%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU826^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:32 AM UTC 2026
% Result : Theorem 1.79s 1.50s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 23 unt; 0 typ; 5 def)
% Number of atoms : 619 ( 108 equ; 0 cnn)
% Maximal formula atoms : 13 ( 8 avg)
% Number of connectives : 453 ( 28 ~; 109 |; 28 &; 277 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 9 con; 0-3 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 56 ( 54 ^; 2 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
seteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
u: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
n: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
a: $i > $o ).
thf(func_def_5,type,
b: $i > $o ).
thf(func_def_6,type,
c: $i > $o ).
thf(f101,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f74,f81,f90,f93,f97,f100]) ).
thf(f100,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f99]) ).
thf(f99,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f78,f89]) ).
thf(f89,plain,
( ( ( c @ sK1 )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl0_5
<=> ( ( c @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f78,plain,
( ( ( c @ sK1 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl0_3
<=> ( ( c @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f97,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f69,f85]) ).
thf(f85,plain,
( ( ( b @ sK1 )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl0_4
<=> ( ( b @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f69,plain,
( ( ( b @ sK1 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl0_1
<=> ( ( b @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f93,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f92]) ).
thf(f92,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f73,f50]) ).
thf(f50,plain,
( $false
= ( a @ sK1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( a @ sK1 ) )
| ( $false
= ( a @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $false
= ( ( b @ sK1 )
| ( a @ sK1 ) ) )
| ( $false
= ( a @ sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false
= ( a @ sK1 ) )
| ( $false
= ( a @ sK1 ) )
| ( $false
= ( ( b @ sK1 )
| ( a @ sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $false
= ( a @ sK1 ) )
| ( $false
= ( ( c @ sK1 )
| ( a @ sK1 ) ) )
| ( $false
= ( ( b @ sK1 )
| ( a @ sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $false
= ( a @ sK1 ) )
| ( $false
= ( ( ( c @ sK1 )
| ( a @ sK1 ) )
& ( ( b @ sK1 )
| ( a @ sK1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $false
= ( ( ( c @ sK1 )
& ( b @ sK1 ) )
| ( a @ sK1 ) ) )
| ( $false
= ( ( ( c @ sK1 )
| ( a @ sK1 ) )
& ( ( b @ sK1 )
| ( a @ sK1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ( c @ sK1 )
| ( a @ sK1 ) )
& ( ( b @ sK1 )
| ( a @ sK1 ) ) )
!= ( ( ( c @ sK1 )
& ( b @ sK1 ) )
| ( a @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( ( ( c @ sK1 )
& ( b @ sK1 ) )
| ( a @ sK1 ) )
= ( ( ( c @ sK1 )
| ( a @ sK1 ) )
& ( ( b @ sK1 )
| ( a @ sK1 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: $i] :
( ( ( ( c @ Y0 )
& ( b @ Y0 ) )
| ( a @ Y0 ) )
= ( ( ( c @ Y0 )
| ( a @ Y0 ) )
& ( ( b @ Y0 )
| ( a @ Y0 ) ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( c @ Y0 )
& ( b @ Y0 ) )
| ( a @ Y0 ) )
= ( ( ( c @ Y0 )
| ( a @ Y0 ) )
& ( ( b @ Y0 )
| ( a @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ a
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ b
@ c ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ a
@ b )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ a
@ c ) ) ) ),
inference(definition_unfolding,[status(thm)],[f16,f18,f19,f17,f17,f19,f19]) ).
thf(f17,plain,
( n
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( n
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( n
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( n
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2THF_28008.p',n) ).
thf(f19,plain,
( u
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( u
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= u ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= u ),
file('/export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2THF_28008.p',u) ).
thf(f18,plain,
( seteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( seteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= seteq ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= seteq ),
file('/export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2THF_28008.p',seteq) ).
thf(f16,plain,
( ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ),
file('/export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2THF_28008.p',conj) ).
thf(f73,plain,
( ( $true
= ( a @ sK1 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f71,definition,
( spl0_2
<=> ( $true
= ( a @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f90,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f36,f87,f83]) ).
thf(f36,plain,
( ( ( b @ sK1 )
= $false )
| ( ( c @ sK1 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( c @ sK1 )
= $false )
| ( ( b @ sK1 )
= $false )
| ( ( b @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( c @ sK1 )
= $false )
| ( ( b @ sK1 )
= $false )
| ( $false
= ( ( b @ sK1 )
| ( a @ sK1 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $false
= ( ( b @ sK1 )
| ( a @ sK1 ) ) )
| ( ( c @ sK1 )
= $false )
| ( ( c @ sK1 )
= $false )
| ( ( b @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $false
= ( ( c @ sK1 )
| ( a @ sK1 ) ) )
| ( ( c @ sK1 )
= $false )
| ( $false
= ( ( b @ sK1 )
| ( a @ sK1 ) ) )
| ( ( b @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( b @ sK1 )
= $false )
| ( ( c @ sK1 )
= $false )
| ( $false
= ( ( ( c @ sK1 )
| ( a @ sK1 ) )
& ( ( b @ sK1 )
| ( a @ sK1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( ( c @ sK1 )
& ( b @ sK1 ) )
= $false )
| ( $false
= ( ( ( c @ sK1 )
| ( a @ sK1 ) )
& ( ( b @ sK1 )
| ( a @ sK1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f81,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f57,f76,f71]) ).
thf(f57,plain,
( ( $true
= ( a @ sK1 ) )
| ( ( c @ sK1 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true
= ( a @ sK1 ) )
| ( ( c @ sK1 )
= $true )
| ( ( c @ sK1 )
= $true )
| ( $true
= ( a @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ( c @ sK1 )
| ( a @ sK1 ) )
= $true )
| ( $true
= ( a @ sK1 ) )
| ( ( c @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true
= ( a @ sK1 ) )
| ( ( ( c @ sK1 )
& ( b @ sK1 ) )
= $true )
| ( ( ( c @ sK1 )
| ( a @ sK1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true
= ( ( ( c @ sK1 )
& ( b @ sK1 ) )
| ( a @ sK1 ) ) )
| ( ( ( c @ sK1 )
| ( a @ sK1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ( ( c @ sK1 )
| ( a @ sK1 ) )
& ( ( b @ sK1 )
| ( a @ sK1 ) ) )
= $true )
| ( $true
= ( ( ( c @ sK1 )
& ( b @ sK1 ) )
| ( a @ sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f74,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f65,f71,f67]) ).
thf(f65,plain,
( ( ( b @ sK1 )
= $true )
| ( $true
= ( a @ sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( b @ sK1 )
= $true )
| ( $true
= ( a @ sK1 ) )
| ( ( b @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
= ( a @ sK1 ) )
| ( ( b @ sK1 )
= $true )
| ( ( ( c @ sK1 )
& ( b @ sK1 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( ( c @ sK1 )
& ( b @ sK1 ) )
= $true )
| ( $true
= ( a @ sK1 ) )
| ( ( b @ sK1 )
= $true )
| ( $true
= ( a @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
= ( a @ sK1 ) )
| ( $true
= ( ( ( c @ sK1 )
& ( b @ sK1 ) )
| ( a @ sK1 ) ) )
| ( ( b @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true
= ( ( b @ sK1 )
| ( a @ sK1 ) ) )
| ( $true
= ( ( ( c @ sK1 )
& ( b @ sK1 ) )
| ( a @ sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU826^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n015.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:35:31 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.36/0.49 ---- Original DTF file ---
% 0.36/0.49 thf(spec,logic,$$dhol).
% 0.36/0.49 %------------------------------------------------------------------------------
% 0.36/0.49 % File : SEU826^1 : TPTP v9.2.1. Released v3.7.0.
% 0.36/0.49 % Domain : Set Theory
% 0.36/0.49 % Problem : About sets 1
% 0.36/0.49 % Version : Especial.
% 0.36/0.49 % English :
% 0.36/0.49
% 0.36/0.49 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.36/0.49 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.36/0.49 % Source : [Ben09]
% 0.36/0.49 % Names : Example 22a [BB05]
% 0.36/0.49
% 0.36/0.49 % Status : Theorem
% 0.36/0.49 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.00 v6.2.0, 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 v3.7.0
% 0.36/0.49 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.36/0.49 % Number of atoms : 19 ( 3 equ; 0 cnn)
% 0.36/0.49 % Maximal formula atoms : 13 ( 4 avg)
% 0.36/0.49 % Number of connectives : 21 ( 0 ~; 1 |; 1 &; 18 @)
% 0.36/0.49 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.36/0.49 % Maximal formula depth : 6 ( 2 avg)
% 0.36/0.49 % Number of types : 2 ( 0 usr)
% 0.36/0.49 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.36/0.49 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.36/0.49 % Number of variables : 9 ( 8 ^; 1 !; 0 ?; 9 :)
% 0.36/0.49 % SPC : TH0_THM_EQU_NAR
% 0.36/0.49
% 0.36/0.49 % Comments :
% 0.36/0.49 %------------------------------------------------------------------------------
% 0.36/0.49 thf(seteq_type,type,
% 0.36/0.49 seteq: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.36/0.49
% 0.36/0.49 thf(seteq,definition,
% 0.36/0.49 ( seteq
% 0.36/0.49 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.36/0.49 ! [U: $i] :
% 0.36/0.49 ( ( X @ U )
% 0.36/0.49 <=> ( Y @ U ) ) ) ) ).
% 0.36/0.49
% 0.36/0.49 thf(u_type,type,
% 0.36/0.49 u: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.36/0.49
% 0.36/0.49 thf(u,definition,
% 0.36/0.49 ( u
% 0.36/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.36/0.49 ( ( X @ U )
% 0.36/0.49 | ( Y @ U ) ) ) ) ).
% 0.36/0.49
% 0.36/0.49 thf(n_type,type,
% 0.36/0.49 n: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.36/0.49
% 0.36/0.49 thf(n,definition,
% 0.36/0.49 ( n
% 0.36/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.36/0.49 ( ( X @ U )
% 0.36/0.49 & ( Y @ U ) ) ) ) ).
% 0.36/0.49
% 0.36/0.49 thf(a_type,type,
% 0.36/0.49 a: $i > $o ).
% 0.36/0.49
% 0.36/0.49 thf(b_type,type,
% 0.36/0.49 b: $i > $o ).
% 0.36/0.49
% 0.36/0.49 thf(c_type,type,
% 0.36/0.49 c: $i > $o ).
% 0.36/0.49
% 0.36/0.49 thf(conj,conjecture,
% 0.36/0.49 seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ).
% 0.36/0.49
% 0.36/0.49 %------------------------------------------------------------------------------
% 0.36/0.49 ------------------------
% 1.65/1.46 ---- Embedded in THF ---
% 1.65/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.46 %%% Generated on Tue Feb 24 12:35:32 EST 2026
% 1.65/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.46 %%% Logic specification used:
% 1.65/1.46 %%% thf(spec, logic, $$dhol).
% 1.65/1.46
% 1.65/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2DTF28008.p
% See solution above
% 1.65/1.46 ------------------------
% 1.65/1.47 ---- Cleaned THF ---
% 1.65/1.47 thf(seteq_type,type,
% 1.65/1.47 seteq: ( $i > $o ) > ( $i > $o ) > $o ).
% 1.65/1.47
% 1.65/1.47 thf(seteq,definition,
% 1.65/1.47 ( seteq
% 1.65/1.47 = ( ^ [X: $i > $o,Y: $i > $o] :
% 1.65/1.47 ! [U: $i] :
% 1.65/1.47 ( ( X @ U )
% 1.65/1.47 <=> ( Y @ U ) ) ) ) ).
% 1.65/1.47
% 1.65/1.47 thf(u_type,type,
% 1.65/1.47 u: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.65/1.47
% 1.65/1.47 thf(u,definition,
% 1.65/1.47 ( u
% 1.65/1.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.65/1.47 ( ( X @ U )
% 1.65/1.47 | ( Y @ U ) ) ) ) ).
% 1.65/1.47
% 1.65/1.47 thf(n_type,type,
% 1.65/1.47 n: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.65/1.47
% 1.65/1.47 thf(n,definition,
% 1.65/1.47 ( n
% 1.65/1.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.65/1.47 ( ( X @ U )
% 1.65/1.47 & ( Y @ U ) ) ) ) ).
% 1.65/1.47
% 1.65/1.47 thf(a_type,type,
% 1.65/1.47 a: $i > $o ).
% 1.65/1.47
% 1.65/1.47 thf(b_type,type,
% 1.65/1.47 b: $i > $o ).
% 1.65/1.47
% 1.65/1.47 thf(c_type,type,
% 1.65/1.47 c: $i > $o ).
% 1.65/1.47
% 1.65/1.47 thf(conj,conjecture,
% 1.65/1.47 seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ).
% 1.65/1.47 ------------------------
% 1.65/1.49 % (28108)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_28008 for (2999ds/27Mi)
% 1.65/1.49 % (28112)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28008 for (2999ds/18Mi)
% 1.65/1.49 % (28107)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_28008 for (2999ds/4Mi)
% 1.65/1.49 % (28111)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_28008 for (2999ds/275Mi)
% 1.65/1.49 % (28109)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28008 for (2999ds/2Mi)
% 1.65/1.49 % (28110)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_28008 for (2999ds/2Mi)
% 1.65/1.49 % (28106)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28008 for (2999ds/183Mi)
% 1.65/1.49 % (28109)Instruction limit reached!
% 1.65/1.49 % (28109)------------------------------
% 1.65/1.49 % (28109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (28109)Termination reason: Unknown
% 1.65/1.49 % (28109)Termination phase: Saturation
% 1.65/1.49
% 1.65/1.49 % (28109)Memory used [KB]: 5373
% 1.65/1.49 % (28109)Time elapsed: 0.003 s
% 1.65/1.49 % (28109)Instructions burned: 2 (million)
% 1.65/1.49 % (28109)------------------------------
% 1.65/1.49 % (28109)------------------------------
% 1.65/1.49 % (28110)Instruction limit reached!
% 1.65/1.49 % (28110)------------------------------
% 1.65/1.49 % (28110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (28110)Termination reason: Unknown
% 1.65/1.49 % (28110)Termination phase: Saturation
% 1.65/1.49
% 1.65/1.49 % (28110)Memory used [KB]: 5500
% 1.65/1.49 % (28110)Time elapsed: 0.003 s
% 1.65/1.49 % (28110)Instructions burned: 2 (million)
% 1.65/1.49 % (28110)------------------------------
% 1.65/1.49 % (28110)------------------------------
% 1.65/1.49 % (28111)Refutation not found, incomplete strategy
% 1.65/1.49 % (28111)------------------------------
% 1.65/1.49 % (28111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (28111)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.49
% 1.65/1.49
% 1.65/1.49 % (28111)Memory used [KB]: 5373
% 1.65/1.49 % (28111)Time elapsed: 0.003 s
% 1.65/1.49 % (28111)Instructions burned: 1 (million)
% 1.65/1.49 % (28111)------------------------------
% 1.65/1.49 % (28111)------------------------------
% 1.65/1.49 % (28107)Instruction limit reached!
% 1.65/1.49 % (28107)------------------------------
% 1.65/1.49 % (28107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (28107)Termination reason: Unknown
% 1.65/1.49 % (28107)Termination phase: Saturation
% 1.65/1.49
% 1.65/1.49 % (28107)Memory used [KB]: 5500
% 1.65/1.49 % (28107)Time elapsed: 0.004 s
% 1.65/1.49 % (28107)Instructions burned: 4 (million)
% 1.65/1.49 % (28107)------------------------------
% 1.65/1.49 % (28107)------------------------------
% 1.65/1.49 % (28112)First to succeed.
% 1.65/1.50 % (28106)Also succeeded, but the first one will report.
% 1.79/1.50 % (28108)Also succeeded, but the first one will report.
% 1.79/1.50 % (28112)Refutation found. Thanks to Tanya!
% 1.79/1.50 % SZS status Theorem for DTF2THF_28008
% 1.79/1.50 % SZS output start Proof for DTF2THF_28008
% 1.79/1.50 thf(func_def_0, type, seteq: ($i > $o) > ($i > $o) > $o).
% 1.79/1.50 thf(func_def_2, type, u: ($i > $o) > ($i > $o) > $i > $o).
% 1.79/1.50 thf(func_def_3, type, n: ($i > $o) > ($i > $o) > $i > $o).
% 1.79/1.50 thf(func_def_4, type, a: $i > $o).
% 1.79/1.50 thf(func_def_5, type, b: $i > $o).
% 1.79/1.50 thf(func_def_6, type, c: $i > $o).
% 1.79/1.50 thf(f101,plain,(
% 1.79/1.50 $false),
% 1.79/1.50 inference(avatar_sat_refutation,[status(thm)],[f74,f81,f90,f93,f97,f100])).
% 1.79/1.50 thf(f100,plain,(
% 1.79/1.50 ~spl0_3 | ~spl0_5),
% 1.79/1.50 inference(avatar_contradiction_clause,[status(thm)],[f99])).
% 1.79/1.50 thf(f99,plain,(
% 1.79/1.50 $false | (~spl0_3 | ~spl0_5)),
% 1.79/1.50 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.79/1.50 thf(f98,plain,(
% 1.79/1.50 ($false = $true) | (~spl0_3 | ~spl0_5)),
% 1.79/1.50 inference(backward_demodulation,[status(thm)],[f78,f89])).
% 1.79/1.50 thf(f89,plain,(
% 1.79/1.50 ((c @ sK1) = $false) | ~spl0_5),
% 1.79/1.50 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.79/1.50 thf(f87,definition,(
% 1.79/1.50 spl0_5 <=> ((c @ sK1) = $false)),
% 1.79/1.50 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.79/1.50 thf(f78,plain,(
% 1.79/1.50 ((c @ sK1) = $true) | ~spl0_3),
% 1.79/1.50 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.79/1.50 thf(f76,definition,(
% 1.79/1.50 spl0_3 <=> ((c @ sK1) = $true)),
% 1.79/1.50 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.79/1.50 thf(f97,plain,(
% 1.79/1.50 ~spl0_1 | ~spl0_4),
% 1.79/1.50 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 1.79/1.50 thf(f96,plain,(
% 1.79/1.50 $false | (~spl0_1 | ~spl0_4)),
% 1.79/1.50 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.79/1.50 thf(f95,plain,(
% 1.79/1.50 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 1.79/1.50 inference(forward_demodulation,[status(thm)],[f69,f85])).
% 1.79/1.50 thf(f85,plain,(
% 1.79/1.50 ((b @ sK1) = $false) | ~spl0_4),
% 1.79/1.50 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.79/1.50 thf(f83,definition,(
% 1.79/1.50 spl0_4 <=> ((b @ sK1) = $false)),
% 1.79/1.50 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.79/1.50 thf(f69,plain,(
% 1.79/1.50 ((b @ sK1) = $true) | ~spl0_1),
% 1.79/1.50 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.79/1.50 thf(f67,definition,(
% 1.79/1.50 spl0_1 <=> ((b @ sK1) = $true)),
% 1.79/1.50 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.79/1.50 thf(f93,plain,(
% 1.79/1.50 ~spl0_2),
% 1.79/1.50 inference(avatar_contradiction_clause,[status(thm)],[f92])).
% 1.79/1.50 thf(f92,plain,(
% 1.79/1.50 $false | ~spl0_2),
% 1.79/1.50 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.79/1.50 thf(f91,plain,(
% 1.79/1.50 ($false = $true) | ~spl0_2),
% 1.79/1.50 inference(forward_demodulation,[status(thm)],[f73,f50])).
% 1.79/1.50 thf(f50,plain,(
% 1.79/1.50 ($false = (a @ sK1))),
% 1.79/1.50 inference(duplicate_literal_removal,[status(thm)],[f48])).
% 1.79/1.50 thf(f48,plain,(
% 1.79/1.50 ($false = (a @ sK1)) | ($false = (a @ sK1))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.79/1.50 thf(f47,plain,(
% 1.79/1.50 ($false = ((b @ sK1) | (a @ sK1))) | ($false = (a @ sK1))),
% 1.79/1.50 inference(duplicate_literal_removal,[status(thm)],[f42])).
% 1.79/1.50 thf(f42,plain,(
% 1.79/1.50 ($false = (a @ sK1)) | ($false = (a @ sK1)) | ($false = ((b @ sK1) | (a @ sK1)))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.79/1.50 thf(f41,plain,(
% 1.79/1.50 ($false = (a @ sK1)) | ($false = ((c @ sK1) | (a @ sK1))) | ($false = ((b @ sK1) | (a @ sK1)))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.79/1.50 thf(f27,plain,(
% 1.79/1.50 ($false = (a @ sK1)) | ($false = (((c @ sK1) | (a @ sK1)) & ((b @ sK1) | (a @ sK1))))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.79/1.50 thf(f26,plain,(
% 1.79/1.50 ($false = (((c @ sK1) & (b @ sK1)) | (a @ sK1))) | ($false = (((c @ sK1) | (a @ sK1)) & ((b @ sK1) | (a @ sK1))))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.79/1.50 thf(f24,plain,(
% 1.79/1.50 ((((c @ sK1) | (a @ sK1)) & ((b @ sK1) | (a @ sK1))) != (((c @ sK1) & (b @ sK1)) | (a @ sK1)))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.79/1.50 thf(f23,plain,(
% 1.79/1.50 (((((c @ sK1) & (b @ sK1)) | (a @ sK1)) = (((c @ sK1) | (a @ sK1)) & ((b @ sK1) | (a @ sK1)))) = $false)),
% 1.79/1.50 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.79/1.50 thf(f22,plain,(
% 1.79/1.50 (((^[Y0 : $i]: ((((c @ Y0) & (b @ Y0)) | (a @ Y0)) = (((c @ Y0) | (a @ Y0)) & ((b @ Y0) | (a @ Y0))))) @ sK1) = $false)),
% 1.79/1.50 inference(sigma_clausification,[status(thm)],[f21])).
% 1.79/1.50 thf(f21,plain,(
% 1.79/1.50 ($true != (!! @ $i @ (^[Y0 : $i]: ((((c @ Y0) & (b @ Y0)) | (a @ Y0)) = (((c @ Y0) | (a @ Y0)) & ((b @ Y0) | (a @ Y0)))))))),
% 1.79/1.50 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.79/1.50 thf(f20,plain,(
% 1.79/1.50 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ a @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ b @ c)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ a @ b) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ a @ c))))),
% 1.79/1.50 inference(definition_unfolding,[status(thm)],[f16,f18,f19,f17,f17,f19,f19])).
% 1.79/1.50 thf(f17,plain,(
% 1.79/1.50 (n = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.79/1.50 inference(cnf_transformation,[status(thm)],[f10])).
% 1.79/1.50 thf(f10,plain,(
% 1.79/1.50 (n = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.79/1.50 inference(fool_elimination,[status(thm)],[f9])).
% 1.79/1.50 thf(f9,plain,(
% 1.79/1.50 (n = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))))),
% 1.79/1.50 inference(rectify,[status(thm)],[f3])).
% 1.79/1.50 thf(f3,axiom,(
% 1.79/1.50 (n = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))))),
% 1.79/1.50 file('/export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2THF_28008.p',n)).
% 1.79/1.50 thf(f19,plain,(
% 1.79/1.50 (u = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.79/1.50 inference(cnf_transformation,[status(thm)],[f14])).
% 1.79/1.50 thf(f14,plain,(
% 1.79/1.50 (u = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.79/1.50 inference(fool_elimination,[status(thm)],[f13])).
% 1.79/1.50 thf(f13,plain,(
% 1.79/1.50 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = u)),
% 1.79/1.50 inference(rectify,[status(thm)],[f2])).
% 1.79/1.50 thf(f2,axiom,(
% 1.79/1.50 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = u)),
% 1.79/1.50 file('/export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2THF_28008.p',u)).
% 1.79/1.50 thf(f18,plain,(
% 1.79/1.50 (seteq = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.79/1.50 inference(cnf_transformation,[status(thm)],[f12])).
% 1.79/1.50 thf(f12,plain,(
% 1.79/1.50 (seteq = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.79/1.50 inference(fool_elimination,[status(thm)],[f11])).
% 1.79/1.50 thf(f11,plain,(
% 1.79/1.50 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) <=> (X1 @ X2)))) = seteq)),
% 1.79/1.50 inference(rectify,[status(thm)],[f1])).
% 1.79/1.50 thf(f1,axiom,(
% 1.79/1.50 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) <=> (X1 @ X2)))) = seteq)),
% 1.79/1.50 file('/export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2THF_28008.p',seteq)).
% 1.79/1.50 thf(f16,plain,(
% 1.79/1.50 ((seteq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c))) != $true)),
% 1.79/1.50 inference(cnf_transformation,[status(thm)],[f15])).
% 1.79/1.50 thf(f15,plain,(
% 1.79/1.50 ((seteq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c))) != $true)),
% 1.79/1.50 inference(flattening,[status(thm)],[f8])).
% 1.79/1.50 thf(f8,plain,(
% 1.79/1.50 ~((seteq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c))) = $true)),
% 1.79/1.50 inference(fool_elimination,[status(thm)],[f7])).
% 1.79/1.50 thf(f7,plain,(
% 1.79/1.50 ~(seteq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c)))),
% 1.79/1.50 inference(rectify,[status(thm)],[f5])).
% 1.79/1.50 thf(f5,negated_conjecture,(
% 1.79/1.50 ~(seteq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c)))),
% 1.79/1.50 inference(negated_conjecture,[status(cth)],[f4])).
% 1.79/1.50 thf(f4,conjecture,(
% 1.79/1.50 (seteq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c)))),
% 1.79/1.50 file('/export/starexec/sandbox/tmp/tmp.qGCOihAaoc/DTF2THF_28008.p',conj)).
% 1.79/1.50 thf(f73,plain,(
% 1.79/1.50 ($true = (a @ sK1)) | ~spl0_2),
% 1.79/1.50 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.79/1.50 thf(f71,definition,(
% 1.79/1.50 spl0_2 <=> ($true = (a @ sK1))),
% 1.79/1.50 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.79/1.50 thf(f90,plain,(
% 1.79/1.50 spl0_4 | spl0_5),
% 1.79/1.50 inference(avatar_split_clause,[status(thm)],[f36,f87,f83])).
% 1.79/1.50 thf(f36,plain,(
% 1.79/1.50 ((b @ sK1) = $false) | ((c @ sK1) = $false)),
% 1.79/1.50 inference(duplicate_literal_removal,[status(thm)],[f35])).
% 1.79/1.50 thf(f35,plain,(
% 1.79/1.50 ((c @ sK1) = $false) | ((b @ sK1) = $false) | ((b @ sK1) = $false)),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.79/1.50 thf(f33,plain,(
% 1.79/1.50 ((c @ sK1) = $false) | ((b @ sK1) = $false) | ($false = ((b @ sK1) | (a @ sK1)))),
% 1.79/1.50 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.79/1.50 thf(f32,plain,(
% 1.79/1.50 ($false = ((b @ sK1) | (a @ sK1))) | ((c @ sK1) = $false) | ((c @ sK1) = $false) | ((b @ sK1) = $false)),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.79/1.50 thf(f30,plain,(
% 1.79/1.50 ($false = ((c @ sK1) | (a @ sK1))) | ((c @ sK1) = $false) | ($false = ((b @ sK1) | (a @ sK1))) | ((b @ sK1) = $false)),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.79/1.50 thf(f29,plain,(
% 1.79/1.50 ((b @ sK1) = $false) | ((c @ sK1) = $false) | ($false = (((c @ sK1) | (a @ sK1)) & ((b @ sK1) | (a @ sK1))))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.79/1.50 thf(f28,plain,(
% 1.79/1.50 (((c @ sK1) & (b @ sK1)) = $false) | ($false = (((c @ sK1) | (a @ sK1)) & ((b @ sK1) | (a @ sK1))))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.79/1.50 thf(f81,plain,(
% 1.79/1.50 spl0_2 | spl0_3),
% 1.79/1.50 inference(avatar_split_clause,[status(thm)],[f57,f76,f71])).
% 1.79/1.50 thf(f57,plain,(
% 1.79/1.50 ($true = (a @ sK1)) | ((c @ sK1) = $true)),
% 1.79/1.50 inference(duplicate_literal_removal,[status(thm)],[f56])).
% 1.79/1.50 thf(f56,plain,(
% 1.79/1.50 ($true = (a @ sK1)) | ((c @ sK1) = $true) | ((c @ sK1) = $true) | ($true = (a @ sK1))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.79/1.50 thf(f55,plain,(
% 1.79/1.50 (((c @ sK1) | (a @ sK1)) = $true) | ($true = (a @ sK1)) | ((c @ sK1) = $true)),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.79/1.50 thf(f53,plain,(
% 1.79/1.50 ($true = (a @ sK1)) | (((c @ sK1) & (b @ sK1)) = $true) | (((c @ sK1) | (a @ sK1)) = $true)),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.79/1.50 thf(f52,plain,(
% 1.79/1.50 ($true = (((c @ sK1) & (b @ sK1)) | (a @ sK1))) | (((c @ sK1) | (a @ sK1)) = $true)),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.79/1.50 thf(f25,plain,(
% 1.79/1.50 ((((c @ sK1) | (a @ sK1)) & ((b @ sK1) | (a @ sK1))) = $true) | ($true = (((c @ sK1) & (b @ sK1)) | (a @ sK1)))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.79/1.50 thf(f74,plain,(
% 1.79/1.50 spl0_1 | spl0_2),
% 1.79/1.50 inference(avatar_split_clause,[status(thm)],[f65,f71,f67])).
% 1.79/1.50 thf(f65,plain,(
% 1.79/1.50 ((b @ sK1) = $true) | ($true = (a @ sK1))),
% 1.79/1.50 inference(duplicate_literal_removal,[status(thm)],[f63])).
% 1.79/1.50 thf(f63,plain,(
% 1.79/1.50 ((b @ sK1) = $true) | ($true = (a @ sK1)) | ((b @ sK1) = $true)),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.79/1.50 thf(f62,plain,(
% 1.79/1.50 ($true = (a @ sK1)) | ((b @ sK1) = $true) | (((c @ sK1) & (b @ sK1)) = $true)),
% 1.79/1.50 inference(duplicate_literal_removal,[status(thm)],[f61])).
% 1.79/1.50 thf(f61,plain,(
% 1.79/1.50 (((c @ sK1) & (b @ sK1)) = $true) | ($true = (a @ sK1)) | ((b @ sK1) = $true) | ($true = (a @ sK1))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.79/1.50 thf(f60,plain,(
% 1.79/1.50 ($true = (a @ sK1)) | ($true = (((c @ sK1) & (b @ sK1)) | (a @ sK1))) | ((b @ sK1) = $true)),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.79/1.50 thf(f51,plain,(
% 1.79/1.50 ($true = ((b @ sK1) | (a @ sK1))) | ($true = (((c @ sK1) & (b @ sK1)) | (a @ sK1)))),
% 1.79/1.50 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.79/1.50 % SZS output end Proof for DTF2THF_28008
% 1.79/1.50 % (28112)------------------------------
% 1.79/1.50 % (28112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.50 % (28112)Termination reason: Refutation
% 1.79/1.50
% 1.79/1.50 % (28112)Memory used [KB]: 5500
% 1.79/1.50 % (28112)Time elapsed: 0.006 s
% 1.79/1.50 % (28112)Instructions burned: 4 (million)
% 1.79/1.50 % (28112)------------------------------
% 1.79/1.50 % (28112)------------------------------
% 1.79/1.50 % (28105)Success in time 0.021 s
%------------------------------------------------------------------------------