%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV082^5 : 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 : n002.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 1.11s 1.11s
% Output : Refutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 2 unt; 0 typ; 2 def)
% Number of atoms : 484 ( 198 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 416 ( 61 ~; 65 |; 33 &; 246 @)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 234 ( 234 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 261 ( 200 ^; 38 !; 23 ?; 261 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_5,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_6,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_7,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_9,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f129,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f51,f85,f128]) ).
thf(f128,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f127]) ).
thf(f127,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f126,f45]) ).
thf(f45,plain,
( ( ( ^ [Y0: $i] : $true )
!= ( ^ [Y0: $i] : $false ) )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl4_1
<=> ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f126,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f125,f111]) ).
thf(f111,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f99,f45]) ).
thf(f99,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ( $true
!= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true
!= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $true
!= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true != $true ) ),
inference(boolean_simplification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( $true
!= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $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 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f13,f12]) ).
thf(f12,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(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X4 @ X2 )
= $true )
& ( $true
= ( X0 @ X3 @ X4 ) ) )
=> ( ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X4 @ X2 )
= $true )
& ( $true
= ( X0 @ X3 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ? [X2: $i > $o,X4: $i > $o,X3: $i > $o] :
( ( ( X0 @ X4 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X2 )
= $true )
& ( $true
= ( X0 @ X4 @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( X0 @ X4 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X2 )
= $true )
& ( $true
= ( X0 @ X4 @ X3 ) ) )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
!= $true )
& ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( ( X0 @ X3 @ X2 )
= $true )
& ( $true
= ( X0 @ X4 @ X3 ) ) )
=> ( ( X0 @ X4 @ X2 )
= $true ) )
& ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true )
& ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
!= $true )
& ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( ( X0 @ X3 @ X2 )
= $true )
& ( $true
= ( X0 @ X4 @ X3 ) ) )
=> ( ( X0 @ X4 @ X2 )
= $true ) ) ),
inference(true_and_false_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( $false
| ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true )
& ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
!= $true )
& ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( ( X0 @ X3 @ X2 )
= $true )
& ( $true
= ( X0 @ X4 @ X3 ) ) )
=> ( ( X0 @ X4 @ X2 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( $false
| ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
= $true )
& ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
!= $true )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( ( X0 @ X6 @ X5 )
= $true )
& ( $true
= ( X0 @ X5 @ X4 ) ) )
=> ( ( X0 @ X6 @ X4 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( $false
| ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ~ ( X0
@ ^ [X2: $i] : $true
@ ^ [X3: $i] : $false )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X6 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X0 @ X6 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( $false
| ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false )
& ! [X3: $i > $o,X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( $false
| ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false )
& ! [X3: $i > $o,X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vNTgD7aOft/DTF2THF_3268.p',cTHM120_4_pme) ).
thf(f125,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 ) )
| ~ spl4_2 ),
inference(equality_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl4_2 ),
inference(equality_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $true != $true )
| ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ~ spl4_2 ),
inference(boolean_simplification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [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] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ~ spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [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 ) ) ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f16,f50]) ).
thf(f50,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl4_2
<=> ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f85,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $false
@ X1 )
= ( ^ [Y0: $i] : $true
@ X1 ) )
| ~ spl4_1 ),
inference(argument_congruence,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( ^ [Y0: $i] : $true )
= ( ^ [Y0: $i] : $false ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f51,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f36,f48,f44]) ).
thf(f36,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)],[f35]) ).
thf(f35,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true != $true )
| ( ( ( ^ [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 ) ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [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 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV082^5 : 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
% 0.13/0.32 % Computer : n002.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:40:03 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEV082^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.42 % Domain : Set Theory (Relations)
% 0.15/0.42 % Problem : TPS problem from RELN-THMS
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : tps_0872 [Bro09]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.25 v9.1.0, 0.12 v9.0.0, 0.25 v8.2.0, 0.27 v8.1.0, 0.42 v7.5.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.2.0, 0.25 v5.1.0, 0.50 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.15/0.42 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.15/0.42 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 3 ( 3 avg)
% 0.15/0.42 % Number of connectives : 16 ( 1 ~; 1 |; 3 &; 10 @)
% 0.15/0.42 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 12 ( 12 avg)
% 0.15/0.42 % Number of types : 2 ( 0 usr)
% 0.15/0.42 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 2 ( 0 usr; 2 con; 0-0 aty)
% 0.15/0.42 % Number of variables : 7 ( 2 ^; 4 !; 1 ?; 7 :)
% 0.15/0.42 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(cTHM120_4_pme,conjecture,
% 0.15/0.42 ( ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.15/0.42 ( ~ ( R
% 0.15/0.42 @ ^ [Xx: $i] : $true
% 0.15/0.42 @ ^ [Xx: $i] : $false )
% 0.15/0.42 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.15/0.42 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.15/0.42 ( ( ( R @ Xx @ Xy )
% 0.15/0.42 & ( R @ Xy @ Xz ) )
% 0.15/0.42 => ( R @ Xx @ Xz ) ) )
% 0.15/0.42 | $false ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.11/1.08 ---- Embedded in THF ---
% 1.11/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.11/1.08 %%% Generated on Tue Feb 24 12:40:04 EST 2026
% 1.11/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.11/1.08 %%% Logic specification used:
% 1.11/1.08 %%% thf(spec, logic, $$dhol).
% 1.11/1.08
% 1.11/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vNTgD7aOft/DTF2DTF3268.p
% See solution above
% 1.11/1.08 ------------------------
% 1.11/1.09 ---- Cleaned THF ---
% 1.11/1.09 thf(cTHM120_4_pme,conjecture,
% 1.11/1.09 ( ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.11/1.09 ( ~ ( R
% 1.11/1.09 @ ^ [Xx: $i] : $true
% 1.11/1.09 @ ^ [Xx: $i] : $false )
% 1.11/1.09 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 1.11/1.09 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.11/1.09 ( ( ( R @ Xx @ Xy )
% 1.11/1.09 & ( R @ Xy @ Xz ) )
% 1.11/1.09 => ( R @ Xx @ Xz ) ) )
% 1.11/1.09 | $false ) ).
% 1.11/1.09 ------------------------
% 1.11/1.10 % (3378)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_3268 for (3000ds/275Mi)
% 1.11/1.10 % (3379)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3268 for (3000ds/18Mi)
% 1.11/1.10 % (3374)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_3268 for (3000ds/4Mi)
% 1.11/1.10 % (3375)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_3268 for (3000ds/27Mi)
% 1.11/1.10 % (3377)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_3268 for (3000ds/2Mi)
% 1.11/1.10 % (3376)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3268 for (3000ds/2Mi)
% 1.11/1.10 % (3373)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3268 for (3000ds/183Mi)
% 1.11/1.10 % (3375)Refutation not found, incomplete strategy
% 1.11/1.10 % (3375)------------------------------
% 1.11/1.10 % (3375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.10 % (3375)Termination reason: Refutation not found, incomplete strategy
% 1.11/1.10
% 1.11/1.10
% 1.11/1.10 % (3375)Memory used [KB]: 5500
% 1.11/1.10 % (3375)Time elapsed: 0.002 s
% 1.11/1.10 % (3375)Instructions burned: 1 (million)
% 1.11/1.10 % (3375)------------------------------
% 1.11/1.10 % (3375)------------------------------
% 1.11/1.10 % (3376)Instruction limit reached!
% 1.11/1.10 % (3376)------------------------------
% 1.11/1.10 % (3376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.10 % (3376)Termination reason: Unknown
% 1.11/1.10 % (3376)Termination phase: Saturation
% 1.11/1.10
% 1.11/1.10 % (3376)Memory used [KB]: 5500
% 1.11/1.10 % (3376)Time elapsed: 0.003 s
% 1.11/1.10 % (3376)Instructions burned: 3 (million)
% 1.11/1.10 % (3376)------------------------------
% 1.11/1.10 % (3376)------------------------------
% 1.11/1.10 % (3377)Instruction limit reached!
% 1.11/1.10 % (3377)------------------------------
% 1.11/1.10 % (3377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.10 % (3377)Termination reason: Unknown
% 1.11/1.10 % (3377)Termination phase: Saturation
% 1.11/1.10
% 1.11/1.10 % (3377)Memory used [KB]: 5500
% 1.11/1.10 % (3377)Time elapsed: 0.003 s
% 1.11/1.10 % (3377)Instructions burned: 3 (million)
% 1.11/1.10 % (3377)------------------------------
% 1.11/1.10 % (3377)------------------------------
% 1.11/1.11 % (3374)Instruction limit reached!
% 1.11/1.11 % (3374)------------------------------
% 1.11/1.11 % (3374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.11 % (3374)Termination reason: Unknown
% 1.11/1.11 % (3374)Termination phase: Saturation
% 1.11/1.11
% 1.11/1.11 % (3374)Memory used [KB]: 5500
% 1.11/1.11 % (3374)Time elapsed: 0.004 s
% 1.11/1.11 % (3374)Instructions burned: 6 (million)
% 1.11/1.11 % (3374)------------------------------
% 1.11/1.11 % (3374)------------------------------
% 1.11/1.11 % (3378)First to succeed.
% 1.11/1.11 % (3378)Refutation found. Thanks to Tanya!
% 1.11/1.11 % SZS status Theorem for DTF2THF_3268
% 1.11/1.11 % SZS output start Proof for DTF2THF_3268
% 1.11/1.11 thf(func_def_4, type, sK0: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.11/1.11 thf(func_def_5, type, sK1: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.11/1.11 thf(func_def_6, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.11/1.11 thf(func_def_7, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.11/1.11 thf(func_def_9, type, ph5: !>[X0: $tType]:(X0)).
% 1.11/1.11 thf(f129,plain,(
% 1.11/1.11 $false),
% 1.11/1.11 inference(avatar_sat_refutation,[status(thm)],[f51,f85,f128])).
% 1.11/1.11 thf(f128,plain,(
% 1.11/1.11 spl4_1 | ~spl4_2),
% 1.11/1.11 inference(avatar_contradiction_clause,[status(thm)],[f127])).
% 1.11/1.11 thf(f127,plain,(
% 1.11/1.11 $false | (spl4_1 | ~spl4_2)),
% 1.11/1.11 inference(subsumption_resolution,[status(thm)],[f126,f45])).
% 1.11/1.11 thf(f45,plain,(
% 1.11/1.11 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl4_1),
% 1.11/1.11 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.11/1.11 thf(f44,definition,(
% 1.11/1.11 spl4_1 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.11/1.11 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.11/1.11 thf(f126,plain,(
% 1.11/1.11 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (spl4_1 | ~spl4_2)),
% 1.11/1.11 inference(subsumption_resolution,[status(thm)],[f125,f111])).
% 1.11/1.11 thf(f111,plain,(
% 1.11/1.11 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | spl4_1),
% 1.11/1.11 inference(subsumption_resolution,[status(thm)],[f99,f45])).
% 1.11/1.11 thf(f99,plain,(
% 1.11/1.11 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.11/1.11 inference(equality_proxy_clausification,[status(thm)],[f98])).
% 1.11/1.11 thf(f98,plain,(
% 1.11/1.11 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.11/1.11 inference(equality_proxy_clausification,[status(thm)],[f97])).
% 1.11/1.11 thf(f97,plain,(
% 1.11/1.11 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.11/1.11 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.11/1.11 thf(f96,plain,(
% 1.11/1.11 ($true != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true != $true)),
% 1.11/1.11 inference(boolean_simplification,[status(thm)],[f95])).
% 1.11/1.11 thf(f95,plain,(
% 1.11/1.11 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true != ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.11/1.11 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.11/1.11 thf(f86,plain,(
% 1.11/1.11 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.11/1.11 inference(primitive_instantiation,[status(thm)],[f17])).
% 1.11/1.11 thf(f17,plain,(
% 1.11/1.11 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ((X0 @ (sK2 @ X0) @ (sK1 @ X0)) != $true)) )),
% 1.11/1.11 inference(cnf_transformation,[status(thm)],[f14])).
% 1.11/1.11 thf(f14,plain,(
% 1.11/1.11 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))) | (((X0 @ (sK2 @ X0) @ (sK1 @ X0)) != $true) & ((X0 @ (sK3 @ X0) @ (sK1 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true)))),
% 1.11/1.11 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f13,f12])).
% 1.11/1.11 thf(f12,plain,(
% 1.11/1.11 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))))),
% 1.11/1.11 introduced(definition,[],[choice_axiom])).
% 1.11/1.11 thf(f13,plain,(
% 1.11/1.11 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (((X0 @ X3 @ X2) != $true) & ((X0 @ X4 @ X2) = $true) & ($true = (X0 @ X3 @ X4))) => (((X0 @ (sK2 @ X0) @ (sK1 @ X0)) != $true) & ((X0 @ (sK3 @ X0) @ (sK1 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true)))),
% 1.11/1.11 introduced(definition,[],[choice_axiom])).
% 1.11/1.11 thf(f11,plain,(
% 1.11/1.11 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (((X0 @ X3 @ X2) != $true) & ((X0 @ X4 @ X2) = $true) & ($true = (X0 @ X3 @ X4))))),
% 1.11/1.11 inference(rectify,[status(thm)],[f10])).
% 1.11/1.11 thf(f10,plain,(
% 1.11/1.11 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ? [X2 : $i > $o,X4 : $i > $o,X3 : $i > $o] : (((X0 @ X4 @ X2) != $true) & ((X0 @ X3 @ X2) = $true) & ($true = (X0 @ X4 @ X3))))),
% 1.11/1.11 inference(flattening,[status(thm)],[f9])).
% 1.11/1.11 thf(f9,plain,(
% 1.11/1.11 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (((X0 @ X4 @ X2) != $true) & (((X0 @ X3 @ X2) = $true) & ($true = (X0 @ X4 @ X3)))) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true))),
% 1.11/1.11 inference(ennf_transformation,[status(thm)],[f8])).
% 1.11/1.11 thf(f8,plain,(
% 1.11/1.11 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) != $true) & ! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : ((((X0 @ X3 @ X2) = $true) & ($true = (X0 @ X4 @ X3))) => ((X0 @ X4 @ X2) = $true)) & ! [X1 : $i > $o] : ((X0 @ X1 @ X1) = $true))),
% 1.11/1.11 inference(flattening,[status(thm)],[f7])).
% 1.11/1.11 thf(f7,plain,(
% 1.11/1.11 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : ((X0 @ X1 @ X1) = $true) & ~((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) & ! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : ((((X0 @ X3 @ X2) = $true) & ($true = (X0 @ X4 @ X3))) => ((X0 @ X4 @ X2) = $true)))),
% 1.11/1.11 inference(true_and_false_elimination,[status(thm)],[f6])).
% 1.11/1.11 thf(f6,plain,(
% 1.11/1.11 ~($false | ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : ((X0 @ X1 @ X1) = $true) & ~((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) & ! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : ((((X0 @ X3 @ X2) = $true) & ($true = (X0 @ X4 @ X3))) => ((X0 @ X4 @ X2) = $true))))),
% 1.11/1.11 inference(rectify,[status(thm)],[f5])).
% 1.11/1.11 thf(f5,plain,(
% 1.11/1.11 ~($false | ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : ((X0 @ X1 @ X1) = $true) & ~((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : ((((X0 @ X6 @ X5) = $true) & ($true = (X0 @ X5 @ X4))) => ((X0 @ X6 @ X4) = $true))))),
% 1.11/1.11 inference(fool_elimination,[status(thm)],[f4])).
% 1.11/1.11 thf(f4,plain,(
% 1.11/1.11 ~($false | ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : (X0 @ X1 @ X1) & ~(X0 @ (^[X2 : $i] : ($true)) @ (^[X3 : $i] : ($false))) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (((X0 @ X6 @ X5) & (X0 @ X5 @ X4)) => (X0 @ X6 @ X4))))),
% 1.11/1.11 inference(rectify,[status(thm)],[f2])).
% 1.11/1.11 thf(f2,negated_conjecture,(
% 1.11/1.11 ~($false | ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : (X0 @ X1 @ X1) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))) & ! [X3 : $i > $o,X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3))))),
% 1.11/1.11 inference(negated_conjecture,[status(cth)],[f1])).
% 1.11/1.11 thf(f1,conjecture,(
% 1.11/1.11 $false | ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : (X0 @ X1 @ X1) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))) & ! [X3 : $i > $o,X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))),
% 1.11/1.11 file('/export/starexec/sandbox/tmp/tmp.vNTgD7aOft/DTF2THF_3268.p',cTHM120_4_pme)).
% 1.11/1.11 thf(f125,plain,(
% 1.11/1.11 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl4_2),
% 1.11/1.11 inference(equality_proxy_clausification,[status(thm)],[f124])).
% 1.11/1.11 thf(f124,plain,(
% 1.11/1.11 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl4_2),
% 1.11/1.11 inference(equality_proxy_clausification,[status(thm)],[f123])).
% 1.11/1.11 thf(f123,plain,(
% 1.11/1.11 ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ~spl4_2),
% 1.11/1.11 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.11/1.11 thf(f122,plain,(
% 1.11/1.11 ($true != $true) | ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ~spl4_2),
% 1.11/1.11 inference(boolean_simplification,[status(thm)],[f121])).
% 1.11/1.11 thf(f121,plain,(
% 1.11/1.11 ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[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 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ~spl4_2),
% 1.11/1.11 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.11/1.11 thf(f116,plain,(
% 1.11/1.11 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[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))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ~spl4_2),
% 1.11/1.11 inference(superposition,[status(thm)],[f16,f50])).
% 1.11/1.11 thf(f50,plain,(
% 1.11/1.11 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl4_2),
% 1.11/1.11 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.11/1.11 thf(f48,definition,(
% 1.11/1.11 spl4_2 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.11/1.11 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.11/1.11 thf(f16,plain,(
% 1.11/1.11 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK3 @ X0) @ (sK1 @ X0)) = $true) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true)) )),
% 1.11/1.11 inference(cnf_transformation,[status(thm)],[f14])).
% 1.11/1.11 thf(f85,plain,(
% 1.11/1.11 ~spl4_1),
% 1.11/1.11 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.11/1.11 thf(f84,plain,(
% 1.11/1.11 $false | ~spl4_1),
% 1.11/1.11 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.11/1.11 thf(f83,plain,(
% 1.11/1.11 ($false = $true) | ~spl4_1),
% 1.11/1.11 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.11/1.11 thf(f82,plain,(
% 1.11/1.11 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X1) = ((^[Y0 : $i]: ($true)) @ X1))) ) | ~spl4_1),
% 1.11/1.11 inference(argument_congruence,[status(thm)],[f46])).
% 1.11/1.11 thf(f46,plain,(
% 1.11/1.11 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl4_1),
% 1.11/1.11 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.11/1.11 thf(f51,plain,(
% 1.11/1.11 spl4_1 | spl4_2),
% 1.11/1.11 inference(avatar_split_clause,[status(thm)],[f36,f48,f44])).
% 1.11/1.11 thf(f36,plain,(
% 1.11/1.11 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 1.11/1.11 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.11/1.11 thf(f35,plain,(
% 1.11/1.11 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 1.11/1.11 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.11/1.11 thf(f34,plain,(
% 1.11/1.11 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 1.11/1.11 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.11/1.11 thf(f33,plain,(
% 1.11/1.11 ($true != $true) | (((^[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)))))) = $true)),
% 1.11/1.11 inference(boolean_simplification,[status(thm)],[f32])).
% 1.11/1.11 thf(f32,plain,(
% 1.11/1.11 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true)),
% 1.11/1.11 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.11/1.11 thf(f18,plain,(
% 1.11/1.11 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[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 > $o]: (Y1 = Y0)))))))),
% 1.11/1.11 inference(primitive_instantiation,[status(thm)],[f15])).
% 1.11/1.11 thf(f15,plain,(
% 1.11/1.11 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0)))) )),
% 1.11/1.11 inference(cnf_transformation,[status(thm)],[f14])).
% 1.11/1.11 % SZS output end Proof for DTF2THF_3268
% 1.11/1.11 % (3378)------------------------------
% 1.11/1.11 % (3378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.11 % (3378)Termination reason: Refutation
% 1.11/1.11
% 1.11/1.11 % (3378)Memory used [KB]: 5500
% 1.11/1.11 % (3378)Time elapsed: 0.007 s
% 1.11/1.11 % (3378)Instructions burned: 10 (million)
% 1.11/1.11 % (3378)------------------------------
% 1.11/1.11 % (3378)------------------------------
% 1.11/1.11 % (3371)Success in time 0.014 s
%------------------------------------------------------------------------------