%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV239^5 : 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 : n009.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 09:40:38 AM UTC 2026
% Result : Theorem 1.47s 1.28s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 10 unt; 0 typ; 6 def)
% Number of atoms : 363 ( 139 equ; 23 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 350 ( 50 ~; 74 |; 36 &; 162 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 12 usr; 12 con; 0-2 aty)
% ( 0 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 72 ( 46 ^; 20 !; 6 ?; 72 :)
% 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_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK2: a ).
thf(func_def_15,type,
sK3: a > $o ).
thf(func_def_16,type,
sK4: a ).
thf(f89,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f37,f42,f47,f55,f58,f63,f88]) ).
thf(f88,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f85,f51]) ).
thf(f51,plain,
( ( ( y @ sK2 )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_5
<=> ( ( y @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f85,plain,
( ( ( y @ sK2 )
= $true )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f32,f81]) ).
thf(f81,plain,
( ( sK4 = sK2 )
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true = $false )
| ( sK4 = sK2 )
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f46,f69]) ).
thf(f69,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $false )
| ( sK4 = X1 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $false )
| ( ( sK4 = X1 )
= $true ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( sK4 = X1 ) )
| ~ spl0_3 ),
inference(argument_congruence,[status(thm)],[f41]) ).
thf(f41,plain,
( ( sK3
= ( (=) @ sK4 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl0_3
<=> ( sK3
= ( (=) @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f46,plain,
( ( ( sK3 @ sK2 )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl0_4
<=> ( ( sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f32,plain,
( ( ( y @ sK4 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl0_1
<=> ( ( y @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f63,plain,
( spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f62,f53,f49]) ).
thf(f53,definition,
( spl0_6
<=> ! [X2: a,X1: a > $o] :
( ( ( y @ X2 )
= $false )
| ( ( X1 @ sK2 )
= $false )
| ( ( (=) @ X2 )
!= X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f62,plain,
( ( ( y @ sK2 )
= $false )
| ~ spl0_6 ),
inference(equality_resolution,[status(thm)],[f61]) ).
thf(f61,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( ( y @ X0 )
= $false ) )
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X0: a] :
( ( ( y @ X0 )
= $false )
| ( $false
= ( X0 = sK2 ) ) )
| ~ spl0_6 ),
inference(equality_resolution,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X2: a,X1: a > $o] :
( ( ( (=) @ X2 )
!= X1 )
| ( ( y @ X2 )
= $false )
| ( ( X1 @ sK2 )
= $false ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f58,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f36,f51]) ).
thf(f36,plain,
( ( ( y @ sK2 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl0_2
<=> ( ( y @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f55,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f19,f53,f49]) ).
thf(f19,plain,
! [X2: a,X1: a > $o] :
( ( ( y @ X2 )
= $false )
| ( ( (=) @ X2 )
!= X1 )
| ( ( y @ sK2 )
= $false )
| ( ( X1 @ sK2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: a,X1: a > $o] :
( ( ( y @ sK2 )
= $false )
| ( ( y @ X2 )
= $false )
| ( $false
= ( ( (=) @ X2 )
= X1 ) )
| ( ( X1 @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( ( ( (=) @ X2 )
= X1 )
& ( y @ X2 ) ) )
| ( ( y @ sK2 )
= $false )
| ( ( X1 @ sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( ^ [Y0: a] :
( ( ( (=) @ Y0 )
= X1 )
& ( y @ Y0 ) )
@ X2 ) )
| ( ( X1 @ sK2 )
= $false )
| ( ( y @ sK2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: a > $o] :
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( ( (=) @ Y0 )
= X1 )
& ( y @ Y0 ) ) )
= $false )
| ( ( X1 @ sK2 )
= $false )
| ( ( y @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: a > $o] :
( ( $false
= ( ( X1 @ sK2 )
& ( ?? @ a
@ ^ [Y0: a] :
( ( ( (=) @ Y0 )
= X1 )
& ( y @ Y0 ) ) ) ) )
| ( ( y @ sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: a > $o] :
( ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ a
@ ^ [Y1: a] :
( ( ( (=) @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) )
@ X1 )
= $false )
| ( ( y @ sK2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( y @ sK2 )
= $false )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ a
@ ^ [Y1: a] :
( ( ( (=) @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( y @ sK2 )
!= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ a
@ ^ [Y1: a] :
( ( ( (=) @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
( ( y @ sK2 )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ a
@ ^ [Y2: a] :
( ( ( (=) @ Y2 )
= Y1 )
& ( y @ Y2 ) ) ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f8]) ).
thf(f8,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ a
@ ^ [Y2: a] :
( ( ( (=) @ Y2 )
= Y1 )
& ( y @ Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ a
@ ^ [Y2: a] :
( ( ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 )
= Y1 )
& ( y @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ a
@ ^ [Y2: a] :
( ( ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 )
= Y1 )
& ( y @ Y2 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ a
@ ^ [Y2: a] :
( ( ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 )
= Y1 )
& ( y @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( y
!= ( ^ [X0: a] :
? [X1: a > $o] :
( ? [X2: a] :
( ( y @ X2 )
& ( ( ^ [X3: a,X4: a] : ( X3 = X4 )
@ X2 )
= X1 ) )
& ( X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( y
!= ( ^ [X0: a] :
? [X1: a > $o] :
( ? [X2: a] :
( ( y @ X2 )
& ( ( ^ [X0: a,X3: a] : ( X0 = X3 )
@ X2 )
= X1 ) )
& ( X1 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( y
= ( ^ [X0: a] :
? [X1: a > $o] :
( ? [X2: a] :
( ( y @ X2 )
& ( ( ^ [X0: a,X3: a] : ( X0 = X3 )
@ X2 )
= X1 ) )
& ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.S3QhFCAZ6t/DTF2THF_29962.p',cX5211_pme) ).
thf(f47,plain,
( spl0_2
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f23,f44,f34]) ).
thf(f23,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( ( y @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( y @ sK2 )
= $true )
| ( ( ( sK3 @ sK2 )
& ( ?? @ a
@ ^ [Y0: a] :
( ( ( (=) @ Y0 )
= sK3 )
& ( y @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( y @ sK2 )
= $true )
| ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ a
@ ^ [Y1: a] :
( ( ( (=) @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) )
@ sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ a
@ ^ [Y1: a] :
( ( ( (=) @ Y1 )
= Y0 )
& ( y @ Y1 ) ) ) ) ) )
| ( ( y @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f42,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f28,f39,f34]) ).
thf(f28,plain,
( ( sK3
= ( (=) @ sK4 ) )
| ( ( y @ sK2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( y @ sK2 )
= $true )
| ( $true
= ( ( (=) @ sK4 )
= sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ( ( (=) @ sK4 )
= sK3 )
& ( y @ sK4 ) )
= $true )
| ( ( y @ sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( y @ sK2 )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ( ( (=) @ Y0 )
= sK3 )
& ( y @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( ( (=) @ Y0 )
= sK3 )
& ( y @ Y0 ) ) )
= $true )
| ( ( y @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f37,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f34,f30]) ).
thf(f26,plain,
( ( ( y @ sK4 )
= $true )
| ( ( y @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV239^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:42:25 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEV239^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory (Sets of sets)
% 0.30/0.46 % Problem : TPS problem X5211
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0492 [Bro09]
% 0.30/0.46 % : X5211 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.30/0.46 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 1 ( 5 avg)
% 0.30/0.46 % Number of connectives : 5 ( 0 ~; 0 |; 2 &; 3 @)
% 0.30/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 1 ( 1 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 5 ( 3 ^; 0 !; 2 ?; 5 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % : Polymorphic definitions expanded.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(y,type,
% 0.30/0.46 y: a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cX5211_pme,conjecture,
% 0.30/0.46 ( y
% 0.30/0.46 = ( ^ [Xx: a] :
% 0.30/0.46 ? [S: a > $o] :
% 0.30/0.46 ( ? [Xx0: a] :
% 0.30/0.46 ( ( y @ Xx0 )
% 0.30/0.46 & ( S
% 0.30/0.46 = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 0.30/0.46 @ Xx0 ) ) )
% 0.30/0.46 & ( S @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 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 12:42:26 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.S3QhFCAZ6t/DTF2DTF29962.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 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: a > $o ).
% 1.47/1.26
% 1.47/1.26 thf(cX5211_pme,conjecture,
% 1.47/1.26 ( y
% 1.47/1.26 = ( ^ [Xx: a] :
% 1.47/1.26 ? [S: a > $o] :
% 1.47/1.26 ( ? [Xx0: a] :
% 1.47/1.26 ( ( y @ Xx0 )
% 1.47/1.26 & ( S
% 1.47/1.26 = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 1.47/1.26 @ Xx0 ) ) )
% 1.47/1.26 & ( S @ Xx ) ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (30248)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_29962 for (3000ds/27Mi)
% 1.47/1.28 % (30248)First to succeed.
% 1.47/1.28 % (30248)Refutation found. Thanks to Tanya!
% 1.47/1.28 % SZS status Theorem for DTF2THF_29962
% 1.47/1.28 % SZS output start Proof for DTF2THF_29962
% 1.47/1.28 thf(type_def_5, type, a: $tType).
% 1.47/1.28 thf(func_def_0, type, a: $tType).
% 1.47/1.28 thf(func_def_1, type, y: a > $o).
% 1.47/1.28 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.47/1.28 thf(func_def_13, type, ph1: !>[X0: $tType]:(X0)).
% 1.47/1.28 thf(func_def_14, type, sK2: a).
% 1.47/1.28 thf(func_def_15, type, sK3: a > $o).
% 1.47/1.28 thf(func_def_16, type, sK4: a).
% 1.47/1.28 thf(f89,plain,(
% 1.47/1.28 $false),
% 1.47/1.28 inference(avatar_sat_refutation,[status(thm)],[f37,f42,f47,f55,f58,f63,f88])).
% 1.47/1.28 thf(f88,plain,(
% 1.47/1.28 ~spl0_1 | ~spl0_3 | ~spl0_4 | ~spl0_5),
% 1.47/1.28 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.47/1.28 thf(f87,plain,(
% 1.47/1.28 $false | (~spl0_1 | ~spl0_3 | ~spl0_4 | ~spl0_5)),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.47/1.28 thf(f86,plain,(
% 1.47/1.28 ($true = $false) | (~spl0_1 | ~spl0_3 | ~spl0_4 | ~spl0_5)),
% 1.47/1.28 inference(forward_demodulation,[status(thm)],[f85,f51])).
% 1.47/1.28 thf(f51,plain,(
% 1.47/1.28 ((y @ sK2) = $false) | ~spl0_5),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.47/1.28 thf(f49,definition,(
% 1.47/1.28 spl0_5 <=> ((y @ sK2) = $false)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.47/1.28 thf(f85,plain,(
% 1.47/1.28 ((y @ sK2) = $true) | (~spl0_1 | ~spl0_3 | ~spl0_4)),
% 1.47/1.28 inference(backward_demodulation,[status(thm)],[f32,f81])).
% 1.47/1.28 thf(f81,plain,(
% 1.47/1.28 (sK4 = sK2) | (~spl0_3 | ~spl0_4)),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.47/1.28 thf(f80,plain,(
% 1.47/1.28 ($true = $false) | (sK4 = sK2) | (~spl0_3 | ~spl0_4)),
% 1.47/1.28 inference(superposition,[status(thm)],[f46,f69])).
% 1.47/1.28 thf(f69,plain,(
% 1.47/1.28 ( ! [X1 : a] : (((sK3 @ X1) = $false) | (sK4 = X1)) ) | ~spl0_3),
% 1.47/1.28 inference(equality_proxy_clausification,[status(thm)],[f68])).
% 1.47/1.28 thf(f68,plain,(
% 1.47/1.28 ( ! [X1 : a] : (((sK3 @ X1) = $false) | ((sK4 = X1) = $true)) ) | ~spl0_3),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.47/1.28 thf(f65,plain,(
% 1.47/1.28 ( ! [X1 : a] : (((sK3 @ X1) = (sK4 = X1))) ) | ~spl0_3),
% 1.47/1.28 inference(argument_congruence,[status(thm)],[f41])).
% 1.47/1.28 thf(f41,plain,(
% 1.47/1.28 (sK3 = (= @ sK4)) | ~spl0_3),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.47/1.28 thf(f39,definition,(
% 1.47/1.28 spl0_3 <=> (sK3 = (= @ sK4))),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.47/1.28 thf(f46,plain,(
% 1.47/1.28 ((sK3 @ sK2) = $true) | ~spl0_4),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.47/1.28 thf(f44,definition,(
% 1.47/1.28 spl0_4 <=> ((sK3 @ sK2) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.47/1.28 thf(f32,plain,(
% 1.47/1.28 ((y @ sK4) = $true) | ~spl0_1),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.47/1.28 thf(f30,definition,(
% 1.47/1.28 spl0_1 <=> ((y @ sK4) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.47/1.28 thf(f63,plain,(
% 1.47/1.28 spl0_5 | ~spl0_6),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f62,f53,f49])).
% 1.47/1.28 thf(f53,definition,(
% 1.47/1.28 spl0_6 <=> ! [X2 : a,X1 : a > $o] : (((y @ X2) = $false) | ((X1 @ sK2) = $false) | ((= @ X2) != X1))),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.47/1.28 thf(f62,plain,(
% 1.47/1.28 ((y @ sK2) = $false) | ~spl0_6),
% 1.47/1.28 inference(equality_resolution,[status(thm)],[f61])).
% 1.47/1.28 thf(f61,plain,(
% 1.47/1.28 ( ! [X0 : a] : ((sK2 != X0) | ((y @ X0) = $false)) ) | ~spl0_6),
% 1.47/1.28 inference(equality_proxy_clausification,[status(thm)],[f60])).
% 1.47/1.28 thf(f60,plain,(
% 1.47/1.28 ( ! [X0 : a] : (((y @ X0) = $false) | ($false = (X0 = sK2))) ) | ~spl0_6),
% 1.47/1.28 inference(equality_resolution,[status(thm)],[f54])).
% 1.47/1.28 thf(f54,plain,(
% 1.47/1.28 ( ! [X2 : a,X1 : a > $o] : (((= @ X2) != X1) | ((y @ X2) = $false) | ((X1 @ sK2) = $false)) ) | ~spl0_6),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.47/1.28 thf(f58,plain,(
% 1.47/1.28 ~spl0_2 | ~spl0_5),
% 1.47/1.28 inference(avatar_contradiction_clause,[status(thm)],[f57])).
% 1.47/1.28 thf(f57,plain,(
% 1.47/1.28 $false | (~spl0_2 | ~spl0_5)),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.47/1.28 thf(f56,plain,(
% 1.47/1.28 ($true = $false) | (~spl0_2 | ~spl0_5)),
% 1.47/1.28 inference(forward_demodulation,[status(thm)],[f36,f51])).
% 1.47/1.28 thf(f36,plain,(
% 1.47/1.28 ((y @ sK2) = $true) | ~spl0_2),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.47/1.28 thf(f34,definition,(
% 1.47/1.28 spl0_2 <=> ((y @ sK2) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.47/1.28 thf(f55,plain,(
% 1.47/1.28 spl0_5 | spl0_6),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f19,f53,f49])).
% 1.47/1.28 thf(f19,plain,(
% 1.47/1.28 ( ! [X2 : a,X1 : a > $o] : (((y @ X2) = $false) | ((= @ X2) != X1) | ((y @ sK2) = $false) | ((X1 @ sK2) = $false)) )),
% 1.47/1.28 inference(equality_proxy_clausification,[status(thm)],[f18])).
% 1.47/1.28 thf(f18,plain,(
% 1.47/1.28 ( ! [X2 : a,X1 : a > $o] : (((y @ sK2) = $false) | ((y @ X2) = $false) | ($false = ((= @ X2) = X1)) | ((X1 @ sK2) = $false)) )),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.47/1.28 thf(f17,plain,(
% 1.47/1.28 ( ! [X2 : a,X1 : a > $o] : (($false = (((= @ X2) = X1) & (y @ X2))) | ((y @ sK2) = $false) | ((X1 @ sK2) = $false)) )),
% 1.47/1.28 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.47/1.28 thf(f16,plain,(
% 1.47/1.28 ( ! [X2 : a,X1 : a > $o] : (($false = ((^[Y0 : a]: (((= @ Y0) = X1) & (y @ Y0))) @ X2)) | ((X1 @ sK2) = $false) | ((y @ sK2) = $false)) )),
% 1.47/1.28 inference(pi_clausification,[status(thm)],[f15])).
% 1.47/1.28 thf(f15,plain,(
% 1.47/1.28 ( ! [X1 : a > $o] : (((?? @ a @ (^[Y0 : a]: (((= @ Y0) = X1) & (y @ Y0)))) = $false) | ((X1 @ sK2) = $false) | ((y @ sK2) = $false)) )),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.47/1.28 thf(f14,plain,(
% 1.47/1.28 ( ! [X1 : a > $o] : (($false = ((X1 @ sK2) & (?? @ a @ (^[Y0 : a]: (((= @ Y0) = X1) & (y @ Y0)))))) | ((y @ sK2) = $false)) )),
% 1.47/1.28 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.47/1.28 thf(f13,plain,(
% 1.47/1.28 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ a @ (^[Y1 : a]: (((= @ Y1) = Y0) & (y @ Y1)))))) @ X1) = $false) | ((y @ sK2) = $false)) )),
% 1.47/1.28 inference(pi_clausification,[status(thm)],[f12])).
% 1.47/1.28 thf(f12,plain,(
% 1.47/1.28 ((y @ sK2) = $false) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ a @ (^[Y1 : a]: (((= @ Y1) = Y0) & (y @ Y1))))))))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.47/1.28 thf(f10,plain,(
% 1.47/1.28 ((y @ sK2) != (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ a @ (^[Y1 : a]: (((= @ Y1) = Y0) & (y @ Y1))))))))),
% 1.47/1.28 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.47/1.28 thf(f9,plain,(
% 1.47/1.28 ((y @ sK2) != ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ a @ (^[Y2 : a]: (((= @ Y2) = Y1) & (y @ Y2)))))))) @ sK2))),
% 1.47/1.28 inference(negative_extensionality,[status(thm)],[f8])).
% 1.47/1.28 thf(f8,plain,(
% 1.47/1.28 (y != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ a @ (^[Y2 : a]: (((= @ Y2) = Y1) & (y @ Y2)))))))))),
% 1.47/1.28 inference(beta_eta_normalization,[status(thm)],[f7])).
% 1.47/1.28 thf(f7,plain,(
% 1.47/1.28 (y != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ a @ (^[Y2 : a]: ((((^[Y3 : a]: ((^[Y4 : a]: (Y3 = Y4)))) @ Y2) = Y1) & (y @ Y2)))))))))),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f6])).
% 1.47/1.28 thf(f6,plain,(
% 1.47/1.28 (y != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ a @ (^[Y2 : a]: ((((^[Y3 : a]: ((^[Y4 : a]: (Y3 = Y4)))) @ Y2) = Y1) & (y @ Y2)))))))))),
% 1.47/1.28 inference(flattening,[status(thm)],[f5])).
% 1.47/1.28 thf(f5,plain,(
% 1.47/1.28 ~(y = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ a @ (^[Y2 : a]: ((((^[Y3 : a]: ((^[Y4 : a]: (Y3 = Y4)))) @ Y2) = Y1) & (y @ Y2)))))))))),
% 1.47/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.28 thf(f4,plain,(
% 1.47/1.28 ~(y = (^[X0 : a] : (? [X1 : a > $o] : (? [X2 : a] : ((y @ X2) & (((^[X3 : a, X4 : a] : ((X3 = X4))) @ X2) = X1)) & (X1 @ X0)))))),
% 1.47/1.28 inference(rectify,[status(thm)],[f2])).
% 1.47/1.28 thf(f2,negated_conjecture,(
% 1.47/1.28 ~(y = (^[X0 : a] : (? [X1 : a > $o] : (? [X2 : a] : ((y @ X2) & (((^[X0 : a, X3 : a] : ((X0 = X3))) @ X2) = X1)) & (X1 @ X0)))))),
% 1.47/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.28 thf(f1,conjecture,(
% 1.47/1.28 (y = (^[X0 : a] : (? [X1 : a > $o] : (? [X2 : a] : ((y @ X2) & (((^[X0 : a, X3 : a] : ((X0 = X3))) @ X2) = X1)) & (X1 @ X0)))))),
% 1.47/1.28 file('/export/starexec/sandbox/tmp/tmp.S3QhFCAZ6t/DTF2THF_29962.p',cX5211_pme)).
% 1.47/1.28 thf(f47,plain,(
% 1.47/1.28 spl0_2 | spl0_4),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f23,f44,f34])).
% 1.47/1.28 thf(f23,plain,(
% 1.47/1.28 ((sK3 @ sK2) = $true) | ((y @ sK2) = $true)),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.47/1.28 thf(f21,plain,(
% 1.47/1.28 ((y @ sK2) = $true) | (((sK3 @ sK2) & (?? @ a @ (^[Y0 : a]: (((= @ Y0) = sK3) & (y @ Y0))))) = $true)),
% 1.47/1.28 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.47/1.28 thf(f20,plain,(
% 1.47/1.28 ((y @ sK2) = $true) | ($true = ((^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ a @ (^[Y1 : a]: (((= @ Y1) = Y0) & (y @ Y1)))))) @ sK3))),
% 1.47/1.28 inference(sigma_clausification,[status(thm)],[f11])).
% 1.47/1.28 thf(f11,plain,(
% 1.47/1.28 ($true = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ a @ (^[Y1 : a]: (((= @ Y1) = Y0) & (y @ Y1)))))))) | ((y @ sK2) = $true)),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.47/1.28 thf(f42,plain,(
% 1.47/1.28 spl0_2 | spl0_3),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f28,f39,f34])).
% 1.47/1.28 thf(f28,plain,(
% 1.47/1.28 (sK3 = (= @ sK4)) | ((y @ sK2) = $true)),
% 1.47/1.28 inference(equality_proxy_clausification,[status(thm)],[f27])).
% 1.47/1.28 thf(f27,plain,(
% 1.47/1.28 ((y @ sK2) = $true) | ($true = ((= @ sK4) = sK3))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.47/1.28 thf(f25,plain,(
% 1.47/1.28 ((((= @ sK4) = sK3) & (y @ sK4)) = $true) | ((y @ sK2) = $true)),
% 1.47/1.28 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.47/1.28 thf(f24,plain,(
% 1.47/1.28 ((y @ sK2) = $true) | ($true = ((^[Y0 : a]: (((= @ Y0) = sK3) & (y @ Y0))) @ sK4))),
% 1.47/1.28 inference(sigma_clausification,[status(thm)],[f22])).
% 1.47/1.28 thf(f22,plain,(
% 1.47/1.28 ((?? @ a @ (^[Y0 : a]: (((= @ Y0) = sK3) & (y @ Y0)))) = $true) | ((y @ sK2) = $true)),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.47/1.28 thf(f37,plain,(
% 1.47/1.28 spl0_1 | spl0_2),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f26,f34,f30])).
% 1.47/1.28 thf(f26,plain,(
% 1.47/1.28 ((y @ sK4) = $true) | ((y @ sK2) = $true)),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.47/1.28 % SZS output end Proof for DTF2THF_29962
% 1.47/1.28 % (30248)------------------------------
% 1.47/1.28 % (30248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (30248)Termination reason: Refutation
% 1.47/1.28
% 1.47/1.28 % (30248)Memory used [KB]: 5500
% 1.47/1.28 % (30248)Time elapsed: 0.004 s
% 1.47/1.28 % (30248)Instructions burned: 3 (million)
% 1.47/1.28 % (30248)------------------------------
% 1.47/1.28 % (30248)------------------------------
% 1.47/1.28 % (30245)Success in time 0.013 s
%------------------------------------------------------------------------------