%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV231^5 : 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 : n026.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 09:40:37 AM UTC 2026
% Result : Theorem 1.52s 1.39s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 9 unt; 0 typ; 9 def)
% Number of atoms : 533 ( 168 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 399 ( 77 ~; 142 |; 10 &; 132 @)
% ( 9 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 15 con; 0-2 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 50 ( 27 ^; 23 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
y: a > $o ).
thf(func_def_2,type,
x: a > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a ).
thf(func_def_18,type,
sK3: a > $o ).
thf(func_def_19,type,
sK4: a ).
thf(func_def_20,type,
sK5: a ).
thf(f182,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f43,f52,f53,f66,f75,f79,f80,f85,f89,f93,f112,f181]) ).
thf(f181,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f180]) ).
thf(f180,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f179]) ).
thf(f179,plain,
( ( $false = $true )
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f170,f65]) ).
thf(f65,plain,
( ( ( sK3 @ sK2 )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl0_7
<=> ( ( sK3 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f170,plain,
( ( ( sK3 @ sK2 )
= $true )
| spl0_6
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ( $false != $false )
| ( ( sK3 @ sK2 )
= $true )
| spl0_6
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f60,f136]) ).
thf(f136,plain,
( ! [X1: a] :
( ( $false
= ( x @ X1 ) )
| ( ( sK3 @ X1 )
= $true ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( x @ X1 ) )
| ~ spl0_9 ),
inference(argument_congruence,[status(thm)],[f74]) ).
thf(f74,plain,
( ( x = sK3 )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl0_9
<=> ( x = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f60,plain,
( ( $false
!= ( x @ sK2 ) )
| spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl0_6
<=> ( $false
= ( x @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f112,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f111]) ).
thf(f111,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f101,f65]) ).
thf(f101,plain,
( ( ( sK3 @ sK2 )
= $true )
| ~ spl0_1
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f95,f39]) ).
thf(f39,plain,
( ( $true
= ( y @ sK2 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_1
<=> ( $true
= ( y @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f95,plain,
( ! [X1: a] :
( ( $false
= ( y @ X1 ) )
| ( ( sK3 @ X1 )
= $true ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( y @ X1 ) )
| ~ spl0_8 ),
inference(argument_congruence,[status(thm)],[f70]) ).
thf(f70,plain,
( ( y = sK3 )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl0_8
<=> ( y = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f93,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f92]) ).
thf(f92,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f51,f61]) ).
thf(f61,plain,
( ( $false
= ( x @ sK2 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f51,plain,
( ( $true
= ( x @ sK2 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_4
<=> ( $true
= ( x @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f89,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f88]) ).
thf(f88,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f39,f57]) ).
thf(f57,plain,
( ( $false
= ( y @ sK2 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl0_5
<=> ( $false
= ( y @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f85,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f82,f61]) ).
thf(f82,plain,
( ( $true
= ( x @ sK2 ) )
| ~ spl0_3 ),
inference(equality_resolution,[status(thm)],[f46]) ).
thf(f46,plain,
( ! [X1: a > $o] :
( ( x != X1 )
| ( $true
= ( X1 @ sK2 ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl0_3
<=> ! [X1: a > $o] :
( ( x != X1 )
| ( $true
= ( X1 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f80,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f76,f41,f37]) ).
thf(f41,definition,
( spl0_2
<=> ! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( y != X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f76,plain,
( ( $true
= ( y @ sK2 ) )
| ~ spl0_2 ),
inference(equality_resolution,[status(thm)],[f42]) ).
thf(f42,plain,
( ! [X1: a > $o] :
( ( y != X1 )
| ( $true
= ( X1 @ sK2 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f79,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f76,f57]) ).
thf(f75,plain,
( spl0_5
| spl0_8
| spl0_9
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f19,f59,f72,f68,f55]) ).
thf(f19,plain,
( ( y = sK3 )
| ( $false
= ( y @ sK2 ) )
| ( x = sK3 )
| ( $false
= ( x @ sK2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false
= ( x @ sK2 ) )
| ( $false
= ( y @ sK2 ) )
| ( ( x = sK3 )
= $true )
| ( y = sK3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( y @ sK2 ) )
| ( $false
= ( x @ sK2 ) )
| ( ( y = sK3 )
= $true )
| ( ( x = sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( y @ sK2 ) )
| ( ( ( x = sK3 )
| ( y = sK3 ) )
= $true )
| ( $false
= ( x @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( y @ sK2 ) )
| ( $false
= ( x @ sK2 ) )
| ( $false
= ( ( ( x = sK3 )
| ( y = sK3 ) )
=> ( sK3 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) )
@ sK3 ) )
| ( $false
= ( y @ sK2 ) )
| ( $false
= ( x @ sK2 ) ) ),
inference(sigma_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) ) )
= $false )
| ( $false
= ( y @ sK2 ) )
| ( $false
= ( x @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $false
= ( ( x @ sK2 )
& ( y @ sK2 ) ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) ) )
!= ( ( x @ sK2 )
& ( y @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( x @ Y0 )
& ( y @ Y0 ) )
@ sK2 )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( x = Y1 )
| ( y = Y1 ) )
=> ( Y1 @ Y0 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( x @ Y0 )
& ( y @ Y0 ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( x = Y1 )
| ( y = Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( x @ Y0 )
& ( y @ Y0 ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( x = Y1 )
| ( y = Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ( x @ Y0 )
& ( y @ Y0 ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( x = Y1 )
| ( y = Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a] :
( ( y @ X0 )
& ( x @ X0 ) ) )
!= ( ^ [X1: a] :
! [X2: a > $o] :
( ( ( y = X2 )
| ( x = X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
( ( y @ X0 )
& ( x @ X0 ) ) )
!= ( ^ [X0: a] :
! [X1: a > $o] :
( ( ( y = X1 )
| ( x = X1 ) )
=> ( X1 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a] :
( ( y @ X0 )
& ( x @ X0 ) ) )
= ( ^ [X0: a] :
! [X1: a > $o] :
( ( ( y = X1 )
| ( x = X1 ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HvX4ohfTSJ/DTF2THF_24713.p',cX5201_pme) ).
thf(f66,plain,
( spl0_5
| spl0_6
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f15,f63,f59,f55]) ).
thf(f15,plain,
( ( $false
= ( y @ sK2 ) )
| ( ( sK3 @ sK2 )
= $false )
| ( $false
= ( x @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f53,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f27,f49,f45]) ).
thf(f27,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $true
= ( x @ sK2 ) )
| ( x != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: a > $o] :
( ( $true
= ( x @ sK2 ) )
| ( ( x = X1 )
= $false )
| ( $true
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: a > $o] :
( ( $true
= ( x @ sK2 ) )
| ( $false
= ( ( x = X1 )
| ( y = X1 ) ) )
| ( $true
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: a > $o] :
( ( $true
= ( ( ( x = X1 )
| ( y = X1 ) )
=> ( X1 @ sK2 ) ) )
| ( $true
= ( x @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: a > $o] :
( ( $true
= ( x @ sK2 ) )
| ( $true
= ( ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
= ( x @ sK2 ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( x @ sK2 )
& ( y @ sK2 ) )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f52,plain,
( spl0_2
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f28,f49,f41]) ).
thf(f28,plain,
! [X1: a > $o] :
( ( y != X1 )
| ( $true
= ( x @ sK2 ) )
| ( $true
= ( X1 @ sK2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $true
= ( x @ sK2 ) )
| ( $false
= ( y = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f35,f41,f37]) ).
thf(f35,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $true
= ( y @ sK2 ) )
| ( y != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $true
= ( y @ sK2 ) )
| ( $false
= ( y = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $true
= ( y @ sK2 ) )
| ( $false
= ( ( x = X1 )
| ( y = X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: a > $o] :
( ( $true
= ( ( ( x = X1 )
| ( y = X1 ) )
=> ( X1 @ sK2 ) ) )
| ( $true
= ( y @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: a > $o] :
( ( $true
= ( ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) )
@ X1 ) )
| ( $true
= ( y @ sK2 ) ) ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
=> ( Y0 @ sK2 ) ) )
= $true )
| ( $true
= ( y @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV231^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n026.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:42:40 EST 2026
% 0.11/0.31 % CPUTime :
% 0.11/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.41 ---- Original DTF file ---
% 0.17/0.41 thf(spec,logic,$$dhol).
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 % File : SEV231^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.41 % Domain : Set Theory (Sets of sets)
% 0.17/0.41 % Problem : TPS problem X5201
% 0.17/0.41 % Version : Especial.
% 0.17/0.41 % English :
% 0.17/0.41
% 0.17/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.41 % Source : [Bro09]
% 0.17/0.41 % Names : tps_0343 [Bro09]
% 0.17/0.41 % : X5201 [TPS]
% 0.17/0.41
% 0.17/0.41 % Status : Theorem
% 0.17/0.41 % 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, 0.14 v5.5.0, 0.17 v5.4.0, 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
% 0.17/0.41 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.17/0.41 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.17/0.41 % Maximal formula atoms : 1 ( 7 avg)
% 0.17/0.41 % Number of connectives : 6 ( 0 ~; 1 |; 1 &; 3 @)
% 0.17/0.41 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.17/0.41 % Maximal formula depth : 1 ( 1 avg)
% 0.17/0.41 % Number of types : 2 ( 1 usr)
% 0.17/0.41 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.41 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.17/0.41 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.17/0.41 % SPC : TH0_THM_EQU_NAR
% 0.17/0.41
% 0.17/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.41 % : Polymorphic definitions expanded.
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 thf(a_type,type,
% 0.17/0.41 a: $tType ).
% 0.17/0.41
% 0.17/0.41 thf(y,type,
% 0.17/0.41 y: a > $o ).
% 0.17/0.41
% 0.17/0.41 thf(x,type,
% 0.17/0.41 x: a > $o ).
% 0.17/0.41
% 0.17/0.41 thf(cX5201_pme,conjecture,
% 0.17/0.41 ( ( ^ [Xx0: a] :
% 0.17/0.41 ( ( x @ Xx0 )
% 0.17/0.41 & ( y @ Xx0 ) ) )
% 0.17/0.41 = ( ^ [Xx0: a] :
% 0.17/0.41 ! [S: a > $o] :
% 0.17/0.41 ( ( ( S = x )
% 0.17/0.41 | ( S = y ) )
% 0.17/0.41 => ( S @ Xx0 ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 ------------------------
% 1.52/1.35 ---- Embedded in THF ---
% 1.52/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.35 %%% Generated on Tue Feb 24 12:42:41 EST 2026
% 1.52/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.35 %%% Logic specification used:
% 1.52/1.35 %%% thf(spec, logic, $$dhol).
% 1.52/1.35
% 1.52/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.HvX4ohfTSJ/DTF2DTF24713.p
% See solution above
% 1.52/1.35 ------------------------
% 1.52/1.36 ---- Cleaned THF ---
% 1.52/1.36 thf(a_type,type,
% 1.52/1.36 a: $tType ).
% 1.52/1.36
% 1.52/1.36 thf(y,type,
% 1.52/1.36 y: a > $o ).
% 1.52/1.36
% 1.52/1.36 thf(x,type,
% 1.52/1.36 x: a > $o ).
% 1.52/1.36
% 1.52/1.36 thf(cX5201_pme,conjecture,
% 1.52/1.36 ( ( ^ [Xx0: a] :
% 1.52/1.36 ( ( x @ Xx0 )
% 1.52/1.36 & ( y @ Xx0 ) ) )
% 1.52/1.36 = ( ^ [Xx0: a] :
% 1.52/1.36 ! [S: a > $o] :
% 1.52/1.36 ( ( ( S = x )
% 1.52/1.36 | ( S = y ) )
% 1.52/1.36 => ( S @ Xx0 ) ) ) ) ).
% 1.52/1.36 ------------------------
% 1.52/1.38 % (24816)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_24713 for (3000ds/2Mi)
% 1.52/1.38 % (24812)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24713 for (3000ds/183Mi)
% 1.52/1.38 % (24818)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24713 for (3000ds/18Mi)
% 1.52/1.38 % (24813)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_24713 for (3000ds/4Mi)
% 1.52/1.38 % (24814)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_24713 for (3000ds/27Mi)
% 1.52/1.38 % (24817)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_24713 for (3000ds/275Mi)
% 1.52/1.38 % (24816)Instruction limit reached!
% 1.52/1.38 % (24816)------------------------------
% 1.52/1.38 % (24816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.38 % (24816)Termination reason: Unknown
% 1.52/1.38 % (24816)Termination phase: Saturation
% 1.52/1.38
% 1.52/1.38 % (24816)Memory used [KB]: 5373
% 1.52/1.38 % (24816)Time elapsed: 0.003 s
% 1.52/1.38 % (24816)Instructions burned: 2 (million)
% 1.52/1.38 % (24816)------------------------------
% 1.52/1.38 % (24816)------------------------------
% 1.52/1.38 % (24813)Instruction limit reached!
% 1.52/1.38 % (24813)------------------------------
% 1.52/1.38 % (24813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.38 % (24813)Termination reason: Unknown
% 1.52/1.38 % (24813)Termination phase: Saturation
% 1.52/1.38
% 1.52/1.38 % (24813)Memory used [KB]: 5500
% 1.52/1.38 % (24813)Time elapsed: 0.005 s
% 1.52/1.38 % (24813)Instructions burned: 4 (million)
% 1.52/1.38 % (24813)------------------------------
% 1.52/1.38 % (24813)------------------------------
% 1.52/1.38 % (24815)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24713 for (3000ds/2Mi)
% 1.52/1.39 % (24815)Instruction limit reached!
% 1.52/1.39 % (24815)------------------------------
% 1.52/1.39 % (24815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.39 % (24815)Termination reason: Unknown
% 1.52/1.39 % (24815)Termination phase: Saturation
% 1.52/1.39
% 1.52/1.39 % (24815)Memory used [KB]: 5373
% 1.52/1.39 % (24815)Time elapsed: 0.003 s
% 1.52/1.39 % (24815)Instructions burned: 2 (million)
% 1.52/1.39 % (24815)------------------------------
% 1.52/1.39 % (24815)------------------------------
% 1.52/1.39 % (24814)First to succeed.
% 1.52/1.39 % (24818)Also succeeded, but the first one will report.
% 1.52/1.39 % (24814)Refutation found. Thanks to Tanya!
% 1.52/1.39 % SZS status Theorem for DTF2THF_24713
% 1.52/1.39 % SZS output start Proof for DTF2THF_24713
% 1.52/1.39 thf(type_def_5, type, a: $tType).
% 1.52/1.39 thf(func_def_0, type, a: $tType).
% 1.52/1.39 thf(func_def_1, type, y: a > $o).
% 1.52/1.39 thf(func_def_2, type, x: a > $o).
% 1.52/1.39 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.52/1.39 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.52/1.39 thf(func_def_17, type, sK2: a).
% 1.52/1.39 thf(func_def_18, type, sK3: a > $o).
% 1.52/1.39 thf(func_def_19, type, sK4: a).
% 1.52/1.39 thf(func_def_20, type, sK5: a).
% 1.52/1.39 thf(f182,plain,(
% 1.52/1.39 $false),
% 1.52/1.39 inference(avatar_sat_refutation,[status(thm)],[f43,f52,f53,f66,f75,f79,f80,f85,f89,f93,f112,f181])).
% 1.52/1.39 thf(f181,plain,(
% 1.52/1.39 spl0_6 | ~spl0_7 | ~spl0_9),
% 1.52/1.39 inference(avatar_contradiction_clause,[status(thm)],[f180])).
% 1.52/1.39 thf(f180,plain,(
% 1.52/1.39 $false | (spl0_6 | ~spl0_7 | ~spl0_9)),
% 1.52/1.39 inference(trivial_inequality_removal,[status(thm)],[f179])).
% 1.52/1.39 thf(f179,plain,(
% 1.52/1.39 ($false = $true) | (spl0_6 | ~spl0_7 | ~spl0_9)),
% 1.52/1.39 inference(forward_demodulation,[status(thm)],[f170,f65])).
% 1.52/1.39 thf(f65,plain,(
% 1.52/1.39 ((sK3 @ sK2) = $false) | ~spl0_7),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.52/1.39 thf(f63,definition,(
% 1.52/1.39 spl0_7 <=> ((sK3 @ sK2) = $false)),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.52/1.39 thf(f170,plain,(
% 1.52/1.39 ((sK3 @ sK2) = $true) | (spl0_6 | ~spl0_9)),
% 1.52/1.39 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.52/1.39 thf(f166,plain,(
% 1.52/1.39 ($false != $false) | ((sK3 @ sK2) = $true) | (spl0_6 | ~spl0_9)),
% 1.52/1.39 inference(superposition,[status(thm)],[f60,f136])).
% 1.52/1.39 thf(f136,plain,(
% 1.52/1.39 ( ! [X1 : a] : (($false = (x @ X1)) | ((sK3 @ X1) = $true)) ) | ~spl0_9),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.52/1.39 thf(f134,plain,(
% 1.52/1.39 ( ! [X1 : a] : (((sK3 @ X1) = (x @ X1))) ) | ~spl0_9),
% 1.52/1.39 inference(argument_congruence,[status(thm)],[f74])).
% 1.52/1.39 thf(f74,plain,(
% 1.52/1.39 (x = sK3) | ~spl0_9),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.52/1.39 thf(f72,definition,(
% 1.52/1.39 spl0_9 <=> (x = sK3)),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.52/1.39 thf(f60,plain,(
% 1.52/1.39 ($false != (x @ sK2)) | spl0_6),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.52/1.39 thf(f59,definition,(
% 1.52/1.39 spl0_6 <=> ($false = (x @ sK2))),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.52/1.39 thf(f112,plain,(
% 1.52/1.39 ~spl0_1 | ~spl0_7 | ~spl0_8),
% 1.52/1.39 inference(avatar_contradiction_clause,[status(thm)],[f111])).
% 1.52/1.39 thf(f111,plain,(
% 1.52/1.39 $false | (~spl0_1 | ~spl0_7 | ~spl0_8)),
% 1.52/1.39 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.52/1.39 thf(f110,plain,(
% 1.52/1.39 ($false = $true) | (~spl0_1 | ~spl0_7 | ~spl0_8)),
% 1.52/1.39 inference(forward_demodulation,[status(thm)],[f101,f65])).
% 1.52/1.39 thf(f101,plain,(
% 1.52/1.39 ((sK3 @ sK2) = $true) | (~spl0_1 | ~spl0_8)),
% 1.52/1.39 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.52/1.39 thf(f98,plain,(
% 1.52/1.39 ((sK3 @ sK2) = $true) | ($false = $true) | (~spl0_1 | ~spl0_8)),
% 1.52/1.39 inference(superposition,[status(thm)],[f95,f39])).
% 1.52/1.39 thf(f39,plain,(
% 1.52/1.39 ($true = (y @ sK2)) | ~spl0_1),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.52/1.39 thf(f37,definition,(
% 1.52/1.39 spl0_1 <=> ($true = (y @ sK2))),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.52/1.39 thf(f95,plain,(
% 1.52/1.39 ( ! [X1 : a] : (($false = (y @ X1)) | ((sK3 @ X1) = $true)) ) | ~spl0_8),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.52/1.39 thf(f94,plain,(
% 1.52/1.39 ( ! [X1 : a] : (((sK3 @ X1) = (y @ X1))) ) | ~spl0_8),
% 1.52/1.39 inference(argument_congruence,[status(thm)],[f70])).
% 1.52/1.39 thf(f70,plain,(
% 1.52/1.39 (y = sK3) | ~spl0_8),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.52/1.39 thf(f68,definition,(
% 1.52/1.39 spl0_8 <=> (y = sK3)),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.52/1.39 thf(f93,plain,(
% 1.52/1.39 ~spl0_4 | ~spl0_6),
% 1.52/1.39 inference(avatar_contradiction_clause,[status(thm)],[f92])).
% 1.52/1.39 thf(f92,plain,(
% 1.52/1.39 $false | (~spl0_4 | ~spl0_6)),
% 1.52/1.39 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.52/1.39 thf(f91,plain,(
% 1.52/1.39 ($false = $true) | (~spl0_4 | ~spl0_6)),
% 1.52/1.39 inference(forward_demodulation,[status(thm)],[f51,f61])).
% 1.52/1.39 thf(f61,plain,(
% 1.52/1.39 ($false = (x @ sK2)) | ~spl0_6),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.52/1.39 thf(f51,plain,(
% 1.52/1.39 ($true = (x @ sK2)) | ~spl0_4),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.52/1.39 thf(f49,definition,(
% 1.52/1.39 spl0_4 <=> ($true = (x @ sK2))),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.52/1.39 thf(f89,plain,(
% 1.52/1.39 ~spl0_1 | ~spl0_5),
% 1.52/1.39 inference(avatar_contradiction_clause,[status(thm)],[f88])).
% 1.52/1.39 thf(f88,plain,(
% 1.52/1.39 $false | (~spl0_1 | ~spl0_5)),
% 1.52/1.39 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.52/1.39 thf(f87,plain,(
% 1.52/1.39 ($false = $true) | (~spl0_1 | ~spl0_5)),
% 1.52/1.39 inference(backward_demodulation,[status(thm)],[f39,f57])).
% 1.52/1.39 thf(f57,plain,(
% 1.52/1.39 ($false = (y @ sK2)) | ~spl0_5),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.52/1.39 thf(f55,definition,(
% 1.52/1.39 spl0_5 <=> ($false = (y @ sK2))),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.52/1.39 thf(f85,plain,(
% 1.52/1.39 ~spl0_3 | ~spl0_6),
% 1.52/1.39 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.52/1.39 thf(f84,plain,(
% 1.52/1.39 $false | (~spl0_3 | ~spl0_6)),
% 1.52/1.39 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.52/1.39 thf(f83,plain,(
% 1.52/1.39 ($false = $true) | (~spl0_3 | ~spl0_6)),
% 1.52/1.39 inference(forward_demodulation,[status(thm)],[f82,f61])).
% 1.52/1.39 thf(f82,plain,(
% 1.52/1.39 ($true = (x @ sK2)) | ~spl0_3),
% 1.52/1.39 inference(equality_resolution,[status(thm)],[f46])).
% 1.52/1.39 thf(f46,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : ((x != X1) | ($true = (X1 @ sK2))) ) | ~spl0_3),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.52/1.39 thf(f45,definition,(
% 1.52/1.39 spl0_3 <=> ! [X1 : a > $o] : ((x != X1) | ($true = (X1 @ sK2)))),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.52/1.39 thf(f80,plain,(
% 1.52/1.39 spl0_1 | ~spl0_2),
% 1.52/1.39 inference(avatar_split_clause,[status(thm)],[f76,f41,f37])).
% 1.52/1.39 thf(f41,definition,(
% 1.52/1.39 spl0_2 <=> ! [X1 : a > $o] : (($true = (X1 @ sK2)) | (y != X1))),
% 1.52/1.39 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.52/1.39 thf(f76,plain,(
% 1.52/1.39 ($true = (y @ sK2)) | ~spl0_2),
% 1.52/1.39 inference(equality_resolution,[status(thm)],[f42])).
% 1.52/1.39 thf(f42,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : ((y != X1) | ($true = (X1 @ sK2))) ) | ~spl0_2),
% 1.52/1.39 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.52/1.39 thf(f79,plain,(
% 1.52/1.39 ~spl0_2 | ~spl0_5),
% 1.52/1.39 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.52/1.39 thf(f78,plain,(
% 1.52/1.39 $false | (~spl0_2 | ~spl0_5)),
% 1.52/1.39 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.52/1.39 thf(f77,plain,(
% 1.52/1.39 ($false = $true) | (~spl0_2 | ~spl0_5)),
% 1.52/1.39 inference(forward_demodulation,[status(thm)],[f76,f57])).
% 1.52/1.39 thf(f75,plain,(
% 1.52/1.39 spl0_5 | spl0_8 | spl0_9 | spl0_6),
% 1.52/1.39 inference(avatar_split_clause,[status(thm)],[f19,f59,f72,f68,f55])).
% 1.52/1.39 thf(f19,plain,(
% 1.52/1.39 (y = sK3) | ($false = (y @ sK2)) | (x = sK3) | ($false = (x @ sK2))),
% 1.52/1.39 inference(equality_proxy_clausification,[status(thm)],[f18])).
% 1.52/1.39 thf(f18,plain,(
% 1.52/1.39 ($false = (x @ sK2)) | ($false = (y @ sK2)) | ((x = sK3) = $true) | (y = sK3)),
% 1.52/1.39 inference(equality_proxy_clausification,[status(thm)],[f17])).
% 1.52/1.39 thf(f17,plain,(
% 1.52/1.39 ($false = (y @ sK2)) | ($false = (x @ sK2)) | ((y = sK3) = $true) | ((x = sK3) = $true)),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.52/1.39 thf(f16,plain,(
% 1.52/1.39 ($false = (y @ sK2)) | (((x = sK3) | (y = sK3)) = $true) | ($false = (x @ sK2))),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.52/1.39 thf(f14,plain,(
% 1.52/1.39 ($false = (y @ sK2)) | ($false = (x @ sK2)) | ($false = (((x = sK3) | (y = sK3)) => (sK3 @ sK2)))),
% 1.52/1.39 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.52/1.39 thf(f13,plain,(
% 1.52/1.39 ($false = ((^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2))) @ sK3)) | ($false = (y @ sK2)) | ($false = (x @ sK2))),
% 1.52/1.39 inference(sigma_clausification,[status(thm)],[f12])).
% 1.52/1.39 thf(f12,plain,(
% 1.52/1.39 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2)))) = $false) | ($false = (y @ sK2)) | ($false = (x @ sK2))),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.52/1.39 thf(f11,plain,(
% 1.52/1.39 ($false = ((x @ sK2) & (y @ sK2))) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2)))) = $false)),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.52/1.39 thf(f9,plain,(
% 1.52/1.39 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2)))) != ((x @ sK2) & (y @ sK2)))),
% 1.52/1.39 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.52/1.39 thf(f8,plain,(
% 1.52/1.39 (((^[Y0 : a]: ((x @ Y0) & (y @ Y0))) @ sK2) != ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((x = Y1) | (y = Y1)) => (Y1 @ Y0))))) @ sK2))),
% 1.52/1.39 inference(negative_extensionality,[status(thm)],[f7])).
% 1.52/1.39 thf(f7,plain,(
% 1.52/1.39 ((^[Y0 : a]: ((x @ Y0) & (y @ Y0))) != (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((x = Y1) | (y = Y1)) => (Y1 @ Y0))))))),
% 1.52/1.39 inference(cnf_transformation,[status(thm)],[f6])).
% 1.52/1.39 thf(f6,plain,(
% 1.52/1.39 ((^[Y0 : a]: ((x @ Y0) & (y @ Y0))) != (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((x = Y1) | (y = Y1)) => (Y1 @ Y0))))))),
% 1.52/1.39 inference(flattening,[status(thm)],[f5])).
% 1.52/1.39 thf(f5,plain,(
% 1.52/1.39 ~((^[Y0 : a]: ((x @ Y0) & (y @ Y0))) = (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((x = Y1) | (y = Y1)) => (Y1 @ Y0))))))),
% 1.52/1.39 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.39 thf(f4,plain,(
% 1.52/1.39 ~((^[X0 : a] : ((y @ X0) & (x @ X0))) = (^[X1 : a] : (! [X2 : a > $o] : (((y = X2) | (x = X2)) => (X2 @ X1)))))),
% 1.52/1.39 inference(rectify,[status(thm)],[f2])).
% 1.52/1.39 thf(f2,negated_conjecture,(
% 1.52/1.39 ~((^[X0 : a] : ((y @ X0) & (x @ X0))) = (^[X0 : a] : (! [X1 : a > $o] : (((y = X1) | (x = X1)) => (X1 @ X0)))))),
% 1.52/1.39 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.39 thf(f1,conjecture,(
% 1.52/1.39 ((^[X0 : a] : ((y @ X0) & (x @ X0))) = (^[X0 : a] : (! [X1 : a > $o] : (((y = X1) | (x = X1)) => (X1 @ X0)))))),
% 1.52/1.39 file('/export/starexec/sandbox2/tmp/tmp.HvX4ohfTSJ/DTF2THF_24713.p',cX5201_pme)).
% 1.52/1.39 thf(f66,plain,(
% 1.52/1.39 spl0_5 | spl0_6 | spl0_7),
% 1.52/1.39 inference(avatar_split_clause,[status(thm)],[f15,f63,f59,f55])).
% 1.52/1.39 thf(f15,plain,(
% 1.52/1.39 ($false = (y @ sK2)) | ((sK3 @ sK2) = $false) | ($false = (x @ sK2))),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.52/1.39 thf(f53,plain,(
% 1.52/1.39 spl0_3 | spl0_4),
% 1.52/1.39 inference(avatar_split_clause,[status(thm)],[f27,f49,f45])).
% 1.52/1.39 thf(f27,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (X1 @ sK2)) | ($true = (x @ sK2)) | (x != X1)) )),
% 1.52/1.39 inference(equality_proxy_clausification,[status(thm)],[f26])).
% 1.52/1.39 thf(f26,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (x @ sK2)) | ((x = X1) = $false) | ($true = (X1 @ sK2))) )),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.52/1.39 thf(f24,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (x @ sK2)) | ($false = ((x = X1) | (y = X1))) | ($true = (X1 @ sK2))) )),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.52/1.39 thf(f23,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (((x = X1) | (y = X1)) => (X1 @ sK2))) | ($true = (x @ sK2))) )),
% 1.52/1.39 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.52/1.39 thf(f22,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (x @ sK2)) | ($true = ((^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2))) @ X1))) )),
% 1.52/1.39 inference(pi_clausification,[status(thm)],[f21])).
% 1.52/1.39 thf(f21,plain,(
% 1.52/1.39 ($true = (x @ sK2)) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2)))) = $true)),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.52/1.39 thf(f10,plain,(
% 1.52/1.39 (((x @ sK2) & (y @ sK2)) = $true) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2)))) = $true)),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.52/1.39 thf(f52,plain,(
% 1.52/1.39 spl0_2 | spl0_4),
% 1.52/1.39 inference(avatar_split_clause,[status(thm)],[f28,f49,f41])).
% 1.52/1.39 thf(f28,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : ((y != X1) | ($true = (x @ sK2)) | ($true = (X1 @ sK2))) )),
% 1.52/1.39 inference(equality_proxy_clausification,[status(thm)],[f25])).
% 1.52/1.39 thf(f25,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (X1 @ sK2)) | ($true = (x @ sK2)) | ($false = (y = X1))) )),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.52/1.39 thf(f43,plain,(
% 1.52/1.39 spl0_1 | spl0_2),
% 1.52/1.39 inference(avatar_split_clause,[status(thm)],[f35,f41,f37])).
% 1.52/1.39 thf(f35,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (X1 @ sK2)) | ($true = (y @ sK2)) | (y != X1)) )),
% 1.52/1.39 inference(equality_proxy_clausification,[status(thm)],[f32])).
% 1.52/1.39 thf(f32,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (X1 @ sK2)) | ($true = (y @ sK2)) | ($false = (y = X1))) )),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.52/1.39 thf(f31,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (X1 @ sK2)) | ($true = (y @ sK2)) | ($false = ((x = X1) | (y = X1)))) )),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.52/1.39 thf(f30,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = (((x = X1) | (y = X1)) => (X1 @ sK2))) | ($true = (y @ sK2))) )),
% 1.52/1.39 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.52/1.39 thf(f29,plain,(
% 1.52/1.39 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2))) @ X1)) | ($true = (y @ sK2))) )),
% 1.52/1.39 inference(pi_clausification,[status(thm)],[f20])).
% 1.52/1.39 thf(f20,plain,(
% 1.52/1.39 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) => (Y0 @ sK2)))) = $true) | ($true = (y @ sK2))),
% 1.52/1.39 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.52/1.39 % SZS output end Proof for DTF2THF_24713
% 1.52/1.39 % (24814)------------------------------
% 1.52/1.39 % (24814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.39 % (24814)Termination reason: Refutation
% 1.52/1.39
% 1.52/1.39 % (24814)Memory used [KB]: 5628
% 1.52/1.39 % (24814)Time elapsed: 0.009 s
% 1.52/1.39 % (24814)Instructions burned: 8 (million)
% 1.52/1.39 % (24814)------------------------------
% 1.52/1.39 % (24814)------------------------------
% 1.52/1.39 % (24811)Success in time 0.021 s
%------------------------------------------------------------------------------