 1.38/1.30 thf(f41,plain,(
% 1.38/1.30 ((sK0 @ sK4) = $true) | ((sK0 @ sK4) = $true) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4))))),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.38/1.30 thf(f40,plain,(
% 1.38/1.30 ((sK0 @ sK4) = $true) | (((~ (sK1 @ sK4)) & (sK0 @ sK4)) = $true) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4))))),
% 1.38/1.30 inference(duplicate_literal_removal,[status(thm)],[f39])).
% 1.38/1.30 thf(f39,plain,(
% 1.38/1.30 (((~ (sK1 @ sK4)) & (sK0 @ sK4)) = $true) | ((sK0 @ sK4) = $true) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4))))),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.38/1.30 thf(f38,plain,(
% 1.38/1.30 ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4))) = $true) | ((sK0 @ sK4) = $true) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4))))),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.38/1.30 thf(f36,plain,(
% 1.38/1.30 (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $true) | ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4))) = $true) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4))))),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.38/1.30 thf(f12,plain,(
% 1.38/1.30 ((((sK0 @ sK4) & (~ (sK1 @ sK4))) | ((sK1 @ sK4) & (~ (sK0 @ sK4)))) = $true) | ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4))) = $true)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.38/1.30 thf(f96,plain,(
% 1.38/1.30 spl2_2 | spl2_3),
% 1.38/1.30 inference(avatar_split_clause,[status(thm)],[f82,f92,f88])).
% 1.38/1.30 thf(f82,plain,(
% 1.38/1.30 ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $false)),
% 1.38/1.30 inference(duplicate_literal_removal,[status(thm)],[f81])).
% 1.38/1.30 thf(f81,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ((sK1 @ sK4) = $false) | ($false = (sK0 @ sK4))),
% 1.38/1.30 inference(not_proxy_clausification,[status(thm)],[f80])).
% 1.38/1.30 thf(f80,plain,(
% 1.38/1.30 ((~ (sK1 @ sK4)) = $true) | ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $false)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.38/1.30 thf(f78,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | (((~ (sK1 @ sK4)) & (sK0 @ sK4)) = $true) | ($false = (sK0 @ sK4))),
% 1.38/1.30 inference(duplicate_literal_removal,[status(thm)],[f77])).
% 1.38/1.30 thf(f77,plain,(
% 1.38/1.30 (((~ (sK1 @ sK4)) & (sK0 @ sK4)) = $true) | ((sK1 @ sK4) = $false) | ($false = (sK0 @ sK4)) | ($false = (sK0 @ sK4))),
% 1.38/1.30 inference(not_proxy_clausification,[status(thm)],[f71])).
% 1.38/1.30 thf(f71,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ($false = (sK0 @ sK4)) | ((~ (sK0 @ sK4)) = $true) | (((~ (sK1 @ sK4)) & (sK0 @ sK4)) = $true)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.38/1.30 thf(f70,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | ($false = (sK0 @ sK4)) | (((~ (sK1 @ sK4)) & (sK0 @ sK4)) = $true)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.38/1.30 thf(f69,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4))) = $true) | ($false = (sK0 @ sK4))),
% 1.38/1.30 inference(not_proxy_clausification,[status(thm)],[f68])).
% 1.38/1.30 thf(f68,plain,(
% 1.38/1.30 ((sK1 @ sK4) = $false) | ((~ (sK0 @ sK4)) = $true) | ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4))) = $true)),
% 1.38/1.30 inference(not_proxy_clausification,[status(thm)],[f52])).
% 1.38/1.30 thf(f52,plain,(
% 1.38/1.30 ((~ (sK1 @ sK4)) = $true) | ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4))) = $true) | ((~ (sK0 @ sK4)) = $true)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.38/1.30 thf(f37,plain,(
% 1.38/1.30 ($true = ((sK1 @ sK4) & (~ (sK0 @ sK4)))) | ((((sK1 @ sK4) & (~ (sK0 @ sK4))) | ((~ (sK1 @ sK4)) & (sK0 @ sK4))) = $true) | ((~ (sK1 @ sK4)) = $true)),
% 1.38/1.30 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.38/1.30 % SZS output end Proof for DTF2THF_32590
% 1.38/1.30 % (32692)------------------------------
% 1.38/1.30 % (32692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.30 % (32692)Termination reason: Refutation
% 1.38/1.30
% 1.38/1.30 % (32692)Memory used [KB]: 5500
% 1.38/1.30 % (32692)Time elapsed: 0.005 s
% 1.38/1.30 % (32692)Instructions burned: 4 (million)
% 1.38/1.30 % (32692)------------------------------
% 1.38/1.30 % (32692)------------------------------
% 1.38/1.30 % (32686)Success in time 0.019 s
%------------------------------------------------------------------------------