%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU896^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:41 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 73 ( 8 unt; 0 typ; 7 def)
% Number of atoms : 360 ( 240 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 390 ( 76 ~; 141 |; 20 &; 135 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 14 con; 0-2 aty)
% ( 0 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 48 ( 26 ^; 20 !; 2 ?; 48 :)
% 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,
y: b ).
thf(func_def_3,type,
g: b > a ).
thf(func_def_4,type,
x: b ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a ).
thf(func_def_18,type,
sK3: b ).
thf(f96,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f59,f64,f72,f73,f74,f77,f80,f88,f95]) ).
thf(f95,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f94]) ).
thf(f94,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( sK2 != sK2 )
| ( x != x )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f67,f50]) ).
thf(f50,plain,
( ( ( g @ x )
= sK2 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl0_2
<=> ( ( g @ x )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f67,plain,
( ! [X1: b] :
( ( ( g @ X1 )
!= sK2 )
| ( x != X1 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f66]) ).
thf(f66,definition,
( spl0_6
<=> ! [X1: b] :
( ( x != X1 )
| ( ( g @ X1 )
!= sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f88,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( y != y )
| ( sK2 != sK2 )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f71,f58]) ).
thf(f58,plain,
( ( ( g @ y )
= sK2 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl0_4
<=> ( ( g @ y )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f71,plain,
( ! [X1: b] :
( ( ( g @ X1 )
!= sK2 )
| ( y != X1 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl0_7
<=> ! [X1: b] :
( ( ( g @ X1 )
!= sK2 )
| ( y != X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f80,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f79]) ).
thf(f79,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f78,f49]) ).
thf(f49,plain,
( ( ( g @ x )
!= sK2 )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f78,plain,
( ( ( g @ x )
= sK2 )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f63,f46]) ).
thf(f46,plain,
( ( x = sK3 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl0_1
<=> ( x = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f63,plain,
( ( sK2
= ( g @ sK3 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl0_5
<=> ( sK2
= ( g @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f77,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f76]) ).
thf(f76,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f75,f57]) ).
thf(f57,plain,
( ( ( g @ y )
!= sK2 )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f75,plain,
( ( ( g @ y )
= sK2 )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f63,f54]) ).
thf(f54,plain,
( ( y = sK3 )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl0_3
<=> ( y = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f74,plain,
( spl0_7
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f48,f70]) ).
thf(f20,plain,
! [X1: b] :
( ( ( g @ X1 )
!= sK2 )
| ( y != X1 )
| ( ( g @ x )
!= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: b] :
( ( ( g @ x )
!= sK2 )
| ( ( y = X1 )
= $false )
| ( ( g @ X1 )
!= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: b] :
( ( $false
= ( ( y = X1 )
| ( x = X1 ) ) )
| ( ( g @ X1 )
!= sK2 )
| ( ( g @ x )
!= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: b] :
( ( ( ( g @ X1 )
= sK2 )
= $false )
| ( ( g @ x )
!= sK2 )
| ( $false
= ( ( y = X1 )
| ( x = X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: b] :
( ( ( ( g @ x )
= sK2 )
= $false )
| ( $false
= ( ( y = X1 )
| ( x = X1 ) ) )
| ( ( ( g @ X1 )
= sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: b] :
( ( ( ( ( g @ X1 )
= sK2 )
& ( ( y = X1 )
| ( x = X1 ) ) )
= $false )
| ( ( ( g @ x )
= sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: b] :
( ( ( ( g @ x )
= sK2 )
= $false )
| ( ( ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) ) )
= $false )
| ( ( ( g @ x )
= sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( ( g @ x )
= sK2 )
| ( ( g @ y )
= sK2 ) )
= $false )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ?? @ b
@ ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) ) )
!= ( ( ( g @ x )
= sK2 )
| ( ( g @ y )
= sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( g @ Y1 )
= Y0 )
& ( ( y = Y1 )
| ( x = Y1 ) ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ( ( g @ x )
= Y0 )
| ( ( g @ y )
= Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( ( g @ x )
= Y0 )
| ( ( g @ y )
= Y0 ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( g @ Y1 )
= Y0 )
& ( ( y = Y1 )
| ( x = Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ( ( g @ x )
= Y0 )
| ( ( g @ y )
= Y0 ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( g @ Y1 )
= Y0 )
& ( ( y = Y1 )
| ( x = Y1 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [Y0: a] :
( ( ( g @ x )
= Y0 )
| ( ( g @ y )
= Y0 ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( g @ Y1 )
= Y0 )
& ( ( y = Y1 )
| ( x = Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( ( x = X1 )
| ( y = X1 ) )
& ( ( g @ X1 )
= X0 ) ) )
!= ( ^ [X2: a] :
( ( ( g @ y )
= X2 )
| ( ( g @ x )
= X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( ( x = X1 )
| ( y = X1 ) )
& ( ( g @ X1 )
= X0 ) ) )
= ( ^ [X2: a] :
( ( ( g @ y )
= X2 )
| ( ( g @ x )
= X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1jUUj0q93U/DTF2THF_30502.p',cTHM500_pme) ).
thf(f73,plain,
( spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f48,f66]) ).
thf(f21,plain,
! [X1: b] :
( ( x != X1 )
| ( ( g @ X1 )
!= sK2 )
| ( ( g @ x )
!= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: b] :
( ( ( x = X1 )
= $false )
| ( ( g @ x )
!= sK2 )
| ( ( g @ X1 )
!= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f72,plain,
( spl0_7
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f29,f56,f70]) ).
thf(f29,plain,
! [X1: b] :
( ( ( g @ X1 )
!= sK2 )
| ( ( g @ y )
!= sK2 )
| ( y != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: b] :
( ( ( g @ X1 )
!= sK2 )
| ( ( g @ y )
!= sK2 )
| ( ( y = X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: b] :
( ( ( g @ y )
!= sK2 )
| ( ( g @ X1 )
!= sK2 )
| ( $false
= ( ( y = X1 )
| ( x = X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: b] :
( ( ( ( g @ X1 )
= sK2 )
= $false )
| ( $false
= ( ( y = X1 )
| ( x = X1 ) ) )
| ( ( g @ y )
!= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: b] :
( ( ( g @ y )
!= sK2 )
| ( ( ( ( g @ X1 )
= sK2 )
& ( ( y = X1 )
| ( x = X1 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: b] :
( ( ( ( g @ y )
= sK2 )
= $false )
| ( ( ( ( g @ X1 )
= sK2 )
& ( ( y = X1 )
| ( x = X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: b] :
( ( ( ( g @ y )
= sK2 )
= $false )
| ( ( ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) ) )
= $false )
| ( ( ( g @ y )
= sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f64,plain,
( spl0_5
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f48,f56,f61]) ).
thf(f38,plain,
( ( sK2
= ( g @ sK3 ) )
| ( ( g @ x )
= sK2 )
| ( ( g @ y )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( ( g @ x )
= sK2 )
= $true )
| ( ( g @ y )
= sK2 )
| ( sK2
= ( g @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( g @ y )
= sK2 )
| ( ( ( g @ sK3 )
= sK2 )
= $true )
| ( ( ( g @ x )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ( ( g @ sK3 )
= sK2 )
& ( ( y = sK3 )
| ( x = sK3 ) ) )
= $true )
| ( ( g @ y )
= sK2 )
| ( ( ( g @ x )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) )
@ sK3 )
= $true )
| ( ( ( g @ x )
= sK2 )
= $true )
| ( ( g @ y )
= sK2 ) ),
inference(sigma_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( g @ y )
= sK2 )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) ) )
= $true )
| ( ( ( g @ x )
= sK2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( ( g @ y )
= sK2 )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) ) )
= $true )
| ( ( ( g @ x )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( ( ( g @ x )
= sK2 )
| ( ( g @ y )
= sK2 ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( g @ Y0 )
= sK2 )
& ( ( y = Y0 )
| ( x = Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f59,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f42,f56,f52,f48,f44]) ).
thf(f42,plain,
( ( y = sK3 )
| ( ( g @ y )
= sK2 )
| ( ( g @ x )
= sK2 )
| ( x = sK3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( x = sK3 )
| ( ( y = sK3 )
= $true )
| ( ( g @ x )
= sK2 )
| ( ( g @ y )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( g @ y )
= sK2 )
| ( ( g @ x )
= sK2 )
| ( ( x = sK3 )
= $true )
| ( ( y = sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( g @ y )
= sK2 )
| ( ( g @ x )
= sK2 )
| ( ( ( y = sK3 )
| ( x = sK3 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ( g @ x )
= sK2 )
= $true )
| ( ( ( y = sK3 )
| ( x = sK3 ) )
= $true )
| ( ( g @ y )
= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU896^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:36:31 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEU896^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : TPS problem THM500
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0412 [Bro09]
% 0.29/0.45 % : THM500 [TPS]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % 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
% 0.29/0.45 % Syntax : Number of formulae : 6 ( 1 unt; 5 typ; 0 def)
% 0.29/0.45 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 1 ( 6 avg)
% 0.29/0.45 % Number of connectives : 6 ( 0 ~; 2 |; 1 &; 3 @)
% 0.29/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 1 ( 1 avg)
% 0.29/0.45 % Number of types : 2 ( 2 usr)
% 0.29/0.45 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.29/0.45 % Number of variables : 3 ( 2 ^; 0 !; 1 ?; 3 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 % : Polymorphic definitions expanded.
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(b_type,type,
% 0.29/0.45 b: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(a_type,type,
% 0.29/0.45 a: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(y,type,
% 0.29/0.45 y: b ).
% 0.29/0.45
% 0.29/0.45 thf(g,type,
% 0.29/0.45 g: b > a ).
% 0.29/0.45
% 0.29/0.45 thf(x,type,
% 0.29/0.45 x: b ).
% 0.29/0.45
% 0.29/0.45 thf(cTHM500_pme,conjecture,
% 0.29/0.45 ( ( ^ [Xz: a] :
% 0.29/0.45 ? [Xt: b] :
% 0.29/0.45 ( ( ( Xt = x )
% 0.29/0.45 | ( Xt = y ) )
% 0.29/0.45 & ( Xz
% 0.29/0.45 = ( g @ Xt ) ) ) )
% 0.29/0.45 = ( ^ [Xv: a] :
% 0.29/0.45 ( ( Xv
% 0.29/0.45 = ( g @ x ) )
% 0.29/0.45 | ( Xv
% 0.29/0.45 = ( g @ y ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 12:36:32 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1jUUj0q93U/DTF2DTF30502.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(b_type,type,
% 1.47/1.26 b: $tType ).
% 1.47/1.26
% 1.47/1.26 thf(a_type,type,
% 1.47/1.26 a: $tType ).
% 1.47/1.26
% 1.47/1.26 thf(y,type,
% 1.47/1.26 y: b ).
% 1.47/1.26
% 1.47/1.26 thf(g,type,
% 1.47/1.26 g: b > a ).
% 1.47/1.26
% 1.47/1.26 thf(x,type,
% 1.47/1.26 x: b ).
% 1.47/1.26
% 1.47/1.26 thf(cTHM500_pme,conjecture,
% 1.47/1.26 ( ( ^ [Xz: a] :
% 1.47/1.26 ? [Xt: b] :
% 1.47/1.26 ( ( ( Xt = x )
% 1.47/1.26 | ( Xt = y ) )
% 1.47/1.26 & ( Xz
% 1.47/1.26 = ( g @ Xt ) ) ) )
% 1.47/1.26 = ( ^ [Xv: a] :
% 1.47/1.26 ( ( Xv
% 1.47/1.26 = ( g @ x ) )
% 1.47/1.26 | ( Xv
% 1.47/1.26 = ( g @ y ) ) ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (30603)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30502 for (2999ds/2Mi)
% 1.47/1.28 % (30603)Instruction limit reached!
% 1.47/1.28 % (30603)------------------------------
% 1.47/1.28 % (30603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (30603)Termination reason: Unknown
% 1.47/1.28 % (30603)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (30603)Memory used [KB]: 5373
% 1.47/1.28 % (30603)Time elapsed: 0.002 s
% 1.47/1.28 % (30603)Instructions burned: 2 (million)
% 1.47/1.28 % (30603)------------------------------
% 1.47/1.28 % (30603)------------------------------
% 1.47/1.28 % (30600)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30502 for (2999ds/183Mi)
% 1.47/1.28 % (30601)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_30502 for (2999ds/4Mi)
% 1.47/1.28 % (30602)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_30502 for (2999ds/27Mi)
% 1.47/1.28 % (30604)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_30502 for (2999ds/2Mi)
% 1.47/1.28 % (30606)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30502 for (2999ds/18Mi)
% 1.47/1.28 % (30604)Instruction limit reached!
% 1.47/1.28 % (30604)------------------------------
% 1.47/1.28 % (30604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (30604)Termination reason: Unknown
% 1.47/1.28 % (30604)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (30604)Memory used [KB]: 895
% 1.47/1.28 % (30604)Time elapsed: 0.003 s
% 1.47/1.28 % (30604)Instructions burned: 2 (million)
% 1.47/1.28 % (30604)------------------------------
% 1.47/1.28 % (30604)------------------------------
% 1.47/1.28 % (30605)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_30502 for (2999ds/275Mi)
% 1.47/1.28 % (30607)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30502 for (2999ds/3Mi)
% 1.47/1.29 % (30601)Instruction limit reached!
% 1.47/1.29 % (30601)------------------------------
% 1.47/1.29 % (30601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30601)Termination reason: Unknown
% 1.47/1.29 % (30601)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (30601)Memory used [KB]: 5500
% 1.47/1.29 % (30601)Time elapsed: 0.005 s
% 1.47/1.29 % (30601)Instructions burned: 4 (million)
% 1.47/1.29 % (30601)------------------------------
% 1.47/1.29 % (30601)------------------------------
% 1.47/1.29 % (30607)Refutation not found, incomplete strategy
% 1.47/1.29 % (30607)------------------------------
% 1.47/1.29 % (30607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30607)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29 % (30600)First to succeed.
% 1.47/1.29
% 1.47/1.29 % (30607)Memory used [KB]: 5500
% 1.47/1.29 % (30607)Time elapsed: 0.001 s
% 1.47/1.29 % (30607)Instructions burned: 1 (million)
% 1.47/1.29 % (30607)------------------------------
% 1.47/1.29 % (30607)------------------------------
% 1.47/1.29 % (30606)Also succeeded, but the first one will report.
% 1.47/1.29 % (30600)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_30502
% 1.47/1.29 % SZS output start Proof for DTF2THF_30502
% 1.47/1.29 thf(type_def_5, type, b: $tType).
% 1.47/1.29 thf(type_def_6, type, a: $tType).
% 1.47/1.29 thf(func_def_0, type, b: $tType).
% 1.47/1.29 thf(func_def_1, type, a: $tType).
% 1.47/1.29 thf(func_def_2, type, y: b).
% 1.47/1.29 thf(func_def_3, type, g: b > a).
% 1.47/1.29 thf(func_def_4, type, x: b).
% 1.47/1.29 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.47/1.29 thf(func_def_17, type, sK2: a).
% 1.47/1.29 thf(func_def_18, type, sK3: b).
% 1.47/1.29 thf(f96,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(avatar_sat_refutation,[status(thm)],[f59,f64,f72,f73,f74,f77,f80,f88,f95])).
% 1.47/1.29 thf(f95,plain,(
% 1.47/1.29 ~spl0_2 | ~spl0_6),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f94])).
% 1.47/1.29 thf(f94,plain,(
% 1.47/1.29 $false | (~spl0_2 | ~spl0_6)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.47/1.29 thf(f92,plain,(
% 1.47/1.29 (sK2 != sK2) | (x != x) | (~spl0_2 | ~spl0_6)),
% 1.47/1.29 inference(superposition,[status(thm)],[f67,f50])).
% 1.47/1.29 thf(f50,plain,(
% 1.47/1.29 ((g @ x) = sK2) | ~spl0_2),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.47/1.29 thf(f48,definition,(
% 1.47/1.29 spl0_2 <=> ((g @ x) = sK2)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.47/1.29 thf(f67,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((g @ X1) != sK2) | (x != X1)) ) | ~spl0_6),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f66])).
% 1.47/1.29 thf(f66,definition,(
% 1.47/1.29 spl0_6 <=> ! [X1 : b] : ((x != X1) | ((g @ X1) != sK2))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.47/1.29 thf(f88,plain,(
% 1.47/1.29 ~spl0_4 | ~spl0_7),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.47/1.29 thf(f87,plain,(
% 1.47/1.29 $false | (~spl0_4 | ~spl0_7)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.47/1.29 thf(f86,plain,(
% 1.47/1.29 (y != y) | (sK2 != sK2) | (~spl0_4 | ~spl0_7)),
% 1.47/1.29 inference(superposition,[status(thm)],[f71,f58])).
% 1.47/1.29 thf(f58,plain,(
% 1.47/1.29 ((g @ y) = sK2) | ~spl0_4),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.47/1.29 thf(f56,definition,(
% 1.47/1.29 spl0_4 <=> ((g @ y) = sK2)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.47/1.29 thf(f71,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((g @ X1) != sK2) | (y != X1)) ) | ~spl0_7),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.47/1.29 thf(f70,definition,(
% 1.47/1.29 spl0_7 <=> ! [X1 : b] : (((g @ X1) != sK2) | (y != X1))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.47/1.29 thf(f80,plain,(
% 1.47/1.29 ~spl0_1 | spl0_2 | ~spl0_5),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f79])).
% 1.47/1.29 thf(f79,plain,(
% 1.47/1.29 $false | (~spl0_1 | spl0_2 | ~spl0_5)),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f78,f49])).
% 1.47/1.29 thf(f49,plain,(
% 1.47/1.29 ((g @ x) != sK2) | spl0_2),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.47/1.29 thf(f78,plain,(
% 1.47/1.29 ((g @ x) = sK2) | (~spl0_1 | ~spl0_5)),
% 1.47/1.29 inference(superposition,[status(thm)],[f63,f46])).
% 1.47/1.29 thf(f46,plain,(
% 1.47/1.29 (x = sK3) | ~spl0_1),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.47/1.29 thf(f44,definition,(
% 1.47/1.29 spl0_1 <=> (x = sK3)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.47/1.29 thf(f63,plain,(
% 1.47/1.29 (sK2 = (g @ sK3)) | ~spl0_5),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.47/1.29 thf(f61,definition,(
% 1.47/1.29 spl0_5 <=> (sK2 = (g @ sK3))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.47/1.29 thf(f77,plain,(
% 1.47/1.29 ~spl0_3 | spl0_4 | ~spl0_5),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f76])).
% 1.47/1.29 thf(f76,plain,(
% 1.47/1.29 $false | (~spl0_3 | spl0_4 | ~spl0_5)),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f75,f57])).
% 1.47/1.29 thf(f57,plain,(
% 1.47/1.29 ((g @ y) != sK2) | spl0_4),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.47/1.29 thf(f75,plain,(
% 1.47/1.29 ((g @ y) = sK2) | (~spl0_3 | ~spl0_5)),
% 1.47/1.29 inference(superposition,[status(thm)],[f63,f54])).
% 1.47/1.29 thf(f54,plain,(
% 1.47/1.29 (y = sK3) | ~spl0_3),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.47/1.29 thf(f52,definition,(
% 1.47/1.29 spl0_3 <=> (y = sK3)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.47/1.29 thf(f74,plain,(
% 1.47/1.29 spl0_7 | ~spl0_2),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f20,f48,f70])).
% 1.47/1.29 thf(f20,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((g @ X1) != sK2) | (y != X1) | ((g @ x) != sK2)) )),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f19])).
% 1.47/1.29 thf(f19,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((g @ x) != sK2) | ((y = X1) = $false) | ((g @ X1) != sK2)) )),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 ( ! [X1 : b] : (($false = ((y = X1) | (x = X1))) | ((g @ X1) != sK2) | ((g @ x) != sK2)) )),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 ( ! [X1 : b] : ((((g @ X1) = sK2) = $false) | ((g @ x) != sK2) | ($false = ((y = X1) | (x = X1)))) )),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f15])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 ( ! [X1 : b] : ((((g @ x) = sK2) = $false) | ($false = ((y = X1) | (x = X1))) | (((g @ X1) = sK2) = $false)) )),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((((g @ X1) = sK2) & ((y = X1) | (x = X1))) = $false) | (((g @ x) = sK2) = $false)) )),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ( ! [X1 : b] : ((((g @ x) = sK2) = $false) | (((^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0)))) @ X1) = $false)) )),
% 1.47/1.29 inference(pi_clausification,[status(thm)],[f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 ((?? @ b @ (^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0))))) = $false) | (((g @ x) = sK2) = $false)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 ((((g @ x) = sK2) | ((g @ y) = sK2)) = $false) | ((?? @ b @ (^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0))))) = $false)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ((?? @ b @ (^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0))))) != (((g @ x) = sK2) | ((g @ y) = sK2)))),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 (((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((g @ Y1) = Y0) & ((y = Y1) | (x = Y1)))))) @ sK2) != ((^[Y0 : a]: (((g @ x) = Y0) | ((g @ y) = Y0))) @ sK2))),
% 1.47/1.29 inference(negative_extensionality,[status(thm)],[f6])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ((^[Y0 : a]: (((g @ x) = Y0) | ((g @ y) = Y0))) != (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((g @ Y1) = Y0) & ((y = Y1) | (x = Y1)))))))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ((^[Y0 : a]: (((g @ x) = Y0) | ((g @ y) = Y0))) != (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((g @ Y1) = Y0) & ((y = Y1) | (x = Y1)))))))),
% 1.47/1.29 inference(flattening,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,plain,(
% 1.47/1.29 ~((^[Y0 : a]: (((g @ x) = Y0) | ((g @ y) = Y0))) = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((g @ Y1) = Y0) & ((y = Y1) | (x = Y1)))))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,negated_conjecture,(
% 1.47/1.29 ~((^[X0 : a] : (? [X1 : b] : (((x = X1) | (y = X1)) & ((g @ X1) = X0)))) = (^[X2 : a] : (((g @ y) = X2) | ((g @ x) = X2))))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.29 thf(f1,conjecture,(
% 1.47/1.29 ((^[X0 : a] : (? [X1 : b] : (((x = X1) | (y = X1)) & ((g @ X1) = X0)))) = (^[X2 : a] : (((g @ y) = X2) | ((g @ x) = X2))))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.1jUUj0q93U/DTF2THF_30502.p',cTHM500_pme)).
% 1.47/1.29 thf(f73,plain,(
% 1.47/1.29 spl0_6 | ~spl0_2),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f21,f48,f66])).
% 1.47/1.29 thf(f21,plain,(
% 1.47/1.29 ( ! [X1 : b] : ((x != X1) | ((g @ X1) != sK2) | ((g @ x) != sK2)) )),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((x = X1) = $false) | ((g @ x) != sK2) | ((g @ X1) != sK2)) )),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.47/1.29 thf(f72,plain,(
% 1.47/1.29 spl0_7 | ~spl0_4),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f29,f56,f70])).
% 1.47/1.29 thf(f29,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((g @ X1) != sK2) | ((g @ y) != sK2) | (y != X1)) )),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.47/1.29 thf(f28,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((g @ X1) != sK2) | ((g @ y) != sK2) | ((y = X1) = $false)) )),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.47/1.29 thf(f26,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((g @ y) != sK2) | ((g @ X1) != sK2) | ($false = ((y = X1) | (x = X1)))) )),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f25])).
% 1.47/1.29 thf(f25,plain,(
% 1.47/1.29 ( ! [X1 : b] : ((((g @ X1) = sK2) = $false) | ($false = ((y = X1) | (x = X1))) | ((g @ y) != sK2)) )),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.47/1.29 thf(f24,plain,(
% 1.47/1.29 ( ! [X1 : b] : (((g @ y) != sK2) | ((((g @ X1) = sK2) & ((y = X1) | (x = X1))) = $false)) )),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 1.47/1.29 thf(f23,plain,(
% 1.47/1.29 ( ! [X1 : b] : ((((g @ y) = sK2) = $false) | ((((g @ X1) = sK2) & ((y = X1) | (x = X1))) = $false)) )),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.47/1.29 thf(f22,plain,(
% 1.47/1.29 ( ! [X1 : b] : ((((g @ y) = sK2) = $false) | (((^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0)))) @ X1) = $false)) )),
% 1.47/1.29 inference(pi_clausification,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 ((?? @ b @ (^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0))))) = $false) | (((g @ y) = sK2) = $false)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.47/1.29 thf(f64,plain,(
% 1.47/1.29 spl0_5 | spl0_4 | spl0_2),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f38,f48,f56,f61])).
% 1.47/1.29 thf(f38,plain,(
% 1.47/1.29 (sK2 = (g @ sK3)) | ((g @ x) = sK2) | ((g @ y) = sK2)),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.47/1.29 thf(f37,plain,(
% 1.47/1.29 (((g @ x) = sK2) = $true) | ((g @ y) = sK2) | (sK2 = (g @ sK3))),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f36])).
% 1.47/1.29 thf(f36,plain,(
% 1.47/1.29 ((g @ y) = sK2) | (((g @ sK3) = sK2) = $true) | (((g @ x) = sK2) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.47/1.29 thf(f34,plain,(
% 1.47/1.29 ((((g @ sK3) = sK2) & ((y = sK3) | (x = sK3))) = $true) | ((g @ y) = sK2) | (((g @ x) = sK2) = $true)),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.47/1.29 thf(f33,plain,(
% 1.47/1.29 (((^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0)))) @ sK3) = $true) | (((g @ x) = sK2) = $true) | ((g @ y) = sK2)),
% 1.47/1.29 inference(sigma_clausification,[status(thm)],[f32])).
% 1.47/1.29 thf(f32,plain,(
% 1.47/1.29 ((g @ y) = sK2) | ((?? @ b @ (^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0))))) = $true) | (((g @ x) = sK2) = $true)),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.47/1.29 thf(f31,plain,(
% 1.47/1.29 (((g @ y) = sK2) = $true) | ((?? @ b @ (^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0))))) = $true) | (((g @ x) = sK2) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ((((g @ x) = sK2) | ((g @ y) = sK2)) = $true) | ((?? @ b @ (^[Y0 : b]: (((g @ Y0) = sK2) & ((y = Y0) | (x = Y0))))) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.47/1.29 thf(f59,plain,(
% 1.47/1.29 spl0_1 | spl0_2 | spl0_3 | spl0_4),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f42,f56,f52,f48,f44])).
% 1.47/1.29 thf(f42,plain,(
% 1.47/1.29 (y = sK3) | ((g @ y) = sK2) | ((g @ x) = sK2) | (x = sK3)),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f41])).
% 1.47/1.29 thf(f41,plain,(
% 1.47/1.29 (x = sK3) | ((y = sK3) = $true) | ((g @ x) = sK2) | ((g @ y) = sK2)),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.47/1.29 thf(f40,plain,(
% 1.47/1.29 ((g @ y) = sK2) | ((g @ x) = sK2) | ((x = sK3) = $true) | ((y = sK3) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.47/1.29 thf(f39,plain,(
% 1.47/1.29 ((g @ y) = sK2) | ((g @ x) = sK2) | (((y = sK3) | (x = sK3)) = $true)),
% 1.47/1.29 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.47/1.29 thf(f35,plain,(
% 1.47/1.29 (((g @ x) = sK2) = $true) | (((y = sK3) | (x = sK3)) = $true) | ((g @ y) = sK2)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_30502
% 1.47/1.29 % (30600)------------------------------
% 1.47/1.29 % (30600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30600)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (30600)Memory used [KB]: 5500
% 1.47/1.29 % (30600)Time elapsed: 0.007 s
% 1.47/1.29 % (30600)Instructions burned: 4 (million)
% 1.47/1.29 % (30600)------------------------------
% 1.47/1.29 % (30600)------------------------------
% 1.47/1.29 % (30599)Success in time 0.022 s
%------------------------------------------------------------------------------