%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU895^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 09:37:41 AM UTC 2026
% Result : Theorem 1.31s 1.19s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 126 ( 9 unt; 0 typ; 13 def)
% Number of atoms : 892 ( 347 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 982 ( 105 ~; 266 |; 88 &; 467 @)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 23 usr; 22 con; 0-2 aty)
% ( 0 !!; 43 ??; 0 @@+; 0 @@-)
% Number of variables : 111 ( 66 ^; 36 !; 9 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
f: b > a ).
thf(func_def_3,type,
y: b > $o ).
thf(func_def_4,type,
x: b > $o ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a ).
thf(func_def_18,type,
sK3: b ).
thf(func_def_19,type,
sK4: b ).
thf(func_def_20,type,
sK5: b ).
thf(func_def_21,type,
sK6: b ).
thf(func_def_22,type,
sK7: b ).
thf(f193,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f86,f91,f100,f105,f114,f119,f120,f121,f125,f131,f139,f148,f156,f164,f179,f192]) ).
thf(f192,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f191]) ).
thf(f191,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f187,f113]) ).
thf(f113,plain,
( ( ( f @ sK5 )
= sK2 )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f111]) ).
thf(f111,definition,
( spl0_10
<=> ( ( f @ sK5 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f187,plain,
( ( ( f @ sK5 )
!= sK2 )
| ~ spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f186]) ).
thf(f186,plain,
( ( ( f @ sK5 )
!= sK2 )
| ( $false = $true )
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f128,f118]) ).
thf(f118,plain,
( ( ( x @ sK5 )
= $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f116,definition,
( spl0_11
<=> ( ( x @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f128,plain,
( ! [X2: b] :
( ( $false
= ( x @ X2 ) )
| ( sK2
!= ( f @ X2 ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f127]) ).
thf(f127,definition,
( spl0_13
<=> ! [X2: b] :
( ( $false
= ( x @ X2 ) )
| ( sK2
!= ( f @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f179,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f178]) ).
thf(f178,plain,
( $false
| ~ spl0_7
| ~ spl0_8
| ~ spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f174,f99]) ).
thf(f99,plain,
( ( sK2
= ( f @ sK6 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f97]) ).
thf(f97,definition,
( spl0_7
<=> ( sK2
= ( f @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f174,plain,
( ( sK2
!= ( f @ sK6 ) )
| ~ spl0_8
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f173]) ).
thf(f173,plain,
( ( $false = $true )
| ( sK2
!= ( f @ sK6 ) )
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f128,f104]) ).
thf(f104,plain,
( ( ( x @ sK6 )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f102]) ).
thf(f102,definition,
( spl0_8
<=> ( ( x @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f164,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f163]) ).
thf(f163,plain,
( $false
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f159,f109]) ).
thf(f109,plain,
( ( ( f @ sK3 )
= sK2 )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl0_9
<=> ( ( f @ sK3 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f159,plain,
( ( ( f @ sK3 )
!= sK2 )
| ~ spl0_1
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ( $false = $true )
| ( ( f @ sK3 )
!= sK2 )
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f128,f73]) ).
thf(f73,plain,
( ( ( x @ sK3 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f71,definition,
( spl0_1
<=> ( ( x @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f156,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f155]) ).
thf(f155,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_12 ),
inference(subsumption_resolution,[status(thm)],[f151,f109]) ).
thf(f151,plain,
( ( ( f @ sK3 )
!= sK2 )
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( ( f @ sK3 )
!= sK2 )
| ( $false = $true )
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f81,f124]) ).
thf(f124,plain,
( ! [X2: b] :
( ( ( y @ X2 )
= $false )
| ( sK2
!= ( f @ X2 ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f123,definition,
( spl0_12
<=> ! [X2: b] :
( ( ( y @ X2 )
= $false )
| ( sK2
!= ( f @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f81,plain,
( ( ( y @ sK3 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f79]) ).
thf(f79,definition,
( spl0_3
<=> ( ( y @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f148,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f147]) ).
thf(f147,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f143,f85]) ).
thf(f85,plain,
( ( ( f @ sK7 )
= sK2 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl0_4
<=> ( ( f @ sK7 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f143,plain,
( ( ( f @ sK7 )
!= sK2 )
| ~ spl0_5
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
( ( $false = $true )
| ( ( f @ sK7 )
!= sK2 )
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f90,f128]) ).
thf(f90,plain,
( ( ( x @ sK7 )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f88,definition,
( spl0_5
<=> ( ( x @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f139,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f138]) ).
thf(f138,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_12 ),
inference(subsumption_resolution,[status(thm)],[f134,f95]) ).
thf(f95,plain,
( ( sK2
= ( f @ sK4 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl0_6
<=> ( sK2
= ( f @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f134,plain,
( ( sK2
!= ( f @ sK4 ) )
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( sK2
!= ( f @ sK4 ) )
| ( $false = $true )
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f124,f77]) ).
thf(f77,plain,
( ( ( y @ sK4 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f75]) ).
thf(f75,definition,
( spl0_2
<=> ( ( y @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f131,plain,
( spl0_13
| spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f23,f127,f127]) ).
thf(f23,plain,
! [X2: b,X1: b] :
( ( ( x @ X1 )
= $false )
| ( sK2
!= ( f @ X2 ) )
| ( $false
= ( x @ X2 ) )
| ( ( f @ X1 )
!= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: b,X1: b] :
( ( sK2
!= ( f @ X2 ) )
| ( ( x @ X1 )
= $false )
| ( ( f @ X1 )
!= sK2 )
| ( $false
= ( ( x @ X2 )
| ( y @ X2 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: b,X1: b] :
( ( ( x @ X1 )
= $false )
| ( ( ( f @ X1 )
= sK2 )
= $false )
| ( sK2
!= ( f @ X2 ) )
| ( $false
= ( ( x @ X2 )
| ( y @ X2 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: b,X1: b] :
( ( ( ( f @ X2 )
= sK2 )
= $false )
| ( ( ( f @ X1 )
= sK2 )
= $false )
| ( $false
= ( ( x @ X2 )
| ( y @ X2 ) ) )
| ( ( x @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: b,X1: b] :
( ( ( x @ X1 )
= $false )
| ( $false
= ( ( ( f @ X2 )
= sK2 )
& ( ( x @ X2 )
| ( y @ X2 ) ) ) )
| ( ( ( f @ X1 )
= sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( x @ X1 )
& ( ( f @ X1 )
= sK2 ) ) )
| ( $false
= ( ( ( f @ X2 )
= sK2 )
& ( ( x @ X2 )
| ( y @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: b,X1: b] :
( ( ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) )
@ X2 )
= $false )
| ( $false
= ( ( x @ X1 )
& ( ( f @ X1 )
= sK2 ) ) ) ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: b] :
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( x @ X1 )
& ( ( f @ X1 )
= sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: b] :
( ( ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) )
@ X1 )
= $false )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $false )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) ) ) )
= $false )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) ) ) )
!= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( ( x @ Y1 )
| ( y @ Y1 ) ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( ( x @ Y1 )
| ( y @ Y1 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( ( x @ Y1 )
| ( y @ Y1 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( ( x @ Y1 )
| ( y @ Y1 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a] :
? [X1: b] :
( ( ( y @ X1 )
| ( x @ X1 ) )
& ( ( f @ X1 )
= X0 ) ) )
!= ( ^ [X2: a] :
( ? [X3: b] :
( ( y @ X3 )
& ( ( f @ X3 )
= X2 ) )
| ? [X4: b] :
( ( ( f @ X4 )
= X2 )
& ( x @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( ( y @ X1 )
| ( x @ X1 ) )
& ( ( f @ X1 )
= X0 ) ) )
!= ( ^ [X0: a] :
( ? [X1: b] :
( ( y @ X1 )
& ( ( f @ X1 )
= X0 ) )
| ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( x @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( ( y @ X1 )
| ( x @ X1 ) )
& ( ( f @ X1 )
= X0 ) ) )
= ( ^ [X0: a] :
( ? [X1: b] :
( ( y @ X1 )
& ( ( f @ X1 )
= X0 ) )
| ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( x @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sUH9rlcmPK/DTF2THF_14558.p',cX5202_pme) ).
thf(f125,plain,
( spl0_12
| spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f34,f123,f123]) ).
thf(f34,plain,
! [X2: b,X1: b] :
( ( ( y @ X2 )
= $false )
| ( ( y @ X1 )
= $false )
| ( sK2
!= ( f @ X2 ) )
| ( ( f @ X1 )
!= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: b,X1: b] :
( ( ( ( f @ X2 )
= sK2 )
= $false )
| ( ( f @ X1 )
!= sK2 )
| ( ( y @ X2 )
= $false )
| ( ( y @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: b,X1: b] :
( ( ( y @ X1 )
= $false )
| ( $false
= ( ( x @ X2 )
| ( y @ X2 ) ) )
| ( ( f @ X1 )
!= sK2 )
| ( ( ( f @ X2 )
= sK2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: b,X1: b] :
( ( ( y @ X1 )
= $false )
| ( ( ( f @ X1 )
= sK2 )
= $false )
| ( ( ( f @ X2 )
= sK2 )
= $false )
| ( $false
= ( ( x @ X2 )
| ( y @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( ( f @ X2 )
= sK2 )
& ( ( x @ X2 )
| ( y @ X2 ) ) ) )
| ( ( ( f @ X1 )
= sK2 )
= $false )
| ( ( y @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: b,X1: b] :
( ( ( ( ( f @ X1 )
= sK2 )
& ( y @ X1 ) )
= $false )
| ( $false
= ( ( ( f @ X2 )
= sK2 )
& ( ( x @ X2 )
| ( y @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: b,X1: b] :
( ( ( ( ( f @ X1 )
= sK2 )
& ( y @ X1 ) )
= $false )
| ( ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: b] :
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) )
= $false )
| ( ( ( ( f @ X1 )
= sK2 )
& ( y @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: b] :
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) ) )
= $false )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f121,plain,
( spl0_6
| spl0_11
| spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f49,f107,f116,f93]) ).
thf(f49,plain,
( ( ( x @ sK5 )
= $true )
| ( sK2
= ( f @ sK4 ) )
| ( ( f @ sK3 )
= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( f @ sK3 )
= sK2 )
| ( ( ( x @ sK5 )
& ( ( f @ sK5 )
= sK2 ) )
= $true )
| ( sK2
= ( f @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( ( f @ sK3 )
= sK2 )
= $true )
| ( sK2
= ( f @ sK4 ) )
| ( ( ( x @ sK5 )
& ( ( f @ sK5 )
= sK2 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( ( f @ sK4 )
= sK2 )
= $true )
| ( ( ( x @ sK5 )
& ( ( f @ sK5 )
= sK2 ) )
= $true )
| ( ( ( f @ sK3 )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ( ( f @ sK4 )
= sK2 )
& ( y @ sK4 ) )
= $true )
| ( ( ( x @ sK5 )
& ( ( f @ sK5 )
= sK2 ) )
= $true )
| ( ( ( f @ sK3 )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) )
@ sK5 )
= $true )
| ( ( ( ( f @ sK4 )
= sK2 )
& ( y @ sK4 ) )
= $true )
| ( ( ( f @ sK3 )
= sK2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true )
| ( ( ( f @ sK3 )
= sK2 )
= $true )
| ( ( ( ( f @ sK4 )
= sK2 )
& ( y @ sK4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ( ( f @ sK3 )
= sK2 )
& ( ( x @ sK3 )
| ( y @ sK3 ) ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true )
| ( ( ( ( f @ sK4 )
= sK2 )
& ( y @ sK4 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( ( ( f @ sK3 )
= sK2 )
& ( ( x @ sK3 )
| ( y @ sK3 ) ) )
= $true )
| ( ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) )
@ sK4 )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true )
| ( ( ( ( f @ sK3 )
= sK2 )
& ( ( x @ sK3 )
| ( y @ sK3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) ) ) )
= $true )
| ( ( ( ( f @ sK3 )
= sK2 )
& ( ( x @ sK3 )
| ( y @ sK3 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) )
@ sK3 )
= $true )
| ( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( ( x @ Y0 )
| ( y @ Y0 ) ) ) )
= $true )
| ( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( y @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f120,plain,
( spl0_10
| spl0_9
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f50,f93,f107,f111]) ).
thf(f50,plain,
( ( ( f @ sK5 )
= sK2 )
| ( ( f @ sK3 )
= sK2 )
| ( sK2
= ( f @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( ( f @ sK5 )
= sK2 )
= $true )
| ( sK2
= ( f @ sK4 ) )
| ( ( f @ sK3 )
= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f119,plain,
( spl0_9
| spl0_2
| spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f53,f116,f75,f107]) ).
thf(f53,plain,
( ( ( x @ sK5 )
= $true )
| ( ( y @ sK4 )
= $true )
| ( ( f @ sK3 )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( y @ sK4 )
= $true )
| ( ( x @ sK5 )
= $true )
| ( ( ( f @ sK3 )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ( x @ sK5 )
& ( ( f @ sK5 )
= sK2 ) )
= $true )
| ( ( ( f @ sK3 )
= sK2 )
= $true )
| ( ( y @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f114,plain,
( spl0_9
| spl0_2
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f55,f111,f75,f107]) ).
thf(f55,plain,
( ( ( f @ sK3 )
= sK2 )
| ( ( y @ sK4 )
= $true )
| ( ( f @ sK5 )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( ( f @ sK5 )
= sK2 )
= $true )
| ( ( f @ sK3 )
= sK2 )
| ( ( y @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( ( f @ sK3 )
= sK2 )
= $true )
| ( ( ( f @ sK5 )
= sK2 )
= $true )
| ( ( y @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f105,plain,
( spl0_3
| spl0_8
| spl0_1
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f63,f93,f71,f102,f79]) ).
thf(f63,plain,
( ( sK2
= ( f @ sK4 ) )
| ( ( y @ sK3 )
= $true )
| ( ( x @ sK3 )
= $true )
| ( ( x @ sK6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( sK2
= ( f @ sK4 ) )
| ( ( y @ sK3 )
= $true )
| ( ( ( x @ sK6 )
& ( ( f @ sK6 )
= sK2 ) )
= $true )
| ( ( x @ sK3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( x @ sK3 )
= $true )
| ( sK2
= ( f @ sK4 ) )
| ( ( y @ sK3 )
= $true )
| ( ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) )
@ sK6 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true )
| ( sK2
= ( f @ sK4 ) )
| ( ( y @ sK3 )
= $true )
| ( ( x @ sK3 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( y @ sK3 )
= $true )
| ( ( ( f @ sK4 )
= sK2 )
= $true )
| ( ( x @ sK3 )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( ( ( f @ sK4 )
= sK2 )
& ( y @ sK4 ) )
= $true )
| ( ( x @ sK3 )
= $true )
| ( ( y @ sK3 )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( ( x @ sK3 )
| ( y @ sK3 ) )
= $true )
| ( ( ( ( f @ sK4 )
= sK2 )
& ( y @ sK4 ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f100,plain,
( spl0_6
| spl0_3
| spl0_1
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f64,f97,f71,f79,f93]) ).
thf(f64,plain,
( ( sK2
= ( f @ sK4 ) )
| ( ( x @ sK3 )
= $true )
| ( ( y @ sK3 )
= $true )
| ( sK2
= ( f @ sK6 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( y @ sK3 )
= $true )
| ( ( ( f @ sK6 )
= sK2 )
= $true )
| ( ( x @ sK3 )
= $true )
| ( sK2
= ( f @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f91,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f68,f88,f71,f75,f79]) ).
thf(f68,plain,
( ( ( y @ sK3 )
= $true )
| ( ( x @ sK3 )
= $true )
| ( ( y @ sK4 )
= $true )
| ( ( x @ sK7 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( y @ sK3 )
= $true )
| ( ( y @ sK4 )
= $true )
| ( $true
= ( ( x @ sK7 )
& ( ( f @ sK7 )
= sK2 ) ) )
| ( ( x @ sK3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( x @ sK3 )
= $true )
| ( ( y @ sK3 )
= $true )
| ( ( y @ sK4 )
= $true )
| ( ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) )
@ sK7 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( x @ sK3 )
= $true )
| ( ( y @ sK3 )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true )
| ( ( y @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f86,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f69,f83,f79,f75,f71]) ).
thf(f69,plain,
( ( ( x @ sK3 )
= $true )
| ( ( f @ sK7 )
= sK2 )
| ( ( y @ sK3 )
= $true )
| ( ( y @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( y @ sK4 )
= $true )
| ( ( ( f @ sK7 )
= sK2 )
= $true )
| ( ( x @ sK3 )
= $true )
| ( ( y @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU895^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Feb 24 12:37:18 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.42 ---- Original DTF file ---
% 0.17/0.42 thf(spec,logic,$$dhol).
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 % File : SEU895^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.42 % Domain : Set Theory
% 0.17/0.42 % Problem : TPS problem X5202
% 0.17/0.42 % Version : Especial.
% 0.17/0.42 % English :
% 0.17/0.42
% 0.17/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.42 % Source : [Bro09]
% 0.17/0.42 % Names : tps_0392 [Bro09]
% 0.17/0.42 % : X5202 [TPS]
% 0.17/0.42 % : X5206 [TPS]
% 0.17/0.42
% 0.17/0.42 % Status : Theorem
% 0.17/0.42 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.17/0.42 % Syntax : Number of formulae : 6 ( 1 unt; 5 typ; 0 def)
% 0.17/0.42 % Number of atoms : 8 ( 4 equ; 0 cnn)
% 0.17/0.42 % Maximal formula atoms : 1 ( 8 avg)
% 0.17/0.42 % Number of connectives : 12 ( 0 ~; 2 |; 3 &; 7 @)
% 0.17/0.42 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.42 % Maximal formula depth : 1 ( 1 avg)
% 0.17/0.42 % Number of types : 3 ( 2 usr)
% 0.17/0.42 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.42 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.17/0.42 % Number of variables : 5 ( 2 ^; 0 !; 3 ?; 5 :)
% 0.17/0.42 % SPC : TH0_THM_EQU_NAR
% 0.17/0.42
% 0.17/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.42 % : Polymorphic definitions expanded.
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 thf(b_type,type,
% 0.17/0.42 b: $tType ).
% 0.17/0.42
% 0.17/0.42 thf(a_type,type,
% 0.17/0.42 a: $tType ).
% 0.17/0.42
% 0.17/0.42 thf(f,type,
% 0.17/0.42 f: b > a ).
% 0.17/0.42
% 0.17/0.42 thf(y,type,
% 0.17/0.42 y: b > $o ).
% 0.17/0.42
% 0.17/0.42 thf(x,type,
% 0.17/0.42 x: b > $o ).
% 0.17/0.42
% 0.17/0.42 thf(cX5202_pme,conjecture,
% 0.17/0.42 ( ( ^ [Xz: a] :
% 0.17/0.42 ? [Xt: b] :
% 0.17/0.42 ( ( ( x @ Xt )
% 0.17/0.42 | ( y @ Xt ) )
% 0.17/0.42 & ( Xz
% 0.17/0.42 = ( f @ Xt ) ) ) )
% 0.17/0.42 = ( ^ [Xz: a] :
% 0.17/0.42 ( ? [Xt: b] :
% 0.17/0.42 ( ( x @ Xt )
% 0.17/0.42 & ( Xz
% 0.17/0.42 = ( f @ Xt ) ) )
% 0.17/0.42 | ? [Xt: b] :
% 0.17/0.42 ( ( y @ Xt )
% 0.17/0.42 & ( Xz
% 0.17/0.42 = ( f @ Xt ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 ------------------------
% 1.31/1.16 ---- Embedded in THF ---
% 1.31/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.31/1.17 %%% Generated on Tue Feb 24 12:37:19 EST 2026
% 1.31/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.31/1.17 %%% Logic specification used:
% 1.31/1.17 %%% thf(spec, logic, $$dhol).
% 1.31/1.17
% 1.31/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.sUH9rlcmPK/DTF2DTF14558.p
% See solution above
% 1.31/1.17 ------------------------
% 1.31/1.17 ---- Cleaned THF ---
% 1.31/1.17 thf(b_type,type,
% 1.31/1.17 b: $tType ).
% 1.31/1.17
% 1.31/1.17 thf(a_type,type,
% 1.31/1.17 a: $tType ).
% 1.31/1.17
% 1.31/1.17 thf(f,type,
% 1.31/1.17 f: b > a ).
% 1.31/1.17
% 1.31/1.17 thf(y,type,
% 1.31/1.17 y: b > $o ).
% 1.31/1.17
% 1.31/1.17 thf(x,type,
% 1.31/1.17 x: b > $o ).
% 1.31/1.17
% 1.31/1.17 thf(cX5202_pme,conjecture,
% 1.31/1.17 ( ( ^ [Xz: a] :
% 1.31/1.17 ? [Xt: b] :
% 1.31/1.17 ( ( ( x @ Xt )
% 1.31/1.17 | ( y @ Xt ) )
% 1.31/1.17 & ( Xz
% 1.31/1.17 = ( f @ Xt ) ) ) )
% 1.31/1.17 = ( ^ [Xz: a] :
% 1.31/1.17 ( ? [Xt: b] :
% 1.31/1.17 ( ( x @ Xt )
% 1.31/1.17 & ( Xz
% 1.31/1.17 = ( f @ Xt ) ) )
% 1.31/1.17 | ? [Xt: b] :
% 1.31/1.17 ( ( y @ Xt )
% 1.31/1.17 & ( Xz
% 1.31/1.17 = ( f @ Xt ) ) ) ) ) ) ).
% 1.31/1.17 ------------------------
% 1.31/1.19 % (14658)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14558 for (2999ds/183Mi)
% 1.31/1.19 % (14658)First to succeed.
% 1.31/1.19 % (14664)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14558 for (2999ds/18Mi)
% 1.31/1.19 % (14661)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14558 for (2999ds/2Mi)
% 1.31/1.19 % (14660)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_14558 for (2999ds/27Mi)
% 1.31/1.19 % (14663)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_14558 for (2999ds/275Mi)
% 1.31/1.19 % (14662)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_14558 for (2999ds/2Mi)
% 1.31/1.19 % (14658)Refutation found. Thanks to Tanya!
% 1.31/1.19 % SZS status Theorem for DTF2THF_14558
% 1.31/1.19 % SZS output start Proof for DTF2THF_14558
% 1.31/1.19 thf(type_def_5, type, b: $tType).
% 1.31/1.19 thf(type_def_6, type, a: $tType).
% 1.31/1.19 thf(func_def_0, type, b: $tType).
% 1.31/1.19 thf(func_def_1, type, a: $tType).
% 1.31/1.19 thf(func_def_2, type, f: b > a).
% 1.31/1.19 thf(func_def_3, type, y: b > $o).
% 1.31/1.19 thf(func_def_4, type, x: b > $o).
% 1.31/1.19 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.31/1.19 thf(func_def_17, type, sK2: a).
% 1.31/1.19 thf(func_def_18, type, sK3: b).
% 1.31/1.19 thf(func_def_19, type, sK4: b).
% 1.31/1.19 thf(func_def_20, type, sK5: b).
% 1.31/1.19 thf(func_def_21, type, sK6: b).
% 1.31/1.19 thf(func_def_22, type, sK7: b).
% 1.31/1.19 thf(f193,plain,(
% 1.31/1.19 $false),
% 1.31/1.19 inference(avatar_sat_refutation,[status(thm)],[f86,f91,f100,f105,f114,f119,f120,f121,f125,f131,f139,f148,f156,f164,f179,f192])).
% 1.31/1.19 thf(f192,plain,(
% 1.31/1.19 ~spl0_10 | ~spl0_11 | ~spl0_13),
% 1.31/1.19 inference(avatar_contradiction_clause,[status(thm)],[f191])).
% 1.31/1.19 thf(f191,plain,(
% 1.31/1.19 $false | (~spl0_10 | ~spl0_11 | ~spl0_13)),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f187,f113])).
% 1.31/1.19 thf(f113,plain,(
% 1.31/1.20 ((f @ sK5) = sK2) | ~spl0_10),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f111])).
% 1.31/1.20 thf(f111,definition,(
% 1.31/1.20 spl0_10 <=> ((f @ sK5) = sK2)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.31/1.20 thf(f187,plain,(
% 1.31/1.20 ((f @ sK5) != sK2) | (~spl0_11 | ~spl0_13)),
% 1.31/1.20 inference(trivial_inequality_removal,[status(thm)],[f186])).
% 1.31/1.20 thf(f186,plain,(
% 1.31/1.20 ((f @ sK5) != sK2) | ($false = $true) | (~spl0_11 | ~spl0_13)),
% 1.31/1.20 inference(superposition,[status(thm)],[f128,f118])).
% 1.31/1.20 thf(f118,plain,(
% 1.31/1.20 ((x @ sK5) = $true) | ~spl0_11),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.31/1.20 thf(f116,definition,(
% 1.31/1.20 spl0_11 <=> ((x @ sK5) = $true)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.31/1.20 thf(f128,plain,(
% 1.31/1.20 ( ! [X2 : b] : (($false = (x @ X2)) | (sK2 != (f @ X2))) ) | ~spl0_13),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f127])).
% 1.31/1.20 thf(f127,definition,(
% 1.31/1.20 spl0_13 <=> ! [X2 : b] : (($false = (x @ X2)) | (sK2 != (f @ X2)))),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.31/1.20 thf(f179,plain,(
% 1.31/1.20 ~spl0_7 | ~spl0_8 | ~spl0_13),
% 1.31/1.20 inference(avatar_contradiction_clause,[status(thm)],[f178])).
% 1.31/1.20 thf(f178,plain,(
% 1.31/1.20 $false | (~spl0_7 | ~spl0_8 | ~spl0_13)),
% 1.31/1.20 inference(subsumption_resolution,[status(thm)],[f174,f99])).
% 1.31/1.20 thf(f99,plain,(
% 1.31/1.20 (sK2 = (f @ sK6)) | ~spl0_7),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f97])).
% 1.31/1.20 thf(f97,definition,(
% 1.31/1.20 spl0_7 <=> (sK2 = (f @ sK6))),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.31/1.20 thf(f174,plain,(
% 1.31/1.20 (sK2 != (f @ sK6)) | (~spl0_8 | ~spl0_13)),
% 1.31/1.20 inference(trivial_inequality_removal,[status(thm)],[f173])).
% 1.31/1.20 thf(f173,plain,(
% 1.31/1.20 ($false = $true) | (sK2 != (f @ sK6)) | (~spl0_8 | ~spl0_13)),
% 1.31/1.20 inference(superposition,[status(thm)],[f128,f104])).
% 1.31/1.20 thf(f104,plain,(
% 1.31/1.20 ((x @ sK6) = $true) | ~spl0_8),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f102])).
% 1.31/1.20 thf(f102,definition,(
% 1.31/1.20 spl0_8 <=> ((x @ sK6) = $true)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.31/1.20 thf(f164,plain,(
% 1.31/1.20 ~spl0_1 | ~spl0_9 | ~spl0_13),
% 1.31/1.20 inference(avatar_contradiction_clause,[status(thm)],[f163])).
% 1.31/1.20 thf(f163,plain,(
% 1.31/1.20 $false | (~spl0_1 | ~spl0_9 | ~spl0_13)),
% 1.31/1.20 inference(subsumption_resolution,[status(thm)],[f159,f109])).
% 1.31/1.20 thf(f109,plain,(
% 1.31/1.20 ((f @ sK3) = sK2) | ~spl0_9),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.31/1.20 thf(f107,definition,(
% 1.31/1.20 spl0_9 <=> ((f @ sK3) = sK2)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.31/1.20 thf(f159,plain,(
% 1.31/1.20 ((f @ sK3) != sK2) | (~spl0_1 | ~spl0_13)),
% 1.31/1.20 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.31/1.20 thf(f158,plain,(
% 1.31/1.20 ($false = $true) | ((f @ sK3) != sK2) | (~spl0_1 | ~spl0_13)),
% 1.31/1.20 inference(superposition,[status(thm)],[f128,f73])).
% 1.31/1.20 thf(f73,plain,(
% 1.31/1.20 ((x @ sK3) = $true) | ~spl0_1),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.31/1.20 thf(f71,definition,(
% 1.31/1.20 spl0_1 <=> ((x @ sK3) = $true)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.31/1.20 thf(f156,plain,(
% 1.31/1.20 ~spl0_3 | ~spl0_9 | ~spl0_12),
% 1.31/1.20 inference(avatar_contradiction_clause,[status(thm)],[f155])).
% 1.31/1.20 thf(f155,plain,(
% 1.31/1.20 $false | (~spl0_3 | ~spl0_9 | ~spl0_12)),
% 1.31/1.20 inference(subsumption_resolution,[status(thm)],[f151,f109])).
% 1.31/1.20 thf(f151,plain,(
% 1.31/1.20 ((f @ sK3) != sK2) | (~spl0_3 | ~spl0_12)),
% 1.31/1.20 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.31/1.20 thf(f149,plain,(
% 1.31/1.20 ((f @ sK3) != sK2) | ($false = $true) | (~spl0_3 | ~spl0_12)),
% 1.31/1.20 inference(superposition,[status(thm)],[f81,f124])).
% 1.31/1.20 thf(f124,plain,(
% 1.31/1.20 ( ! [X2 : b] : (((y @ X2) = $false) | (sK2 != (f @ X2))) ) | ~spl0_12),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f123])).
% 1.31/1.20 thf(f123,definition,(
% 1.31/1.20 spl0_12 <=> ! [X2 : b] : (((y @ X2) = $false) | (sK2 != (f @ X2)))),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.31/1.20 thf(f81,plain,(
% 1.31/1.20 ((y @ sK3) = $true) | ~spl0_3),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f79])).
% 1.31/1.20 thf(f79,definition,(
% 1.31/1.20 spl0_3 <=> ((y @ sK3) = $true)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.31/1.20 thf(f148,plain,(
% 1.31/1.20 ~spl0_4 | ~spl0_5 | ~spl0_13),
% 1.31/1.20 inference(avatar_contradiction_clause,[status(thm)],[f147])).
% 1.31/1.20 thf(f147,plain,(
% 1.31/1.20 $false | (~spl0_4 | ~spl0_5 | ~spl0_13)),
% 1.31/1.20 inference(subsumption_resolution,[status(thm)],[f143,f85])).
% 1.31/1.20 thf(f85,plain,(
% 1.31/1.20 ((f @ sK7) = sK2) | ~spl0_4),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.31/1.20 thf(f83,definition,(
% 1.31/1.20 spl0_4 <=> ((f @ sK7) = sK2)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.31/1.20 thf(f143,plain,(
% 1.31/1.20 ((f @ sK7) != sK2) | (~spl0_5 | ~spl0_13)),
% 1.31/1.20 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.31/1.20 thf(f142,plain,(
% 1.31/1.20 ($false = $true) | ((f @ sK7) != sK2) | (~spl0_5 | ~spl0_13)),
% 1.31/1.20 inference(superposition,[status(thm)],[f90,f128])).
% 1.31/1.20 thf(f90,plain,(
% 1.31/1.20 ((x @ sK7) = $true) | ~spl0_5),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.31/1.20 thf(f88,definition,(
% 1.31/1.20 spl0_5 <=> ((x @ sK7) = $true)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.31/1.20 thf(f139,plain,(
% 1.31/1.20 ~spl0_2 | ~spl0_6 | ~spl0_12),
% 1.31/1.20 inference(avatar_contradiction_clause,[status(thm)],[f138])).
% 1.31/1.20 thf(f138,plain,(
% 1.31/1.20 $false | (~spl0_2 | ~spl0_6 | ~spl0_12)),
% 1.31/1.20 inference(subsumption_resolution,[status(thm)],[f134,f95])).
% 1.31/1.20 thf(f95,plain,(
% 1.31/1.20 (sK2 = (f @ sK4)) | ~spl0_6),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.31/1.20 thf(f93,definition,(
% 1.31/1.20 spl0_6 <=> (sK2 = (f @ sK4))),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.31/1.20 thf(f134,plain,(
% 1.31/1.20 (sK2 != (f @ sK4)) | (~spl0_2 | ~spl0_12)),
% 1.31/1.20 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.31/1.20 thf(f132,plain,(
% 1.31/1.20 (sK2 != (f @ sK4)) | ($false = $true) | (~spl0_2 | ~spl0_12)),
% 1.31/1.20 inference(superposition,[status(thm)],[f124,f77])).
% 1.31/1.20 thf(f77,plain,(
% 1.31/1.20 ((y @ sK4) = $true) | ~spl0_2),
% 1.31/1.20 inference(avatar_component_clause,[status(thm)],[f75])).
% 1.31/1.20 thf(f75,definition,(
% 1.31/1.20 spl0_2 <=> ((y @ sK4) = $true)),
% 1.31/1.20 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.31/1.20 thf(f131,plain,(
% 1.31/1.20 spl0_13 | spl0_13),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f23,f127,f127])).
% 1.31/1.20 thf(f23,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (((x @ X1) = $false) | (sK2 != (f @ X2)) | ($false = (x @ X2)) | ((f @ X1) != sK2)) )),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.31/1.20 thf(f21,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : ((sK2 != (f @ X2)) | ((x @ X1) = $false) | ((f @ X1) != sK2) | ($false = ((x @ X2) | (y @ X2)))) )),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f20])).
% 1.31/1.20 thf(f20,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (((x @ X1) = $false) | (((f @ X1) = sK2) = $false) | (sK2 != (f @ X2)) | ($false = ((x @ X2) | (y @ X2)))) )),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f19])).
% 1.31/1.20 thf(f19,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : ((((f @ X2) = sK2) = $false) | (((f @ X1) = sK2) = $false) | ($false = ((x @ X2) | (y @ X2))) | ((x @ X1) = $false)) )),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.31/1.20 thf(f18,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (((x @ X1) = $false) | ($false = (((f @ X2) = sK2) & ((x @ X2) | (y @ X2)))) | (((f @ X1) = sK2) = $false)) )),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.31/1.20 thf(f17,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (($false = ((x @ X1) & ((f @ X1) = sK2))) | ($false = (((f @ X2) = sK2) & ((x @ X2) | (y @ X2))))) )),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.31/1.20 thf(f16,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : ((((^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0)))) @ X2) = $false) | ($false = ((x @ X1) & ((f @ X1) = sK2)))) )),
% 1.31/1.20 inference(pi_clausification,[status(thm)],[f15])).
% 1.31/1.20 thf(f15,plain,(
% 1.31/1.20 ( ! [X1 : b] : (((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))) = $false) | ($false = ((x @ X1) & ((f @ X1) = sK2)))) )),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.31/1.20 thf(f14,plain,(
% 1.31/1.20 ( ! [X1 : b] : ((((^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2))) @ X1) = $false) | ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))) = $false)) )),
% 1.31/1.20 inference(pi_clausification,[status(thm)],[f13])).
% 1.31/1.20 thf(f13,plain,(
% 1.31/1.20 ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $false) | ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))) = $false)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.31/1.20 thf(f11,plain,(
% 1.31/1.20 (((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) | (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0))))) = $false) | ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))) = $false)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.31/1.20 thf(f9,plain,(
% 1.31/1.20 (((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) | (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0))))) != (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))))),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.31/1.20 thf(f8,plain,(
% 1.31/1.20 (((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & ((x @ Y1) | (y @ Y1)))))) @ sK2) != ((^[Y0 : a]: ((?? @ b @ (^[Y1 : b]: ((x @ Y1) & ((f @ Y1) = Y0)))) | (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & (y @ Y1)))))) @ sK2))),
% 1.31/1.20 inference(negative_extensionality,[status(thm)],[f7])).
% 1.31/1.20 thf(f7,plain,(
% 1.31/1.20 ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & ((x @ Y1) | (y @ Y1)))))) != (^[Y0 : a]: ((?? @ b @ (^[Y1 : b]: ((x @ Y1) & ((f @ Y1) = Y0)))) | (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & (y @ Y1)))))))),
% 1.31/1.20 inference(cnf_transformation,[status(thm)],[f6])).
% 1.31/1.20 thf(f6,plain,(
% 1.31/1.20 ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & ((x @ Y1) | (y @ Y1)))))) != (^[Y0 : a]: ((?? @ b @ (^[Y1 : b]: ((x @ Y1) & ((f @ Y1) = Y0)))) | (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & (y @ Y1)))))))),
% 1.31/1.20 inference(flattening,[status(thm)],[f5])).
% 1.31/1.20 thf(f5,plain,(
% 1.31/1.20 ~((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & ((x @ Y1) | (y @ Y1)))))) = (^[Y0 : a]: ((?? @ b @ (^[Y1 : b]: ((x @ Y1) & ((f @ Y1) = Y0)))) | (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & (y @ Y1)))))))),
% 1.31/1.20 inference(fool_elimination,[status(thm)],[f4])).
% 1.31/1.20 thf(f4,plain,(
% 1.31/1.20 ~((^[X0 : a] : (? [X1 : b] : (((y @ X1) | (x @ X1)) & ((f @ X1) = X0)))) = (^[X2 : a] : (? [X3 : b] : ((y @ X3) & ((f @ X3) = X2)) | ? [X4 : b] : (((f @ X4) = X2) & (x @ X4)))))),
% 1.31/1.20 inference(rectify,[status(thm)],[f2])).
% 1.31/1.20 thf(f2,negated_conjecture,(
% 1.31/1.20 ~((^[X0 : a] : (? [X1 : b] : (((y @ X1) | (x @ X1)) & ((f @ X1) = X0)))) = (^[X0 : a] : (? [X1 : b] : ((y @ X1) & ((f @ X1) = X0)) | ? [X1 : b] : (((f @ X1) = X0) & (x @ X1)))))),
% 1.31/1.20 inference(negated_conjecture,[status(cth)],[f1])).
% 1.31/1.20 thf(f1,conjecture,(
% 1.31/1.20 ((^[X0 : a] : (? [X1 : b] : (((y @ X1) | (x @ X1)) & ((f @ X1) = X0)))) = (^[X0 : a] : (? [X1 : b] : ((y @ X1) & ((f @ X1) = X0)) | ? [X1 : b] : (((f @ X1) = X0) & (x @ X1)))))),
% 1.31/1.20 file('/export/starexec/sandbox2/tmp/tmp.sUH9rlcmPK/DTF2THF_14558.p',cX5202_pme)).
% 1.31/1.20 thf(f125,plain,(
% 1.31/1.20 spl0_12 | spl0_12),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f34,f123,f123])).
% 1.31/1.20 thf(f34,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (((y @ X2) = $false) | ((y @ X1) = $false) | (sK2 != (f @ X2)) | ((f @ X1) != sK2)) )),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.31/1.20 thf(f31,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : ((((f @ X2) = sK2) = $false) | ((f @ X1) != sK2) | ((y @ X2) = $false) | ((y @ X1) = $false)) )),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.31/1.20 thf(f30,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (((y @ X1) = $false) | ($false = ((x @ X2) | (y @ X2))) | ((f @ X1) != sK2) | (((f @ X2) = sK2) = $false)) )),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.31/1.20 thf(f29,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (((y @ X1) = $false) | (((f @ X1) = sK2) = $false) | (((f @ X2) = sK2) = $false) | ($false = ((x @ X2) | (y @ X2)))) )),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.31/1.20 thf(f28,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (($false = (((f @ X2) = sK2) & ((x @ X2) | (y @ X2)))) | (((f @ X1) = sK2) = $false) | ((y @ X1) = $false)) )),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.31/1.20 thf(f27,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (((((f @ X1) = sK2) & (y @ X1)) = $false) | ($false = (((f @ X2) = sK2) & ((x @ X2) | (y @ X2))))) )),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.31/1.20 thf(f26,plain,(
% 1.31/1.20 ( ! [X2 : b,X1 : b] : (((((f @ X1) = sK2) & (y @ X1)) = $false) | (((^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0)))) @ X2) = $false)) )),
% 1.31/1.20 inference(pi_clausification,[status(thm)],[f25])).
% 1.31/1.20 thf(f25,plain,(
% 1.31/1.20 ( ! [X1 : b] : (((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))) = $false) | ((((f @ X1) = sK2) & (y @ X1)) = $false)) )),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.31/1.20 thf(f24,plain,(
% 1.31/1.20 ( ! [X1 : b] : (((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))) = $false) | (((^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0))) @ X1) = $false)) )),
% 1.31/1.20 inference(pi_clausification,[status(thm)],[f12])).
% 1.31/1.20 thf(f12,plain,(
% 1.31/1.20 ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0)))) = $false) | ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))) = $false)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.31/1.20 thf(f121,plain,(
% 1.31/1.20 spl0_6 | spl0_11 | spl0_9),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f49,f107,f116,f93])).
% 1.31/1.20 thf(f49,plain,(
% 1.31/1.20 ((x @ sK5) = $true) | (sK2 = (f @ sK4)) | ((f @ sK3) = sK2)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.31/1.20 thf(f47,plain,(
% 1.31/1.20 ((f @ sK3) = sK2) | (((x @ sK5) & ((f @ sK5) = sK2)) = $true) | (sK2 = (f @ sK4))),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.31/1.20 thf(f46,plain,(
% 1.31/1.20 (((f @ sK3) = sK2) = $true) | (sK2 = (f @ sK4)) | (((x @ sK5) & ((f @ sK5) = sK2)) = $true)),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f45])).
% 1.31/1.20 thf(f45,plain,(
% 1.31/1.20 (((f @ sK4) = sK2) = $true) | (((x @ sK5) & ((f @ sK5) = sK2)) = $true) | (((f @ sK3) = sK2) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.31/1.20 thf(f43,plain,(
% 1.31/1.20 ((((f @ sK4) = sK2) & (y @ sK4)) = $true) | (((x @ sK5) & ((f @ sK5) = sK2)) = $true) | (((f @ sK3) = sK2) = $true)),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.31/1.20 thf(f42,plain,(
% 1.31/1.20 (((^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2))) @ sK5) = $true) | ((((f @ sK4) = sK2) & (y @ sK4)) = $true) | (((f @ sK3) = sK2) = $true)),
% 1.31/1.20 inference(sigma_clausification,[status(thm)],[f41])).
% 1.31/1.20 thf(f41,plain,(
% 1.31/1.20 ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true) | (((f @ sK3) = sK2) = $true) | ((((f @ sK4) = sK2) & (y @ sK4)) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.31/1.20 thf(f39,plain,(
% 1.31/1.20 ((((f @ sK3) = sK2) & ((x @ sK3) | (y @ sK3))) = $true) | ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true) | ((((f @ sK4) = sK2) & (y @ sK4)) = $true)),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.31/1.20 thf(f38,plain,(
% 1.31/1.20 ((((f @ sK3) = sK2) & ((x @ sK3) | (y @ sK3))) = $true) | (((^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0))) @ sK4) = $true) | ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true)),
% 1.31/1.20 inference(sigma_clausification,[status(thm)],[f37])).
% 1.31/1.20 thf(f37,plain,(
% 1.31/1.20 ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0)))) = $true) | ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true) | ((((f @ sK3) = sK2) & ((x @ sK3) | (y @ sK3))) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.31/1.20 thf(f36,plain,(
% 1.31/1.20 (((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) | (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0))))) = $true) | ((((f @ sK3) = sK2) & ((x @ sK3) | (y @ sK3))) = $true)),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.31/1.20 thf(f35,plain,(
% 1.31/1.20 (((^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0)))) @ sK3) = $true) | (((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) | (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0))))) = $true)),
% 1.31/1.20 inference(sigma_clausification,[status(thm)],[f10])).
% 1.31/1.20 thf(f10,plain,(
% 1.31/1.20 ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & ((x @ Y0) | (y @ Y0))))) = $true) | (((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) | (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (y @ Y0))))) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.31/1.20 thf(f120,plain,(
% 1.31/1.20 spl0_10 | spl0_9 | spl0_6),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f50,f93,f107,f111])).
% 1.31/1.20 thf(f50,plain,(
% 1.31/1.20 ((f @ sK5) = sK2) | ((f @ sK3) = sK2) | (sK2 = (f @ sK4))),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f48])).
% 1.31/1.20 thf(f48,plain,(
% 1.31/1.20 (((f @ sK5) = sK2) = $true) | (sK2 = (f @ sK4)) | ((f @ sK3) = sK2)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.31/1.20 thf(f119,plain,(
% 1.31/1.20 spl0_9 | spl0_2 | spl0_11),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f53,f116,f75,f107])).
% 1.31/1.20 thf(f53,plain,(
% 1.31/1.20 ((x @ sK5) = $true) | ((y @ sK4) = $true) | ((f @ sK3) = sK2)),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f52])).
% 1.31/1.20 thf(f52,plain,(
% 1.31/1.20 ((y @ sK4) = $true) | ((x @ sK5) = $true) | (((f @ sK3) = sK2) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.31/1.20 thf(f44,plain,(
% 1.31/1.20 (((x @ sK5) & ((f @ sK5) = sK2)) = $true) | (((f @ sK3) = sK2) = $true) | ((y @ sK4) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.31/1.20 thf(f114,plain,(
% 1.31/1.20 spl0_9 | spl0_2 | spl0_10),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f55,f111,f75,f107])).
% 1.31/1.20 thf(f55,plain,(
% 1.31/1.20 ((f @ sK3) = sK2) | ((y @ sK4) = $true) | ((f @ sK5) = sK2)),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f54])).
% 1.31/1.20 thf(f54,plain,(
% 1.31/1.20 (((f @ sK5) = sK2) = $true) | ((f @ sK3) = sK2) | ((y @ sK4) = $true)),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 1.31/1.20 thf(f51,plain,(
% 1.31/1.20 (((f @ sK3) = sK2) = $true) | (((f @ sK5) = sK2) = $true) | ((y @ sK4) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.31/1.20 thf(f105,plain,(
% 1.31/1.20 spl0_3 | spl0_8 | spl0_1 | spl0_6),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f63,f93,f71,f102,f79])).
% 1.31/1.20 thf(f63,plain,(
% 1.31/1.20 (sK2 = (f @ sK4)) | ((y @ sK3) = $true) | ((x @ sK3) = $true) | ((x @ sK6) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.31/1.20 thf(f61,plain,(
% 1.31/1.20 (sK2 = (f @ sK4)) | ((y @ sK3) = $true) | (((x @ sK6) & ((f @ sK6) = sK2)) = $true) | ((x @ sK3) = $true)),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.31/1.20 thf(f60,plain,(
% 1.31/1.20 ((x @ sK3) = $true) | (sK2 = (f @ sK4)) | ((y @ sK3) = $true) | (((^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2))) @ sK6) = $true)),
% 1.31/1.20 inference(sigma_clausification,[status(thm)],[f59])).
% 1.31/1.20 thf(f59,plain,(
% 1.31/1.20 ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true) | (sK2 = (f @ sK4)) | ((y @ sK3) = $true) | ((x @ sK3) = $true)),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 1.31/1.20 thf(f58,plain,(
% 1.31/1.20 ((y @ sK3) = $true) | (((f @ sK4) = sK2) = $true) | ((x @ sK3) = $true) | ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.31/1.20 thf(f56,plain,(
% 1.31/1.20 ((((f @ sK4) = sK2) & (y @ sK4)) = $true) | ((x @ sK3) = $true) | ((y @ sK3) = $true) | ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.31/1.20 thf(f40,plain,(
% 1.31/1.20 (((x @ sK3) | (y @ sK3)) = $true) | ((((f @ sK4) = sK2) & (y @ sK4)) = $true) | ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.31/1.20 thf(f100,plain,(
% 1.31/1.20 spl0_6 | spl0_3 | spl0_1 | spl0_7),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f64,f97,f71,f79,f93])).
% 1.31/1.20 thf(f64,plain,(
% 1.31/1.20 (sK2 = (f @ sK4)) | ((x @ sK3) = $true) | ((y @ sK3) = $true) | (sK2 = (f @ sK6))),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f62])).
% 1.31/1.20 thf(f62,plain,(
% 1.31/1.20 ((y @ sK3) = $true) | (((f @ sK6) = sK2) = $true) | ((x @ sK3) = $true) | (sK2 = (f @ sK4))),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.31/1.20 thf(f91,plain,(
% 1.31/1.20 spl0_3 | spl0_2 | spl0_1 | spl0_5),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f68,f88,f71,f75,f79])).
% 1.31/1.20 thf(f68,plain,(
% 1.31/1.20 ((y @ sK3) = $true) | ((x @ sK3) = $true) | ((y @ sK4) = $true) | ((x @ sK7) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.31/1.20 thf(f66,plain,(
% 1.31/1.20 ((y @ sK3) = $true) | ((y @ sK4) = $true) | ($true = ((x @ sK7) & ((f @ sK7) = sK2))) | ((x @ sK3) = $true)),
% 1.31/1.20 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.31/1.20 thf(f65,plain,(
% 1.31/1.20 ((x @ sK3) = $true) | ((y @ sK3) = $true) | ((y @ sK4) = $true) | (((^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2))) @ sK7) = $true)),
% 1.31/1.20 inference(sigma_clausification,[status(thm)],[f57])).
% 1.31/1.20 thf(f57,plain,(
% 1.31/1.20 ((x @ sK3) = $true) | ((y @ sK3) = $true) | ((?? @ b @ (^[Y0 : b]: ((x @ Y0) & ((f @ Y0) = sK2)))) = $true) | ((y @ sK4) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.31/1.20 thf(f86,plain,(
% 1.31/1.20 spl0_1 | spl0_2 | spl0_3 | spl0_4),
% 1.31/1.20 inference(avatar_split_clause,[status(thm)],[f69,f83,f79,f75,f71])).
% 1.31/1.20 thf(f69,plain,(
% 1.31/1.20 ((x @ sK3) = $true) | ((f @ sK7) = sK2) | ((y @ sK3) = $true) | ((y @ sK4) = $true)),
% 1.31/1.20 inference(equality_proxy_clausification,[status(thm)],[f67])).
% 1.31/1.20 thf(f67,plain,(
% 1.31/1.20 ((y @ sK4) = $true) | (((f @ sK7) = sK2) = $true) | ((x @ sK3) = $true) | ((y @ sK3) = $true)),
% 1.31/1.20 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.31/1.20 % SZS output end Proof for DTF2THF_14558
% 1.31/1.20 % (14658)------------------------------
% 1.31/1.20 % (14658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.20 % (14658)Termination reason: Refutation
% 1.31/1.20
% 1.31/1.20 % (14658)Memory used [KB]: 5628
% 1.31/1.20 % (14658)Time elapsed: 0.007 s
% 1.31/1.20 % (14658)Instructions burned: 9 (million)
% 1.31/1.20 % (14658)------------------------------
% 1.31/1.20 % (14658)------------------------------
% 1.31/1.20 % (14657)Success in time 0.017 s
%------------------------------------------------------------------------------