%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV052^5 : 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 : n016.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 09:40:10 AM UTC 2026
% Result : Theorem 1.59s 1.38s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 2 unt; 0 typ; 5 def)
% Number of atoms : 423 ( 169 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 411 ( 69 ~; 53 |; 34 &; 242 @)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 241 ( 241 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 219 ( 150 ^; 40 !; 29 ?; 219 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sP0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $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_8,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_10,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f88,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f52,f70,f75,f80,f81,f87]) ).
thf(f87,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $false = $true )
| ~ spl5_1 ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $true
@ X1 )
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ~ spl5_1 ),
inference(argument_congruence,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl5_1
<=> ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f81,plain,
( ( ( sK2
@ ^ [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 ) )
!= ( sK3
@ ^ [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 ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f80,plain,
( ~ spl5_5
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f59,f49,f77]) ).
thf(f77,definition,
( spl5_5
<=> ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f49,definition,
( spl5_2
<=> ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f59,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl5_2 ),
inference(equality_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ~ spl5_2 ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ^ [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 )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true != $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 )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f19,f51]) ).
thf(f51,plain,
( ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f19,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
!= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
!= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f13,f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X2 @ X1 )
!= $true ) )
=> ( ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X2 @ X1 )
!= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X1 @ X3 )
!= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X1 @ X3 )
!= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f75,plain,
( spl5_4
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f62,f49,f72]) ).
thf(f72,definition,
( spl5_4
<=> ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f62,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl5_2 ),
inference(equality_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl5_2 ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( ^ [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 )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $true != $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 )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f20,f51]) ).
thf(f20,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f70,plain,
( spl5_3
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f65,f49,f67]) ).
thf(f67,definition,
( spl5_3
<=> ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f65,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl5_2 ),
inference(equality_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl5_2 ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( ^ [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 )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( ^ [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 )
| ( $true != $true )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f21,f51]) ).
thf(f21,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f52,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f49,f45]) ).
thf(f34,plain,
( ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $true != $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK4 @ X0 ) @ ( sK4 @ X0 ) )
!= $true )
| ( ( sP0 @ X0 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( sP0 @ X0 )
= $true )
| ( ( X0 @ ( sK4 @ X0 ) @ ( sK4 @ X0 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f16,f17]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
=> ( ( X0 @ ( sK4 @ X0 ) @ ( sK4 @ X0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( sP0 @ X0 )
= $true )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ( ( sP0 @ X0 )
= $true )
| ? [X4: $i > $o] :
( ( X0 @ X4 @ X4 )
!= $true ) ),
inference(definition_folding,[status(thm)],[f9,f10]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true )
| ? [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X1 @ X3 )
!= $true ) )
| ? [X4: $i > $o] :
( ( X0 @ X4 @ X4 )
!= $true ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X4: $i > $o] :
( ( X0 @ X4 @ X4 )
!= $true )
| ? [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 @ X3 )
!= $true )
& ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X4: $i > $o] :
( ( X0 @ X4 @ X4 )
= $true )
& ! [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) )
=> ( ( X0 @ X1 @ X3 )
= $true ) )
& ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false )
!= $true )
& ! [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( ( X0 @ X2 @ X3 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) )
=> ( ( X0 @ X1 @ X3 )
= $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] : $true
@ ^ [Y0: $i] : $false )
!= $true )
& ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ( ( X0 @ X3 @ X4 )
= $true )
& ( $true
= ( X0 @ X4 @ X5 ) ) )
=> ( ( X0 @ X3 @ X5 )
= $true ) )
& ! [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] : $true
@ ^ [X2: $i] : $false )
& ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X3 @ X5 ) )
& ! [X6: $i > $o] : ( X0 @ X6 @ X6 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( X0
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $false )
& ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( 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] : $true
@ ^ [X1: $i] : $false )
& ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.Bl9oTMKEeS/DTF2THF_20067.p',cTHM120B_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV052^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:39:51 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SEV052^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.47 % Domain : Set Theory (Relations)
% 0.29/0.47 % Problem : TPS problem THM120B
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : tps_0251 [Bro09]
% 0.29/0.47 % : THM120B [TPS]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % 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 v5.3.0, 0.25 v5.2.0, 0.50 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.29/0.47 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.29/0.47 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.29/0.47 % Number of connectives : 15 ( 1 ~; 0 |; 3 &; 10 @)
% 0.29/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 11 ( 11 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 2 ( 0 usr; 2 con; 0-0 aty)
% 0.29/0.47 % Number of variables : 7 ( 2 ^; 4 !; 1 ?; 7 :)
% 0.29/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.47 % : Polymorphic definitions expanded.
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(cTHM120B_pme,conjecture,
% 0.29/0.47 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.29/0.47 ( ~ ( R
% 0.29/0.47 @ ^ [Xx: $i] : $true
% 0.29/0.47 @ ^ [Xx: $i] : $false )
% 0.29/0.47 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.29/0.47 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.29/0.47 ( ( ( R @ Xx @ Xy )
% 0.29/0.47 & ( R @ Xy @ Xz ) )
% 0.29/0.47 => ( R @ Xx @ Xz ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.59/1.34 ---- Embedded in THF ---
% 1.59/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.34 %%% Generated on Tue Feb 24 12:39:52 EST 2026
% 1.59/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.34 %%% Logic specification used:
% 1.59/1.34 %%% thf(spec, logic, $$dhol).
% 1.59/1.34
% 1.59/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Bl9oTMKEeS/DTF2DTF20067.p
% See solution above
% 1.59/1.34 ------------------------
% 1.59/1.35 ---- Cleaned THF ---
% 1.59/1.35 thf(cTHM120B_pme,conjecture,
% 1.59/1.35 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.59/1.35 ( ~ ( R
% 1.59/1.35 @ ^ [Xx: $i] : $true
% 1.59/1.35 @ ^ [Xx: $i] : $false )
% 1.59/1.35 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 1.59/1.35 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.59/1.35 ( ( ( R @ Xx @ Xy )
% 1.59/1.35 & ( R @ Xy @ Xz ) )
% 1.59/1.35 => ( R @ Xx @ Xz ) ) ) ).
% 1.59/1.35 ------------------------
% 1.59/1.36 % (20351)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_20067 for (2999ds/4Mi)
% 1.59/1.36 % (20353)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20067 for (2999ds/2Mi)
% 1.59/1.36 % (20354)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_20067 for (2999ds/2Mi)
% 1.59/1.36 % (20353)Instruction limit reached!
% 1.59/1.36 % (20353)------------------------------
% 1.59/1.36 % (20353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (20353)Termination reason: Unknown
% 1.59/1.36 % (20353)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (20353)Memory used [KB]: 5500
% 1.59/1.36 % (20353)Time elapsed: 0.002 s
% 1.59/1.36 % (20353)Instructions burned: 2 (million)
% 1.59/1.36 % (20353)------------------------------
% 1.59/1.36 % (20353)------------------------------
% 1.59/1.36 % (20354)Instruction limit reached!
% 1.59/1.36 % (20354)------------------------------
% 1.59/1.36 % (20354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (20354)Termination reason: Unknown
% 1.59/1.36 % (20354)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (20354)Memory used [KB]: 5500
% 1.59/1.36 % (20354)Time elapsed: 0.002 s
% 1.59/1.36 % (20354)Instructions burned: 2 (million)
% 1.59/1.36 % (20354)------------------------------
% 1.59/1.36 % (20354)------------------------------
% 1.59/1.37 % (20351)Instruction limit reached!
% 1.59/1.37 % (20351)------------------------------
% 1.59/1.37 % (20351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (20351)Termination reason: Unknown
% 1.59/1.37 % (20351)Termination phase: Saturation
% 1.59/1.37
% 1.59/1.37 % (20351)Memory used [KB]: 5500
% 1.59/1.37 % (20351)Time elapsed: 0.003 s
% 1.59/1.37 % (20351)Instructions burned: 5 (million)
% 1.59/1.37 % (20351)------------------------------
% 1.59/1.37 % (20351)------------------------------
% 1.59/1.37 % (20350)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20067 for (2999ds/183Mi)
% 1.59/1.37 % (20352)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_20067 for (2999ds/27Mi)
% 1.59/1.37 % (20355)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_20067 for (2999ds/275Mi)
% 1.59/1.37 % (20356)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20067 for (2999ds/18Mi)
% 1.59/1.37 % (20352)Refutation not found, incomplete strategy
% 1.59/1.37 % (20352)------------------------------
% 1.59/1.37 % (20352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (20352)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.37
% 1.59/1.37
% 1.59/1.37 % (20352)Memory used [KB]: 5500
% 1.59/1.37 % (20352)Time elapsed: 0.004 s
% 1.59/1.37 % (20352)Instructions burned: 2 (million)
% 1.59/1.37 % (20352)------------------------------
% 1.59/1.37 % (20352)------------------------------
% 1.59/1.38 % (20357)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20067 for (2999ds/3Mi)
% 1.59/1.38 % (20358)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_20067 for (2999ds/37Mi)
% 1.59/1.38 % (20359)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_20067 for (2999ds/15Mi)
% 1.59/1.38 % (20357)Instruction limit reached!
% 1.59/1.38 % (20357)------------------------------
% 1.59/1.38 % (20357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (20357)Termination reason: Unknown
% 1.59/1.38 % (20357)Termination phase: Saturation
% 1.59/1.38
% 1.59/1.38 % (20357)Memory used [KB]: 5500
% 1.59/1.38 % (20357)Time elapsed: 0.003 s
% 1.59/1.38 % (20357)Instructions burned: 3 (million)
% 1.59/1.38 % (20357)------------------------------
% 1.59/1.38 % (20357)------------------------------
% 1.59/1.38 % (20359)First to succeed.
% 1.59/1.38 % (20355)Also succeeded, but the first one will report.
% 1.59/1.38 % (20359)Refutation found. Thanks to Tanya!
% 1.59/1.38 % SZS status Theorem for DTF2THF_20067
% 1.59/1.38 % SZS output start Proof for DTF2THF_20067
% 1.59/1.38 thf(func_def_4, type, sP0: (($i > $o) > ($i > $o) > $o) > $o).
% 1.59/1.38 thf(func_def_5, type, sK1: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.59/1.38 thf(func_def_6, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.59/1.38 thf(func_def_7, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.59/1.38 thf(func_def_8, type, sK4: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.59/1.38 thf(func_def_10, type, ph6: !>[X0: $tType]:(X0)).
% 1.59/1.38 thf(f88,plain,(
% 1.59/1.38 $false),
% 1.59/1.38 inference(avatar_sat_refutation,[status(thm)],[f52,f70,f75,f80,f81,f87])).
% 1.59/1.38 thf(f87,plain,(
% 1.59/1.38 ~spl5_1),
% 1.59/1.38 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.59/1.38 thf(f86,plain,(
% 1.59/1.38 $false | ~spl5_1),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.59/1.38 thf(f85,plain,(
% 1.59/1.38 ($false = $true) | ~spl5_1),
% 1.59/1.38 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.59/1.38 thf(f84,plain,(
% 1.59/1.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X1) = ((^[Y0 : $i]: ($false)) @ X1))) ) | ~spl5_1),
% 1.59/1.38 inference(argument_congruence,[status(thm)],[f47])).
% 1.59/1.38 thf(f47,plain,(
% 1.59/1.38 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl5_1),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.59/1.38 thf(f45,definition,(
% 1.59/1.38 spl5_1 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.59/1.38 thf(f81,plain,(
% 1.59/1.38 ((sK2 @ (^[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))))) != (sK3 @ (^[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))))))),
% 1.59/1.38 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.59/1.38 thf(f80,plain,(
% 1.59/1.38 ~spl5_5 | ~spl5_2),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f59,f49,f77])).
% 1.59/1.38 thf(f77,definition,(
% 1.59/1.38 spl5_5 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.59/1.38 thf(f49,definition,(
% 1.59/1.38 spl5_2 <=> ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.59/1.38 thf(f59,plain,(
% 1.59/1.38 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl5_2),
% 1.59/1.38 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 1.59/1.38 thf(f58,plain,(
% 1.59/1.38 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl5_2),
% 1.59/1.38 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.59/1.38 thf(f57,plain,(
% 1.59/1.38 (((^[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)))))) != $true) | ~spl5_2),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.59/1.38 thf(f55,plain,(
% 1.59/1.38 ($true != $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) | ~spl5_2),
% 1.59/1.38 inference(superposition,[status(thm)],[f19,f51])).
% 1.59/1.38 thf(f51,plain,(
% 1.59/1.38 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ~spl5_2),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.59/1.38 thf(f19,plain,(
% 1.59/1.38 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK2 @ X0) @ (sK1 @ X0)) != $true) | ((sP0 @ X0) != $true)) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f15])).
% 1.59/1.38 thf(f15,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK3 @ X0) @ (sK1 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK1 @ X0)) != $true)) | ((sP0 @ X0) != $true))),
% 1.59/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f13,f14])).
% 1.59/1.38 thf(f14,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X1) = $true) & ((X0 @ X2 @ X3) = $true) & ((X0 @ X2 @ X1) != $true)) => (((X0 @ (sK3 @ X0) @ (sK1 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK1 @ X0)) != $true)))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f13,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X1) = $true) & ((X0 @ X2 @ X3) = $true) & ((X0 @ X2 @ X1) != $true)) | ((sP0 @ X0) != $true))),
% 1.59/1.38 inference(rectify,[status(thm)],[f12])).
% 1.59/1.38 thf(f12,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X3) != $true)) | ((sP0 @ X0) != $true))),
% 1.59/1.38 inference(nnf_transformation,[status(thm)],[f10])).
% 1.59/1.38 thf(f10,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X3) != $true)) | ~((sP0 @ X0) = $true))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.59/1.38 thf(f75,plain,(
% 1.59/1.38 spl5_4 | ~spl5_2),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f62,f49,f72])).
% 1.59/1.38 thf(f72,definition,(
% 1.59/1.38 spl5_4 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.59/1.38 thf(f62,plain,(
% 1.59/1.38 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl5_2),
% 1.59/1.38 inference(equality_proxy_clausification,[status(thm)],[f61])).
% 1.59/1.38 thf(f61,plain,(
% 1.59/1.38 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl5_2),
% 1.59/1.38 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.59/1.38 thf(f60,plain,(
% 1.59/1.38 (((^[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)))))) = $true) | ~spl5_2),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.59/1.38 thf(f54,plain,(
% 1.59/1.38 ($true != $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)))))) = $true) | ~spl5_2),
% 1.59/1.38 inference(superposition,[status(thm)],[f20,f51])).
% 1.59/1.38 thf(f20,plain,(
% 1.59/1.38 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f15])).
% 1.59/1.38 thf(f70,plain,(
% 1.59/1.38 spl5_3 | ~spl5_2),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f65,f49,f67])).
% 1.59/1.38 thf(f67,definition,(
% 1.59/1.38 spl5_3 <=> ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.59/1.38 thf(f65,plain,(
% 1.59/1.38 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl5_2),
% 1.59/1.38 inference(equality_proxy_clausification,[status(thm)],[f64])).
% 1.59/1.38 thf(f64,plain,(
% 1.59/1.38 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl5_2),
% 1.59/1.38 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.59/1.38 thf(f63,plain,(
% 1.59/1.38 (((^[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) | ~spl5_2),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.59/1.38 thf(f56,plain,(
% 1.59/1.38 (((^[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)))))) = $true) | ($true != $true) | ~spl5_2),
% 1.59/1.38 inference(superposition,[status(thm)],[f21,f51])).
% 1.59/1.38 thf(f21,plain,(
% 1.59/1.38 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK3 @ X0) @ (sK1 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f15])).
% 1.59/1.38 thf(f52,plain,(
% 1.59/1.38 spl5_1 | spl5_2),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f34,f49,f45])).
% 1.59/1.38 thf(f34,plain,(
% 1.59/1.38 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 1.59/1.38 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.59/1.38 thf(f33,plain,(
% 1.59/1.38 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.59/1.38 thf(f32,plain,(
% 1.59/1.38 ($true != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)),
% 1.59/1.38 inference(boolean_simplification,[status(thm)],[f31])).
% 1.59/1.38 thf(f31,plain,(
% 1.59/1.38 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)),
% 1.59/1.38 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.59/1.38 thf(f24,plain,(
% 1.59/1.38 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true)),
% 1.59/1.38 inference(primitive_instantiation,[status(thm)],[f22])).
% 1.59/1.38 thf(f22,plain,(
% 1.59/1.38 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK4 @ X0) @ (sK4 @ X0)) != $true) | ((sP0 @ X0) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true)) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f18])).
% 1.59/1.38 thf(f18,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ((sP0 @ X0) = $true) | ((X0 @ (sK4 @ X0) @ (sK4 @ X0)) != $true))),
% 1.59/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f16,f17])).
% 1.59/1.38 thf(f17,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ((X0 @ (sK4 @ X0) @ (sK4 @ X0)) != $true))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f16,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ((sP0 @ X0) = $true) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true))),
% 1.59/1.38 inference(rectify,[status(thm)],[f11])).
% 1.59/1.38 thf(f11,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ((sP0 @ X0) = $true) | ? [X4 : $i > $o] : ((X0 @ X4 @ X4) != $true))),
% 1.59/1.38 inference(definition_folding,[status(thm)],[f9,f10])).
% 1.59/1.38 thf(f9,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) | ? [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X3) != $true)) | ? [X4 : $i > $o] : ((X0 @ X4 @ X4) != $true))),
% 1.59/1.38 inference(flattening,[status(thm)],[f8])).
% 1.59/1.38 thf(f8,plain,(
% 1.59/1.38 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X4 : $i > $o] : ((X0 @ X4 @ X4) != $true) | ? [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1 @ X3) != $true) & (((X0 @ X2 @ X3) = $true) & ((X0 @ X1 @ X2) = $true))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true))),
% 1.59/1.38 inference(ennf_transformation,[status(thm)],[f7])).
% 1.59/1.38 thf(f7,plain,(
% 1.59/1.38 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X4 : $i > $o] : ((X0 @ X4 @ X4) = $true) & ! [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : ((((X0 @ X2 @ X3) = $true) & ((X0 @ X1 @ X2) = $true)) => ((X0 @ X1 @ X3) = $true)) & ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) != $true))),
% 1.59/1.38 inference(flattening,[status(thm)],[f6])).
% 1.59/1.38 thf(f6,plain,(
% 1.59/1.38 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (~((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) & ! [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : ((((X0 @ X2 @ X3) = $true) & ((X0 @ X1 @ X2) = $true)) => ((X0 @ X1 @ X3) = $true)) & ! [X4 : $i > $o] : ((X0 @ X4 @ X4) = $true))),
% 1.59/1.38 inference(rectify,[status(thm)],[f5])).
% 1.59/1.38 thf(f5,plain,(
% 1.59/1.38 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (~((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))) = $true) & ! [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : ((((X0 @ X3 @ X4) = $true) & ($true = (X0 @ X4 @ X5))) => ((X0 @ X3 @ X5) = $true)) & ! [X6 : $i > $o] : ((X0 @ X6 @ X6) = $true))),
% 1.59/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.59/1.38 thf(f4,plain,(
% 1.59/1.38 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (~(X0 @ (^[X1 : $i] : ($true)) @ (^[X2 : $i] : ($false))) & ! [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)) & ! [X6 : $i > $o] : (X0 @ X6 @ X6))),
% 1.59/1.38 inference(rectify,[status(thm)],[f2])).
% 1.59/1.38 thf(f2,negated_conjecture,(
% 1.59/1.38 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))) & ! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1))),
% 1.59/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.38 thf(f1,conjecture,(
% 1.59/1.38 ? [X0 : ($i > $o) > ($i > $o) > $o] : (~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))) & ! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1))),
% 1.59/1.38 file('/export/starexec/sandbox/tmp/tmp.Bl9oTMKEeS/DTF2THF_20067.p',cTHM120B_pme)).
% 1.59/1.38 % SZS output end Proof for DTF2THF_20067
% 1.59/1.38 % (20359)------------------------------
% 1.59/1.38 % (20359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (20359)Termination reason: Refutation
% 1.59/1.38
% 1.59/1.38 % (20359)Memory used [KB]: 5628
% 1.59/1.38 % (20359)Time elapsed: 0.005 s
% 1.59/1.38 % (20359)Instructions burned: 6 (million)
% 1.59/1.38 % (20359)------------------------------
% 1.59/1.38 % (20359)------------------------------
% 1.59/1.38 % (20349)Success in time 0.024 s
%------------------------------------------------------------------------------