%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV387^5 : 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 : n021.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 09:41:08 AM UTC 2026
% Result : Theorem 1.12s 1.11s
% Output : Refutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 95 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 943 ( 223 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 1203 ( 184 ~; 213 |; 260 &; 539 @)
% ( 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(f336,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f272,f300,f311,f318,f324,f328,f332,f335]) ).
thf(f335,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f334]) ).
thf(f334,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f333]) ).
thf(f333,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[status(thm)],[f256,f261]) ).
thf(f261,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f259]) ).
thf(f259,definition,
( spl3_3
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f256,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f254]) ).
thf(f254,definition,
( spl3_2
<=> ( $true
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f332,plain,
( ~ spl3_5
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f331]) ).
thf(f331,plain,
( $false
| ~ spl3_5
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f330]) ).
thf(f330,plain,
( ( $true = $false )
| ~ spl3_5
| ~ spl3_6 ),
inference(backward_demodulation,[status(thm)],[f270,f276]) ).
thf(f276,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f274]) ).
thf(f274,definition,
( spl3_6
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f270,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f268]) ).
thf(f268,definition,
( spl3_5
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f328,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f327]) ).
thf(f327,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f326]) ).
thf(f326,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f252,f265]) ).
thf(f265,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f263]) ).
thf(f263,definition,
( spl3_4
<=> ( ( sK1 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f252,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f250]) ).
thf(f250,definition,
( spl3_1
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f324,plain,
( spl3_4
| spl3_5
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f29,f259,f268,f263]) ).
thf(f29,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK2 @ sK5 ) )
= $false )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( ~ ( sK2 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $false
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( ~ ( sK2 @ sK5 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $false
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( ~ ( sK2 @ sK5 ) )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( ~ ( sK2 @ sK5 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( ~ ( sK2 @ sK5 ) )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
| ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( $false
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK1 @ sK5 ) ) )
| ( $false
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) ) )
| ( $false
= ( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) )
!= ( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK1 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ( sK1 @ Y0 ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
& ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( ( X1 @ Y0 )
& ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
& ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( ( X1 @ Y0 )
& ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( X0 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( ~ ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
& ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( ( X1 @ Y0 )
& ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( X1 @ X3 )
& ~ ( ( X0 @ X3 )
& ( X1 @ X3 ) )
& ( X2 @ X3 ) )
| ( ( X0 @ X3 )
& ( X1 @ X3 )
& ~ ( ( X2 @ X3 )
& ( X1 @ X3 ) ) ) ) )
= ( ^ [X4: a] :
( ( X1 @ X4 )
& ( ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) )
| ( ~ ( X2 @ X4 )
& ( X0 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( ( X2 @ X4 )
& ( X0 @ X4 ) )
& ( X1 @ X4 ) )
| ( ( X2 @ X4 )
& ( X0 @ X4 )
& ~ ( ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
& ( ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( ( X2 @ X4 )
& ( X0 @ X4 ) )
& ( X1 @ X4 ) )
| ( ( X2 @ X4 )
& ( X0 @ X4 )
& ~ ( ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
& ( ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.watkrFNOZD/DTF2THF_13052.p',cGAZING_THM44_pme) ).
thf(f318,plain,
( spl3_2
| spl3_6
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f58,f263,f274,f254]) ).
thf(f58,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( ( ~ ( sK0 @ sK5 ) )
= $false )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK1 @ sK5 ) ) )
| ( $false
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f311,plain,
( spl3_3
| spl3_6
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f108,f263,f274,f259]) ).
thf(f108,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( ( ~ ( sK0 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f103]) ).
thf(f103,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( ~ ( sK2 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| ( ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $true
= ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $false
= ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
= $true )
| ( $true
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( $true
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
= ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
& ( sK1 @ sK5 ) ) )
| ( $true
= ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f300,plain,
( spl3_5
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f146,f254,f268]) ).
thf(f146,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f143]) ).
thf(f143,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f141]) ).
thf(f141,plain,
( ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( ( ( sK0 @ sK5 )
& ~ ( sK2 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f272,plain,
spl3_1,
inference(avatar_split_clause,[status(thm)],[f241,f250]) ).
thf(f241,plain,
( ( sK1 @ sK5 )
= $true ),
inference(duplicate_literal_removal,[status(thm)],[f237]) ).
thf(f237,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f236,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f220]) ).
thf(f220,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f219]) ).
thf(f219,plain,
( ( $true
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) )
| ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
( ( $true
= ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| ( $true
= ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true
= ( ( ~ ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
& ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
& ~ ( ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
& ( sK1 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV387^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n021.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:45:53 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SEV387^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.41 % Domain : Set Theory
% 0.16/0.41 % Problem : TPS problem GAZING-THM44
% 0.16/0.41 % Version : Especial.
% 0.16/0.41 % English :
% 0.16/0.41
% 0.16/0.41 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.16/0.41 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.41 % Source : [Bro09]
% 0.16/0.41 % Names : tps_0489 [Bro09]
% 0.16/0.41 % : 44 [Bar92]
% 0.16/0.41 % : GAZING-THM44 [TPS]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % 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, 0.14 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
% 0.16/0.41 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.41 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 1 ( 1 avg)
% 0.16/0.41 % Number of connectives : 28 ( 4 ~; 2 |; 9 &; 13 @)
% 0.16/0.41 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 4 ( 4 avg)
% 0.16/0.41 % Number of types : 2 ( 1 usr)
% 0.16/0.41 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.41 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.16/0.41 % SPC : TH0_THM_EQU_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.41 % : Polymorphic definitions expanded.
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(a_type,type,
% 0.16/0.41 a: $tType ).
% 0.16/0.41
% 0.16/0.41 thf(cGAZING_THM44_pme,conjecture,
% 0.16/0.41 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.16/0.41 ( ( ^ [Xx: a] :
% 0.16/0.41 ( ( S @ Xx )
% 0.16/0.41 & ( ( ( T @ Xx )
% 0.16/0.41 & ~ ( U @ Xx ) )
% 0.16/0.41 | ( ( U @ Xx )
% 0.16/0.41 & ~ ( T @ Xx ) ) ) ) )
% 0.16/0.41 = ( ^ [Xz: a] :
% 0.16/0.41 ( ( ( S @ Xz )
% 0.16/0.41 & ( T @ Xz )
% 0.16/0.41 & ~ ( ( S @ Xz )
% 0.16/0.41 & ( U @ Xz ) ) )
% 0.16/0.41 | ( ( S @ Xz )
% 0.16/0.41 & ( U @ Xz )
% 0.16/0.41 & ~ ( ( S @ Xz )
% 0.16/0.41 & ( T @ Xz ) ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.12/1.08 ---- Embedded in THF ---
% 1.12/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.08 %%% Generated on Tue Feb 24 12:45:54 EST 2026
% 1.12/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.08 %%% Logic specification used:
% 1.12/1.08 %%% thf(spec, logic, $$dhol).
% 1.12/1.08
% 1.12/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.watkrFNOZD/DTF2DTF13052.p
% See solution above
% 1.12/1.08 ------------------------
% 1.12/1.09 ---- Cleaned THF ---
% 1.12/1.09 thf(a_type,type,
% 1.12/1.09 a: $tType ).
% 1.12/1.09
% 1.12/1.09 thf(cGAZING_THM44_pme,conjecture,
% 1.12/1.09 ! [S: a > $o,T: a > $o,U: a > $o] :
% 1.12/1.09 ( ( ^ [Xx: a] :
% 1.12/1.09 ( ( S @ Xx )
% 1.12/1.09 & ( ( ( T @ Xx )
% 1.12/1.09 & ~ ( U @ Xx ) )
% 1.12/1.09 | ( ( U @ Xx )
% 1.12/1.09 & ~ ( T @ Xx ) ) ) ) )
% 1.12/1.09 = ( ^ [Xz: a] :
% 1.12/1.09 ( ( ( S @ Xz )
% 1.12/1.09 & ( T @ Xz )
% 1.12/1.09 & ~ ( ( S @ Xz )
% 1.12/1.09 & ( U @ Xz ) ) )
% 1.12/1.09 | ( ( S @ Xz )
% 1.12/1.09 & ( U @ Xz )
% 1.12/1.09 & ~ ( ( S @ Xz )
% 1.12/1.09 & ( T @ Xz ) ) ) ) ) ) ).
% 1.12/1.09 ------------------------
% 1.12/1.10 % (13189)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13052 for (3000ds/18Mi)
% 1.12/1.10 % (13185)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_13052 for (3000ds/27Mi)
% 1.12/1.10 % (13184)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_13052 for (3000ds/4Mi)
% 1.12/1.10 % (13188)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_13052 for (3000ds/275Mi)
% 1.12/1.10 % (13186)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13052 for (3000ds/2Mi)
% 1.12/1.10 % (13187)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_13052 for (3000ds/2Mi)
% 1.12/1.10 % (13183)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13052 for (3000ds/183Mi)
% 1.12/1.10 % (13186)Instruction limit reached!
% 1.12/1.10 % (13186)------------------------------
% 1.12/1.10 % (13186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.10 % (13186)Termination reason: Unknown
% 1.12/1.10 % (13186)Termination phase: Preprocessing 3
% 1.12/1.10
% 1.12/1.10 % (13186)Memory used [KB]: 895
% 1.12/1.10 % (13186)Time elapsed: 0.002 s
% 1.12/1.10 % (13186)Instructions burned: 2 (million)
% 1.12/1.10 % (13186)------------------------------
% 1.12/1.10 % (13186)------------------------------
% 1.12/1.10 % (13187)Instruction limit reached!
% 1.12/1.10 % (13187)------------------------------
% 1.12/1.10 % (13187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.10 % (13187)Termination reason: Unknown
% 1.12/1.10 % (13187)Termination phase: Saturation
% 1.12/1.10
% 1.12/1.10 % (13187)Memory used [KB]: 895
% 1.12/1.10 % (13187)Time elapsed: 0.002 s
% 1.12/1.10 % (13187)Instructions burned: 2 (million)
% 1.12/1.10 % (13187)------------------------------
% 1.12/1.10 % (13187)------------------------------
% 1.12/1.10 % (13184)Instruction limit reached!
% 1.12/1.10 % (13184)------------------------------
% 1.12/1.10 % (13184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.10 % (13184)Termination reason: Unknown
% 1.12/1.10 % (13184)Termination phase: Saturation
% 1.12/1.10
% 1.12/1.10 % (13184)Memory used [KB]: 5500
% 1.12/1.10 % (13184)Time elapsed: 0.003 s
% 1.12/1.10 % (13184)Instructions burned: 4 (million)
% 1.12/1.10 % (13184)------------------------------
% 1.12/1.10 % (13184)------------------------------
% 1.12/1.10 % (13185)First to succeed.
% 1.12/1.11 % (13183)Also succeeded, but the first one will report.
% 1.12/1.11 % (13188)Also succeeded, but the first one will report.
% 1.12/1.11 % (13185)Refutation found. Thanks to Tanya!
% 1.12/1.11 % SZS status Theorem for DTF2THF_13052
% 1.12/1.11 % SZS output start Proof for DTF2THF_13052
% 1.12/1.11 thf(type_def_5, type, a: $tType).
% 1.12/1.11 thf(func_def_0, type, a: $tType).
% 1.12/1.11 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.12/1.11 thf(func_def_10, type, sK0: a > $o).
% 1.12/1.11 thf(func_def_11, type, sK1: a > $o).
% 1.12/1.11 thf(func_def_12, type, sK2: a > $o).
% 1.12/1.11 thf(func_def_14, type, ph4: !>[X0: $tType]:(X0)).
% 1.12/1.11 thf(func_def_15, type, sK5: a).
% 1.12/1.11 thf(f336,plain,(
% 1.12/1.11 $false),
% 1.12/1.11 inference(avatar_sat_refutation,[status(thm)],[f272,f300,f311,f318,f324,f328,f332,f335])).
% 1.12/1.11 thf(f335,plain,(
% 1.12/1.11 ~spl3_2 | ~spl3_3),
% 1.12/1.11 inference(avatar_contradiction_clause,[status(thm)],[f334])).
% 1.12/1.11 thf(f334,plain,(
% 1.12/1.11 $false | (~spl3_2 | ~spl3_3)),
% 1.12/1.11 inference(trivial_inequality_removal,[status(thm)],[f333])).
% 1.12/1.11 thf(f333,plain,(
% 1.12/1.11 ($true = $false) | (~spl3_2 | ~spl3_3)),
% 1.12/1.11 inference(backward_demodulation,[status(thm)],[f256,f261])).
% 1.12/1.11 thf(f261,plain,(
% 1.12/1.11 ($false = (sK0 @ sK5)) | ~spl3_3),
% 1.12/1.11 inference(avatar_component_clause,[status(thm)],[f259])).
% 1.12/1.11 thf(f259,definition,(
% 1.12/1.11 spl3_3 <=> ($false = (sK0 @ sK5))),
% 1.12/1.11 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.12/1.11 thf(f256,plain,(
% 1.12/1.11 ($true = (sK0 @ sK5)) | ~spl3_2),
% 1.12/1.11 inference(avatar_component_clause,[status(thm)],[f254])).
% 1.12/1.11 thf(f254,definition,(
% 1.12/1.11 spl3_2 <=> ($true = (sK0 @ sK5))),
% 1.12/1.11 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.12/1.11 thf(f332,plain,(
% 1.12/1.11 ~spl3_5 | ~spl3_6),
% 1.12/1.11 inference(avatar_contradiction_clause,[status(thm)],[f331])).
% 1.12/1.11 thf(f331,plain,(
% 1.12/1.11 $false | (~spl3_5 | ~spl3_6)),
% 1.12/1.11 inference(trivial_inequality_removal,[status(thm)],[f330])).
% 1.12/1.11 thf(f330,plain,(
% 1.12/1.11 ($true = $false) | (~spl3_5 | ~spl3_6)),
% 1.12/1.11 inference(backward_demodulation,[status(thm)],[f270,f276])).
% 1.12/1.11 thf(f276,plain,(
% 1.12/1.11 ($false = (sK2 @ sK5)) | ~spl3_6),
% 1.12/1.11 inference(avatar_component_clause,[status(thm)],[f274])).
% 1.12/1.11 thf(f274,definition,(
% 1.12/1.11 spl3_6 <=> ($false = (sK2 @ sK5))),
% 1.12/1.11 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.12/1.11 thf(f270,plain,(
% 1.12/1.11 ($true = (sK2 @ sK5)) | ~spl3_5),
% 1.12/1.11 inference(avatar_component_clause,[status(thm)],[f268])).
% 1.12/1.11 thf(f268,definition,(
% 1.12/1.11 spl3_5 <=> ($true = (sK2 @ sK5))),
% 1.12/1.11 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.12/1.11 thf(f328,plain,(
% 1.12/1.11 ~spl3_1 | ~spl3_4),
% 1.12/1.11 inference(avatar_contradiction_clause,[status(thm)],[f327])).
% 1.12/1.11 thf(f327,plain,(
% 1.12/1.11 $false | (~spl3_1 | ~spl3_4)),
% 1.12/1.11 inference(trivial_inequality_removal,[status(thm)],[f326])).
% 1.12/1.11 thf(f326,plain,(
% 1.12/1.11 ($true = $false) | (~spl3_1 | ~spl3_4)),
% 1.12/1.11 inference(backward_demodulation,[status(thm)],[f252,f265])).
% 1.12/1.11 thf(f265,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ~spl3_4),
% 1.12/1.11 inference(avatar_component_clause,[status(thm)],[f263])).
% 1.12/1.11 thf(f263,definition,(
% 1.12/1.11 spl3_4 <=> ((sK1 @ sK5) = $false)),
% 1.12/1.11 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.12/1.11 thf(f252,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $true) | ~spl3_1),
% 1.12/1.11 inference(avatar_component_clause,[status(thm)],[f250])).
% 1.12/1.11 thf(f250,definition,(
% 1.12/1.11 spl3_1 <=> ((sK1 @ sK5) = $true)),
% 1.12/1.11 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.12/1.11 thf(f324,plain,(
% 1.12/1.11 spl3_4 | spl3_5 | spl3_3),
% 1.12/1.11 inference(avatar_split_clause,[status(thm)],[f29,f259,f268,f263])).
% 1.12/1.11 thf(f29,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f28])).
% 1.12/1.11 thf(f28,plain,(
% 1.12/1.11 ($true = (sK2 @ sK5)) | ($false = (sK0 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $false)),
% 1.12/1.11 inference(not_proxy_clausification,[status(thm)],[f25])).
% 1.12/1.11 thf(f25,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($true = (sK2 @ sK5)) | ((~ (sK2 @ sK5)) = $false) | ($false = (sK0 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.12/1.11 thf(f24,plain,(
% 1.12/1.11 ($true = ((sK1 @ sK5) & (sK2 @ sK5))) | ($false = (sK0 @ sK5)) | ((sK1 @ sK5) = $false) | ((~ (sK2 @ sK5)) = $false)),
% 1.12/1.11 inference(not_proxy_clausification,[status(thm)],[f23])).
% 1.12/1.11 thf(f23,plain,(
% 1.12/1.11 ($false = (~ ((sK1 @ sK5) & (sK2 @ sK5)))) | ((sK1 @ sK5) = $false) | ($false = (sK0 @ sK5)) | ((~ (sK2 @ sK5)) = $false)),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f22])).
% 1.12/1.11 thf(f22,plain,(
% 1.12/1.11 ($false = (~ ((sK1 @ sK5) & (sK2 @ sK5)))) | ((~ (sK2 @ sK5)) = $false) | ((sK1 @ sK5) = $false) | ((sK1 @ sK5) = $false) | ($false = (sK0 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.12/1.11 thf(f21,plain,(
% 1.12/1.11 (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) = $false) | ($false = (sK0 @ sK5)) | ((sK1 @ sK5) = $false) | ((~ (sK2 @ sK5)) = $false)),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.12/1.11 thf(f20,plain,(
% 1.12/1.11 ((~ (sK2 @ sK5)) = $false) | ((sK1 @ sK5) = $false) | ($false = (sK0 @ sK5)) | ($false = (sK0 @ sK5)) | (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) = $false)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.12/1.11 thf(f19,plain,(
% 1.12/1.11 ($false = (sK0 @ sK5)) | ((sK1 @ sK5) = $false) | ($false = ((sK0 @ sK5) & (~ (sK2 @ sK5)))) | (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) = $false)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.12/1.11 thf(f17,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($false = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) = $false) | ($false = (sK0 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.12/1.11 thf(f16,plain,(
% 1.12/1.11 ($false = (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5))) | ($false = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ((sK1 @ sK5) = $false)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.12/1.11 thf(f15,plain,(
% 1.12/1.11 ($false = ((((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (sK1 @ sK5))) | ($false = (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5)))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.12/1.11 thf(f13,plain,(
% 1.12/1.11 ($false = ((((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5)) | (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5)))) | ($false = ((((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (sK1 @ sK5)))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.12/1.11 thf(f11,plain,(
% 1.12/1.11 (((((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5)) | (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5))) != ((((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (sK1 @ sK5)))),
% 1.12/1.11 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.12/1.11 thf(f10,plain,(
% 1.12/1.11 (((^[Y0 : a]: ((((~ ((sK1 @ Y0) & (sK2 @ Y0))) & (sK1 @ Y0)) & (sK0 @ Y0)) | (((sK2 @ Y0) & (~ ((sK1 @ Y0) & (sK0 @ Y0)))) & (sK1 @ Y0)))) @ sK5) != ((^[Y0 : a]: ((((sK0 @ Y0) & (~ (sK2 @ Y0))) | ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (sK1 @ Y0))) @ sK5))),
% 1.12/1.11 inference(negative_extensionality,[status(thm)],[f9])).
% 1.12/1.11 thf(f9,plain,(
% 1.12/1.11 ((^[Y0 : a]: ((((sK0 @ Y0) & (~ (sK2 @ Y0))) | ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (sK1 @ Y0))) != (^[Y0 : a]: ((((~ ((sK1 @ Y0) & (sK2 @ Y0))) & (sK1 @ Y0)) & (sK0 @ Y0)) | (((sK2 @ Y0) & (~ ((sK1 @ Y0) & (sK0 @ Y0)))) & (sK1 @ Y0)))))),
% 1.12/1.11 inference(cnf_transformation,[status(thm)],[f8])).
% 1.12/1.11 thf(f8,plain,(
% 1.12/1.11 ((^[Y0 : a]: ((((sK0 @ Y0) & (~ (sK2 @ Y0))) | ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (sK1 @ Y0))) != (^[Y0 : a]: ((((~ ((sK1 @ Y0) & (sK2 @ Y0))) & (sK1 @ Y0)) & (sK0 @ Y0)) | (((sK2 @ Y0) & (~ ((sK1 @ Y0) & (sK0 @ Y0)))) & (sK1 @ Y0)))))),
% 1.12/1.11 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.12/1.11 thf(f7,plain,(
% 1.12/1.11 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X0 @ Y0) & (~ (X2 @ Y0))) | ((~ (X0 @ Y0)) & (X2 @ Y0))) & (X1 @ Y0))) != (^[Y0 : a]: ((((~ ((X1 @ Y0) & (X2 @ Y0))) & (X1 @ Y0)) & (X0 @ Y0)) | (((X2 @ Y0) & (~ ((X1 @ Y0) & (X0 @ Y0)))) & (X1 @ Y0))))) => ((^[Y0 : a]: ((((sK0 @ Y0) & (~ (sK2 @ Y0))) | ((~ (sK0 @ Y0)) & (sK2 @ Y0))) & (sK1 @ Y0))) != (^[Y0 : a]: ((((~ ((sK1 @ Y0) & (sK2 @ Y0))) & (sK1 @ Y0)) & (sK0 @ Y0)) | (((sK2 @ Y0) & (~ ((sK1 @ Y0) & (sK0 @ Y0)))) & (sK1 @ Y0)))))),
% 1.12/1.11 introduced(definition,[],[choice_axiom])).
% 1.12/1.11 thf(f6,plain,(
% 1.12/1.11 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X0 @ Y0) & (~ (X2 @ Y0))) | ((~ (X0 @ Y0)) & (X2 @ Y0))) & (X1 @ Y0))) != (^[Y0 : a]: ((((~ ((X1 @ Y0) & (X2 @ Y0))) & (X1 @ Y0)) & (X0 @ Y0)) | (((X2 @ Y0) & (~ ((X1 @ Y0) & (X0 @ Y0)))) & (X1 @ Y0)))))),
% 1.12/1.11 inference(ennf_transformation,[status(thm)],[f5])).
% 1.12/1.11 thf(f5,plain,(
% 1.12/1.11 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X0 @ Y0) & (~ (X2 @ Y0))) | ((~ (X0 @ Y0)) & (X2 @ Y0))) & (X1 @ Y0))) = (^[Y0 : a]: ((((~ ((X1 @ Y0) & (X2 @ Y0))) & (X1 @ Y0)) & (X0 @ Y0)) | (((X2 @ Y0) & (~ ((X1 @ Y0) & (X0 @ Y0)))) & (X1 @ Y0)))))),
% 1.12/1.11 inference(fool_elimination,[status(thm)],[f4])).
% 1.12/1.11 thf(f4,plain,(
% 1.12/1.11 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((X1 @ X3) & ~((X0 @ X3) & (X1 @ X3)) & (X2 @ X3)) | ((X0 @ X3) & (X1 @ X3) & ~((X2 @ X3) & (X1 @ X3))))) = (^[X4 : a] : ((X1 @ X4) & (((X2 @ X4) & ~(X0 @ X4)) | (~(X2 @ X4) & (X0 @ X4))))))),
% 1.12/1.11 inference(rectify,[status(thm)],[f2])).
% 1.12/1.11 thf(f2,negated_conjecture,(
% 1.12/1.11 ~! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : ((^[X4 : a] : (((X0 @ X4) & ~((X2 @ X4) & (X0 @ X4)) & (X1 @ X4)) | ((X2 @ X4) & (X0 @ X4) & ~((X1 @ X4) & (X0 @ X4))))) = (^[X3 : a] : ((X0 @ X3) & (((X1 @ X3) & ~(X2 @ X3)) | (~(X1 @ X3) & (X2 @ X3))))))),
% 1.12/1.11 inference(negated_conjecture,[status(cth)],[f1])).
% 1.12/1.11 thf(f1,conjecture,(
% 1.12/1.11 ! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : ((^[X4 : a] : (((X0 @ X4) & ~((X2 @ X4) & (X0 @ X4)) & (X1 @ X4)) | ((X2 @ X4) & (X0 @ X4) & ~((X1 @ X4) & (X0 @ X4))))) = (^[X3 : a] : ((X0 @ X3) & (((X1 @ X3) & ~(X2 @ X3)) | (~(X1 @ X3) & (X2 @ X3))))))),
% 1.12/1.11 file('/export/starexec/sandbox/tmp/tmp.watkrFNOZD/DTF2THF_13052.p',cGAZING_THM44_pme)).
% 1.12/1.11 thf(f318,plain,(
% 1.12/1.11 spl3_2 | spl3_6 | spl3_4),
% 1.12/1.11 inference(avatar_split_clause,[status(thm)],[f58,f263,f274,f254])).
% 1.12/1.11 thf(f58,plain,(
% 1.12/1.11 ($false = (sK2 @ sK5)) | ($true = (sK0 @ sK5)) | ((sK1 @ sK5) = $false)),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f57])).
% 1.12/1.11 thf(f57,plain,(
% 1.12/1.11 ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ($true = (sK0 @ sK5)) | ($true = (sK0 @ sK5))),
% 1.12/1.11 inference(not_proxy_clausification,[status(thm)],[f56])).
% 1.12/1.11 thf(f56,plain,(
% 1.12/1.11 ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ((~ (sK0 @ sK5)) = $false) | ($true = (sK0 @ sK5))),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f55])).
% 1.12/1.11 thf(f55,plain,(
% 1.12/1.11 ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false) | ($true = (sK0 @ sK5)) | ($false = (sK2 @ sK5)) | ((~ (sK0 @ sK5)) = $false)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.12/1.11 thf(f50,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($false = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = (sK0 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.12/1.11 thf(f49,plain,(
% 1.12/1.11 (((sK1 @ sK5) & (sK0 @ sK5)) = $true) | ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($false = ((~ (sK0 @ sK5)) & (sK2 @ sK5)))),
% 1.12/1.11 inference(not_proxy_clausification,[status(thm)],[f48])).
% 1.12/1.11 thf(f48,plain,(
% 1.12/1.11 ($false = (sK2 @ sK5)) | ((~ ((sK1 @ sK5) & (sK0 @ sK5))) = $false) | ($false = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ((sK1 @ sK5) = $false)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.12/1.11 thf(f40,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($false = ((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5))))) | ($false = ((~ (sK0 @ sK5)) & (sK2 @ sK5)))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.12/1.11 thf(f39,plain,(
% 1.12/1.11 ($false = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($false = ((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5))))) | ((sK1 @ sK5) = $false)),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f38])).
% 1.12/1.11 thf(f38,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($false = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ((sK1 @ sK5) = $false) | ($false = ((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.12/1.11 thf(f37,plain,(
% 1.12/1.11 ($false = (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5))) | ((sK1 @ sK5) = $false) | ($false = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.12/1.11 thf(f14,plain,(
% 1.12/1.11 ($false = ((((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (sK1 @ sK5))) | ($false = (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5)))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.12/1.11 thf(f311,plain,(
% 1.12/1.11 spl3_3 | spl3_6 | spl3_4),
% 1.12/1.11 inference(avatar_split_clause,[status(thm)],[f108,f263,f274,f259])).
% 1.12/1.11 thf(f108,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f107])).
% 1.12/1.11 thf(f107,plain,(
% 1.12/1.11 ($false = (sK0 @ sK5)) | ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.12/1.11 inference(not_proxy_clausification,[status(thm)],[f106])).
% 1.12/1.11 thf(f106,plain,(
% 1.12/1.11 ((~ (sK0 @ sK5)) = $true) | ((sK1 @ sK5) = $false) | ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.12/1.11 thf(f104,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($false = (sK0 @ sK5)) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($false = (sK2 @ sK5))),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f103])).
% 1.12/1.11 thf(f103,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ((sK1 @ sK5) = $false) | ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.12/1.11 thf(f102,plain,(
% 1.12/1.11 (((sK1 @ sK5) & (sK0 @ sK5)) = $false) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($false = (sK2 @ sK5)) | ((sK1 @ sK5) = $false)),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f101])).
% 1.12/1.11 thf(f101,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5)) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($false = (sK2 @ sK5)) | (((sK1 @ sK5) & (sK0 @ sK5)) = $false)),
% 1.12/1.11 inference(not_proxy_clausification,[status(thm)],[f92])).
% 1.12/1.11 thf(f92,plain,(
% 1.12/1.11 ((~ (sK2 @ sK5)) = $true) | ((sK1 @ sK5) = $false) | (((sK1 @ sK5) & (sK0 @ sK5)) = $false) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($false = (sK2 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.12/1.11 thf(f91,plain,(
% 1.12/1.11 ($true = ((sK0 @ sK5) & (~ (sK2 @ sK5)))) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ((sK1 @ sK5) = $false) | ($false = (sK2 @ sK5)) | (((sK1 @ sK5) & (sK0 @ sK5)) = $false)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.12/1.11 thf(f90,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $false) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($false = (sK2 @ sK5)) | (((sK1 @ sK5) & (sK0 @ sK5)) = $false)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.12/1.11 thf(f89,plain,(
% 1.12/1.11 ($false = ((sK1 @ sK5) & (sK2 @ sK5))) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | (((sK1 @ sK5) & (sK0 @ sK5)) = $false)),
% 1.12/1.11 inference(not_proxy_clausification,[status(thm)],[f88])).
% 1.12/1.11 thf(f88,plain,(
% 1.12/1.11 ($true = (~ ((sK1 @ sK5) & (sK2 @ sK5)))) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | (((sK1 @ sK5) & (sK0 @ sK5)) = $false)),
% 1.12/1.11 inference(not_proxy_clausification,[status(thm)],[f68])).
% 1.12/1.11 thf(f68,plain,(
% 1.12/1.11 ((~ ((sK1 @ sK5) & (sK0 @ sK5))) = $true) | ($true = (~ ((sK1 @ sK5) & (sK2 @ sK5)))) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.12/1.11 thf(f67,plain,(
% 1.12/1.11 ($true = ((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5))))) | ($true = (~ ((sK1 @ sK5) & (sK2 @ sK5)))) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.12/1.11 thf(f65,plain,(
% 1.12/1.11 (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) = $true) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($true = ((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.12/1.11 thf(f63,plain,(
% 1.12/1.11 ($true = (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5))) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($true = ((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.12/1.11 thf(f61,plain,(
% 1.12/1.11 ($true = (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5))) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($true = (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5)))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.12/1.11 thf(f60,plain,(
% 1.12/1.11 ($true = ((((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5)) | (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5)))) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.12/1.11 thf(f12,plain,(
% 1.12/1.11 ($true = ((((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))) & (sK1 @ sK5))) | ($true = ((((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5)) | (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.12/1.11 thf(f300,plain,(
% 1.12/1.11 spl3_5 | spl3_2),
% 1.12/1.11 inference(avatar_split_clause,[status(thm)],[f146,f254,f268])).
% 1.12/1.11 thf(f146,plain,(
% 1.12/1.11 ($true = (sK2 @ sK5)) | ($true = (sK0 @ sK5))),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f143])).
% 1.12/1.11 thf(f143,plain,(
% 1.12/1.11 ($true = (sK2 @ sK5)) | ($true = (sK2 @ sK5)) | ($true = (sK0 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 1.12/1.11 thf(f142,plain,(
% 1.12/1.11 ($true = (sK0 @ sK5)) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = (sK2 @ sK5))),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f141])).
% 1.12/1.11 thf(f141,plain,(
% 1.12/1.11 ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = (sK0 @ sK5)) | ($true = (sK2 @ sK5)) | ($true = (sK0 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 1.12/1.11 thf(f139,plain,(
% 1.12/1.11 ($true = (sK2 @ sK5)) | ($true = ((sK0 @ sK5) & (~ (sK2 @ sK5)))) | ($true = ((~ (sK0 @ sK5)) & (sK2 @ sK5))) | ($true = (sK0 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f138])).
% 1.12/1.11 thf(f138,plain,(
% 1.12/1.11 ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5)))) | ($true = (sK2 @ sK5)) | ($true = (sK0 @ sK5))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.12/1.11 thf(f64,plain,(
% 1.12/1.11 ($true = ((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5))))) | ($true = (sK0 @ sK5)) | ($true = (((sK0 @ sK5) & (~ (sK2 @ sK5))) | ((~ (sK0 @ sK5)) & (sK2 @ sK5))))),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.12/1.11 thf(f272,plain,(
% 1.12/1.11 spl3_1),
% 1.12/1.11 inference(avatar_split_clause,[status(thm)],[f241,f250])).
% 1.12/1.11 thf(f241,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $true)),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f237])).
% 1.12/1.11 thf(f237,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 1.12/1.11 thf(f236,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $true) | (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) = $true)),
% 1.12/1.11 inference(duplicate_literal_removal,[status(thm)],[f220])).
% 1.12/1.11 thf(f220,plain,(
% 1.12/1.11 ((sK1 @ sK5) = $true) | ((sK1 @ sK5) = $true) | (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) = $true)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f219])).
% 1.12/1.11 thf(f219,plain,(
% 1.12/1.11 ($true = (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5))) | (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) = $true) | ((sK1 @ sK5) = $true)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f217])).
% 1.12/1.11 thf(f217,plain,(
% 1.12/1.11 ($true = (((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5))) | ($true = (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5))) | ((sK1 @ sK5) = $true)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.12/1.11 thf(f59,plain,(
% 1.12/1.11 ($true = ((((~ ((sK1 @ sK5) & (sK2 @ sK5))) & (sK1 @ sK5)) & (sK0 @ sK5)) | (((sK2 @ sK5) & (~ ((sK1 @ sK5) & (sK0 @ sK5)))) & (sK1 @ sK5)))) | ((sK1 @ sK5) = $true)),
% 1.12/1.11 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.12/1.11 % SZS output end Proof for DTF2THF_13052
% 1.12/1.11 % (13185)------------------------------
% 1.12/1.11 % (13185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.11 % (13185)Termination reason: Refutation
% 1.12/1.11
% 1.12/1.11 % (13185)Memory used [KB]: 5628
% 1.12/1.11 % (13185)Time elapsed: 0.007 s
% 1.12/1.11 % (13185)Instructions burned: 11 (million)
% 1.12/1.11 % (13185)------------------------------
% 1.12/1.11 % (13185)------------------------------
% 1.12/1.11 % (13181)Success in time 0.015 s
%------------------------------------------------------------------------------