%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU827^1 : 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 : n020.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 1.59s 1.37s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 27 unt; 0 typ; 6 def)
% Number of atoms : 630 ( 104 equ; 0 cnn)
% Maximal formula atoms : 13 ( 8 avg)
% Number of connectives : 513 ( 35 ~; 117 |; 37 &; 306 @)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 10 con; 0-3 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 70 ( 68 ^; 2 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: ( $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(func_def_18,type,
sK1: ( $i > $o ) > $o ).
thf(func_def_20,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f130,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f81,f88,f97,f108,f114,f121,f129]) ).
thf(f129,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f128]) ).
thf(f128,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f80,f96]) ).
thf(f96,plain,
( ( $false
= ( c @ sK3 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f94,definition,
( spl0_5
<=> ( $false
= ( c @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
= ( c @ sK3 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl0_2
<=> ( $true
= ( c @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f121,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f120]) ).
thf(f120,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f76,f101]) ).
thf(f101,plain,
( ( $false
= ( a @ sK3 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl0_6
<=> ( $false
= ( a @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f76,plain,
( ( $true
= ( a @ sK3 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f74,definition,
( spl0_1
<=> ( $true
= ( a @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f114,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f113]) ).
thf(f113,plain,
( $false
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f85,f92]) ).
thf(f92,plain,
( ( $false
= ( b @ sK3 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl0_4
<=> ( $false
= ( b @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f85,plain,
( ( ( b @ sK3 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl0_3
<=> ( ( b @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f108,plain,
spl0_6,
inference(avatar_split_clause,[status(thm)],[f42,f99]) ).
thf(f42,plain,
( $false
= ( a @ sK3 ) ),
inference(duplicate_literal_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $false
= ( a @ sK3 ) )
| ( $false
= ( a @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $false
= ( a @ sK3 ) )
| ( $false
= ( ( a @ sK3 )
| ( b @ sK3 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $false
= ( a @ sK3 ) )
| ( $false
= ( a @ sK3 ) )
| ( $false
= ( ( a @ sK3 )
| ( b @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ( a @ sK3 )
| ( ( b @ sK3 )
& ( c @ sK3 ) ) )
= $false )
| ( $false
= ( a @ sK3 ) )
| ( $false
= ( ( a @ sK3 )
| ( b @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ( a @ sK3 )
| ( c @ sK3 ) )
= $false )
| ( $false
= ( ( a @ sK3 )
| ( b @ sK3 ) ) )
| ( ( ( a @ sK3 )
| ( ( b @ sK3 )
& ( c @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $false
= ( ( ( a @ sK3 )
| ( b @ sK3 ) )
& ( ( a @ sK3 )
| ( c @ sK3 ) ) ) )
| ( ( ( a @ sK3 )
| ( ( b @ sK3 )
& ( c @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( a @ sK3 )
| ( ( b @ sK3 )
& ( c @ sK3 ) ) )
!= ( ( ( a @ sK3 )
| ( b @ sK3 ) )
& ( ( a @ sK3 )
| ( c @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ^ [Y0: $i] :
( ( a @ Y0 )
| ( ( b @ Y0 )
& ( c @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: $i] :
( ( ( a @ Y0 )
| ( b @ Y0 ) )
& ( ( a @ Y0 )
| ( c @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ^ [Y0: $i] :
( ( ( a @ Y0 )
| ( b @ Y0 ) )
& ( ( a @ Y0 )
| ( c @ Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( a @ Y0 )
| ( ( b @ Y0 )
& ( c @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( ^ [Y0: $i] :
( ( ( a @ Y0 )
| ( b @ Y0 ) )
& ( ( a @ Y0 )
| ( c @ Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( a @ Y0 )
| ( ( b @ Y0 )
& ( c @ Y0 ) ) ) ) )
| ( $false = $true ) ),
inference(constrained_superposition,[status(thm)],[f25,f24]) ).
thf(f24,plain,
( ( sK1
@ ^ [Y0: $i] :
( ( ( a @ Y0 )
| ( b @ Y0 ) )
& ( ( a @ Y0 )
| ( c @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( sK1
@ ^ [Y0: $i] :
( ( a @ Y0 )
| ( ( b @ Y0 )
& ( c @ Y0 ) ) ) )
=> ( sK1
@ ^ [Y0: $i] :
( ( ( a @ Y0 )
| ( b @ Y0 ) )
& ( ( a @ Y0 )
| ( c @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( Y0
@ ^ [Y1: $i] :
( ( a @ Y1 )
| ( ( b @ Y1 )
& ( c @ Y1 ) ) ) )
=> ( Y0
@ ^ [Y1: $i] :
( ( ( a @ Y1 )
| ( b @ Y1 ) )
& ( ( a @ Y1 )
| ( c @ Y1 ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
!= ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( Y0
@ ^ [Y1: $i] :
( ( a @ Y1 )
| ( ( b @ Y1 )
& ( c @ Y1 ) ) ) )
=> ( Y0
@ ^ [Y1: $i] :
( ( ( a @ Y1 )
| ( b @ Y1 ) )
& ( ( a @ Y1 )
| ( c @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ a
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ b
@ c ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ a
@ b )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ a
@ c ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f17,f19,f16,f18,f18,f16,f16]) ).
thf(f18,plain,
( n
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( n
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= n ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= n ),
file('/export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2THF_22168.p',n) ).
thf(f16,plain,
( u
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( u
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= u ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X0 @ X3 ) ) )
= u ),
file('/export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2THF_22168.p',u) ).
thf(f19,plain,
( leibeq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( leibeq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: ( $i > $o ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: ( $i > $o ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
file('/export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2THF_22168.p',leibeq) ).
thf(f17,plain,
( ( leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ),
file('/export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2THF_22168.p',conj) ).
thf(f25,plain,
( $true
= ( sK1
@ ^ [Y0: $i] :
( ( a @ Y0 )
| ( ( b @ Y0 )
& ( c @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f97,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f58,f94,f90]) ).
thf(f58,plain,
( ( $false
= ( b @ sK3 ) )
| ( $false
= ( c @ sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $false
= ( b @ sK3 ) )
| ( $false
= ( c @ sK3 ) )
| ( $false
= ( c @ sK3 ) )
| ( $false
= ( b @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ( b @ sK3 )
& ( c @ sK3 ) )
= $false )
| ( $false
= ( b @ sK3 ) )
| ( $false
= ( c @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( b @ sK3 ) )
| ( $false
= ( c @ sK3 ) )
| ( ( ( a @ sK3 )
| ( ( b @ sK3 )
& ( c @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $false
= ( ( a @ sK3 )
| ( b @ sK3 ) ) )
| ( $false
= ( c @ sK3 ) )
| ( ( ( a @ sK3 )
| ( ( b @ sK3 )
& ( c @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f88,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f66,f83,f74]) ).
thf(f66,plain,
( ( ( b @ sK3 )
= $true )
| ( $true
= ( a @ sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( b @ sK3 )
= $true )
| ( ( b @ sK3 )
= $true )
| ( $true
= ( a @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( b @ sK3 )
= $true )
| ( $true
= ( a @ sK3 ) )
| ( ( ( b @ sK3 )
& ( c @ sK3 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
= ( a @ sK3 ) )
| ( $true
= ( a @ sK3 ) )
| ( ( b @ sK3 )
= $true )
| ( ( ( b @ sK3 )
& ( c @ sK3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true
= ( a @ sK3 ) )
| ( $true
= ( ( a @ sK3 )
| ( b @ sK3 ) ) )
| ( ( ( b @ sK3 )
& ( c @ sK3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true
= ( a @ sK3 ) )
| ( $true
= ( ( ( a @ sK3 )
| ( b @ sK3 ) )
& ( ( a @ sK3 )
| ( c @ sK3 ) ) ) )
| ( ( ( b @ sK3 )
& ( c @ sK3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( ( a @ sK3 )
| ( ( b @ sK3 )
& ( c @ sK3 ) ) )
= $true )
| ( $true
= ( ( ( a @ sK3 )
| ( b @ sK3 ) )
& ( ( a @ sK3 )
| ( c @ sK3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f81,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f72,f78,f74]) ).
thf(f72,plain,
( ( $true
= ( c @ sK3 ) )
| ( $true
= ( a @ sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true
= ( c @ sK3 ) )
| ( $true
= ( c @ sK3 ) )
| ( $true
= ( a @ sK3 ) )
| ( $true
= ( a @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( ( a @ sK3 )
| ( c @ sK3 ) )
= $true )
| ( $true
= ( c @ sK3 ) )
| ( $true
= ( a @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( ( b @ sK3 )
& ( c @ sK3 ) )
= $true )
| ( $true
= ( a @ sK3 ) )
| ( ( ( a @ sK3 )
| ( c @ sK3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU827^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.08 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.26 % Computer : n020.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Tue Feb 24 12:35:27 EST 2026
% 0.08/0.26 % CPUTime :
% 0.08/0.26 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 ---- Original DTF file ---
% 0.08/0.34 thf(spec,logic,$$dhol).
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 % File : SEU827^1 : TPTP v9.2.1. Released v3.7.0.
% 0.08/0.34 % Domain : Set Theory
% 0.08/0.34 % Problem : About sets 2
% 0.08/0.34 % Version : Especial.
% 0.08/0.34 % English :
% 0.08/0.34
% 0.08/0.34 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.08/0.34 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.08/0.34 % Source : [Ben09]
% 0.08/0.34 % Names : Example 22b [BB05]
% 0.08/0.34
% 0.08/0.34 % Status : Theorem
% 0.08/0.34 % : Without Boolean extensionality : CounterSatisfiable
% 0.08/0.34 % : Without xi extensionality : CounterSatisfiable
% 0.08/0.34 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.44 v7.2.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.0, 0.33 v3.7.0
% 0.08/0.34 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.08/0.34 % Number of atoms : 19 ( 3 equ; 0 cnn)
% 0.08/0.34 % Maximal formula atoms : 13 ( 4 avg)
% 0.08/0.34 % Number of connectives : 21 ( 0 ~; 1 |; 1 &; 18 @)
% 0.08/0.34 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.08/0.34 % Maximal formula depth : 6 ( 2 avg)
% 0.08/0.34 % Number of types : 2 ( 0 usr)
% 0.08/0.34 % Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% 0.08/0.34 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.08/0.34 % Number of variables : 9 ( 8 ^; 1 !; 0 ?; 9 :)
% 0.08/0.34 % SPC : TH0_THM_EQU_NAR
% 0.08/0.34
% 0.08/0.34 % Comments :
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 thf(leibeq_type,type,
% 0.08/0.34 leibeq: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.08/0.34
% 0.08/0.34 thf(leibeq,definition,
% 0.08/0.34 ( leibeq
% 0.08/0.34 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.08/0.34 ! [P: ( $i > $o ) > $o] :
% 0.08/0.34 ( ( P @ X )
% 0.08/0.34 => ( P @ Y ) ) ) ) ).
% 0.08/0.34
% 0.08/0.34 thf(u_type,type,
% 0.08/0.34 u: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.08/0.34
% 0.08/0.34 thf(u,definition,
% 0.08/0.34 ( u
% 0.08/0.34 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.08/0.34 ( ( X @ U )
% 0.08/0.34 | ( Y @ U ) ) ) ) ).
% 0.08/0.34
% 0.08/0.34 thf(n_type,type,
% 0.08/0.34 n: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.08/0.34
% 0.08/0.34 thf(n,definition,
% 0.08/0.34 ( n
% 0.08/0.34 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.08/0.34 ( ( X @ U )
% 0.08/0.34 & ( Y @ U ) ) ) ) ).
% 0.08/0.34
% 0.08/0.34 thf(a_type,type,
% 0.08/0.34 a: $i > $o ).
% 0.08/0.34
% 0.08/0.34 thf(b_type,type,
% 0.08/0.34 b: $i > $o ).
% 0.08/0.34
% 0.08/0.34 thf(c_type,type,
% 0.08/0.34 c: $i > $o ).
% 0.08/0.34
% 0.08/0.34 thf(conj,conjecture,
% 0.08/0.34 leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ).
% 0.08/0.34
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 ------------------------
% 1.59/1.33 ---- Embedded in THF ---
% 1.59/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.33 %%% Generated on Tue Feb 24 12:35:28 EST 2026
% 1.59/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.33 %%% Logic specification used:
% 1.59/1.33 %%% thf(spec, logic, $$dhol).
% 1.59/1.33
% 1.59/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2DTF22168.p
% See solution above
% 1.59/1.33 ------------------------
% 1.59/1.34 ---- Cleaned THF ---
% 1.59/1.34 thf(leibeq_type,type,
% 1.59/1.34 leibeq: ( $i > $o ) > ( $i > $o ) > $o ).
% 1.59/1.34
% 1.59/1.34 thf(leibeq,definition,
% 1.59/1.34 ( leibeq
% 1.59/1.34 = ( ^ [X: $i > $o,Y: $i > $o] :
% 1.59/1.34 ! [P: ( $i > $o ) > $o] :
% 1.59/1.34 ( ( P @ X )
% 1.59/1.34 => ( P @ Y ) ) ) ) ).
% 1.59/1.34
% 1.59/1.34 thf(u_type,type,
% 1.59/1.34 u: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.59/1.34
% 1.59/1.34 thf(u,definition,
% 1.59/1.34 ( u
% 1.59/1.34 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.59/1.34 ( ( X @ U )
% 1.59/1.34 | ( Y @ U ) ) ) ) ).
% 1.59/1.34
% 1.59/1.34 thf(n_type,type,
% 1.59/1.34 n: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.59/1.34
% 1.59/1.34 thf(n,definition,
% 1.59/1.34 ( n
% 1.59/1.34 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.59/1.34 ( ( X @ U )
% 1.59/1.34 & ( Y @ U ) ) ) ) ).
% 1.59/1.34
% 1.59/1.34 thf(a_type,type,
% 1.59/1.34 a: $i > $o ).
% 1.59/1.34
% 1.59/1.34 thf(b_type,type,
% 1.59/1.34 b: $i > $o ).
% 1.59/1.34
% 1.59/1.34 thf(c_type,type,
% 1.59/1.34 c: $i > $o ).
% 1.59/1.34
% 1.59/1.34 thf(conj,conjecture,
% 1.59/1.34 leibeq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ).
% 1.59/1.34 ------------------------
% 1.59/1.36 % (22352)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_22168 for (2999ds/4Mi)
% 1.59/1.36 % (22357)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22168 for (2999ds/18Mi)
% 1.59/1.36 % (22356)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_22168 for (2999ds/275Mi)
% 1.59/1.36 % (22351)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22168 for (2999ds/183Mi)
% 1.59/1.36 % (22354)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22168 for (2999ds/2Mi)
% 1.59/1.36 % (22355)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_22168 for (2999ds/2Mi)
% 1.59/1.36 % (22356)Refutation not found, incomplete strategy
% 1.59/1.36 % (22356)------------------------------
% 1.59/1.36 % (22356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (22356)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.36
% 1.59/1.36
% 1.59/1.36 % (22353)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_22168 for (2999ds/27Mi)
% 1.59/1.36 % (22356)Memory used [KB]: 5500
% 1.59/1.36 % (22356)Time elapsed: 0.003 s
% 1.59/1.36 % (22356)Instructions burned: 2 (million)
% 1.59/1.36 % (22356)------------------------------
% 1.59/1.36 % (22356)------------------------------
% 1.59/1.36 % (22354)Instruction limit reached!
% 1.59/1.36 % (22354)------------------------------
% 1.59/1.36 % (22354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (22354)Termination reason: Unknown
% 1.59/1.36 % (22354)Termination phase: Saturation
% 1.59/1.36 % (22355)Instruction limit reached!
% 1.59/1.36 % (22355)------------------------------
% 1.59/1.36 % (22355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (22355)Termination reason: Unknown
% 1.59/1.36 % (22355)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (22355)Memory used [KB]: 5500
% 1.59/1.36 % (22355)Time elapsed: 0.003 s
% 1.59/1.36 % (22355)Instructions burned: 3 (million)
% 1.59/1.36 % (22355)------------------------------
% 1.59/1.36 % (22355)------------------------------
% 1.59/1.36
% 1.59/1.36 % (22354)Memory used [KB]: 5500
% 1.59/1.36 % (22354)Time elapsed: 0.003 s
% 1.59/1.36 % (22354)Instructions burned: 3 (million)
% 1.59/1.36 % (22354)------------------------------
% 1.59/1.36 % (22354)------------------------------
% 1.59/1.36 % (22352)Refutation not found, incomplete strategy
% 1.59/1.36 % (22352)------------------------------
% 1.59/1.36 % (22352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (22352)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.36
% 1.59/1.36
% 1.59/1.36 % (22352)Memory used [KB]: 5500
% 1.59/1.36 % (22352)Time elapsed: 0.003 s
% 1.59/1.36 % (22352)Instructions burned: 3 (million)
% 1.59/1.36 % (22352)------------------------------
% 1.59/1.36 % (22352)------------------------------
% 1.59/1.37 % (22353)Refutation not found, incomplete strategy
% 1.59/1.37 % (22353)------------------------------
% 1.59/1.37 % (22353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (22353)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.37
% 1.59/1.37
% 1.59/1.37 % (22353)Memory used [KB]: 5500
% 1.59/1.37 % (22353)Time elapsed: 0.003 s
% 1.59/1.37 % (22353)Instructions burned: 2 (million)
% 1.59/1.37 % (22353)------------------------------
% 1.59/1.37 % (22353)------------------------------
% 1.59/1.37 % (22351)First to succeed.
% 1.59/1.37 % (22357)Also succeeded, but the first one will report.
% 1.59/1.37 % (22351)Refutation found. Thanks to Tanya!
% 1.59/1.37 % SZS status Theorem for DTF2THF_22168
% 1.59/1.37 % SZS output start Proof for DTF2THF_22168
% 1.59/1.37 thf(func_def_0, type, leibeq: ($i > $o) > ($i > $o) > $o).
% 1.59/1.37 thf(func_def_2, type, u: ($i > $o) > ($i > $o) > $i > $o).
% 1.59/1.37 thf(func_def_3, type, n: ($i > $o) > ($i > $o) > $i > $o).
% 1.59/1.37 thf(func_def_4, type, a: $i > $o).
% 1.59/1.37 thf(func_def_5, type, b: $i > $o).
% 1.59/1.37 thf(func_def_6, type, c: $i > $o).
% 1.59/1.37 thf(func_def_18, type, sK1: ($i > $o) > $o).
% 1.59/1.37 thf(func_def_20, type, ph2: !>[X0: $tType]:(X0)).
% 1.59/1.37 thf(f130,plain,(
% 1.59/1.37 $false),
% 1.59/1.37 inference(avatar_sat_refutation,[status(thm)],[f81,f88,f97,f108,f114,f121,f129])).
% 1.59/1.37 thf(f129,plain,(
% 1.59/1.37 ~spl0_2 | ~spl0_5),
% 1.59/1.37 inference(avatar_contradiction_clause,[status(thm)],[f128])).
% 1.59/1.37 thf(f128,plain,(
% 1.59/1.37 $false | (~spl0_2 | ~spl0_5)),
% 1.59/1.37 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.59/1.37 thf(f125,plain,(
% 1.59/1.37 ($false = $true) | (~spl0_2 | ~spl0_5)),
% 1.59/1.37 inference(superposition,[status(thm)],[f80,f96])).
% 1.59/1.37 thf(f96,plain,(
% 1.59/1.37 ($false = (c @ sK3)) | ~spl0_5),
% 1.59/1.37 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.59/1.37 thf(f94,definition,(
% 1.59/1.37 spl0_5 <=> ($false = (c @ sK3))),
% 1.59/1.37 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.59/1.37 thf(f80,plain,(
% 1.59/1.37 ($true = (c @ sK3)) | ~spl0_2),
% 1.59/1.37 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.59/1.37 thf(f78,definition,(
% 1.59/1.37 spl0_2 <=> ($true = (c @ sK3))),
% 1.59/1.37 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.59/1.37 thf(f121,plain,(
% 1.59/1.37 ~spl0_1 | ~spl0_6),
% 1.59/1.37 inference(avatar_contradiction_clause,[status(thm)],[f120])).
% 1.59/1.37 thf(f120,plain,(
% 1.59/1.37 $false | (~spl0_1 | ~spl0_6)),
% 1.59/1.37 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.59/1.37 thf(f117,plain,(
% 1.59/1.37 ($false = $true) | (~spl0_1 | ~spl0_6)),
% 1.59/1.37 inference(superposition,[status(thm)],[f76,f101])).
% 1.59/1.37 thf(f101,plain,(
% 1.59/1.37 ($false = (a @ sK3)) | ~spl0_6),
% 1.59/1.37 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.59/1.37 thf(f99,definition,(
% 1.59/1.37 spl0_6 <=> ($false = (a @ sK3))),
% 1.59/1.37 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.59/1.37 thf(f76,plain,(
% 1.59/1.37 ($true = (a @ sK3)) | ~spl0_1),
% 1.59/1.37 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.59/1.37 thf(f74,definition,(
% 1.59/1.37 spl0_1 <=> ($true = (a @ sK3))),
% 1.59/1.37 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.59/1.37 thf(f114,plain,(
% 1.59/1.37 ~spl0_3 | ~spl0_4),
% 1.59/1.37 inference(avatar_contradiction_clause,[status(thm)],[f113])).
% 1.59/1.37 thf(f113,plain,(
% 1.59/1.37 $false | (~spl0_3 | ~spl0_4)),
% 1.59/1.37 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.59/1.37 thf(f110,plain,(
% 1.59/1.37 ($false = $true) | (~spl0_3 | ~spl0_4)),
% 1.59/1.37 inference(superposition,[status(thm)],[f85,f92])).
% 1.59/1.37 thf(f92,plain,(
% 1.59/1.37 ($false = (b @ sK3)) | ~spl0_4),
% 1.59/1.37 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.59/1.37 thf(f90,definition,(
% 1.59/1.37 spl0_4 <=> ($false = (b @ sK3))),
% 1.59/1.37 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.59/1.37 thf(f85,plain,(
% 1.59/1.37 ((b @ sK3) = $true) | ~spl0_3),
% 1.59/1.37 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.59/1.37 thf(f83,definition,(
% 1.59/1.37 spl0_3 <=> ((b @ sK3) = $true)),
% 1.59/1.37 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.59/1.37 thf(f108,plain,(
% 1.59/1.37 spl0_6),
% 1.59/1.37 inference(avatar_split_clause,[status(thm)],[f42,f99])).
% 1.59/1.37 thf(f42,plain,(
% 1.59/1.37 ($false = (a @ sK3))),
% 1.59/1.37 inference(duplicate_literal_removal,[status(thm)],[f41])).
% 1.59/1.37 thf(f41,plain,(
% 1.59/1.37 ($false = (a @ sK3)) | ($false = (a @ sK3))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.59/1.37 thf(f39,plain,(
% 1.59/1.37 ($false = (a @ sK3)) | ($false = ((a @ sK3) | (b @ sK3)))),
% 1.59/1.37 inference(duplicate_literal_removal,[status(thm)],[f38])).
% 1.59/1.37 thf(f38,plain,(
% 1.59/1.37 ($false = (a @ sK3)) | ($false = (a @ sK3)) | ($false = ((a @ sK3) | (b @ sK3)))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.59/1.37 thf(f36,plain,(
% 1.59/1.37 (((a @ sK3) | ((b @ sK3) & (c @ sK3))) = $false) | ($false = (a @ sK3)) | ($false = ((a @ sK3) | (b @ sK3)))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.59/1.37 thf(f34,plain,(
% 1.59/1.37 (((a @ sK3) | (c @ sK3)) = $false) | ($false = ((a @ sK3) | (b @ sK3))) | (((a @ sK3) | ((b @ sK3) & (c @ sK3))) = $false)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.59/1.37 thf(f33,plain,(
% 1.59/1.37 ($false = (((a @ sK3) | (b @ sK3)) & ((a @ sK3) | (c @ sK3)))) | (((a @ sK3) | ((b @ sK3) & (c @ sK3))) = $false)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.59/1.37 thf(f31,plain,(
% 1.59/1.37 (((a @ sK3) | ((b @ sK3) & (c @ sK3))) != (((a @ sK3) | (b @ sK3)) & ((a @ sK3) | (c @ sK3))))),
% 1.59/1.37 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.59/1.37 thf(f30,plain,(
% 1.59/1.37 (((^[Y0 : $i]: ((a @ Y0) | ((b @ Y0) & (c @ Y0)))) @ sK3) != ((^[Y0 : $i]: (((a @ Y0) | (b @ Y0)) & ((a @ Y0) | (c @ Y0)))) @ sK3))),
% 1.59/1.37 inference(negative_extensionality,[status(thm)],[f29])).
% 1.59/1.37 thf(f29,plain,(
% 1.59/1.37 ((^[Y0 : $i]: (((a @ Y0) | (b @ Y0)) & ((a @ Y0) | (c @ Y0)))) != (^[Y0 : $i]: ((a @ Y0) | ((b @ Y0) & (c @ Y0)))))),
% 1.59/1.37 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.59/1.37 thf(f27,plain,(
% 1.59/1.37 ((^[Y0 : $i]: (((a @ Y0) | (b @ Y0)) & ((a @ Y0) | (c @ Y0)))) != (^[Y0 : $i]: ((a @ Y0) | ((b @ Y0) & (c @ Y0))))) | ($false = $true)),
% 1.59/1.37 inference(constrained_superposition,[status(thm)],[f25,f24])).
% 1.59/1.37 thf(f24,plain,(
% 1.59/1.37 ((sK1 @ (^[Y0 : $i]: (((a @ Y0) | (b @ Y0)) & ((a @ Y0) | (c @ Y0))))) = $false)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.59/1.37 thf(f23,plain,(
% 1.59/1.37 (((sK1 @ (^[Y0 : $i]: ((a @ Y0) | ((b @ Y0) & (c @ Y0))))) => (sK1 @ (^[Y0 : $i]: (((a @ Y0) | (b @ Y0)) & ((a @ Y0) | (c @ Y0)))))) = $false)),
% 1.59/1.37 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.59/1.37 thf(f22,plain,(
% 1.59/1.37 (((^[Y0 : ($i > $o) > $o]: ((Y0 @ (^[Y1 : $i]: ((a @ Y1) | ((b @ Y1) & (c @ Y1))))) => (Y0 @ (^[Y1 : $i]: (((a @ Y1) | (b @ Y1)) & ((a @ Y1) | (c @ Y1))))))) @ sK1) = $false)),
% 1.59/1.37 inference(sigma_clausification,[status(thm)],[f21])).
% 1.59/1.37 thf(f21,plain,(
% 1.59/1.37 ($true != (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((Y0 @ (^[Y1 : $i]: ((a @ Y1) | ((b @ Y1) & (c @ Y1))))) => (Y0 @ (^[Y1 : $i]: (((a @ Y1) | (b @ Y1)) & ((a @ Y1) | (c @ Y1)))))))))),
% 1.59/1.37 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.59/1.37 thf(f20,plain,(
% 1.59/1.37 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ a @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ b @ c)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ a @ b) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ a @ c))) != $true)),
% 1.59/1.37 inference(definition_unfolding,[status(thm)],[f17,f19,f16,f18,f18,f16,f16])).
% 1.59/1.37 thf(f18,plain,(
% 1.59/1.37 (n = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.59/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.37 thf(f14,plain,(
% 1.59/1.37 (n = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.59/1.37 inference(fool_elimination,[status(thm)],[f13])).
% 1.59/1.37 thf(f13,plain,(
% 1.59/1.37 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) & (X0 @ X2))) = n)),
% 1.59/1.37 inference(rectify,[status(thm)],[f3])).
% 1.59/1.37 thf(f3,axiom,(
% 1.59/1.37 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) & (X0 @ X3))) = n)),
% 1.59/1.37 file('/export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2THF_22168.p',n)).
% 1.59/1.37 thf(f16,plain,(
% 1.59/1.37 (u = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 1.59/1.37 inference(cnf_transformation,[status(thm)],[f10])).
% 1.59/1.37 thf(f10,plain,(
% 1.59/1.37 (u = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 1.59/1.37 inference(fool_elimination,[status(thm)],[f9])).
% 1.59/1.37 thf(f9,plain,(
% 1.59/1.37 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = u)),
% 1.59/1.37 inference(rectify,[status(thm)],[f2])).
% 1.59/1.37 thf(f2,axiom,(
% 1.59/1.37 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) | (X0 @ X3))) = u)),
% 1.59/1.37 file('/export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2THF_22168.p',u)).
% 1.59/1.37 thf(f19,plain,(
% 1.59/1.37 (leibeq = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.59/1.37 inference(cnf_transformation,[status(thm)],[f8])).
% 1.59/1.37 thf(f8,plain,(
% 1.59/1.37 (leibeq = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.59/1.37 inference(fool_elimination,[status(thm)],[f7])).
% 1.59/1.37 thf(f7,plain,(
% 1.59/1.37 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : ($i > $o) > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.59/1.37 inference(rectify,[status(thm)],[f1])).
% 1.59/1.37 thf(f1,axiom,(
% 1.59/1.37 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : ($i > $o) > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.59/1.37 file('/export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2THF_22168.p',leibeq)).
% 1.59/1.37 thf(f17,plain,(
% 1.59/1.37 ((leibeq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c))) != $true)),
% 1.59/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.59/1.37 thf(f15,plain,(
% 1.59/1.37 ((leibeq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c))) != $true)),
% 1.59/1.37 inference(flattening,[status(thm)],[f12])).
% 1.59/1.37 thf(f12,plain,(
% 1.59/1.37 ~((leibeq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c))) = $true)),
% 1.59/1.37 inference(fool_elimination,[status(thm)],[f11])).
% 1.59/1.37 thf(f11,plain,(
% 1.59/1.37 ~(leibeq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c)))),
% 1.59/1.37 inference(rectify,[status(thm)],[f5])).
% 1.59/1.37 thf(f5,negated_conjecture,(
% 1.59/1.37 ~(leibeq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c)))),
% 1.59/1.37 inference(negated_conjecture,[status(cth)],[f4])).
% 1.59/1.37 thf(f4,conjecture,(
% 1.59/1.37 (leibeq @ (u @ a @ (n @ b @ c)) @ (n @ (u @ a @ b) @ (u @ a @ c)))),
% 1.59/1.37 file('/export/starexec/sandbox/tmp/tmp.NlBGfRVcTX/DTF2THF_22168.p',conj)).
% 1.59/1.37 thf(f25,plain,(
% 1.59/1.37 ($true = (sK1 @ (^[Y0 : $i]: ((a @ Y0) | ((b @ Y0) & (c @ Y0))))))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.59/1.37 thf(f97,plain,(
% 1.59/1.37 spl0_4 | spl0_5),
% 1.59/1.37 inference(avatar_split_clause,[status(thm)],[f58,f94,f90])).
% 1.59/1.37 thf(f58,plain,(
% 1.59/1.37 ($false = (b @ sK3)) | ($false = (c @ sK3))),
% 1.59/1.37 inference(duplicate_literal_removal,[status(thm)],[f57])).
% 1.59/1.37 thf(f57,plain,(
% 1.59/1.37 ($false = (b @ sK3)) | ($false = (c @ sK3)) | ($false = (c @ sK3)) | ($false = (b @ sK3))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.59/1.37 thf(f55,plain,(
% 1.59/1.37 (((b @ sK3) & (c @ sK3)) = $false) | ($false = (b @ sK3)) | ($false = (c @ sK3))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.59/1.37 thf(f48,plain,(
% 1.59/1.37 ($false = (b @ sK3)) | ($false = (c @ sK3)) | (((a @ sK3) | ((b @ sK3) & (c @ sK3))) = $false)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.59/1.37 thf(f35,plain,(
% 1.59/1.37 ($false = ((a @ sK3) | (b @ sK3))) | ($false = (c @ sK3)) | (((a @ sK3) | ((b @ sK3) & (c @ sK3))) = $false)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.59/1.37 thf(f88,plain,(
% 1.59/1.37 spl0_1 | spl0_3),
% 1.59/1.37 inference(avatar_split_clause,[status(thm)],[f66,f83,f74])).
% 1.59/1.37 thf(f66,plain,(
% 1.59/1.37 ((b @ sK3) = $true) | ($true = (a @ sK3))),
% 1.59/1.37 inference(duplicate_literal_removal,[status(thm)],[f65])).
% 1.59/1.37 thf(f65,plain,(
% 1.59/1.37 ((b @ sK3) = $true) | ((b @ sK3) = $true) | ($true = (a @ sK3))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.59/1.37 thf(f63,plain,(
% 1.59/1.37 ((b @ sK3) = $true) | ($true = (a @ sK3)) | (((b @ sK3) & (c @ sK3)) = $true)),
% 1.59/1.37 inference(duplicate_literal_removal,[status(thm)],[f62])).
% 1.59/1.37 thf(f62,plain,(
% 1.59/1.37 ($true = (a @ sK3)) | ($true = (a @ sK3)) | ((b @ sK3) = $true) | (((b @ sK3) & (c @ sK3)) = $true)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.59/1.37 thf(f61,plain,(
% 1.59/1.37 ($true = (a @ sK3)) | ($true = ((a @ sK3) | (b @ sK3))) | (((b @ sK3) & (c @ sK3)) = $true)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.59/1.37 thf(f59,plain,(
% 1.59/1.37 ($true = (a @ sK3)) | ($true = (((a @ sK3) | (b @ sK3)) & ((a @ sK3) | (c @ sK3)))) | (((b @ sK3) & (c @ sK3)) = $true)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.59/1.37 thf(f32,plain,(
% 1.59/1.37 (((a @ sK3) | ((b @ sK3) & (c @ sK3))) = $true) | ($true = (((a @ sK3) | (b @ sK3)) & ((a @ sK3) | (c @ sK3))))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.59/1.37 thf(f81,plain,(
% 1.59/1.37 spl0_1 | spl0_2),
% 1.59/1.37 inference(avatar_split_clause,[status(thm)],[f72,f78,f74])).
% 1.59/1.37 thf(f72,plain,(
% 1.59/1.37 ($true = (c @ sK3)) | ($true = (a @ sK3))),
% 1.59/1.37 inference(duplicate_literal_removal,[status(thm)],[f71])).
% 1.59/1.37 thf(f71,plain,(
% 1.59/1.37 ($true = (c @ sK3)) | ($true = (c @ sK3)) | ($true = (a @ sK3)) | ($true = (a @ sK3))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.59/1.37 thf(f67,plain,(
% 1.59/1.37 (((a @ sK3) | (c @ sK3)) = $true) | ($true = (c @ sK3)) | ($true = (a @ sK3))),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.59/1.37 thf(f60,plain,(
% 1.59/1.37 (((b @ sK3) & (c @ sK3)) = $true) | ($true = (a @ sK3)) | (((a @ sK3) | (c @ sK3)) = $true)),
% 1.59/1.37 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.59/1.37 % SZS output end Proof for DTF2THF_22168
% 1.59/1.37 % (22351)------------------------------
% 1.59/1.37 % (22351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (22351)Termination reason: Refutation
% 1.59/1.37
% 1.59/1.37 % (22351)Memory used [KB]: 5500
% 1.59/1.37 % (22351)Time elapsed: 0.007 s
% 1.59/1.37 % (22351)Instructions burned: 6 (million)
% 1.59/1.37 % (22351)------------------------------
% 1.59/1.37 % (22351)------------------------------
% 1.59/1.37 % (22350)Success in time 0.021 s
%------------------------------------------------------------------------------