%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET601^5 : 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 : n028.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 09:31:52 AM UTC 2026
% Result : Theorem 1.52s 1.30s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 95 ( 10 unt; 0 typ; 6 def)
% Number of atoms : 904 ( 211 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 1011 ( 34 ~; 319 |; 133 &; 518 @)
% ( 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_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK5: a ).
thf(f294,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f231,f236,f245,f255,f273,f279,f284,f288,f293]) ).
thf(f293,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f292]) ).
thf(f292,plain,
( $false
| ~ spl3_2
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f291]) ).
thf(f291,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_6 ),
inference(backward_demodulation,[status(thm)],[f217,f259]) ).
thf(f259,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f257]) ).
thf(f257,definition,
( spl3_6
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f217,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f215]) ).
thf(f215,definition,
( spl3_2
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f288,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f287]) ).
thf(f287,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f286]) ).
thf(f286,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f213,f249]) ).
thf(f249,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f247]) ).
thf(f247,definition,
( spl3_4
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f213,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f211]) ).
thf(f211,definition,
( spl3_1
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f284,plain,
( ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f283]) ).
thf(f283,plain,
( $false
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f282]) ).
thf(f282,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f221,f253]) ).
thf(f253,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f251]) ).
thf(f251,definition,
( spl3_5
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f221,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f219]) ).
thf(f219,definition,
( spl3_3
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f279,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f33,f257,f251]) ).
thf(f33,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
!= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X2 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) ) ) )
=> ( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X2 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X2 @ Y0 )
| ( X1 @ Y0 ) )
& ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ( X2 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
| ( X0 @ X4 ) )
& ( ( X1 @ X4 )
| ( X2 @ X4 ) )
& ( ( X1 @ X4 )
| ( X0 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
| ( ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ( X0 @ X3 )
& ( X1 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( ( X0 @ X4 )
| ( X2 @ X4 ) )
& ( ( X0 @ X4 )
| ( X1 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
| ( ( X2 @ X3 )
& ( X1 @ X3 ) )
| ( ( X0 @ X3 )
& ( X1 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( ( X0 @ X4 )
| ( X2 @ X4 ) )
& ( ( X0 @ X4 )
| ( X1 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2W6kZrcHS1/DTF2THF_21286.p',cBOOL_PROP_72_pme) ).
thf(f273,plain,
( spl3_6
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f59,f247,f257]) ).
thf(f59,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $false
= ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) )
| ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) )
| ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f255,plain,
( spl3_4
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f108,f251,f247]) ).
thf(f108,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $false
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $false
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f245,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f124,f219,f215]) ).
thf(f124,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
= $true )
| ( ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
& ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f236,plain,
( spl3_3
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f156,f211,f219]) ).
thf(f156,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f155]) ).
thf(f155,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
( ( ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
( ( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
( ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $true )
| ( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f231,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f176,f215,f211]) ).
thf(f176,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) )
| ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK2 @ sK5 )
| ( sK1 @ sK5 ) )
& ( ( sK0 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET601^5 : 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
% 0.12/0.29 % Computer : n028.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:00:26 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SET601^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.38 % Domain : Set Theory
% 0.17/0.38 % Problem : TPS problem BOOL-PROP-72
% 0.17/0.38 % Version : Especial.
% 0.17/0.38 % English : Trybulec's 72nd Boolean property of sets
% 0.17/0.38
% 0.17/0.38 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.17/0.38 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.38 % Source : [Bro09]
% 0.17/0.38 % Names : tps_0433 [Bro09]
% 0.17/0.38 % : BOOL-PROP-72 [TPS]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % 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 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.17/0.38 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.17/0.38 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 1 ( 1 avg)
% 0.17/0.38 % Number of connectives : 22 ( 0 ~; 5 |; 5 &; 12 @)
% 0.17/0.38 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 4 ( 4 avg)
% 0.17/0.38 % Number of types : 2 ( 1 usr)
% 0.17/0.38 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.17/0.38 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.38 % : Polymorphic definitions expanded.
% 0.17/0.38 % :
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(a_type,type,
% 0.17/0.38 a: $tType ).
% 0.17/0.38
% 0.17/0.38 thf(cBOOL_PROP_72_pme,conjecture,
% 0.17/0.38 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.17/0.38 ( ( ^ [Xz: a] :
% 0.17/0.38 ( ( ( X @ Xz )
% 0.17/0.38 & ( Y @ Xz ) )
% 0.17/0.38 | ( ( Y @ Xz )
% 0.17/0.38 & ( Z @ Xz ) )
% 0.17/0.38 | ( ( Z @ Xz )
% 0.17/0.38 & ( X @ Xz ) ) ) )
% 0.17/0.38 = ( ^ [Xx: a] :
% 0.17/0.38 ( ( ( X @ Xx )
% 0.17/0.38 | ( Y @ Xx ) )
% 0.17/0.38 & ( ( Y @ Xx )
% 0.17/0.38 | ( Z @ Xx ) )
% 0.17/0.38 & ( ( Z @ Xx )
% 0.17/0.38 | ( X @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 1.37/1.26 ---- Embedded in THF ---
% 1.37/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.26 %%% Generated on Tue Feb 24 12:00:27 EST 2026
% 1.37/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.26 %%% Logic specification used:
% 1.37/1.26 %%% thf(spec, logic, $$dhol).
% 1.37/1.26
% 1.37/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2W6kZrcHS1/DTF2DTF21286.p
% See solution above
% 1.37/1.26 ------------------------
% 1.37/1.27 ---- Cleaned THF ---
% 1.37/1.27 thf(a_type,type,
% 1.37/1.27 a: $tType ).
% 1.37/1.27
% 1.37/1.27 thf(cBOOL_PROP_72_pme,conjecture,
% 1.37/1.27 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.37/1.27 ( ( ^ [Xz: a] :
% 1.37/1.27 ( ( ( X @ Xz )
% 1.37/1.27 & ( Y @ Xz ) )
% 1.37/1.27 | ( ( Y @ Xz )
% 1.37/1.27 & ( Z @ Xz ) )
% 1.37/1.27 | ( ( Z @ Xz )
% 1.37/1.27 & ( X @ Xz ) ) ) )
% 1.37/1.27 = ( ^ [Xx: a] :
% 1.37/1.27 ( ( ( X @ Xx )
% 1.37/1.27 | ( Y @ Xx ) )
% 1.37/1.27 & ( ( Y @ Xx )
% 1.37/1.27 | ( Z @ Xx ) )
% 1.37/1.27 & ( ( Z @ Xx )
% 1.37/1.27 | ( X @ Xx ) ) ) ) ) ).
% 1.37/1.27 ------------------------
% 1.37/1.29 % (21384)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_21286 for (3000ds/4Mi)
% 1.37/1.29 % (21383)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21286 for (3000ds/183Mi)
% 1.37/1.29 % (21385)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_21286 for (3000ds/27Mi)
% 1.37/1.29 % (21386)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21286 for (3000ds/2Mi)
% 1.37/1.29 % (21387)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_21286 for (3000ds/2Mi)
% 1.37/1.29 % (21388)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_21286 for (3000ds/275Mi)
% 1.37/1.29 % (21389)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21286 for (3000ds/18Mi)
% 1.37/1.29 % (21386)Instruction limit reached!
% 1.37/1.29 % (21386)------------------------------
% 1.37/1.29 % (21386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.29 % (21386)Termination reason: Unknown
% 1.37/1.29 % (21387)Instruction limit reached!
% 1.37/1.29 % (21387)------------------------------
% 1.37/1.29 % (21387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.29 % (21386)Termination phase: Saturation
% 1.37/1.29
% 1.37/1.29 % (21386)Memory used [KB]: 5500
% 1.37/1.29 % (21386)Time elapsed: 0.003 s
% 1.37/1.29 % (21386)Instructions burned: 3 (million)
% 1.37/1.29 % (21386)------------------------------
% 1.37/1.29 % (21386)------------------------------
% 1.37/1.29 % (21387)Termination reason: Unknown
% 1.37/1.29 % (21387)Termination phase: Saturation
% 1.37/1.29
% 1.37/1.29 % (21387)Memory used [KB]: 5500
% 1.37/1.29 % (21387)Time elapsed: 0.003 s
% 1.37/1.29 % (21387)Instructions burned: 2 (million)
% 1.37/1.29 % (21387)------------------------------
% 1.37/1.29 % (21387)------------------------------
% 1.37/1.29 % (21384)Instruction limit reached!
% 1.37/1.29 % (21384)------------------------------
% 1.37/1.29 % (21384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.29 % (21384)Termination reason: Unknown
% 1.37/1.29 % (21384)Termination phase: Saturation
% 1.37/1.29
% 1.37/1.29 % (21384)Memory used [KB]: 5500
% 1.37/1.29 % (21384)Time elapsed: 0.004 s
% 1.37/1.29 % (21384)Instructions burned: 4 (million)
% 1.37/1.29 % (21384)------------------------------
% 1.37/1.29 % (21384)------------------------------
% 1.37/1.29 % (21385)First to succeed.
% 1.52/1.30 % (21383)Also succeeded, but the first one will report.
% 1.52/1.30 % (21388)Also succeeded, but the first one will report.
% 1.52/1.30 % (21385)Refutation found. Thanks to Tanya!
% 1.52/1.30 % SZS status Theorem for DTF2THF_21286
% 1.52/1.30 % SZS output start Proof for DTF2THF_21286
% 1.52/1.30 thf(type_def_5, type, a: $tType).
% 1.52/1.30 thf(func_def_0, type, a: $tType).
% 1.52/1.30 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.52/1.30 thf(func_def_9, type, sK0: a > $o).
% 1.52/1.30 thf(func_def_10, type, sK1: a > $o).
% 1.52/1.30 thf(func_def_11, type, sK2: a > $o).
% 1.52/1.30 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.52/1.30 thf(func_def_14, type, sK5: a).
% 1.52/1.30 thf(f294,plain,(
% 1.52/1.30 $false),
% 1.52/1.30 inference(avatar_sat_refutation,[status(thm)],[f231,f236,f245,f255,f273,f279,f284,f288,f293])).
% 1.52/1.30 thf(f293,plain,(
% 1.52/1.30 ~spl3_2 | ~spl3_6),
% 1.52/1.30 inference(avatar_contradiction_clause,[status(thm)],[f292])).
% 1.52/1.30 thf(f292,plain,(
% 1.52/1.30 $false | (~spl3_2 | ~spl3_6)),
% 1.52/1.30 inference(trivial_inequality_removal,[status(thm)],[f291])).
% 1.52/1.30 thf(f291,plain,(
% 1.52/1.30 ($false = $true) | (~spl3_2 | ~spl3_6)),
% 1.52/1.30 inference(backward_demodulation,[status(thm)],[f217,f259])).
% 1.52/1.30 thf(f259,plain,(
% 1.52/1.30 ($false = (sK0 @ sK5)) | ~spl3_6),
% 1.52/1.30 inference(avatar_component_clause,[status(thm)],[f257])).
% 1.52/1.30 thf(f257,definition,(
% 1.52/1.30 spl3_6 <=> ($false = (sK0 @ sK5))),
% 1.52/1.30 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.52/1.30 thf(f217,plain,(
% 1.52/1.30 ((sK0 @ sK5) = $true) | ~spl3_2),
% 1.52/1.30 inference(avatar_component_clause,[status(thm)],[f215])).
% 1.52/1.30 thf(f215,definition,(
% 1.52/1.30 spl3_2 <=> ((sK0 @ sK5) = $true)),
% 1.52/1.30 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.52/1.30 thf(f288,plain,(
% 1.52/1.30 ~spl3_1 | ~spl3_4),
% 1.52/1.30 inference(avatar_contradiction_clause,[status(thm)],[f287])).
% 1.52/1.30 thf(f287,plain,(
% 1.52/1.30 $false | (~spl3_1 | ~spl3_4)),
% 1.52/1.30 inference(trivial_inequality_removal,[status(thm)],[f286])).
% 1.52/1.30 thf(f286,plain,(
% 1.52/1.30 ($false = $true) | (~spl3_1 | ~spl3_4)),
% 1.52/1.30 inference(forward_demodulation,[status(thm)],[f213,f249])).
% 1.52/1.30 thf(f249,plain,(
% 1.52/1.30 ($false = (sK2 @ sK5)) | ~spl3_4),
% 1.52/1.30 inference(avatar_component_clause,[status(thm)],[f247])).
% 1.52/1.30 thf(f247,definition,(
% 1.52/1.30 spl3_4 <=> ($false = (sK2 @ sK5))),
% 1.52/1.30 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.52/1.30 thf(f213,plain,(
% 1.52/1.30 ($true = (sK2 @ sK5)) | ~spl3_1),
% 1.52/1.30 inference(avatar_component_clause,[status(thm)],[f211])).
% 1.52/1.30 thf(f211,definition,(
% 1.52/1.30 spl3_1 <=> ($true = (sK2 @ sK5))),
% 1.52/1.30 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.52/1.30 thf(f284,plain,(
% 1.52/1.30 ~spl3_3 | ~spl3_5),
% 1.52/1.30 inference(avatar_contradiction_clause,[status(thm)],[f283])).
% 1.52/1.30 thf(f283,plain,(
% 1.52/1.30 $false | (~spl3_3 | ~spl3_5)),
% 1.52/1.30 inference(trivial_inequality_removal,[status(thm)],[f282])).
% 1.52/1.30 thf(f282,plain,(
% 1.52/1.30 ($false = $true) | (~spl3_3 | ~spl3_5)),
% 1.52/1.30 inference(backward_demodulation,[status(thm)],[f221,f253])).
% 1.52/1.30 thf(f253,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ~spl3_5),
% 1.52/1.30 inference(avatar_component_clause,[status(thm)],[f251])).
% 1.52/1.30 thf(f251,definition,(
% 1.52/1.30 spl3_5 <=> ($false = (sK1 @ sK5))),
% 1.52/1.30 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.52/1.30 thf(f221,plain,(
% 1.52/1.30 ((sK1 @ sK5) = $true) | ~spl3_3),
% 1.52/1.30 inference(avatar_component_clause,[status(thm)],[f219])).
% 1.52/1.30 thf(f219,definition,(
% 1.52/1.30 spl3_3 <=> ((sK1 @ sK5) = $true)),
% 1.52/1.30 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.52/1.30 thf(f279,plain,(
% 1.52/1.30 spl3_5 | spl3_6),
% 1.52/1.30 inference(avatar_split_clause,[status(thm)],[f33,f257,f251])).
% 1.52/1.30 thf(f33,plain,(
% 1.52/1.30 ($false = (sK0 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.52/1.30 thf(f32,plain,(
% 1.52/1.30 ($false = (sK0 @ sK5)) | ($false = (sK0 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.52/1.30 thf(f30,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5)) | (((sK0 @ sK5) | (sK1 @ sK5)) = $false)),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.52/1.30 thf(f24,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5)) | (((sK0 @ sK5) | (sK1 @ sK5)) = $false) | ($false = (sK1 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.52/1.30 thf(f23,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = ((sK2 @ sK5) | (sK1 @ sK5))) | ($false = (sK0 @ sK5)) | (((sK0 @ sK5) | (sK1 @ sK5)) = $false)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.52/1.30 thf(f22,plain,(
% 1.52/1.30 ($false = (sK0 @ sK5)) | ($false = (sK1 @ sK5)) | ($false = (((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f21])).
% 1.52/1.30 thf(f21,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5)) | ($false = (((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5)))) | ($false = (sK0 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.52/1.30 thf(f19,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ($false = (sK0 @ sK5)) | ($false = (((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.52/1.30 thf(f18,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5)) | ($false = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.52/1.30 thf(f17,plain,(
% 1.52/1.30 ($false = ((sK0 @ sK5) & (sK1 @ sK5))) | ($false = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.52/1.30 thf(f15,plain,(
% 1.52/1.30 ($false = (((sK0 @ sK5) & (sK1 @ sK5)) | ((sK0 @ sK5) & (sK2 @ sK5)))) | ($false = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.52/1.30 thf(f13,plain,(
% 1.52/1.30 ($false = ((((sK0 @ sK5) & (sK1 @ sK5)) | ((sK0 @ sK5) & (sK2 @ sK5))) | ((sK1 @ sK5) & (sK2 @ sK5)))) | ($false = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.52/1.30 thf(f11,plain,(
% 1.52/1.30 (((((sK0 @ sK5) & (sK1 @ sK5)) | ((sK0 @ sK5) & (sK2 @ sK5))) | ((sK1 @ sK5) & (sK2 @ sK5))) != ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.52/1.30 thf(f10,plain,(
% 1.52/1.30 (((^[Y0 : a]: ((((sK0 @ Y0) & (sK1 @ Y0)) | ((sK0 @ Y0) & (sK2 @ Y0))) | ((sK1 @ Y0) & (sK2 @ Y0)))) @ sK5) != ((^[Y0 : a]: ((((sK0 @ Y0) | (sK1 @ Y0)) & ((sK2 @ Y0) | (sK1 @ Y0))) & ((sK0 @ Y0) | (sK2 @ Y0)))) @ sK5))),
% 1.52/1.30 inference(negative_extensionality,[status(thm)],[f9])).
% 1.52/1.30 thf(f9,plain,(
% 1.52/1.30 ((^[Y0 : a]: ((((sK0 @ Y0) & (sK1 @ Y0)) | ((sK0 @ Y0) & (sK2 @ Y0))) | ((sK1 @ Y0) & (sK2 @ Y0)))) != (^[Y0 : a]: ((((sK0 @ Y0) | (sK1 @ Y0)) & ((sK2 @ Y0) | (sK1 @ Y0))) & ((sK0 @ Y0) | (sK2 @ Y0)))))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.52/1.30 thf(f8,plain,(
% 1.52/1.30 ((^[Y0 : a]: ((((sK0 @ Y0) & (sK1 @ Y0)) | ((sK0 @ Y0) & (sK2 @ Y0))) | ((sK1 @ Y0) & (sK2 @ Y0)))) != (^[Y0 : a]: ((((sK0 @ Y0) | (sK1 @ Y0)) & ((sK2 @ Y0) | (sK1 @ Y0))) & ((sK0 @ Y0) | (sK2 @ Y0)))))),
% 1.52/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.52/1.30 thf(f7,plain,(
% 1.52/1.30 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X0 @ Y0) & (X1 @ Y0)) | ((X0 @ Y0) & (X2 @ Y0))) | ((X1 @ Y0) & (X2 @ Y0)))) != (^[Y0 : a]: ((((X0 @ Y0) | (X1 @ Y0)) & ((X2 @ Y0) | (X1 @ Y0))) & ((X0 @ Y0) | (X2 @ Y0))))) => ((^[Y0 : a]: ((((sK0 @ Y0) & (sK1 @ Y0)) | ((sK0 @ Y0) & (sK2 @ Y0))) | ((sK1 @ Y0) & (sK2 @ Y0)))) != (^[Y0 : a]: ((((sK0 @ Y0) | (sK1 @ Y0)) & ((sK2 @ Y0) | (sK1 @ Y0))) & ((sK0 @ Y0) | (sK2 @ Y0)))))),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f6,plain,(
% 1.52/1.30 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X0 @ Y0) & (X1 @ Y0)) | ((X0 @ Y0) & (X2 @ Y0))) | ((X1 @ Y0) & (X2 @ Y0)))) != (^[Y0 : a]: ((((X0 @ Y0) | (X1 @ Y0)) & ((X2 @ Y0) | (X1 @ Y0))) & ((X0 @ Y0) | (X2 @ Y0)))))),
% 1.52/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.30 thf(f5,plain,(
% 1.52/1.30 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: ((((X0 @ Y0) & (X1 @ Y0)) | ((X0 @ Y0) & (X2 @ Y0))) | ((X1 @ Y0) & (X2 @ Y0)))) = (^[Y0 : a]: ((((X0 @ Y0) | (X1 @ Y0)) & ((X2 @ Y0) | (X1 @ Y0))) & ((X0 @ Y0) | (X2 @ Y0)))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.30 thf(f4,plain,(
% 1.52/1.30 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((X2 @ X3) & (X1 @ X3)) | ((X2 @ X3) & (X0 @ X3)) | ((X1 @ X3) & (X0 @ X3)))) = (^[X4 : a] : (((X2 @ X4) | (X0 @ X4)) & ((X1 @ X4) | (X2 @ X4)) & ((X1 @ X4) | (X0 @ X4)))))),
% 1.52/1.30 inference(rectify,[status(thm)],[f2])).
% 1.52/1.30 thf(f2,negated_conjecture,(
% 1.52/1.30 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((X2 @ X3) & (X0 @ X3)) | ((X2 @ X3) & (X1 @ X3)) | ((X0 @ X3) & (X1 @ X3)))) = (^[X4 : a] : (((X2 @ X4) | (X1 @ X4)) & ((X0 @ X4) | (X2 @ X4)) & ((X0 @ X4) | (X1 @ X4)))))),
% 1.52/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.30 thf(f1,conjecture,(
% 1.52/1.30 ! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((^[X3 : a] : (((X2 @ X3) & (X0 @ X3)) | ((X2 @ X3) & (X1 @ X3)) | ((X0 @ X3) & (X1 @ X3)))) = (^[X4 : a] : (((X2 @ X4) | (X1 @ X4)) & ((X0 @ X4) | (X2 @ X4)) & ((X0 @ X4) | (X1 @ X4)))))),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.2W6kZrcHS1/DTF2THF_21286.p',cBOOL_PROP_72_pme)).
% 1.52/1.30 thf(f273,plain,(
% 1.52/1.30 spl3_6 | spl3_4),
% 1.52/1.30 inference(avatar_split_clause,[status(thm)],[f59,f247,f257])).
% 1.52/1.30 thf(f59,plain,(
% 1.52/1.30 ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f58])).
% 1.52/1.30 thf(f58,plain,(
% 1.52/1.30 ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.52/1.30 thf(f56,plain,(
% 1.52/1.30 ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ($false = (sK2 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f55])).
% 1.52/1.30 thf(f55,plain,(
% 1.52/1.30 ($false = (sK0 @ sK5)) | ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.52/1.30 thf(f53,plain,(
% 1.52/1.30 ($false = (sK2 @ sK5)) | ($false = (sK0 @ sK5)) | (((sK0 @ sK5) | (sK1 @ sK5)) = $false) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f52])).
% 1.52/1.30 thf(f52,plain,(
% 1.52/1.30 (((sK0 @ sK5) | (sK1 @ sK5)) = $false) | ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (sK0 @ sK5)) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.52/1.30 thf(f51,plain,(
% 1.52/1.30 ($false = ((sK0 @ sK5) & (sK2 @ sK5))) | (((sK0 @ sK5) | (sK1 @ sK5)) = $false) | ($false = (sK2 @ sK5)) | ($false = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.52/1.30 thf(f49,plain,(
% 1.52/1.30 ($false = ((sK2 @ sK5) | (sK1 @ sK5))) | ($false = ((sK0 @ sK5) & (sK2 @ sK5))) | ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | (((sK0 @ sK5) | (sK1 @ sK5)) = $false)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.52/1.30 thf(f48,plain,(
% 1.52/1.30 ($false = (((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5)))) | ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ($false = ((sK0 @ sK5) & (sK2 @ sK5)))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.52/1.30 thf(f16,plain,(
% 1.52/1.30 ($false = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5)))) | ($false = ((sK0 @ sK5) & (sK2 @ sK5)))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.52/1.30 thf(f255,plain,(
% 1.52/1.30 spl3_4 | spl3_5),
% 1.52/1.30 inference(avatar_split_clause,[status(thm)],[f108,f251,f247])).
% 1.52/1.30 thf(f108,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f107])).
% 1.52/1.30 thf(f107,plain,(
% 1.52/1.30 ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.52/1.30 thf(f105,plain,(
% 1.52/1.30 ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5)) | ($false = ((sK2 @ sK5) | (sK1 @ sK5)))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f99])).
% 1.52/1.30 thf(f99,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = ((sK2 @ sK5) | (sK1 @ sK5))) | ($false = (sK1 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.52/1.30 thf(f98,plain,(
% 1.52/1.30 ($false = (sK2 @ sK5)) | (((sK0 @ sK5) | (sK1 @ sK5)) = $false) | ($false = (sK1 @ sK5)) | ($false = ((sK2 @ sK5) | (sK1 @ sK5)))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.52/1.30 thf(f97,plain,(
% 1.52/1.30 ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f82])).
% 1.52/1.30 thf(f82,plain,(
% 1.52/1.30 ($false = (sK2 @ sK5)) | ($false = (((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5)))) | ($false = (sK2 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.52/1.30 thf(f81,plain,(
% 1.52/1.30 ($false = ((sK0 @ sK5) | (sK2 @ sK5))) | ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.52/1.30 thf(f80,plain,(
% 1.52/1.30 ($false = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5)))) | ($false = (sK1 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.52/1.30 thf(f14,plain,(
% 1.52/1.30 ($false = ((sK1 @ sK5) & (sK2 @ sK5))) | ($false = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.52/1.30 thf(f245,plain,(
% 1.52/1.30 spl3_2 | spl3_3),
% 1.52/1.30 inference(avatar_split_clause,[status(thm)],[f124,f219,f215])).
% 1.52/1.30 thf(f124,plain,(
% 1.52/1.30 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f123])).
% 1.52/1.30 thf(f123,plain,(
% 1.52/1.30 ((sK1 @ sK5) = $true) | ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.52/1.30 thf(f122,plain,(
% 1.52/1.30 (((sK0 @ sK5) | (sK1 @ sK5)) = $true) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f120])).
% 1.52/1.30 thf(f120,plain,(
% 1.52/1.30 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) = $true)),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f119])).
% 1.52/1.30 thf(f119,plain,(
% 1.52/1.30 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.52/1.30 thf(f117,plain,(
% 1.52/1.30 ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $true) | ($true = ((sK0 @ sK5) & (sK2 @ sK5))) | ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.52/1.30 thf(f115,plain,(
% 1.52/1.30 ((sK0 @ sK5) = $true) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5)))) | ((sK1 @ sK5) = $true) | ($true = ((sK0 @ sK5) & (sK2 @ sK5)))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.52/1.30 thf(f113,plain,(
% 1.52/1.30 (((sK0 @ sK5) & (sK1 @ sK5)) = $true) | ((sK1 @ sK5) = $true) | ($true = ((sK0 @ sK5) & (sK2 @ sK5))) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.52/1.30 thf(f111,plain,(
% 1.52/1.30 (((sK1 @ sK5) & (sK2 @ sK5)) = $true) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5)))) | ($true = ((sK0 @ sK5) & (sK2 @ sK5))) | (((sK0 @ sK5) & (sK1 @ sK5)) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.52/1.30 thf(f110,plain,(
% 1.52/1.30 ((((sK0 @ sK5) & (sK1 @ sK5)) | ((sK0 @ sK5) & (sK2 @ sK5))) = $true) | (((sK1 @ sK5) & (sK2 @ sK5)) = $true) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.52/1.30 thf(f12,plain,(
% 1.52/1.30 ($true = ((((sK0 @ sK5) & (sK1 @ sK5)) | ((sK0 @ sK5) & (sK2 @ sK5))) | ((sK1 @ sK5) & (sK2 @ sK5)))) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.52/1.30 thf(f236,plain,(
% 1.52/1.30 spl3_3 | spl3_1),
% 1.52/1.30 inference(avatar_split_clause,[status(thm)],[f156,f211,f219])).
% 1.52/1.30 thf(f156,plain,(
% 1.52/1.30 ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f155])).
% 1.52/1.30 thf(f155,plain,(
% 1.52/1.30 ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f151])).
% 1.52/1.30 thf(f151,plain,(
% 1.52/1.30 (((sK2 @ sK5) | (sK1 @ sK5)) = $true) | ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.52/1.30 thf(f143,plain,(
% 1.52/1.30 ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) = $true) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 1.52/1.30 thf(f142,plain,(
% 1.52/1.30 ($true = ((sK0 @ sK5) & (sK2 @ sK5))) | ((sK1 @ sK5) = $true) | ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.52/1.30 thf(f140,plain,(
% 1.52/1.30 ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5)))) | ($true = ((sK0 @ sK5) & (sK2 @ sK5))) | ((sK1 @ sK5) = $true)),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f114])).
% 1.52/1.30 thf(f114,plain,(
% 1.52/1.30 ($true = ((sK0 @ sK5) & (sK2 @ sK5))) | ((sK1 @ sK5) = $true) | ((sK1 @ sK5) = $true) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.52/1.30 thf(f231,plain,(
% 1.52/1.30 spl3_1 | spl3_2),
% 1.52/1.30 inference(avatar_split_clause,[status(thm)],[f176,f215,f211])).
% 1.52/1.30 thf(f176,plain,(
% 1.52/1.30 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f175])).
% 1.52/1.30 thf(f175,plain,(
% 1.52/1.30 ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 1.52/1.30 thf(f167,plain,(
% 1.52/1.30 ($true = (sK2 @ sK5)) | ((sK0 @ sK5) = $true) | ($true = ((sK0 @ sK5) | (sK2 @ sK5)))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 1.52/1.30 thf(f166,plain,(
% 1.52/1.30 ((sK0 @ sK5) = $true) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5)))) | ($true = (sK2 @ sK5))),
% 1.52/1.30 inference(duplicate_literal_removal,[status(thm)],[f165])).
% 1.52/1.30 thf(f165,plain,(
% 1.52/1.30 ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f163])).
% 1.52/1.30 thf(f163,plain,(
% 1.52/1.30 ((sK0 @ sK5) = $true) | (((sK0 @ sK5) & (sK1 @ sK5)) = $true) | ($true = (sK2 @ sK5)) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f112])).
% 1.52/1.30 thf(f112,plain,(
% 1.52/1.30 ($true = (sK2 @ sK5)) | ($true = ((sK0 @ sK5) & (sK2 @ sK5))) | (((sK0 @ sK5) & (sK1 @ sK5)) = $true) | ($true = ((((sK0 @ sK5) | (sK1 @ sK5)) & ((sK2 @ sK5) | (sK1 @ sK5))) & ((sK0 @ sK5) | (sK2 @ sK5))))),
% 1.52/1.30 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.52/1.30 % SZS output end Proof for DTF2THF_21286
% 1.52/1.30 % (21385)------------------------------
% 1.52/1.30 % (21385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (21385)Termination reason: Refutation
% 1.52/1.30
% 1.52/1.30 % (21385)Memory used [KB]: 5628
% 1.52/1.30 % (21385)Time elapsed: 0.009 s
% 1.52/1.30 % (21385)Instructions burned: 8 (million)
% 1.52/1.30 % (21385)------------------------------
% 1.52/1.30 % (21385)------------------------------
% 1.52/1.30 % (21382)Success in time 0.02 s
%------------------------------------------------------------------------------