%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV227^5 : 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 : n001.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 09:40:36 AM UTC 2026
% Result : Theorem 1.54s 1.22s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 9 unt; 0 typ; 9 def)
% Number of atoms : 493 ( 158 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 370 ( 68 ~; 137 |; 19 &; 127 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 14 con; 0-2 aty)
% ( 0 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 48 ( 27 ^; 18 !; 3 ?; 48 :)
% 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_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK2: a ).
thf(func_def_17,type,
sK3: a > $o ).
thf(func_def_18,type,
sK4: a ).
thf(f170,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f48,f57,f69,f74,f77,f80,f97,f107,f110,f169]) ).
thf(f169,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f168]) ).
thf(f168,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f161,f73]) ).
thf(f73,plain,
( ( $false
= ( y @ sK2 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f71,definition,
( spl0_9
<=> ( $false
= ( y @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f161,plain,
( ( $true
= ( y @ sK2 ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $true
= ( y @ sK2 ) )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f117,f39]) ).
thf(f39,plain,
( ( ( sK3 @ sK2 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_1
<=> ( ( sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f117,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $false )
| ( ( y @ X1 )
= $true ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( y @ X1 ) )
| ~ spl0_5 ),
inference(argument_congruence,[status(thm)],[f56]) ).
thf(f56,plain,
( ( y = sK3 )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl0_5
<=> ( y = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f110,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f109]) ).
thf(f109,plain,
( $false
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f47,f64]) ).
thf(f64,plain,
( ( ( x @ sK2 )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f62,definition,
( spl0_7
<=> ( ( x @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f47,plain,
( ( ( x @ sK2 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl0_3
<=> ( ( x @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f107,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f100,f64]) ).
thf(f100,plain,
( ( ( x @ sK2 )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( x @ sK2 )
= $true )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f85,f39]) ).
thf(f85,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $false )
| ( ( x @ X1 )
= $true ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( x @ X1 ) )
| ~ spl0_4 ),
inference(argument_congruence,[status(thm)],[f52]) ).
thf(f52,plain,
( ( x = sK3 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl0_4
<=> ( x = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f97,plain,
( spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f96,f67,f62]) ).
thf(f67,definition,
( spl0_8
<=> ! [X1: a > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( x != X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f96,plain,
( ( ( x @ sK2 )
= $false )
| ~ spl0_8 ),
inference(equality_resolution,[status(thm)],[f68]) ).
thf(f68,plain,
( ! [X1: a > $o] :
( ( x != X1 )
| ( $false
= ( X1 @ sK2 ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f80,plain,
( ~ spl0_2
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f79]) ).
thf(f79,plain,
( $false
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f43,f73]) ).
thf(f43,plain,
( ( $true
= ( y @ sK2 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl0_2
<=> ( $true
= ( y @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f77,plain,
( spl0_9
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f76,f59,f71]) ).
thf(f59,definition,
( spl0_6
<=> ! [X1: a > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( y != X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f76,plain,
( ( $false
= ( y @ sK2 ) )
| ~ spl0_6 ),
inference(equality_resolution,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X1: a > $o] :
( ( y != X1 )
| ( $false
= ( X1 @ sK2 ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f74,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f20,f59,f71]) ).
thf(f20,plain,
! [X1: a > $o] :
( ( y != X1 )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( y @ sK2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: a > $o] :
( ( ( y = X1 )
= $false )
| ( $false
= ( y @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: a > $o] :
( ( $false
= ( y @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( ( ( x = X1 )
| ( y = X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: a > $o] :
( ( $false
= ( y @ sK2 ) )
| ( $false
= ( ( ( x = X1 )
| ( y = X1 ) )
& ( X1 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: a > $o] :
( ( $false
= ( y @ sK2 ) )
| ( $false
= ( ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( y @ sK2 ) )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $false
= ( ( y @ sK2 )
| ( x @ sK2 ) ) )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( y @ sK2 )
| ( x @ sK2 ) )
!= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( x = Y1 )
| ( y = Y1 ) )
& ( Y1 @ Y0 ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ( y @ Y0 )
| ( x @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( y @ Y0 )
| ( x @ 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] :
( ( y @ Y0 )
| ( x @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( x = Y1 )
| ( y = Y1 ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ( y @ Y0 )
| ( x @ 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] :
( ( x @ X0 )
| ( y @ X0 ) ) )
!= ( ^ [X1: a] :
? [X2: a > $o] :
( ( X2 @ X1 )
& ( ( y = X2 )
| ( x = X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
( ( x @ X0 )
| ( y @ X0 ) ) )
!= ( ^ [X1: a] :
? [X2: a > $o] :
( ( X2 @ X1 )
& ( ( y = X2 )
| ( x = X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a] :
( ( x @ X0 )
| ( y @ X0 ) ) )
= ( ^ [X1: a] :
? [X2: a > $o] :
( ( X2 @ X1 )
& ( ( y = X2 )
| ( x = X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xQYIYUQuWE/DTF2THF_11638.p',cX5200_pme) ).
thf(f69,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f26,f62,f67]) ).
thf(f26,plain,
! [X1: a > $o] :
( ( ( x @ sK2 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( x != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: a > $o] :
( ( ( x = X1 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( ( x @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: a > $o] :
( ( ( ( x = X1 )
| ( y = X1 ) )
= $false )
| ( ( x @ sK2 )
= $false )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: a > $o] :
( ( ( x @ sK2 )
= $false )
| ( $false
= ( ( ( x = X1 )
| ( y = X1 ) )
& ( X1 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: a > $o] :
( ( ( x @ sK2 )
= $false )
| ( $false
= ( ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( x @ sK2 )
= $false )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f57,plain,
( spl0_4
| spl0_5
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f35,f45,f41,f54,f50]) ).
thf(f35,plain,
( ( x = sK3 )
| ( y = sK3 )
| ( $true
= ( y @ sK2 ) )
| ( ( x @ sK2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( x = sK3 )
= $true )
| ( $true
= ( y @ sK2 ) )
| ( y = sK3 )
| ( ( x @ sK2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( y = sK3 )
= $true )
| ( $true
= ( y @ sK2 ) )
| ( ( x = sK3 )
= $true )
| ( ( x @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $true
= ( y @ sK2 ) )
| ( ( ( x = sK3 )
| ( y = sK3 ) )
= $true )
| ( ( x @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ( ( x = sK3 )
| ( y = sK3 ) )
& ( sK3 @ sK2 ) )
= $true )
| ( $true
= ( y @ sK2 ) )
| ( ( x @ sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( x @ sK2 )
= $true )
| ( $true
= ( ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) )
@ sK3 ) )
| ( $true
= ( y @ sK2 ) ) ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( x @ sK2 )
= $true )
| ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) ) ) )
| ( $true
= ( y @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
= ( ( y @ sK2 )
| ( x @ sK2 ) ) )
| ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( x = Y0 )
| ( y = Y0 ) )
& ( Y0 @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f48,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f31,f45,f41,f37]) ).
thf(f31,plain,
( ( $true
= ( y @ sK2 ) )
| ( ( sK3 @ sK2 )
= $true )
| ( ( x @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV227^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:43:05 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEV227^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.45 % Domain : Set Theory (Sets of sets)
% 0.20/0.45 % Problem : TPS problem X5200
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Bro09]
% 0.20/0.45 % Names : tps_0115 [Bro09]
% 0.20/0.45 % : X5200 [TPS]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % 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, 0.14 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
% 0.20/0.45 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.20/0.45 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 1 ( 7 avg)
% 0.20/0.45 % Number of connectives : 6 ( 0 ~; 2 |; 1 &; 3 @)
% 0.20/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 1 ( 1 avg)
% 0.20/0.45 % Number of types : 2 ( 1 usr)
% 0.20/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.20/0.45 % Number of variables : 3 ( 2 ^; 0 !; 1 ?; 3 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.45 % : Polymorphic definitions expanded.
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(a_type,type,
% 0.20/0.45 a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(y,type,
% 0.20/0.45 y: a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(x,type,
% 0.20/0.45 x: a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(cX5200_pme,conjecture,
% 0.20/0.45 ( ( ^ [Xz: a] :
% 0.20/0.45 ( ( x @ Xz )
% 0.20/0.45 | ( y @ Xz ) ) )
% 0.20/0.45 = ( ^ [Xx0: a] :
% 0.20/0.45 ? [S: a > $o] :
% 0.20/0.45 ( ( ( S = x )
% 0.20/0.45 | ( S = y ) )
% 0.20/0.45 & ( S @ Xx0 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.43/1.18 ---- Embedded in THF ---
% 1.43/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.18 %%% Generated on Tue Feb 24 12:43:06 EST 2026
% 1.43/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.18 %%% Logic specification used:
% 1.43/1.18 %%% thf(spec, logic, $$dhol).
% 1.43/1.18
% 1.43/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xQYIYUQuWE/DTF2DTF11638.p
% See solution above
% 1.43/1.18 ------------------------
% 1.43/1.19 ---- Cleaned THF ---
% 1.43/1.20 thf(a_type,type,
% 1.43/1.20 a: $tType ).
% 1.43/1.20
% 1.43/1.20 thf(y,type,
% 1.43/1.20 y: a > $o ).
% 1.43/1.20
% 1.43/1.20 thf(x,type,
% 1.43/1.20 x: a > $o ).
% 1.43/1.20
% 1.43/1.20 thf(cX5200_pme,conjecture,
% 1.43/1.20 ( ( ^ [Xz: a] :
% 1.43/1.20 ( ( x @ Xz )
% 1.43/1.20 | ( y @ Xz ) ) )
% 1.43/1.20 = ( ^ [Xx0: a] :
% 1.43/1.20 ? [S: a > $o] :
% 1.43/1.20 ( ( ( S = x )
% 1.43/1.20 | ( S = y ) )
% 1.43/1.20 & ( S @ Xx0 ) ) ) ) ).
% 1.43/1.20 ------------------------
% 1.54/1.21 % (11830)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11638 for (2999ds/2Mi)
% 1.54/1.21 % (11833)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11638 for (2999ds/18Mi)
% 1.54/1.21 % (11830)Instruction limit reached!
% 1.54/1.21 % (11830)------------------------------
% 1.54/1.21 % (11830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.21 % (11830)Termination reason: Unknown
% 1.54/1.21 % (11830)Termination phase: Saturation
% 1.54/1.21
% 1.54/1.21 % (11830)Memory used [KB]: 5500
% 1.54/1.21 % (11830)Time elapsed: 0.002 s
% 1.54/1.21 % (11830)Instructions burned: 2 (million)
% 1.54/1.21 % (11830)------------------------------
% 1.54/1.21 % (11830)------------------------------
% 1.54/1.21 % (11833)First to succeed.
% 1.54/1.22 % (11833)Refutation found. Thanks to Tanya!
% 1.54/1.22 % SZS status Theorem for DTF2THF_11638
% 1.54/1.22 % SZS output start Proof for DTF2THF_11638
% 1.54/1.22 thf(type_def_5, type, a: $tType).
% 1.54/1.22 thf(func_def_0, type, a: $tType).
% 1.54/1.22 thf(func_def_1, type, y: a > $o).
% 1.54/1.22 thf(func_def_2, type, x: a > $o).
% 1.54/1.22 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.54/1.22 thf(func_def_16, type, sK2: a).
% 1.54/1.22 thf(func_def_17, type, sK3: a > $o).
% 1.54/1.22 thf(func_def_18, type, sK4: a).
% 1.54/1.22 thf(f170,plain,(
% 1.54/1.22 $false),
% 1.54/1.22 inference(avatar_sat_refutation,[status(thm)],[f48,f57,f69,f74,f77,f80,f97,f107,f110,f169])).
% 1.54/1.22 thf(f169,plain,(
% 1.54/1.22 ~spl0_1 | ~spl0_5 | ~spl0_9),
% 1.54/1.22 inference(avatar_contradiction_clause,[status(thm)],[f168])).
% 1.54/1.22 thf(f168,plain,(
% 1.54/1.22 $false | (~spl0_1 | ~spl0_5 | ~spl0_9)),
% 1.54/1.22 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.54/1.22 thf(f167,plain,(
% 1.54/1.22 ($false = $true) | (~spl0_1 | ~spl0_5 | ~spl0_9)),
% 1.54/1.22 inference(forward_demodulation,[status(thm)],[f161,f73])).
% 1.54/1.22 thf(f73,plain,(
% 1.54/1.22 ($false = (y @ sK2)) | ~spl0_9),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.54/1.22 thf(f71,definition,(
% 1.54/1.22 spl0_9 <=> ($false = (y @ sK2))),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.54/1.22 thf(f161,plain,(
% 1.54/1.22 ($true = (y @ sK2)) | (~spl0_1 | ~spl0_5)),
% 1.54/1.22 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.54/1.22 thf(f156,plain,(
% 1.54/1.22 ($true = (y @ sK2)) | ($false = $true) | (~spl0_1 | ~spl0_5)),
% 1.54/1.22 inference(superposition,[status(thm)],[f117,f39])).
% 1.54/1.22 thf(f39,plain,(
% 1.54/1.22 ((sK3 @ sK2) = $true) | ~spl0_1),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.54/1.22 thf(f37,definition,(
% 1.54/1.22 spl0_1 <=> ((sK3 @ sK2) = $true)),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.54/1.22 thf(f117,plain,(
% 1.54/1.22 ( ! [X1 : a] : (((sK3 @ X1) = $false) | ((y @ X1) = $true)) ) | ~spl0_5),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.54/1.22 thf(f113,plain,(
% 1.54/1.22 ( ! [X1 : a] : (((sK3 @ X1) = (y @ X1))) ) | ~spl0_5),
% 1.54/1.22 inference(argument_congruence,[status(thm)],[f56])).
% 1.54/1.22 thf(f56,plain,(
% 1.54/1.22 (y = sK3) | ~spl0_5),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.54/1.22 thf(f54,definition,(
% 1.54/1.22 spl0_5 <=> (y = sK3)),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.54/1.22 thf(f110,plain,(
% 1.54/1.22 ~spl0_3 | ~spl0_7),
% 1.54/1.22 inference(avatar_contradiction_clause,[status(thm)],[f109])).
% 1.54/1.22 thf(f109,plain,(
% 1.54/1.22 $false | (~spl0_3 | ~spl0_7)),
% 1.54/1.22 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.54/1.22 thf(f108,plain,(
% 1.54/1.22 ($false = $true) | (~spl0_3 | ~spl0_7)),
% 1.54/1.22 inference(forward_demodulation,[status(thm)],[f47,f64])).
% 1.54/1.22 thf(f64,plain,(
% 1.54/1.22 ((x @ sK2) = $false) | ~spl0_7),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.54/1.22 thf(f62,definition,(
% 1.54/1.22 spl0_7 <=> ((x @ sK2) = $false)),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.54/1.22 thf(f47,plain,(
% 1.54/1.22 ((x @ sK2) = $true) | ~spl0_3),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.54/1.22 thf(f45,definition,(
% 1.54/1.22 spl0_3 <=> ((x @ sK2) = $true)),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.54/1.22 thf(f107,plain,(
% 1.54/1.22 ~spl0_1 | ~spl0_4 | ~spl0_7),
% 1.54/1.22 inference(avatar_contradiction_clause,[status(thm)],[f106])).
% 1.54/1.22 thf(f106,plain,(
% 1.54/1.22 $false | (~spl0_1 | ~spl0_4 | ~spl0_7)),
% 1.54/1.22 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.54/1.22 thf(f105,plain,(
% 1.54/1.22 ($false = $true) | (~spl0_1 | ~spl0_4 | ~spl0_7)),
% 1.54/1.22 inference(forward_demodulation,[status(thm)],[f100,f64])).
% 1.54/1.22 thf(f100,plain,(
% 1.54/1.22 ((x @ sK2) = $true) | (~spl0_1 | ~spl0_4)),
% 1.54/1.22 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.54/1.22 thf(f98,plain,(
% 1.54/1.22 ((x @ sK2) = $true) | ($false = $true) | (~spl0_1 | ~spl0_4)),
% 1.54/1.22 inference(superposition,[status(thm)],[f85,f39])).
% 1.54/1.22 thf(f85,plain,(
% 1.54/1.22 ( ! [X1 : a] : (((sK3 @ X1) = $false) | ((x @ X1) = $true)) ) | ~spl0_4),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.54/1.22 thf(f82,plain,(
% 1.54/1.22 ( ! [X1 : a] : (((sK3 @ X1) = (x @ X1))) ) | ~spl0_4),
% 1.54/1.22 inference(argument_congruence,[status(thm)],[f52])).
% 1.54/1.22 thf(f52,plain,(
% 1.54/1.22 (x = sK3) | ~spl0_4),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.54/1.22 thf(f50,definition,(
% 1.54/1.22 spl0_4 <=> (x = sK3)),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.54/1.22 thf(f97,plain,(
% 1.54/1.22 spl0_7 | ~spl0_8),
% 1.54/1.22 inference(avatar_split_clause,[status(thm)],[f96,f67,f62])).
% 1.54/1.22 thf(f67,definition,(
% 1.54/1.22 spl0_8 <=> ! [X1 : a > $o] : (($false = (X1 @ sK2)) | (x != X1))),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.54/1.22 thf(f96,plain,(
% 1.54/1.22 ((x @ sK2) = $false) | ~spl0_8),
% 1.54/1.22 inference(equality_resolution,[status(thm)],[f68])).
% 1.54/1.22 thf(f68,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : ((x != X1) | ($false = (X1 @ sK2))) ) | ~spl0_8),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.54/1.22 thf(f80,plain,(
% 1.54/1.22 ~spl0_2 | ~spl0_9),
% 1.54/1.22 inference(avatar_contradiction_clause,[status(thm)],[f79])).
% 1.54/1.22 thf(f79,plain,(
% 1.54/1.22 $false | (~spl0_2 | ~spl0_9)),
% 1.54/1.22 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.54/1.22 thf(f78,plain,(
% 1.54/1.22 ($false = $true) | (~spl0_2 | ~spl0_9)),
% 1.54/1.22 inference(backward_demodulation,[status(thm)],[f43,f73])).
% 1.54/1.22 thf(f43,plain,(
% 1.54/1.22 ($true = (y @ sK2)) | ~spl0_2),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.54/1.22 thf(f41,definition,(
% 1.54/1.22 spl0_2 <=> ($true = (y @ sK2))),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.54/1.22 thf(f77,plain,(
% 1.54/1.22 spl0_9 | ~spl0_6),
% 1.54/1.22 inference(avatar_split_clause,[status(thm)],[f76,f59,f71])).
% 1.54/1.22 thf(f59,definition,(
% 1.54/1.22 spl0_6 <=> ! [X1 : a > $o] : (($false = (X1 @ sK2)) | (y != X1))),
% 1.54/1.22 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.54/1.22 thf(f76,plain,(
% 1.54/1.22 ($false = (y @ sK2)) | ~spl0_6),
% 1.54/1.22 inference(equality_resolution,[status(thm)],[f60])).
% 1.54/1.22 thf(f60,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : ((y != X1) | ($false = (X1 @ sK2))) ) | ~spl0_6),
% 1.54/1.22 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.54/1.22 thf(f74,plain,(
% 1.54/1.22 spl0_9 | spl0_6),
% 1.54/1.22 inference(avatar_split_clause,[status(thm)],[f20,f59,f71])).
% 1.54/1.22 thf(f20,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : ((y != X1) | ($false = (X1 @ sK2)) | ($false = (y @ sK2))) )),
% 1.54/1.22 inference(equality_proxy_clausification,[status(thm)],[f17])).
% 1.54/1.22 thf(f17,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : (((y = X1) = $false) | ($false = (y @ sK2)) | ($false = (X1 @ sK2))) )),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.54/1.22 thf(f16,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : (($false = (y @ sK2)) | ($false = (X1 @ sK2)) | (((x = X1) | (y = X1)) = $false)) )),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.54/1.22 thf(f15,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : (($false = (y @ sK2)) | ($false = (((x = X1) | (y = X1)) & (X1 @ sK2)))) )),
% 1.54/1.22 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.54/1.22 thf(f14,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : (($false = (y @ sK2)) | ($false = ((^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2))) @ X1))) )),
% 1.54/1.22 inference(pi_clausification,[status(thm)],[f13])).
% 1.54/1.22 thf(f13,plain,(
% 1.54/1.22 ($false = (y @ sK2)) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2)))))),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.54/1.22 thf(f11,plain,(
% 1.54/1.22 ($false = ((y @ sK2) | (x @ sK2))) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2)))))),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.54/1.22 thf(f9,plain,(
% 1.54/1.22 (((y @ sK2) | (x @ sK2)) != (?? @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2)))))),
% 1.54/1.22 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.54/1.22 thf(f8,plain,(
% 1.54/1.22 (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((x = Y1) | (y = Y1)) & (Y1 @ Y0))))) @ sK2) != ((^[Y0 : a]: ((y @ Y0) | (x @ Y0))) @ sK2))),
% 1.54/1.22 inference(negative_extensionality,[status(thm)],[f7])).
% 1.54/1.22 thf(f7,plain,(
% 1.54/1.22 ((^[Y0 : a]: ((y @ Y0) | (x @ Y0))) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((x = Y1) | (y = Y1)) & (Y1 @ Y0))))))),
% 1.54/1.22 inference(cnf_transformation,[status(thm)],[f6])).
% 1.54/1.22 thf(f6,plain,(
% 1.54/1.22 ((^[Y0 : a]: ((y @ Y0) | (x @ Y0))) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((x = Y1) | (y = Y1)) & (Y1 @ Y0))))))),
% 1.54/1.22 inference(flattening,[status(thm)],[f5])).
% 1.54/1.22 thf(f5,plain,(
% 1.54/1.22 ~((^[Y0 : a]: ((y @ Y0) | (x @ Y0))) = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((x = Y1) | (y = Y1)) & (Y1 @ Y0))))))),
% 1.54/1.22 inference(fool_elimination,[status(thm)],[f4])).
% 1.54/1.22 thf(f4,plain,(
% 1.54/1.22 ~((^[X0 : a] : ((x @ X0) | (y @ X0))) = (^[X1 : a] : (? [X2 : a > $o] : ((X2 @ X1) & ((y = X2) | (x = X2))))))),
% 1.54/1.22 inference(rectify,[status(thm)],[f2])).
% 1.54/1.22 thf(f2,negated_conjecture,(
% 1.54/1.22 ~((^[X0 : a] : ((x @ X0) | (y @ X0))) = (^[X1 : a] : (? [X2 : a > $o] : ((X2 @ X1) & ((y = X2) | (x = X2))))))),
% 1.54/1.22 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.22 thf(f1,conjecture,(
% 1.54/1.22 ((^[X0 : a] : ((x @ X0) | (y @ X0))) = (^[X1 : a] : (? [X2 : a > $o] : ((X2 @ X1) & ((y = X2) | (x = X2))))))),
% 1.54/1.22 file('/export/starexec/sandbox/tmp/tmp.xQYIYUQuWE/DTF2THF_11638.p',cX5200_pme)).
% 1.54/1.22 thf(f69,plain,(
% 1.54/1.22 spl0_8 | spl0_7),
% 1.54/1.22 inference(avatar_split_clause,[status(thm)],[f26,f62,f67])).
% 1.54/1.22 thf(f26,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : (((x @ sK2) = $false) | ($false = (X1 @ sK2)) | (x != X1)) )),
% 1.54/1.22 inference(equality_proxy_clausification,[status(thm)],[f25])).
% 1.54/1.22 thf(f25,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : (((x = X1) = $false) | ($false = (X1 @ sK2)) | ((x @ sK2) = $false)) )),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.54/1.22 thf(f23,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : ((((x = X1) | (y = X1)) = $false) | ((x @ sK2) = $false) | ($false = (X1 @ sK2))) )),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.54/1.22 thf(f22,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : (((x @ sK2) = $false) | ($false = (((x = X1) | (y = X1)) & (X1 @ sK2)))) )),
% 1.54/1.22 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.54/1.22 thf(f21,plain,(
% 1.54/1.22 ( ! [X1 : a > $o] : (((x @ sK2) = $false) | ($false = ((^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2))) @ X1))) )),
% 1.54/1.22 inference(pi_clausification,[status(thm)],[f12])).
% 1.54/1.22 thf(f12,plain,(
% 1.54/1.22 ((x @ sK2) = $false) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2)))))),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.54/1.22 thf(f57,plain,(
% 1.54/1.22 spl0_4 | spl0_5 | spl0_2 | spl0_3),
% 1.54/1.22 inference(avatar_split_clause,[status(thm)],[f35,f45,f41,f54,f50])).
% 1.54/1.22 thf(f35,plain,(
% 1.54/1.22 (x = sK3) | (y = sK3) | ($true = (y @ sK2)) | ((x @ sK2) = $true)),
% 1.54/1.22 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.54/1.22 thf(f34,plain,(
% 1.54/1.22 ((x = sK3) = $true) | ($true = (y @ sK2)) | (y = sK3) | ((x @ sK2) = $true)),
% 1.54/1.22 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.54/1.22 thf(f33,plain,(
% 1.54/1.22 ((y = sK3) = $true) | ($true = (y @ sK2)) | ((x = sK3) = $true) | ((x @ sK2) = $true)),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.54/1.22 thf(f32,plain,(
% 1.54/1.22 ($true = (y @ sK2)) | (((x = sK3) | (y = sK3)) = $true) | ((x @ sK2) = $true)),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.54/1.22 thf(f30,plain,(
% 1.54/1.22 ((((x = sK3) | (y = sK3)) & (sK3 @ sK2)) = $true) | ($true = (y @ sK2)) | ((x @ sK2) = $true)),
% 1.54/1.22 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.54/1.22 thf(f29,plain,(
% 1.54/1.22 ((x @ sK2) = $true) | ($true = ((^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2))) @ sK3)) | ($true = (y @ sK2))),
% 1.54/1.22 inference(sigma_clausification,[status(thm)],[f28])).
% 1.54/1.22 thf(f28,plain,(
% 1.54/1.22 ((x @ sK2) = $true) | ($true = (?? @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2))))) | ($true = (y @ sK2))),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.54/1.22 thf(f10,plain,(
% 1.54/1.22 ($true = ((y @ sK2) | (x @ sK2))) | ($true = (?? @ (a > $o) @ (^[Y0 : a > $o]: (((x = Y0) | (y = Y0)) & (Y0 @ sK2)))))),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.54/1.22 thf(f48,plain,(
% 1.54/1.22 spl0_1 | spl0_2 | spl0_3),
% 1.54/1.22 inference(avatar_split_clause,[status(thm)],[f31,f45,f41,f37])).
% 1.54/1.22 thf(f31,plain,(
% 1.54/1.22 ($true = (y @ sK2)) | ((sK3 @ sK2) = $true) | ((x @ sK2) = $true)),
% 1.54/1.22 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.54/1.22 % SZS output end Proof for DTF2THF_11638
% 1.54/1.22 % (11833)------------------------------
% 1.54/1.22 % (11833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.22 % (11833)Termination reason: Refutation
% 1.54/1.22
% 1.54/1.22 % (11833)Memory used [KB]: 5628
% 1.54/1.22 % (11833)Time elapsed: 0.005 s
% 1.54/1.22 % (11833)Instructions burned: 7 (million)
% 1.54/1.22 % (11833)------------------------------
% 1.54/1.22 % (11833)------------------------------
% 1.54/1.22 % (11826)Success in time 0.012 s
%------------------------------------------------------------------------------