%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV084^5 : 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 : n008.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 09:40:14 AM UTC 2026
% Result : Theorem 1.47s 1.27s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 2 unt; 0 typ; 4 def)
% Number of atoms : 584 ( 221 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 539 ( 94 ~; 86 |; 43 &; 304 @)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 266 ( 266 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 284 ( 222 ^; 40 !; 22 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_8,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_9,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_10,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_11,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_13,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f141,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f65,f127,f132,f137,f140]) ).
thf(f140,plain,
( ~ spl4_4
| ~ spl4_6
| spl4_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f139]) ).
thf(f139,plain,
( $false
| ~ spl4_4
| ~ spl4_6
| spl4_7 ),
inference(subsumption_resolution,[status(thm)],[f138,f64]) ).
thf(f64,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f62,definition,
( spl4_4
<=> ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f138,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl4_6
| spl4_7 ),
inference(forward_demodulation,[status(thm)],[f136,f131]) ).
thf(f131,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f129]) ).
thf(f129,definition,
( spl4_6
<=> ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f136,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f134]) ).
thf(f134,definition,
( spl4_7
<=> ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f137,plain,
( spl4_2
| ~ spl4_7 ),
inference(avatar_split_clause,[status(thm)],[f122,f134,f53]) ).
thf(f53,definition,
( spl4_2
<=> ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f122,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $true
!= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true
!= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $true
!= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] : $false ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
= $true )
| ( $true
!= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( $true
!= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
=> ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( $true
!= ( X0 @ X4 @ X3 ) )
& ( $true
= ( X0 @ X4 @ X2 ) )
& ( ( X0 @ X2 @ X3 )
= $true ) )
=> ( ( $true
!= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
= $true )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( $true
!= ( X0 @ X4 @ X3 ) )
& ( $true
= ( X0 @ X4 @ X2 ) )
& ( ( X0 @ X2 @ X3 )
= $true ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
= $true )
| ? [X4: $i > $o] :
( ( X0 @ X4 @ X4 )
!= $true )
| ? [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X1 )
!= $true )
& ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X3 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
= $true )
| ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X2 @ X1 )
!= $true )
& ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X2 @ X3 )
= $true ) )
| ? [X4: $i > $o] :
( ( X0 @ X4 @ X4 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
!= $true )
& ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X2 @ X3 )
= $true ) )
=> ( ( X0 @ X2 @ X1 )
= $true ) )
& ! [X4: $i > $o] :
( ( X0 @ X4 @ X4 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
!= $true )
& ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X2 @ X3 )
= $true ) )
=> ( ( X0 @ X2 @ X1 )
= $true ) )
& ! [X4: $i > $o] :
( ( X0 @ X4 @ X4 )
= $true ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
!= $true )
& ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ( $true
= ( X0 @ X5 @ X3 ) )
& ( $true
= ( X0 @ X4 @ X5 ) ) )
=> ( $true
= ( X0 @ X4 @ X3 ) ) )
& ! [X6: $i > $o] :
( ( X0 @ X6 @ X6 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( X0
@ ^ [X1: $i] :
( ~ cP
| cP )
@ ^ [X2: $i] :
( ~ cP
& cP ) )
& ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X3 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X4 @ X3 ) )
& ! [X6: $i > $o] : ( X0 @ X6 @ X6 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( X0
@ ^ [X1: $i] :
( ~ cP
| cP )
@ ^ [X1: $i] :
( ~ cP
& cP ) )
& ! [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( X0
@ ^ [X1: $i] :
( ~ cP
| cP )
@ ^ [X1: $i] :
( ~ cP
& cP ) )
& ! [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.KNNgo5lwuG/DTF2THF_5021.p',cTHM120J_pme) ).
thf(f132,plain,
( spl4_2
| spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f90,f129,f53]) ).
thf(f90,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true != $true )
| ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true
!= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) ) ),
inference(primitive_instantiation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) ) ),
inference(boolean_simplification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] : $false ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
= $true )
| ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f127,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f126]) ).
thf(f126,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f124]) ).
thf(f124,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $true
@ X1 )
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ~ spl4_2 ),
inference(argument_congruence,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f65,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f53,f62]) ).
thf(f34,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true != $true )
| ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
!= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] : $false ) )
| ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) ) )
| ( ( X0
@ ^ [Y0: $i] :
( cP
| ~ cP )
@ ^ [Y0: $i] :
( cP
& ~ cP ) )
= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV084^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:39:54 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEV084^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory (Relations)
% 0.28/0.46 % Problem : TPS problem from RELN-THMS
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0897 [Bro09]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.33 v8.2.0, 0.36 v8.1.0, 0.50 v7.5.0, 0.42 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.50 v6.2.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.75 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.28/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.28/0.46 % Number of connectives : 19 ( 3 ~; 1 |; 4 &; 10 @)
% 0.28/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 11 ( 11 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 1 ( 1 usr; 1 con; 0-0 aty)
% 0.28/0.46 % Number of variables : 7 ( 2 ^; 4 !; 1 ?; 7 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(cP,type,
% 0.28/0.46 cP: $o ).
% 0.28/0.46
% 0.28/0.46 thf(cTHM120J_pme,conjecture,
% 0.28/0.46 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.28/0.46 ( ~ ( R
% 0.28/0.46 @ ^ [Xx: $i] :
% 0.28/0.46 ( cP
% 0.28/0.46 | ~ cP )
% 0.28/0.46 @ ^ [Xx: $i] :
% 0.28/0.46 ( cP
% 0.28/0.46 & ~ cP ) )
% 0.28/0.46 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.28/0.46 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.28/0.46 ( ( ( R @ Xx @ Xy )
% 0.28/0.46 & ( R @ Xy @ Xz ) )
% 0.28/0.46 => ( R @ Xx @ Xz ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.47/1.22 ---- Embedded in THF ---
% 1.47/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.23 %%% Generated on Tue Feb 24 12:39:55 EST 2026
% 1.47/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.23 %%% Logic specification used:
% 1.47/1.23 %%% thf(spec, logic, $$dhol).
% 1.47/1.23
% 1.47/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KNNgo5lwuG/DTF2DTF5021.p
% See solution above
% 1.47/1.23 ------------------------
% 1.47/1.23 ---- Cleaned THF ---
% 1.47/1.24 thf(cP,type,
% 1.47/1.24 cP: $o ).
% 1.47/1.24
% 1.47/1.24 thf(cTHM120J_pme,conjecture,
% 1.47/1.24 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.47/1.24 ( ~ ( R
% 1.47/1.24 @ ^ [Xx: $i] :
% 1.47/1.24 ( cP
% 1.47/1.24 | ~ cP )
% 1.47/1.24 @ ^ [Xx: $i] :
% 1.47/1.24 ( cP
% 1.47/1.24 & ~ cP ) )
% 1.47/1.24 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 1.47/1.24 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.47/1.24 ( ( ( R @ Xx @ Xy )
% 1.47/1.24 & ( R @ Xy @ Xz ) )
% 1.47/1.24 => ( R @ Xx @ Xz ) ) ) ).
% 1.47/1.24 ------------------------
% 1.47/1.25 % (5299)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5021 for (2999ds/2Mi)
% 1.47/1.25 % (5297)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_5021 for (2999ds/4Mi)
% 1.47/1.25 % (5299)Instruction limit reached!
% 1.47/1.25 % (5299)------------------------------
% 1.47/1.25 % (5299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.25 % (5299)Termination reason: Unknown
% 1.47/1.25 % (5299)Termination phase: Clausification
% 1.47/1.25
% 1.47/1.25 % (5299)Memory used [KB]: 895
% 1.47/1.25 % (5299)Time elapsed: 0.002 s
% 1.47/1.25 % (5299)Instructions burned: 2 (million)
% 1.47/1.25 % (5299)------------------------------
% 1.47/1.25 % (5299)------------------------------
% 1.47/1.25 % (5297)Instruction limit reached!
% 1.47/1.25 % (5297)------------------------------
% 1.47/1.25 % (5297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.25 % (5297)Termination reason: Unknown
% 1.47/1.25 % (5297)Termination phase: Saturation
% 1.47/1.25
% 1.47/1.25 % (5297)Memory used [KB]: 5500
% 1.47/1.25 % (5297)Time elapsed: 0.003 s
% 1.47/1.25 % (5297)Instructions burned: 5 (million)
% 1.47/1.25 % (5297)------------------------------
% 1.47/1.25 % (5297)------------------------------
% 1.47/1.26 % (5296)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5021 for (2999ds/183Mi)
% 1.47/1.26 % (5298)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_5021 for (2999ds/27Mi)
% 1.47/1.26 % (5300)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_5021 for (2999ds/2Mi)
% 1.47/1.26 % (5301)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_5021 for (2999ds/275Mi)
% 1.47/1.26 % (5302)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5021 for (2999ds/18Mi)
% 1.47/1.26 % (5300)Instruction limit reached!
% 1.47/1.26 % (5300)------------------------------
% 1.47/1.26 % (5300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.26 % (5300)Termination reason: Unknown
% 1.47/1.26 % (5300)Termination phase: Property scanning
% 1.47/1.26
% 1.47/1.26 % (5300)Memory used [KB]: 895
% 1.47/1.26 % (5300)Time elapsed: 0.003 s
% 1.47/1.26 % (5300)Instructions burned: 2 (million)
% 1.47/1.26 % (5300)------------------------------
% 1.47/1.26 % (5300)------------------------------
% 1.47/1.26 % (5298)Refutation not found, incomplete strategy
% 1.47/1.26 % (5298)------------------------------
% 1.47/1.26 % (5298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.26 % (5298)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.26
% 1.47/1.26
% 1.47/1.26 % (5298)Memory used [KB]: 5500
% 1.47/1.26 % (5298)Time elapsed: 0.004 s
% 1.47/1.26 % (5298)Instructions burned: 2 (million)
% 1.47/1.26 % (5298)------------------------------
% 1.47/1.26 % (5298)------------------------------
% 1.47/1.26 % (5303)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5021 for (2999ds/3Mi)
% 1.47/1.26 % (5303)Instruction limit reached!
% 1.47/1.26 % (5303)------------------------------
% 1.47/1.26 % (5303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.26 % (5303)Termination reason: Unknown
% 1.47/1.26 % (5303)Termination phase: Saturation
% 1.47/1.26
% 1.47/1.26 % (5303)Memory used [KB]: 5500
% 1.47/1.26 % (5303)Time elapsed: 0.002 s
% 1.47/1.26 % (5303)Instructions burned: 3 (million)
% 1.47/1.26 % (5303)------------------------------
% 1.47/1.26 % (5303)------------------------------
% 1.47/1.26 % (5304)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_5021 for (2999ds/37Mi)
% 1.47/1.27 % (5301)First to succeed.
% 1.47/1.27 % (5302)Instruction limit reached!
% 1.47/1.27 % (5302)------------------------------
% 1.47/1.27 % (5302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.27 % (5302)Termination reason: Unknown
% 1.47/1.27 % (5302)Termination phase: Saturation
% 1.47/1.27
% 1.47/1.27 % (5302)Memory used [KB]: 5628
% 1.47/1.27 % (5302)Time elapsed: 0.013 s
% 1.47/1.27 % (5302)Instructions burned: 18 (million)
% 1.47/1.27 % (5302)------------------------------
% 1.47/1.27 % (5302)------------------------------
% 1.47/1.27 % (5301)Refutation found. Thanks to Tanya!
% 1.47/1.27 % SZS status Theorem for DTF2THF_5021
% 1.47/1.27 % SZS output start Proof for DTF2THF_5021
% 1.47/1.27 thf(func_def_8, type, sK0: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.47/1.27 thf(func_def_9, type, sK1: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.47/1.27 thf(func_def_10, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.47/1.27 thf(func_def_11, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.47/1.27 thf(func_def_13, type, ph5: !>[X0: $tType]:(X0)).
% 1.47/1.27 thf(f141,plain,(
% 1.47/1.27 $false),
% 1.47/1.27 inference(avatar_sat_refutation,[status(thm)],[f65,f127,f132,f137,f140])).
% 1.47/1.27 thf(f140,plain,(
% 1.47/1.27 ~spl4_4 | ~spl4_6 | spl4_7),
% 1.47/1.27 inference(avatar_contradiction_clause,[status(thm)],[f139])).
% 1.47/1.27 thf(f139,plain,(
% 1.47/1.27 $false | (~spl4_4 | ~spl4_6 | spl4_7)),
% 1.47/1.27 inference(subsumption_resolution,[status(thm)],[f138,f64])).
% 1.47/1.27 thf(f64,plain,(
% 1.47/1.27 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl4_4),
% 1.47/1.27 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.47/1.27 thf(f62,definition,(
% 1.47/1.27 spl4_4 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.47/1.27 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.47/1.27 thf(f138,plain,(
% 1.47/1.27 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | (~spl4_6 | spl4_7)),
% 1.47/1.27 inference(forward_demodulation,[status(thm)],[f136,f131])).
% 1.47/1.27 thf(f131,plain,(
% 1.47/1.27 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl4_6),
% 1.47/1.27 inference(avatar_component_clause,[status(thm)],[f129])).
% 1.47/1.27 thf(f129,definition,(
% 1.47/1.27 spl4_6 <=> ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.47/1.27 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.47/1.27 thf(f136,plain,(
% 1.47/1.27 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | spl4_7),
% 1.47/1.27 inference(avatar_component_clause,[status(thm)],[f134])).
% 1.47/1.27 thf(f134,definition,(
% 1.47/1.27 spl4_7 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.47/1.27 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.47/1.27 thf(f137,plain,(
% 1.47/1.27 spl4_2 | ~spl4_7),
% 1.47/1.27 inference(avatar_split_clause,[status(thm)],[f122,f134,f53])).
% 1.47/1.27 thf(f53,definition,(
% 1.47/1.27 spl4_2 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.47/1.27 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.47/1.27 thf(f122,plain,(
% 1.47/1.27 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.47/1.27 inference(equality_proxy_clausification,[status(thm)],[f121])).
% 1.47/1.27 thf(f121,plain,(
% 1.47/1.27 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.47/1.27 inference(equality_proxy_clausification,[status(thm)],[f120])).
% 1.47/1.27 thf(f120,plain,(
% 1.47/1.27 ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 1.47/1.27 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.47/1.27 thf(f119,plain,(
% 1.47/1.27 ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f118])).
% 1.47/1.27 thf(f118,plain,(
% 1.47/1.27 ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 1.47/1.27 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.47/1.27 thf(f98,plain,(
% 1.47/1.27 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.47/1.27 inference(primitive_instantiation,[status(thm)],[f22])).
% 1.47/1.27 thf(f22,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK3 @ X0) @ (sK2 @ X0))) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0)))) )),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f21])).
% 1.47/1.27 thf(f21,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: ($false)))) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))) | ($true != (X0 @ (sK3 @ X0) @ (sK2 @ X0)))) )),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f16])).
% 1.47/1.27 thf(f16,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) | ($true != (X0 @ (sK3 @ X0) @ (sK2 @ X0))) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0)))) )),
% 1.47/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.27 thf(f13,plain,(
% 1.47/1.27 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))) | (($true != (X0 @ (sK3 @ X0) @ (sK2 @ X0))) & ($true = (X0 @ (sK3 @ X0) @ (sK1 @ X0))) & ($true = (X0 @ (sK1 @ X0) @ (sK2 @ X0)))))),
% 1.47/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11])).
% 1.47/1.27 thf(f11,plain,(
% 1.47/1.27 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))))),
% 1.47/1.27 introduced(definition,[],[choice_axiom])).
% 1.47/1.27 thf(f12,plain,(
% 1.47/1.27 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (($true != (X0 @ X4 @ X3)) & ($true = (X0 @ X4 @ X2)) & ((X0 @ X2 @ X3) = $true)) => (($true != (X0 @ (sK3 @ X0) @ (sK2 @ X0))) & ($true = (X0 @ (sK3 @ X0) @ (sK1 @ X0))) & ($true = (X0 @ (sK1 @ X0) @ (sK2 @ X0)))))),
% 1.47/1.27 introduced(definition,[],[choice_axiom])).
% 1.47/1.27 thf(f10,plain,(
% 1.47/1.27 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (($true != (X0 @ X4 @ X3)) & ($true = (X0 @ X4 @ X2)) & ((X0 @ X2 @ X3) = $true)))),
% 1.47/1.27 inference(rectify,[status(thm)],[f9])).
% 1.47/1.27 thf(f9,plain,(
% 1.47/1.27 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) | ? [X4 : $i > $o] : ((X0 @ X4 @ X4) != $true) | ? [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) != $true) & ((X0 @ X2 @ X3) = $true) & ((X0 @ X3 @ X1) = $true)))),
% 1.47/1.27 inference(flattening,[status(thm)],[f8])).
% 1.47/1.27 thf(f8,plain,(
% 1.47/1.27 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) | ? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X2 @ X1) != $true) & (((X0 @ X3 @ X1) = $true) & ((X0 @ X2 @ X3) = $true))) | ? [X4 : $i > $o] : ((X0 @ X4 @ X4) != $true))),
% 1.47/1.27 inference(ennf_transformation,[status(thm)],[f7])).
% 1.47/1.27 thf(f7,plain,(
% 1.47/1.27 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) != $true) & ! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : ((((X0 @ X3 @ X1) = $true) & ((X0 @ X2 @ X3) = $true)) => ((X0 @ X2 @ X1) = $true)) & ! [X4 : $i > $o] : ((X0 @ X4 @ X4) = $true))),
% 1.47/1.27 inference(flattening,[status(thm)],[f6])).
% 1.47/1.27 thf(f6,plain,(
% 1.47/1.27 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (~((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) & ! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : ((((X0 @ X3 @ X1) = $true) & ((X0 @ X2 @ X3) = $true)) => ((X0 @ X2 @ X1) = $true)) & ! [X4 : $i > $o] : ((X0 @ X4 @ X4) = $true))),
% 1.47/1.27 inference(rectify,[status(thm)],[f5])).
% 1.47/1.27 thf(f5,plain,(
% 1.47/1.27 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (~((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) & ! [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : ((($true = (X0 @ X5 @ X3)) & ($true = (X0 @ X4 @ X5))) => ($true = (X0 @ X4 @ X3))) & ! [X6 : $i > $o] : ((X0 @ X6 @ X6) = $true))),
% 1.47/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.27 thf(f4,plain,(
% 1.47/1.27 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (~(X0 @ (^[X1 : $i] : (~cP | cP)) @ (^[X2 : $i] : (~cP & cP))) & ! [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X3) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X3)) & ! [X6 : $i > $o] : (X0 @ X6 @ X6))),
% 1.47/1.27 inference(rectify,[status(thm)],[f2])).
% 1.47/1.27 thf(f2,negated_conjecture,(
% 1.47/1.27 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (~(X0 @ (^[X1 : $i] : (~cP | cP)) @ (^[X1 : $i] : (~cP & cP))) & ! [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1))),
% 1.47/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.27 thf(f1,conjecture,(
% 1.47/1.27 ? [X0 : ($i > $o) > ($i > $o) > $o] : (~(X0 @ (^[X1 : $i] : (~cP | cP)) @ (^[X1 : $i] : (~cP & cP))) & ! [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1))),
% 1.47/1.27 file('/export/starexec/sandbox2/tmp/tmp.KNNgo5lwuG/DTF2THF_5021.p',cTHM120J_pme)).
% 1.47/1.27 thf(f132,plain,(
% 1.47/1.27 spl4_2 | spl4_6),
% 1.47/1.27 inference(avatar_split_clause,[status(thm)],[f90,f129,f53])).
% 1.47/1.27 thf(f90,plain,(
% 1.47/1.27 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.47/1.27 inference(equality_proxy_clausification,[status(thm)],[f89])).
% 1.47/1.27 thf(f89,plain,(
% 1.47/1.27 ($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.47/1.27 inference(equality_proxy_clausification,[status(thm)],[f88])).
% 1.47/1.27 thf(f88,plain,(
% 1.47/1.27 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.47/1.27 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.47/1.27 thf(f87,plain,(
% 1.47/1.27 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true != $true) | ($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f86])).
% 1.47/1.27 thf(f86,plain,(
% 1.47/1.27 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.47/1.27 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.47/1.27 thf(f66,plain,(
% 1.47/1.27 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))),
% 1.47/1.27 inference(primitive_instantiation,[status(thm)],[f20])).
% 1.47/1.27 thf(f20,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK1 @ X0) @ (sK2 @ X0))) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))) )),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f19])).
% 1.47/1.27 thf(f19,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK1 @ X0) @ (sK2 @ X0))) | ($true = (X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: ($false)))) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0)))) )),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f14])).
% 1.47/1.27 thf(f14,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) | ($true = (X0 @ (sK1 @ X0) @ (sK2 @ X0))) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0)))) )),
% 1.47/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.27 thf(f127,plain,(
% 1.47/1.27 ~spl4_2),
% 1.47/1.27 inference(avatar_contradiction_clause,[status(thm)],[f126])).
% 1.47/1.27 thf(f126,plain,(
% 1.47/1.27 $false | ~spl4_2),
% 1.47/1.27 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.47/1.27 thf(f125,plain,(
% 1.47/1.27 ($true = $false) | ~spl4_2),
% 1.47/1.27 inference(beta_eta_normalization,[status(thm)],[f124])).
% 1.47/1.27 thf(f124,plain,(
% 1.47/1.27 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X1) = ((^[Y0 : $i]: ($false)) @ X1))) ) | ~spl4_2),
% 1.47/1.27 inference(argument_congruence,[status(thm)],[f54])).
% 1.47/1.27 thf(f54,plain,(
% 1.47/1.27 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl4_2),
% 1.47/1.27 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.47/1.27 thf(f65,plain,(
% 1.47/1.27 spl4_4 | spl4_2),
% 1.47/1.27 inference(avatar_split_clause,[status(thm)],[f34,f53,f62])).
% 1.47/1.27 thf(f34,plain,(
% 1.47/1.27 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.47/1.27 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.47/1.27 thf(f33,plain,(
% 1.47/1.27 ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.47/1.27 inference(equality_proxy_clausification,[status(thm)],[f32])).
% 1.47/1.27 thf(f32,plain,(
% 1.47/1.27 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.47/1.27 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.47/1.27 thf(f31,plain,(
% 1.47/1.27 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true != $true) | ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f30])).
% 1.47/1.27 thf(f30,plain,(
% 1.47/1.27 ($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.47/1.27 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.47/1.27 thf(f23,plain,(
% 1.47/1.27 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.47/1.27 inference(primitive_instantiation,[status(thm)],[f18])).
% 1.47/1.27 thf(f18,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK3 @ X0) @ (sK1 @ X0))) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0)))) )),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f17])).
% 1.47/1.27 thf(f17,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))) | ($true = (X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: ($false)))) | ($true = (X0 @ (sK3 @ X0) @ (sK1 @ X0)))) )),
% 1.47/1.27 inference(boolean_simplification,[status(thm)],[f15])).
% 1.47/1.27 thf(f15,plain,(
% 1.47/1.27 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK3 @ X0) @ (sK1 @ X0))) | ((X0 @ (^[Y0 : $i]: (cP | (~ cP))) @ (^[Y0 : $i]: (cP & (~ cP)))) = $true) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0)))) )),
% 1.47/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.27 % SZS output end Proof for DTF2THF_5021
% 1.47/1.27 % (5301)------------------------------
% 1.47/1.27 % (5301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.27 % (5301)Termination reason: Refutation
% 1.47/1.27
% 1.47/1.27 % (5301)Memory used [KB]: 5500
% 1.47/1.27 % (5301)Time elapsed: 0.012 s
% 1.47/1.27 % (5301)Instructions burned: 11 (million)
% 1.47/1.27 % (5301)------------------------------
% 1.47/1.27 % (5301)------------------------------
% 1.47/1.27 % (5295)Success in time 0.027 s
%------------------------------------------------------------------------------