%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU875^5 : 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 : n005.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 09:37:38 AM UTC 2026
% Result : Theorem 1.71s 1.55s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 17
% Syntax : Number of formulae : 123 ( 1 unt; 0 typ; 9 def)
% Number of atoms : 1725 ( 671 equ; 28 cnn)
% Maximal formula atoms : 20 ( 14 avg)
% Number of connectives : 1920 ( 394 ~; 596 |; 114 &; 762 @)
% ( 9 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 147 ( 147 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 413 ( 183 ^; 193 !; 37 ?; 413 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
t: a ).
thf(func_def_2,type,
cA: ( a > $o ) > $o ).
thf(func_def_10,type,
sP0: ( a > $o ) > $o ).
thf(func_def_12,type,
sK2: a > $o ).
thf(func_def_13,type,
sK3: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_14,type,
sK4: ( a > $o ) > a ).
thf(func_def_15,type,
sK5: ( a > $o ) > a > $o ).
thf(func_def_16,type,
sK6: a > $o ).
thf(func_def_18,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f552,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f46,f47,f51,f66,f70,f74,f78,f82,f86,f551]) ).
thf(f551,plain,
( ~ spl7_3
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f550]) ).
thf(f550,plain,
( $false
| ~ spl7_3
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(trivial_inequality_removal,[status(thm)],[f545]) ).
thf(f545,plain,
( ( $true = $false )
| ( t != t )
| ~ spl7_3
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(superposition,[status(thm)],[f65,f542]) ).
thf(f542,plain,
( ! [X0: a] :
( ( $false
= ( sK2 @ X0 ) )
| ( t != X0 ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(duplicate_literal_removal,[status(thm)],[f541]) ).
thf(f541,plain,
( ! [X0: a] :
( ( t != X0 )
| ( $false
= ( sK2 @ X0 ) )
| ( t != X0 ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(equality_proxy_clausification,[status(thm)],[f540]) ).
thf(f540,plain,
( ! [X0: a] :
( ( $true
!= ( X0 = t ) )
| ( $false
= ( sK2 @ X0 ) )
| ( t != X0 ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(trivial_inequality_removal,[status(thm)],[f531]) ).
thf(f531,plain,
( ! [X0: a] :
( ( $true
!= ( X0 = t ) )
| ( t != X0 )
| ( $true = $false )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(superposition,[status(thm)],[f528,f103]) ).
thf(f103,plain,
! [X0: a > $o] :
( ( ( sP0 @ X0 )
= $false )
| ( ( X0 @ t )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( ( X0 @ t )
!= $true )
| ( ( sP0 @ X0 )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f101]) ).
thf(f101,plain,
! [X0: a > $o] :
( ( $true
!= ( sP0 @ X0 ) )
| ( ( X0 @ t )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
! [X0: a > $o] :
( ( $true
!= ( sP0 @ X0 ) )
| ( $true != $true )
| ( ( X0 @ t )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f98]) ).
thf(f98,plain,
! [X0: a > $o] :
( ( ( X0 @ t )
!= $true )
| ( $true != $true )
| ( $true
!= ( sP0 @ X0 ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f95,f32]) ).
thf(f32,plain,
! [X2: a,X0: a > $o] :
( ( $true
= ( sK5 @ X0 @ X2 ) )
| ( $true
!= ( sP0 @ X0 ) )
| ( $true
!= ( X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: a > $o] :
( ( ( $true
= ( cA @ ( sK5 @ X0 ) ) )
& ( ( $true
!= ( sK5 @ X0 @ t ) )
| ( $true
!= ( cA @ ( sK5 @ X0 ) ) ) )
& ! [X2: a] :
( ( $true
= ( sK5 @ X0 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f19,f20]) ).
thf(f20,plain,
! [X0: a > $o] :
( ? [X1: a > $o] :
( ( ( cA @ X1 )
= $true )
& ( ( $true
!= ( X1 @ t ) )
| ( ( cA @ X1 )
!= $true ) )
& ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) ) )
=> ( ( $true
= ( cA @ ( sK5 @ X0 ) ) )
& ( ( $true
!= ( sK5 @ X0 @ t ) )
| ( $true
!= ( cA @ ( sK5 @ X0 ) ) ) )
& ! [X2: a] :
( ( $true
= ( sK5 @ X0 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X0: a > $o] :
( ? [X1: a > $o] :
( ( ( cA @ X1 )
= $true )
& ( ( $true
!= ( X1 @ t ) )
| ( ( cA @ X1 )
!= $true ) )
& ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: a > $o] :
( ? [X6: a > $o] :
( ( $true
= ( cA @ X6 ) )
& ( ( $true
!= ( X6 @ t ) )
| ( $true
!= ( cA @ X6 ) ) )
& ! [X7: a] :
( ( $true
= ( X6 @ X7 ) )
| ( $true
!= ( X2 @ X7 ) ) ) )
| ( $true
!= ( sP0 @ X2 ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X2: a > $o] :
( ? [X6: a > $o] :
( ( $true
= ( cA @ X6 ) )
& ( ( $true
!= ( X6 @ t ) )
| ( $true
!= ( cA @ X6 ) ) )
& ! [X7: a] :
( ( $true
= ( X6 @ X7 ) )
| ( $true
!= ( X2 @ X7 ) ) ) )
| ( $true
!= ( sP0 @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f95,plain,
! [X0: a > $o] :
( ( $true
!= ( sK5 @ X0 @ t ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
! [X0: a > $o] :
( ( $true
!= ( sK5 @ X0 @ t ) )
| ( $true
!= ( sP0 @ X0 ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X0: a > $o] :
( ( $true
!= ( sP0 @ X0 ) )
| ( $true
!= ( sK5 @ X0 @ t ) )
| ( $true
!= ( sP0 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f33,f34]) ).
thf(f34,plain,
! [X0: a > $o] :
( ( $true
= ( cA @ ( sK5 @ X0 ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f33,plain,
! [X0: a > $o] :
( ( $true
!= ( cA @ ( sK5 @ X0 ) ) )
| ( $true
!= ( sP0 @ X0 ) )
| ( $true
!= ( sK5 @ X0 @ t ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f528,plain,
( ! [X0: a] :
( ( $true
= ( sP0 @ ( (=) @ X0 ) ) )
| ( t != X0 )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10
| ~ spl7_11 ),
inference(superposition,[status(thm)],[f373,f527]) ).
thf(f527,plain,
( ! [X0: a] :
( ( ( sK4 @ ( (=) @ X0 ) )
= X0 )
| ( t != X0 ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(equality_proxy_clausification,[status(thm)],[f526]) ).
thf(f526,plain,
( ! [X0: a] :
( ( $true
!= ( X0 = t ) )
| ( ( sK4 @ ( (=) @ X0 ) )
= X0 ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(trivial_inequality_removal,[status(thm)],[f521]) ).
thf(f521,plain,
( ! [X0: a] :
( ( $true
!= ( X0 = t ) )
| ( ( sK4 @ ( (=) @ X0 ) )
= X0 )
| ( $true != $true ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(superposition,[status(thm)],[f101,f496]) ).
thf(f496,plain,
( ! [X0: a] :
( ( $true
= ( sP0 @ ( (=) @ X0 ) ) )
| ( ( sK4 @ ( (=) @ X0 ) )
= X0 ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(duplicate_literal_removal,[status(thm)],[f495]) ).
thf(f495,plain,
( ! [X0: a] :
( ( ( sK4 @ ( (=) @ X0 ) )
= X0 )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) )
| ( ( sK4 @ ( (=) @ X0 ) )
= X0 ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(equality_proxy_clausification,[status(thm)],[f494]) ).
thf(f494,plain,
( ! [X0: a] :
( ( $true
= ( X0
= ( sK4 @ ( (=) @ X0 ) ) ) )
| ( ( sK4 @ ( (=) @ X0 ) )
= X0 )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(beta_eta_normalization,[status(thm)],[f493]) ).
thf(f493,plain,
( ! [X0: a] :
( ( $true
= ( X0
= ( sK4
@ ^ [Y0: a] : ( X0 = Y0 ) ) ) )
| ( ( sK4 @ ( (=) @ X0 ) )
= X0 )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(boolean_simplification,[status(thm)],[f492]) ).
thf(f492,plain,
( ! [X0: a] :
( ( ( sK4 @ ( (=) @ X0 ) )
= X0 )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) )
| ( $true
= ( X0
= ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(boolean_simplification,[status(thm)],[f491]) ).
thf(f491,plain,
( ! [X0: a] :
( ( ( sK4 @ ( (=) @ X0 ) )
= X0 )
| ( $true
= ( $false
| ( X0
= ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) ) )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(beta_eta_normalization,[status(thm)],[f490]) ).
thf(f490,plain,
( ! [X0: a] :
( ( ( sK4
@ ^ [Y0: a] : ( X0 = Y0 ) )
= X0 )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) )
| ( $true
= ( $false
| ( X0
= ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(boolean_simplification,[status(thm)],[f489]) ).
thf(f489,plain,
( ! [X0: a] :
( ( ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) )
= X0 )
| ( $true
= ( $false
| ( X0
= ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) ) )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(beta_eta_normalization,[status(thm)],[f488]) ).
thf(f488,plain,
( ! [X0: a] :
( ( $true
= ( $false
| ( X0
= ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] : ( X0 = Y0 ) ) )
| ( ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) )
= X0 ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(boolean_simplification,[status(thm)],[f487]) ).
thf(f487,plain,
( ! [X0: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) )
| ( ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) )
= X0 )
| ( $true
= ( $false
| ( X0
= ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(trivial_inequality_removal,[status(thm)],[f486]) ).
thf(f486,plain,
( ! [X0: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) )
| ( $true
= ( $false
| ( X0
= ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) ) )
| ( ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) )
= X0 )
| ( $true = $false ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(beta_eta_normalization,[status(thm)],[f485]) ).
thf(f485,plain,
( ! [X0: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) )
| ( $true
= ( ^ [Y0: a] : $false
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) )
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ( ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) )
= X0 ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(trivial_inequality_removal,[status(thm)],[f484]) ).
thf(f484,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) )
= X0 )
| ( $true
= ( ^ [Y0: a] : $false
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) )
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(duplicate_literal_removal,[status(thm)],[f466]) ).
thf(f466,plain,
( ! [X0: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) )
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: a] : $false
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ( ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) )
= X0 )
| ( $true != $true )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ~ spl7_8
| ~ spl7_9
| ~ spl7_10 ),
inference(superposition,[status(thm)],[f328,f73]) ).
thf(f73,plain,
( ! [X1: a > $o] :
( ( $true
= ( sK3 @ X1
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl7_8
<=> ! [X1: a > $o] :
( ( $true
= ( X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( sK3 @ X1
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sP0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl7_8])],[avatar_definition]) ).
thf(f328,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
= ( X0
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) )
= X1 )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(equality_proxy_clausification,[status(thm)],[f327]) ).
thf(f327,plain,
( ! [X0: a > $o,X1: a] :
( ( ( X1
= ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
= $true )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
= ( X0
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(binary_proxy_clausification,[status(thm)],[f326]) ).
thf(f326,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
= ( ( X0
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( X1
= ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(trivial_inequality_removal,[status(thm)],[f325]) ).
thf(f325,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true != $true )
| ( $true
= ( ( X0
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( X1
= ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(boolean_simplification,[status(thm)],[f324]) ).
thf(f324,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( ( X0 @ X1 )
| $true ) )
| ( $true
= ( ( X0
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( X1
= ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(boolean_simplification,[status(thm)],[f323]) ).
thf(f323,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
= ( ( X0
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( X1
= ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( ( X0 @ X1 )
| ( X1 = X1 ) ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(beta_eta_normalization,[status(thm)],[f322]) ).
thf(f322,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X1 ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(trivial_inequality_removal,[status(thm)],[f321]) ).
thf(f321,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X1 ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( $true = $false ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(duplicate_literal_removal,[status(thm)],[f275]) ).
thf(f275,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( $true = $false )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X1 ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ~ spl7_9
| ~ spl7_10 ),
inference(superposition,[status(thm)],[f77,f121]) ).
thf(f121,plain,
( ! [X1: a > $o] :
( ( ( sK3 @ X1 @ X1 )
= $false )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) ) )
| ~ spl7_10 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ! [X1: a > $o] :
( ( $true != $true )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) )
| ( ( sK3 @ X1 @ X1 )
= $false ) )
| ~ spl7_10 ),
inference(fool_paramodulation,[status(thm)],[f81]) ).
thf(f81,plain,
( ! [X1: a > $o] :
( ( ( sK3 @ X1 @ X1 )
!= $true )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) ) )
| ~ spl7_10 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl7_10
<=> ! [X1: a > $o] :
( ( $true
= ( sP0 @ X1 ) )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) )
| ( ( sK3 @ X1 @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl7_10])],[avatar_definition]) ).
thf(f77,plain,
( ! [X3: a > $o,X1: a > $o,X4: a] :
( ( $true
= ( sK3 @ X1
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) )
| ( ( X1 @ X4 )
!= $true )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
!= ( sK3 @ X1 @ X3 ) )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl7_9
<=> ! [X4: a,X1: a > $o,X3: a > $o] :
( ( $true
= ( sK3 @ X1
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
!= ( sK3 @ X1 @ X3 ) )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) )
| ( ( X1 @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl7_9])],[avatar_definition]) ).
thf(f373,plain,
( ! [X0: a] :
( ( ( sK2 @ ( sK4 @ ( (=) @ X0 ) ) )
= $false )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(trivial_inequality_removal,[status(thm)],[f372]) ).
thf(f372,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( sK2 @ ( sK4 @ ( (=) @ X0 ) ) )
= $false )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(fool_paramodulation,[status(thm)],[f363]) ).
thf(f363,plain,
( ! [X0: a] :
( ( $true
!= ( sK2 @ ( sK4 @ ( (=) @ X0 ) ) ) )
| ( $true
= ( sP0 @ ( (=) @ X0 ) ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(beta_eta_normalization,[status(thm)],[f362]) ).
thf(f362,plain,
( ! [X0: a] :
( ( $true
!= ( sK2 @ ( sK4 @ ( (=) @ X0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] : ( X0 = Y0 ) ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(boolean_simplification,[status(thm)],[f361]) ).
thf(f361,plain,
( ! [X0: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) )
| ( $true
!= ( sK2 @ ( sK4 @ ( (=) @ X0 ) ) ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(beta_eta_normalization,[status(thm)],[f360]) ).
thf(f360,plain,
( ! [X0: a] :
( ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] : ( X0 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(boolean_simplification,[status(thm)],[f359]) ).
thf(f359,plain,
( ! [X0: a] :
( ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( $false
| ( X0 = Y0 ) ) ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(beta_eta_normalization,[status(thm)],[f358]) ).
thf(f358,plain,
( ! [X0: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(trivial_inequality_removal,[status(thm)],[f357]) ).
thf(f357,plain,
( ! [X0: a] :
( ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) )
| ( $true != $true ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(duplicate_literal_removal,[status(thm)],[f333]) ).
thf(f333,plain,
( ! [X0: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( X0 = Y0 ) ) ) ) )
| ( $true != $true ) )
| ~ spl7_3
| ~ spl7_7
| ~ spl7_11 ),
inference(superposition,[status(thm)],[f272,f85]) ).
thf(f85,plain,
( ! [X1: a > $o] :
( ( $true
= ( sK3 @ X1
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) ) )
| ~ spl7_11 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl7_11
<=> ! [X1: a > $o] :
( ( $true
= ( sK3 @ X1
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl7_11])],[avatar_definition]) ).
thf(f272,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f271]) ).
thf(f271,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( $true != $true ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(boolean_simplification,[status(thm)],[f270]) ).
thf(f270,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
!= ( ( X0 @ X1 )
| $true ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(boolean_simplification,[status(thm)],[f269]) ).
thf(f269,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
!= ( ( X0 @ X1 )
| ( X1 = X1 ) ) ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(beta_eta_normalization,[status(thm)],[f268]) ).
thf(f268,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X1 ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f267]) ).
thf(f267,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( $true = $false )
| ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X1 ) ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(duplicate_literal_removal,[status(thm)],[f228]) ).
thf(f228,plain,
( ! [X0: a > $o,X1: a] :
( ( $true
!= ( sK3
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X0 ) )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( $true
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) )
@ X1 ) )
| ( $true = $false )
| ( $true
!= ( sK2
@ ( sK4
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 = Y0 ) ) ) ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(superposition,[status(thm)],[f119,f50]) ).
thf(f50,plain,
( ! [X3: a > $o,X1: a > $o,X4: a] :
( ( $true
= ( sK3 @ X1
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
| ( ( X1 @ X4 )
!= $true )
| ( $true
!= ( sK3 @ X1 @ X3 ) ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl7_3
<=> ! [X4: a,X1: a > $o,X3: a > $o] :
( ( $true
= ( sP0 @ X1 ) )
| ( ( X1 @ X4 )
!= $true )
| ( $true
= ( sK3 @ X1
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
| ( $true
!= ( sK3 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition]) ).
thf(f119,plain,
( ! [X1: a > $o] :
( ( ( sK3 @ X1 @ X1 )
= $false )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) ) )
| ~ spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ! [X1: a > $o] :
( ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
| ( $true
= ( sP0 @ X1 ) )
| ( $true != $true )
| ( ( sK3 @ X1 @ X1 )
= $false ) )
| ~ spl7_7 ),
inference(fool_paramodulation,[status(thm)],[f69]) ).
thf(f69,plain,
( ! [X1: a > $o] :
( ( ( sK3 @ X1 @ X1 )
!= $true )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
| ( $true
= ( sP0 @ X1 ) ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl7_7
<=> ! [X1: a > $o] :
( ( $true
= ( sP0 @ X1 ) )
| ( ( sK3 @ X1 @ X1 )
!= $true )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl7_7])],[avatar_definition]) ).
thf(f65,plain,
( ( $true
= ( sK2 @ t ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl7_6
<=> ( $true
= ( sK2 @ t ) ) ),
introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition]) ).
thf(f86,plain,
( spl7_11
| ~ spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f29,f43,f84]) ).
thf(f43,definition,
( spl7_2
<=> ( $true = sP1 ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f29,plain,
! [X1: a > $o] :
( ( $true
= ( sK3 @ X1
@ ^ [Y0: a] : $false ) )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
| ( $true
= ( sP0 @ X1 ) )
| ( $true != sP1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ! [X1: a > $o] :
( ( ( ( sK3 @ X1 @ X1 )
!= $true )
& ( $true
= ( sK3 @ X1
@ ^ [Y0: a] : $false ) )
& ! [X3: a > $o] :
( ( $true
!= ( sK3 @ X1 @ X3 ) )
| ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( $true
= ( sK3 @ X1
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) ) ) ) )
| ( ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
& ( $true
= ( X1 @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( sP0 @ X1 ) ) )
& ( $true
= ( cA @ sK2 ) )
& ( $true
= ( sK2 @ t ) ) )
| ( $true != sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f13,f16,f15,f14]) ).
thf(f14,plain,
( ? [X0: a > $o] :
( ! [X1: a > $o] :
( ? [X2: ( a > $o ) > $o] :
( ( ( X2 @ X1 )
!= $true )
& ( $true
= ( X2
@ ^ [Y0: a] : $false ) )
& ! [X3: a > $o] :
( ( $true
!= ( X2 @ X3 ) )
| ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( $true
= ( X2
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) ) ) ) )
| ? [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
& ( ( X1 @ X5 )
= $true ) )
| ( $true
= ( sP0 @ X1 ) ) )
& ( ( cA @ X0 )
= $true )
& ( ( X0 @ t )
= $true ) )
=> ( ! [X1: a > $o] :
( ? [X2: ( a > $o ) > $o] :
( ( ( X2 @ X1 )
!= $true )
& ( $true
= ( X2
@ ^ [Y0: a] : $false ) )
& ! [X3: a > $o] :
( ( $true
!= ( X2 @ X3 ) )
| ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( $true
= ( X2
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) ) ) ) )
| ? [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
& ( ( X1 @ X5 )
= $true ) )
| ( $true
= ( sP0 @ X1 ) ) )
& ( $true
= ( cA @ sK2 ) )
& ( $true
= ( sK2 @ t ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X1: a > $o] :
( ? [X2: ( a > $o ) > $o] :
( ( ( X2 @ X1 )
!= $true )
& ( $true
= ( X2
@ ^ [Y0: a] : $false ) )
& ! [X3: a > $o] :
( ( $true
!= ( X2 @ X3 ) )
| ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( $true
= ( X2
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) ) ) ) )
=> ( ( ( sK3 @ X1 @ X1 )
!= $true )
& ( $true
= ( sK3 @ X1
@ ^ [Y0: a] : $false ) )
& ! [X3: a > $o] :
( ( $true
!= ( sK3 @ X1 @ X3 ) )
| ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( $true
= ( sK3 @ X1
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X1: a > $o] :
( ? [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
& ( ( X1 @ X5 )
= $true ) )
=> ( ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
& ( $true
= ( X1 @ ( sK4 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: a > $o] :
( ! [X1: a > $o] :
( ? [X2: ( a > $o ) > $o] :
( ( ( X2 @ X1 )
!= $true )
& ( $true
= ( X2
@ ^ [Y0: a] : $false ) )
& ! [X3: a > $o] :
( ( $true
!= ( X2 @ X3 ) )
| ! [X4: a] :
( ( ( X1 @ X4 )
!= $true )
| ( $true
= ( X2
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) ) ) ) )
| ? [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
& ( ( X1 @ X5 )
= $true ) )
| ( $true
= ( sP0 @ X1 ) ) )
& ( ( cA @ X0 )
= $true )
& ( ( X0 @ t )
= $true ) )
| ( $true != sP1 ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X1: a > $o] :
( ! [X2: a > $o] :
( ? [X3: ( a > $o ) > $o] :
( ( $true
!= ( X3 @ X2 ) )
& ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ! [X4: a > $o] :
( ( $true
!= ( X3 @ X4 ) )
| ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X3
@ ^ [Y0: a] :
( ( X4 @ Y0 )
| ( X5 = Y0 ) ) ) ) ) ) )
| ? [X8: a] :
( ( $true
!= ( X1 @ X8 ) )
& ( $true
= ( X2 @ X8 ) ) )
| ( $true
= ( sP0 @ X2 ) ) )
& ( ( cA @ X1 )
= $true )
& ( $true
= ( X1 @ t ) ) )
| ( $true != sP1 ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X1: a > $o] :
( ! [X2: a > $o] :
( ? [X3: ( a > $o ) > $o] :
( ( $true
!= ( X3 @ X2 ) )
& ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ! [X4: a > $o] :
( ( $true
!= ( X3 @ X4 ) )
| ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X3
@ ^ [Y0: a] :
( ( X4 @ Y0 )
| ( X5 = Y0 ) ) ) ) ) ) )
| ? [X8: a] :
( ( $true
!= ( X1 @ X8 ) )
& ( $true
= ( X2 @ X8 ) ) )
| ( $true
= ( sP0 @ X2 ) ) )
& ( ( cA @ X1 )
= $true )
& ( $true
= ( X1 @ t ) ) )
| ( $true != sP1 ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f82,plain,
( ~ spl7_2
| spl7_10 ),
inference(avatar_split_clause,[status(thm)],[f30,f80,f43]) ).
thf(f30,plain,
! [X1: a > $o] :
( ( $true
= ( sP0 @ X1 ) )
| ( $true != sP1 )
| ( ( sK3 @ X1 @ X1 )
!= $true )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f78,plain,
( spl7_9
| ~ spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f43,f76]) ).
thf(f26,plain,
! [X3: a > $o,X1: a > $o,X4: a] :
( ( $true
= ( sK3 @ X1
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) )
| ( ( X1 @ X4 )
!= $true )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) )
| ( $true != sP1 )
| ( $true
!= ( sK3 @ X1 @ X3 ) )
| ( $true
= ( sP0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f74,plain,
( ~ spl7_2
| spl7_8 ),
inference(avatar_split_clause,[status(thm)],[f28,f72,f43]) ).
thf(f28,plain,
! [X1: a > $o] :
( ( $true != sP1 )
| ( $true
= ( X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( sP0 @ X1 ) )
| ( $true
= ( sK3 @ X1
@ ^ [Y0: a] : $false ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f70,plain,
( spl7_7
| ~ spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f31,f43,f68]) ).
thf(f31,plain,
! [X1: a > $o] :
( ( $true
= ( sP0 @ X1 ) )
| ( $true != sP1 )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
| ( ( sK3 @ X1 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f66,plain,
( ~ spl7_2
| spl7_6 ),
inference(avatar_split_clause,[status(thm)],[f24,f63,f43]) ).
thf(f24,plain,
( ( $true != sP1 )
| ( $true
= ( sK2 @ t ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f51,plain,
( ~ spl7_2
| spl7_3 ),
inference(avatar_split_clause,[status(thm)],[f27,f49,f43]) ).
thf(f27,plain,
! [X3: a > $o,X1: a > $o,X4: a] :
( ( $true
= ( sP0 @ X1 ) )
| ( $true
!= ( sK3 @ X1 @ X3 ) )
| ( $true
!= ( sK2 @ ( sK4 @ X1 ) ) )
| ( $true
= ( sK3 @ X1
@ ^ [Y0: a] :
( ( X3 @ Y0 )
| ( X4 = Y0 ) ) ) )
| ( ( X1 @ X4 )
!= $true )
| ( $true != sP1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f47,plain,
( spl7_2
| spl7_1 ),
inference(avatar_split_clause,[status(thm)],[f35,f39,f43]) ).
thf(f39,definition,
( spl7_1
<=> ( $true
= ( cA @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f35,plain,
( ( $true = sP1 )
| ( $true
= ( cA @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true = sP1 )
| ( ( $true
!= ( cA @ sK6 ) )
& ( $true
= ( sK6 @ t ) )
& ( $true
= ( cA @ sK6 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f11,f22]) ).
thf(f22,plain,
( ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( X0 @ t )
= $true )
& ( ( cA @ X0 )
= $true ) )
=> ( ( $true
!= ( cA @ sK6 ) )
& ( $true
= ( sK6 @ t ) )
& ( $true
= ( cA @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ( $true = sP1 )
| ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( X0 @ t )
= $true )
& ( ( cA @ X0 )
= $true ) ) ),
inference(definition_folding,[status(thm)],[f8,f10,f9]) ).
thf(f8,plain,
( ? [X1: a > $o] :
( ! [X2: a > $o] :
( ? [X3: ( a > $o ) > $o] :
( ( $true
!= ( X3 @ X2 ) )
& ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ! [X4: a > $o] :
( ( $true
!= ( X3 @ X4 ) )
| ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X3
@ ^ [Y0: a] :
( ( X4 @ Y0 )
| ( X5 = Y0 ) ) ) ) ) ) )
| ? [X8: a] :
( ( $true
!= ( X1 @ X8 ) )
& ( $true
= ( X2 @ X8 ) ) )
| ? [X6: a > $o] :
( ( $true
= ( cA @ X6 ) )
& ( ( $true
!= ( X6 @ t ) )
| ( $true
!= ( cA @ X6 ) ) )
& ! [X7: a] :
( ( $true
= ( X6 @ X7 ) )
| ( $true
!= ( X2 @ X7 ) ) ) ) )
& ( ( cA @ X1 )
= $true )
& ( $true
= ( X1 @ t ) ) )
| ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( X0 @ t )
= $true )
& ( ( cA @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X1: a > $o] :
( ! [X2: a > $o] :
( ? [X6: a > $o] :
( ( ( $true
!= ( X6 @ t ) )
| ( $true
!= ( cA @ X6 ) ) )
& ( $true
= ( cA @ X6 ) )
& ! [X7: a] :
( ( $true
= ( X6 @ X7 ) )
| ( $true
!= ( X2 @ X7 ) ) ) )
| ? [X8: a] :
( ( $true
!= ( X1 @ X8 ) )
& ( $true
= ( X2 @ X8 ) ) )
| ? [X3: ( a > $o ) > $o] :
( ( $true
!= ( X3 @ X2 ) )
& ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ! [X4: a > $o] :
( ( $true
!= ( X3 @ X4 ) )
| ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X3
@ ^ [Y0: a] :
( ( X4 @ Y0 )
| ( X5 = Y0 ) ) ) ) ) ) ) )
& ( $true
= ( X1 @ t ) )
& ( ( cA @ X1 )
= $true ) )
| ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true )
& ( ( X0 @ t )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X1: a > $o] :
( ( ( $true
= ( X1 @ t ) )
& ( ( cA @ X1 )
= $true ) )
=> ? [X2: a > $o] :
( ! [X6: a > $o] :
( ( ( $true
= ( cA @ X6 ) )
& ! [X7: a] :
( ( $true
= ( X2 @ X7 ) )
=> ( $true
= ( X6 @ X7 ) ) ) )
=> ( ( $true
= ( X6 @ t ) )
& ( $true
= ( cA @ X6 ) ) ) )
& ! [X8: a] :
( ( $true
= ( X2 @ X8 ) )
=> ( $true
= ( X1 @ X8 ) ) )
& ! [X3: ( a > $o ) > $o] :
( ( ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ! [X4: a > $o] :
( ( $true
= ( X3 @ X4 ) )
=> ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
=> ( $true
= ( X3
@ ^ [Y0: a] :
( ( X4 @ Y0 )
| ( X5 = Y0 ) ) ) ) ) ) )
=> ( $true
= ( X3 @ X2 ) ) ) ) )
& ! [X0: a > $o] :
( ( ( ( cA @ X0 )
= $true )
& ( ( X0 @ t )
= $true ) )
=> ( ( cA @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a > $o] :
( ( ( ( cA @ X0 )
= $true )
& ( ( X0 @ t )
= $true ) )
=> ( ( cA @ X0 )
= $true ) )
& ! [X1: a > $o] :
( ( ( $true
= ( X1 @ t ) )
& ( ( cA @ X1 )
= $true ) )
=> ? [X2: a > $o] :
( ! [X3: ( a > $o ) > $o] :
( ( ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ! [X5: a > $o] :
( ( ( X3 @ X5 )
= $true )
=> ! [X6: a] :
( ( $true
= ( X2 @ X6 ) )
=> ( $true
= ( X3
@ ^ [Y0: a] :
( ( X5 @ Y0 )
| ( X6 = Y0 ) ) ) ) ) ) )
=> ( $true
= ( X3 @ X2 ) ) )
& ! [X8: a > $o] :
( ( ( $true
= ( cA @ X8 ) )
& ! [X9: a] :
( ( $true
= ( X2 @ X9 ) )
=> ( $true
= ( X8 @ X9 ) ) ) )
=> ( ( $true
= ( cA @ X8 ) )
& ( $true
= ( X8 @ t ) ) ) )
& ! [X10: a] :
( ( $true
= ( X2 @ X10 ) )
=> ( $true
= ( X1 @ X10 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o] :
( ( ( X0 @ t )
& ( cA @ X0 ) )
=> ( cA @ X0 ) )
& ! [X1: a > $o] :
( ( ( cA @ X1 )
& ( X1 @ t ) )
=> ? [X2: a > $o] :
( ! [X3: ( a > $o ) > $o] :
( ( ( X3
@ ^ [X4: a] : $false )
& ! [X5: a > $o] :
( ( X3 @ X5 )
=> ! [X6: a] :
( ( X2 @ X6 )
=> ( X3
@ ^ [X7: a] :
( ( X6 = X7 )
| ( X5 @ X7 ) ) ) ) ) )
=> ( X3 @ X2 ) )
& ! [X8: a > $o] :
( ( ( cA @ X8 )
& ! [X9: a] :
( ( X2 @ X9 )
=> ( X8 @ X9 ) ) )
=> ( ( cA @ X8 )
& ( X8 @ t ) ) )
& ! [X10: a] :
( ( X2 @ X10 )
=> ( X1 @ X10 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > $o] :
( ( ( X0 @ t )
& ( cA @ X0 ) )
=> ( cA @ X0 ) )
& ! [X0: a > $o] :
( ( ( cA @ X0 )
& ( X0 @ t ) )
=> ? [X1: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X4: a > $o] :
( ( X2 @ X4 )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2
@ ^ [X6: a] :
( ( X5 = X6 )
| ( X4 @ X6 ) ) ) ) ) )
=> ( X2 @ X1 ) )
& ! [X3: a > $o] :
( ( ( cA @ X3 )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( ( cA @ X3 )
& ( X3 @ t ) ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > $o] :
( ( ( X0 @ t )
& ( cA @ X0 ) )
=> ( cA @ X0 ) )
& ! [X0: a > $o] :
( ( ( cA @ X0 )
& ( X0 @ t ) )
=> ? [X1: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X4: a > $o] :
( ( X2 @ X4 )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2
@ ^ [X6: a] :
( ( X5 = X6 )
| ( X4 @ X6 ) ) ) ) ) )
=> ( X2 @ X1 ) )
& ! [X3: a > $o] :
( ( ( cA @ X3 )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( ( cA @ X3 )
& ( X3 @ t ) ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BIG0Vhr8BN/DTF2THF_30984.p',cDOMLEMMA5_pme) ).
thf(f46,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f37,f43,f39]) ).
thf(f37,plain,
( ( $true
!= ( cA @ sK6 ) )
| ( $true = sP1 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU875^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.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 12:35:44 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
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEU875^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Set Theory (Finite sets)
% 0.20/0.47 % Problem : TPS problem from SET-TOPOLOGY-THMS
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_1044 [Bro09]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.57 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.20/0.47 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 7 ( 7 avg)
% 0.20/0.47 % Number of connectives : 35 ( 0 ~; 1 |; 8 &; 18 @)
% 0.20/0.47 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 17 ( 17 avg)
% 0.20/0.47 % Number of types : 2 ( 1 usr)
% 0.20/0.47 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 4 ( 2 usr; 2 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 11 ( 2 ^; 8 !; 1 ?; 11 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(a_type,type,
% 0.20/0.47 a: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(t,type,
% 0.20/0.47 t: a ).
% 0.20/0.47
% 0.20/0.47 thf(cA,type,
% 0.20/0.47 cA: ( a > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cDOMLEMMA5_pme,conjecture,
% 0.20/0.47 ( ! [Xx: a > $o] :
% 0.20/0.47 ( ( ( cA @ Xx )
% 0.20/0.47 & ( Xx @ t ) )
% 0.20/0.47 => ( cA @ Xx ) )
% 0.20/0.47 & ! [Xx: a > $o] :
% 0.20/0.47 ( ( ( cA @ Xx )
% 0.20/0.47 & ( Xx @ t ) )
% 0.20/0.47 => ? [Xe: a > $o] :
% 0.20/0.47 ( ! [X: ( a > $o ) > $o] :
% 0.20/0.47 ( ( ( X
% 0.20/0.47 @ ^ [Xy: a] : $false )
% 0.20/0.47 & ! [Xx0: a > $o] :
% 0.20/0.47 ( ( X @ Xx0 )
% 0.20/0.47 => ! [Xt0: a] :
% 0.20/0.47 ( ( Xe @ Xt0 )
% 0.20/0.47 => ( X
% 0.20/0.47 @ ^ [Xz: a] :
% 0.20/0.47 ( ( Xx0 @ Xz )
% 0.20/0.47 | ( Xt0 = Xz ) ) ) ) ) )
% 0.20/0.47 => ( X @ Xe ) )
% 0.20/0.47 & ! [Xx0: a] :
% 0.20/0.47 ( ( Xe @ Xx0 )
% 0.20/0.47 => ( Xx @ Xx0 ) )
% 0.20/0.47 & ! [Xy: a > $o] :
% 0.20/0.47 ( ( ( cA @ Xy )
% 0.20/0.47 & ! [Xx0: a] :
% 0.20/0.47 ( ( Xe @ Xx0 )
% 0.20/0.47 => ( Xy @ Xx0 ) ) )
% 0.20/0.47 => ( ( cA @ Xy )
% 0.20/0.47 & ( Xy @ t ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 0.32/1.40 ---- Embedded in THF ---
% 0.32/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.40 %%% Generated on Tue Feb 24 12:35:45 EST 2026
% 0.32/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.40 %%% Logic specification used:
% 0.32/1.40 %%% thf(spec, logic, $$dhol).
% 0.32/1.40
% 0.32/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BIG0Vhr8BN/DTF2DTF30984.p
% See solution above
% 0.32/1.40 ------------------------
% 0.32/1.41 ---- Cleaned THF ---
% 0.32/1.41 thf(a_type,type,
% 0.32/1.41 a: $tType ).
% 0.32/1.41
% 0.32/1.41 thf(t,type,
% 0.32/1.41 t: a ).
% 0.32/1.41
% 0.32/1.41 thf(cA,type,
% 0.32/1.41 cA: ( a > $o ) > $o ).
% 0.32/1.41
% 0.32/1.41 thf(cDOMLEMMA5_pme,conjecture,
% 0.32/1.41 ( ! [Xx: a > $o] :
% 0.32/1.41 ( ( ( cA @ Xx )
% 0.32/1.41 & ( Xx @ t ) )
% 0.32/1.41 => ( cA @ Xx ) )
% 0.32/1.41 & ! [Xx: a > $o] :
% 0.32/1.41 ( ( ( cA @ Xx )
% 0.32/1.41 & ( Xx @ t ) )
% 0.32/1.41 => ? [Xe: a > $o] :
% 0.32/1.41 ( ! [X: ( a > $o ) > $o] :
% 0.32/1.41 ( ( ( X
% 0.32/1.41 @ ^ [Xy: a] : $false )
% 0.32/1.41 & ! [Xx0: a > $o] :
% 0.32/1.41 ( ( X @ Xx0 )
% 0.32/1.41 => ! [Xt0: a] :
% 0.32/1.41 ( ( Xe @ Xt0 )
% 0.32/1.41 => ( X
% 0.32/1.41 @ ^ [Xz: a] :
% 0.32/1.41 ( ( Xx0 @ Xz )
% 0.32/1.41 | ( Xt0 = Xz ) ) ) ) ) )
% 0.32/1.41 => ( X @ Xe ) )
% 0.32/1.41 & ! [Xx0: a] :
% 0.32/1.41 ( ( Xe @ Xx0 )
% 0.32/1.41 => ( Xx @ Xx0 ) )
% 0.32/1.41 & ! [Xy: a > $o] :
% 0.32/1.41 ( ( ( cA @ Xy )
% 0.32/1.41 & ! [Xx0: a] :
% 0.32/1.41 ( ( Xe @ Xx0 )
% 0.32/1.41 => ( Xy @ Xx0 ) ) )
% 0.32/1.41 => ( ( cA @ Xy )
% 0.32/1.41 & ( Xy @ t ) ) ) ) ) ) ).
% 0.32/1.41 ------------------------
% 0.32/1.43 % (31081)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30984 for (3000ds/183Mi)
% 0.32/1.43 % (31082)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_30984 for (3000ds/4Mi)
% 0.32/1.43 % (31083)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_30984 for (3000ds/27Mi)
% 0.32/1.43 % (31084)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30984 for (3000ds/2Mi)
% 0.32/1.43 % (31085)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_30984 for (3000ds/2Mi)
% 0.32/1.43 % (31086)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_30984 for (3000ds/275Mi)
% 0.32/1.43 % (31087)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30984 for (3000ds/18Mi)
% 0.32/1.43 % (31084)Instruction limit reached!
% 0.32/1.43 % (31084)------------------------------
% 0.32/1.43 % (31084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (31084)Termination reason: Unknown
% 0.32/1.43 % (31085)Instruction limit reached!
% 0.32/1.43 % (31085)------------------------------
% 0.32/1.43 % (31085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (31085)Termination reason: Unknown
% 0.32/1.43 % (31085)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (31085)Memory used [KB]: 5500
% 0.32/1.43 % (31085)Time elapsed: 0.003 s
% 0.32/1.43 % (31085)Instructions burned: 3 (million)
% 0.32/1.43 % (31085)------------------------------
% 0.32/1.43 % (31085)------------------------------
% 0.32/1.43 % (31084)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (31084)Memory used [KB]: 5500
% 0.32/1.43 % (31084)Time elapsed: 0.003 s
% 0.32/1.43 % (31084)Instructions burned: 3 (million)
% 0.32/1.43 % (31084)------------------------------
% 0.32/1.43 % (31084)------------------------------
% 0.32/1.43 % (31082)Instruction limit reached!
% 0.32/1.43 % (31082)------------------------------
% 0.32/1.43 % (31082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (31082)Termination reason: Unknown
% 0.32/1.43 % (31082)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (31082)Memory used [KB]: 5500
% 0.32/1.43 % (31082)Time elapsed: 0.004 s
% 0.32/1.43 % (31086)Refutation not found, incomplete strategy
% 0.32/1.43 % (31086)------------------------------
% 0.32/1.43 % (31086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (31082)Instructions burned: 4 (million)
% 0.32/1.43 % (31082)------------------------------
% 0.32/1.43 % (31082)------------------------------
% 0.32/1.43 % (31086)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.43
% 0.32/1.43
% 0.32/1.43 % (31086)Memory used [KB]: 5500
% 0.32/1.43 % (31086)Time elapsed: 0.003 s
% 0.32/1.43 % (31086)Instructions burned: 3 (million)
% 0.32/1.43 % (31086)------------------------------
% 0.32/1.43 % (31086)------------------------------
% 0.32/1.44 % (31087)Instruction limit reached!
% 0.32/1.44 % (31087)------------------------------
% 0.32/1.44 % (31087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.44 % (31087)Termination reason: Unknown
% 0.32/1.44 % (31087)Termination phase: Saturation
% 0.32/1.44
% 0.32/1.44 % (31087)Memory used [KB]: 5628
% 0.32/1.44 % (31087)Time elapsed: 0.012 s
% 0.32/1.44 % (31087)Instructions burned: 19 (million)
% 0.32/1.44 % (31087)------------------------------
% 0.32/1.44 % (31087)------------------------------
% 0.32/1.44 % (31083)Instruction limit reached!
% 0.32/1.44 % (31083)------------------------------
% 0.32/1.44 % (31083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.44 % (31083)Termination reason: Unknown
% 0.32/1.44 % (31083)Termination phase: Saturation
% 0.32/1.44
% 0.32/1.44 % (31083)Memory used [KB]: 5756
% 0.32/1.44 % (31083)Time elapsed: 0.016 s
% 0.32/1.44 % (31083)Instructions burned: 27 (million)
% 0.32/1.44 % (31083)------------------------------
% 0.32/1.44 % (31083)------------------------------
% 0.32/1.45 % (31088)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/3Mi)
% 0.32/1.45 % (31089)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_30984 for (2999ds/37Mi)
% 0.32/1.45 % (31090)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_30984 for (2999ds/15Mi)
% 0.32/1.45 % (31091)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/3Mi)
% 0.32/1.45 % (31088)Instruction limit reached!
% 0.32/1.45 % (31088)------------------------------
% 0.32/1.45 % (31088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.45 % (31088)Termination reason: Unknown
% 0.32/1.45 % (31088)Termination phase: Saturation
% 0.32/1.45
% 0.32/1.45 % (31088)Memory used [KB]: 5500
% 0.32/1.45 % (31088)Time elapsed: 0.003 s
% 0.32/1.45 % (31088)Instructions burned: 3 (million)
% 0.32/1.45 % (31088)------------------------------
% 0.32/1.45 % (31088)------------------------------
% 0.32/1.45 % (31091)Instruction limit reached!
% 0.32/1.45 % (31091)------------------------------
% 0.32/1.45 % (31091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.45 % (31091)Termination reason: Unknown
% 0.32/1.45 % (31091)Termination phase: Saturation
% 0.32/1.45
% 0.32/1.45 % (31091)Memory used [KB]: 5500
% 0.32/1.45 % (31091)Time elapsed: 0.003 s
% 0.32/1.45 % (31091)Instructions burned: 3 (million)
% 0.32/1.45 % (31091)------------------------------
% 0.32/1.45 % (31091)------------------------------
% 0.32/1.46 % (31092)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/1041Mi)
% 0.32/1.46 % (31090)Instruction limit reached!
% 0.32/1.46 % (31090)------------------------------
% 0.32/1.46 % (31090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (31090)Termination reason: Unknown
% 0.32/1.46 % (31090)Termination phase: Saturation
% 0.32/1.46
% 0.32/1.46 % (31090)Memory used [KB]: 5628
% 0.32/1.46 % (31090)Time elapsed: 0.010 s
% 0.32/1.46 % (31090)Instructions burned: 15 (million)
% 0.32/1.46 % (31090)------------------------------
% 0.32/1.46 % (31090)------------------------------
% 0.32/1.46 % (31093)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/7Mi)
% 0.32/1.46 % (31093)Instruction limit reached!
% 0.32/1.46 % (31093)------------------------------
% 0.32/1.46 % (31093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (31093)Termination reason: Unknown
% 0.32/1.46 % (31093)Termination phase: Saturation
% 0.32/1.46
% 0.32/1.46 % (31093)Memory used [KB]: 1023
% 0.32/1.46 % (31093)Time elapsed: 0.005 s
% 0.32/1.46 % (31093)Instructions burned: 7 (million)
% 0.32/1.46 % (31093)------------------------------
% 0.32/1.46 % (31093)------------------------------
% 0.32/1.46 % (31094)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/16Mi)
% 0.32/1.46 % (31089)Instruction limit reached!
% 0.32/1.46 % (31089)------------------------------
% 0.32/1.46 % (31089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (31089)Termination reason: Unknown
% 0.32/1.46 % (31089)Termination phase: Saturation
% 0.32/1.46
% 0.32/1.46 % (31089)Memory used [KB]: 5628
% 0.32/1.46 % (31089)Time elapsed: 0.020 s
% 0.32/1.46 % (31095)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/3Mi)
% 0.32/1.46 % (31089)Instructions burned: 38 (million)
% 0.32/1.46 % (31089)------------------------------
% 0.32/1.46 % (31089)------------------------------
% 0.32/1.47 % (31095)Instruction limit reached!
% 0.32/1.47 % (31095)------------------------------
% 0.32/1.47 % (31095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.47 % (31095)Termination reason: Unknown
% 0.32/1.47 % (31095)Termination phase: Saturation
% 0.32/1.47
% 0.32/1.47 % (31095)Memory used [KB]: 1023
% 0.32/1.47 % (31095)Time elapsed: 0.003 s
% 0.32/1.47 % (31095)Instructions burned: 3 (million)
% 0.32/1.47 % (31095)------------------------------
% 0.32/1.47 % (31095)------------------------------
% 0.32/1.47 % (31096)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/3Mi)
% 0.32/1.47 % (31094)Instruction limit reached!
% 0.32/1.47 % (31094)------------------------------
% 0.32/1.47 % (31094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.47 % (31094)Termination reason: Unknown
% 0.32/1.47 % (31094)Termination phase: Saturation
% 0.32/1.47
% 0.32/1.47 % (31094)Memory used [KB]: 5628
% 0.32/1.47 % (31094)Time elapsed: 0.010 s
% 0.32/1.47 % (31094)Instructions burned: 16 (million)
% 0.32/1.47 % (31094)------------------------------
% 0.32/1.47 % (31094)------------------------------
% 0.32/1.47 % (31096)Instruction limit reached!
% 0.32/1.47 % (31096)------------------------------
% 0.32/1.47 % (31096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.47 % (31096)Termination reason: Unknown
% 0.32/1.47 % (31096)Termination phase: Property scanning
% 0.32/1.47
% 0.32/1.47 % (31096)Memory used [KB]: 1023
% 0.32/1.47 % (31096)Time elapsed: 0.003 s
% 0.32/1.47 % (31096)Instructions burned: 3 (million)
% 0.32/1.47 % (31096)------------------------------
% 0.32/1.47 % (31096)------------------------------
% 0.32/1.48 % (31097)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/7Mi)
% 0.32/1.48 % (31098)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/3Mi)
% 0.32/1.48 % (31098)Instruction limit reached!
% 0.32/1.48 % (31098)------------------------------
% 0.32/1.48 % (31098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (31098)Termination reason: Unknown
% 0.32/1.48 % (31098)Termination phase: Saturation
% 0.32/1.48 % (31099)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/4Mi)
% 0.32/1.48
% 0.32/1.48 % (31098)Memory used [KB]: 5500
% 0.32/1.48 % (31098)Time elapsed: 0.003 s
% 0.32/1.48 % (31098)Instructions burned: 3 (million)
% 0.32/1.48 % (31098)------------------------------
% 0.32/1.48 % (31098)------------------------------
% 0.32/1.48 % (31097)Instruction limit reached!
% 0.32/1.48 % (31097)------------------------------
% 0.32/1.48 % (31097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (31097)Termination reason: Unknown
% 0.32/1.48 % (31097)Termination phase: Saturation
% 0.32/1.48
% 0.32/1.48 % (31097)Memory used [KB]: 5500
% 0.32/1.48 % (31097)Time elapsed: 0.006 s
% 0.32/1.48 % (31097)Instructions burned: 8 (million)
% 0.32/1.48 % (31097)------------------------------
% 0.32/1.48 % (31097)------------------------------
% 0.32/1.48 % (31099)Instruction limit reached!
% 0.32/1.48 % (31099)------------------------------
% 0.32/1.48 % (31099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (31099)Termination reason: Unknown
% 0.32/1.48 % (31099)Termination phase: Saturation
% 0.32/1.48
% 0.32/1.48 % (31099)Memory used [KB]: 5500
% 0.32/1.48 % (31099)Time elapsed: 0.004 s
% 0.32/1.48 % (31099)Instructions burned: 4 (million)
% 0.32/1.48 % (31099)------------------------------
% 0.32/1.48 % (31099)------------------------------
% 0.32/1.49 % (31100)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/18Mi)
% 0.32/1.49 % (31101)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/710Mi)
% 1.71/1.50 % (31100)Instruction limit reached!
% 1.71/1.50 % (31100)------------------------------
% 1.71/1.50 % (31100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.50 % (31100)Termination reason: Unknown
% 1.71/1.50 % (31100)Termination phase: Saturation
% 1.71/1.50
% 1.71/1.50 % (31100)Memory used [KB]: 5628
% 1.71/1.50 % (31100)Time elapsed: 0.011 s
% 1.71/1.50 % (31100)Instructions burned: 18 (million)
% 1.71/1.50 % (31100)------------------------------
% 1.71/1.50 % (31100)------------------------------
% 1.71/1.50 % (31102)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/6Mi)
% 1.71/1.50 % (31103)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/902Mi)
% 1.71/1.50 % (31103)Refutation not found, incomplete strategy
% 1.71/1.50 % (31103)------------------------------
% 1.71/1.50 % (31103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.50 % (31103)Termination reason: Refutation not found, incomplete strategy
% 1.71/1.50
% 1.71/1.50
% 1.71/1.50 % (31103)Memory used [KB]: 5500
% 1.71/1.50 % (31103)Time elapsed: 0.003 s
% 1.71/1.50 % (31104)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/21Mi)
% 1.71/1.50 % (31103)Instructions burned: 3 (million)
% 1.71/1.50 % (31103)------------------------------
% 1.71/1.50 % (31103)------------------------------
% 1.71/1.50 % (31102)Instruction limit reached!
% 1.71/1.50 % (31102)------------------------------
% 1.71/1.50 % (31102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.50 % (31102)Termination reason: Unknown
% 1.71/1.50 % (31102)Termination phase: Saturation
% 1.71/1.50
% 1.71/1.50 % (31102)Memory used [KB]: 5500
% 1.71/1.50 % (31102)Time elapsed: 0.005 s
% 1.71/1.50 % (31102)Instructions burned: 7 (million)
% 1.71/1.50 % (31102)------------------------------
% 1.71/1.50 % (31102)------------------------------
% 1.71/1.50 % (31081)Instruction limit reached!
% 1.71/1.50 % (31081)------------------------------
% 1.71/1.50 % (31081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.50 % (31081)Termination reason: Unknown
% 1.71/1.50 % (31081)Termination phase: Saturation
% 1.71/1.50
% 1.71/1.50 % (31081)Memory used [KB]: 6524
% 1.71/1.50 % (31081)Time elapsed: 0.076 s
% 1.71/1.50 % (31081)Instructions burned: 185 (million)
% 1.71/1.50 % (31081)------------------------------
% 1.71/1.50 % (31081)------------------------------
% 1.71/1.51 % (31104)Instruction limit reached!
% 1.71/1.51 % (31104)------------------------------
% 1.71/1.51 % (31104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.51 % (31104)Termination reason: Unknown
% 1.71/1.51 % (31104)Termination phase: Saturation
% 1.71/1.51
% 1.71/1.51 % (31104)Memory used [KB]: 5756
% 1.71/1.51 % (31104)Time elapsed: 0.014 s
% 1.71/1.51 % (31104)Instructions burned: 22 (million)
% 1.71/1.51 % (31104)------------------------------
% 1.71/1.51 % (31104)------------------------------
% 1.71/1.51 % (31105)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/5Mi)
% 1.71/1.52 % (31105)Instruction limit reached!
% 1.71/1.52 % (31105)------------------------------
% 1.71/1.52 % (31105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.52 % (31105)Termination reason: Unknown
% 1.71/1.52 % (31105)Termination phase: Saturation
% 1.71/1.52
% 1.71/1.52 % (31105)Memory used [KB]: 5500
% 1.71/1.52 % (31105)Time elapsed: 0.004 s
% 1.71/1.52 % (31105)Instructions burned: 5 (million)
% 1.71/1.52 % (31105)------------------------------
% 1.71/1.52 % (31105)------------------------------
% 1.71/1.52 % (31106)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/6Mi)
% 1.71/1.52 % (31107)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/377Mi)
% 1.71/1.52 % (31108)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/779Mi)
% 1.71/1.52 % (31106)Instruction limit reached!
% 1.71/1.52 % (31106)------------------------------
% 1.71/1.52 % (31106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.52 % (31106)Termination reason: Unknown
% 1.71/1.52 % (31106)Termination phase: Saturation
% 1.71/1.52
% 1.71/1.52 % (31106)Memory used [KB]: 5500
% 1.71/1.52 % (31106)Time elapsed: 0.004 s
% 1.71/1.52 % (31106)Instructions burned: 6 (million)
% 1.71/1.52 % (31106)------------------------------
% 1.71/1.52 % (31106)------------------------------
% 1.71/1.53 % (31109)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/19Mi)
% 1.71/1.53 % (31110)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/879Mi)
% 1.71/1.54 % (31111)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30984 for (2999ds/17Mi)
% 1.71/1.54 % (31109)Instruction limit reached!
% 1.71/1.54 % (31109)------------------------------
% 1.71/1.54 % (31109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.54 % (31109)Termination reason: Unknown
% 1.71/1.54 % (31109)Termination phase: Saturation
% 1.71/1.54
% 1.71/1.54 % (31109)Memory used [KB]: 5500
% 1.71/1.54 % (31109)Time elapsed: 0.011 s
% 1.71/1.54 % (31109)Instructions burned: 19 (million)
% 1.71/1.54 % (31109)------------------------------
% 1.71/1.54 % (31109)------------------------------
% 1.71/1.54 % (31107)First to succeed.
% 1.71/1.55 % (31111)Instruction limit reached!
% 1.71/1.55 % (31111)------------------------------
% 1.71/1.55 % (31111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.55 % (31111)Termination reason: Unknown
% 1.71/1.55 % (31111)Termination phase: Saturation
% 1.71/1.55
% 1.71/1.55 % (31111)Memory used [KB]: 5628
% 1.71/1.55 % (31111)Time elapsed: 0.011 s
% 1.71/1.55 % (31111)Instructions burned: 18 (million)
% 1.71/1.55 % (31111)------------------------------
% 1.71/1.55 % (31111)------------------------------
% 1.71/1.55 % (31107)Refutation found. Thanks to Tanya!
% 1.71/1.55 % SZS status Theorem for DTF2THF_30984
% 1.71/1.55 % SZS output start Proof for DTF2THF_30984
% 1.71/1.55 thf(type_def_5, type, a: $tType).
% 1.71/1.55 thf(func_def_0, type, a: $tType).
% 1.71/1.55 thf(func_def_1, type, t: a).
% 1.71/1.55 thf(func_def_2, type, cA: (a > $o) > $o).
% 1.71/1.55 thf(func_def_10, type, sP0: (a > $o) > $o).
% 1.71/1.55 thf(func_def_12, type, sK2: a > $o).
% 1.71/1.55 thf(func_def_13, type, sK3: (a > $o) > (a > $o) > $o).
% 1.71/1.55 thf(func_def_14, type, sK4: (a > $o) > a).
% 1.71/1.55 thf(func_def_15, type, sK5: (a > $o) > a > $o).
% 1.71/1.55 thf(func_def_16, type, sK6: a > $o).
% 1.71/1.55 thf(func_def_18, type, ph8: !>[X0: $tType]:(X0)).
% 1.71/1.55 thf(f552,plain,(
% 1.71/1.55 $false),
% 1.71/1.55 inference(avatar_sat_refutation,[status(thm)],[f46,f47,f51,f66,f70,f74,f78,f82,f86,f551])).
% 1.71/1.55 thf(f551,plain,(
% 1.71/1.55 ~spl7_3 | ~spl7_6 | ~spl7_7 | ~spl7_8 | ~spl7_9 | ~spl7_10 | ~spl7_11),
% 1.71/1.55 inference(avatar_contradiction_clause,[status(thm)],[f550])).
% 1.71/1.55 thf(f550,plain,(
% 1.71/1.55 $false | (~spl7_3 | ~spl7_6 | ~spl7_7 | ~spl7_8 | ~spl7_9 | ~spl7_10 | ~spl7_11)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f545])).
% 1.71/1.55 thf(f545,plain,(
% 1.71/1.55 ($true = $false) | (t != t) | (~spl7_3 | ~spl7_6 | ~spl7_7 | ~spl7_8 | ~spl7_9 | ~spl7_10 | ~spl7_11)),
% 1.71/1.55 inference(superposition,[status(thm)],[f65,f542])).
% 1.71/1.55 thf(f542,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($false = (sK2 @ X0)) | (t != X0)) ) | (~spl7_3 | ~spl7_7 | ~spl7_8 | ~spl7_9 | ~spl7_10 | ~spl7_11)),
% 1.71/1.55 inference(duplicate_literal_removal,[status(thm)],[f541])).
% 1.71/1.55 thf(f541,plain,(
% 1.71/1.55 ( ! [X0 : a] : ((t != X0) | ($false = (sK2 @ X0)) | (t != X0)) ) | (~spl7_3 | ~spl7_7 | ~spl7_8 | ~spl7_9 | ~spl7_10 | ~spl7_11)),
% 1.71/1.55 inference(equality_proxy_clausification,[status(thm)],[f540])).
% 1.71/1.55 thf(f540,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (X0 = t)) | ($false = (sK2 @ X0)) | (t != X0)) ) | (~spl7_3 | ~spl7_7 | ~spl7_8 | ~spl7_9 | ~spl7_10 | ~spl7_11)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f531])).
% 1.71/1.55 thf(f531,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (X0 = t)) | (t != X0) | ($true = $false) | ($false = (sK2 @ X0))) ) | (~spl7_3 | ~spl7_7 | ~spl7_8 | ~spl7_9 | ~spl7_10 | ~spl7_11)),
% 1.71/1.55 inference(superposition,[status(thm)],[f528,f103])).
% 1.71/1.55 thf(f103,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (((sP0 @ X0) = $false) | ((X0 @ t) != $true)) )),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.71/1.55 thf(f102,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (($true != $true) | ((X0 @ t) != $true) | ((sP0 @ X0) = $false)) )),
% 1.71/1.55 inference(fool_paramodulation,[status(thm)],[f101])).
% 1.71/1.55 thf(f101,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (($true != (sP0 @ X0)) | ((X0 @ t) != $true)) )),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.71/1.55 thf(f100,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (($true != (sP0 @ X0)) | ($true != $true) | ((X0 @ t) != $true)) )),
% 1.71/1.55 inference(duplicate_literal_removal,[status(thm)],[f98])).
% 1.71/1.55 thf(f98,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (((X0 @ t) != $true) | ($true != $true) | ($true != (sP0 @ X0)) | ($true != (sP0 @ X0))) )),
% 1.71/1.55 inference(superposition,[status(thm)],[f95,f32])).
% 1.71/1.55 thf(f32,plain,(
% 1.71/1.55 ( ! [X2 : a,X0 : a > $o] : (($true = (sK5 @ X0 @ X2)) | ($true != (sP0 @ X0)) | ($true != (X0 @ X2))) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f21])).
% 1.71/1.55 thf(f21,plain,(
% 1.71/1.55 ! [X0 : a > $o] : ((($true = (cA @ (sK5 @ X0))) & (($true != (sK5 @ X0 @ t)) | ($true != (cA @ (sK5 @ X0)))) & ! [X2 : a] : (($true = (sK5 @ X0 @ X2)) | ($true != (X0 @ X2)))) | ($true != (sP0 @ X0)))),
% 1.71/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f19,f20])).
% 1.71/1.55 thf(f20,plain,(
% 1.71/1.55 ! [X0 : a > $o] : (? [X1 : a > $o] : (((cA @ X1) = $true) & (($true != (X1 @ t)) | ((cA @ X1) != $true)) & ! [X2 : a] : (($true = (X1 @ X2)) | ($true != (X0 @ X2)))) => (($true = (cA @ (sK5 @ X0))) & (($true != (sK5 @ X0 @ t)) | ($true != (cA @ (sK5 @ X0)))) & ! [X2 : a] : (($true = (sK5 @ X0 @ X2)) | ($true != (X0 @ X2)))))),
% 1.71/1.55 introduced(definition,[],[choice_axiom])).
% 1.71/1.55 thf(f19,plain,(
% 1.71/1.55 ! [X0 : a > $o] : (? [X1 : a > $o] : (((cA @ X1) = $true) & (($true != (X1 @ t)) | ((cA @ X1) != $true)) & ! [X2 : a] : (($true = (X1 @ X2)) | ($true != (X0 @ X2)))) | ($true != (sP0 @ X0)))),
% 1.71/1.55 inference(rectify,[status(thm)],[f18])).
% 1.71/1.55 thf(f18,plain,(
% 1.71/1.55 ! [X2 : a > $o] : (? [X6 : a > $o] : (($true = (cA @ X6)) & (($true != (X6 @ t)) | ($true != (cA @ X6))) & ! [X7 : a] : (($true = (X6 @ X7)) | ($true != (X2 @ X7)))) | ($true != (sP0 @ X2)))),
% 1.71/1.55 inference(nnf_transformation,[status(thm)],[f9])).
% 1.71/1.55 thf(f9,plain,(
% 1.71/1.55 ! [X2 : a > $o] : (? [X6 : a > $o] : (($true = (cA @ X6)) & (($true != (X6 @ t)) | ($true != (cA @ X6))) & ! [X7 : a] : (($true = (X6 @ X7)) | ($true != (X2 @ X7)))) | ~($true = (sP0 @ X2)))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.71/1.55 thf(f95,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (($true != (sK5 @ X0 @ t)) | ($true != (sP0 @ X0))) )),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.71/1.55 thf(f94,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (($true != (sK5 @ X0 @ t)) | ($true != (sP0 @ X0)) | ($true != $true)) )),
% 1.71/1.55 inference(duplicate_literal_removal,[status(thm)],[f93])).
% 1.71/1.55 thf(f93,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (($true != (sP0 @ X0)) | ($true != (sK5 @ X0 @ t)) | ($true != (sP0 @ X0)) | ($true != $true)) )),
% 1.71/1.55 inference(superposition,[status(thm)],[f33,f34])).
% 1.71/1.55 thf(f34,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (($true = (cA @ (sK5 @ X0))) | ($true != (sP0 @ X0))) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f21])).
% 1.71/1.55 thf(f33,plain,(
% 1.71/1.55 ( ! [X0 : a > $o] : (($true != (cA @ (sK5 @ X0))) | ($true != (sP0 @ X0)) | ($true != (sK5 @ X0 @ t))) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f21])).
% 1.71/1.55 thf(f528,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (sP0 @ (= @ X0))) | (t != X0) | ($false = (sK2 @ X0))) ) | (~spl7_3 | ~spl7_7 | ~spl7_8 | ~spl7_9 | ~spl7_10 | ~spl7_11)),
% 1.71/1.55 inference(superposition,[status(thm)],[f373,f527])).
% 1.71/1.55 thf(f527,plain,(
% 1.71/1.55 ( ! [X0 : a] : (((sK4 @ (= @ X0)) = X0) | (t != X0)) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(equality_proxy_clausification,[status(thm)],[f526])).
% 1.71/1.55 thf(f526,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (X0 = t)) | ((sK4 @ (= @ X0)) = X0)) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f521])).
% 1.71/1.55 thf(f521,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (X0 = t)) | ((sK4 @ (= @ X0)) = X0) | ($true != $true)) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(superposition,[status(thm)],[f101,f496])).
% 1.71/1.55 thf(f496,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (sP0 @ (= @ X0))) | ((sK4 @ (= @ X0)) = X0)) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(duplicate_literal_removal,[status(thm)],[f495])).
% 1.71/1.55 thf(f495,plain,(
% 1.71/1.55 ( ! [X0 : a] : (((sK4 @ (= @ X0)) = X0) | ($true = (sP0 @ (= @ X0))) | ((sK4 @ (= @ X0)) = X0)) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(equality_proxy_clausification,[status(thm)],[f494])).
% 1.71/1.55 thf(f494,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (X0 = (sK4 @ (= @ X0)))) | ((sK4 @ (= @ X0)) = X0) | ($true = (sP0 @ (= @ X0)))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f493])).
% 1.71/1.55 thf(f493,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (X0 = (sK4 @ (^[Y0 : a]: (X0 = Y0))))) | ((sK4 @ (= @ X0)) = X0) | ($true = (sP0 @ (= @ X0)))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f492])).
% 1.71/1.55 thf(f492,plain,(
% 1.71/1.55 ( ! [X0 : a] : (((sK4 @ (= @ X0)) = X0) | ($true = (sP0 @ (= @ X0))) | ($true = (X0 = (sK4 @ (^[Y0 : a]: ($false | (X0 = Y0))))))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f491])).
% 1.71/1.55 thf(f491,plain,(
% 1.71/1.55 ( ! [X0 : a] : (((sK4 @ (= @ X0)) = X0) | ($true = ($false | (X0 = (sK4 @ (^[Y0 : a]: ($false | (X0 = Y0))))))) | ($true = (sP0 @ (= @ X0)))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f490])).
% 1.71/1.55 thf(f490,plain,(
% 1.71/1.55 ( ! [X0 : a] : (((sK4 @ (^[Y0 : a]: (X0 = Y0))) = X0) | ($true = (sP0 @ (= @ X0))) | ($true = ($false | (X0 = (sK4 @ (^[Y0 : a]: ($false | (X0 = Y0)))))))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f489])).
% 1.71/1.55 thf(f489,plain,(
% 1.71/1.55 ( ! [X0 : a] : (((sK4 @ (^[Y0 : a]: ($false | (X0 = Y0)))) = X0) | ($true = ($false | (X0 = (sK4 @ (^[Y0 : a]: ($false | (X0 = Y0))))))) | ($true = (sP0 @ (= @ X0)))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f488])).
% 1.71/1.55 thf(f488,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = ($false | (X0 = (sK4 @ (^[Y0 : a]: ($false | (X0 = Y0))))))) | ($true = (sP0 @ (^[Y0 : a]: (X0 = Y0)))) | ((sK4 @ (^[Y0 : a]: ($false | (X0 = Y0)))) = X0)) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f487])).
% 1.71/1.55 thf(f487,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (sP0 @ (^[Y0 : a]: ($false | (X0 = Y0))))) | ((sK4 @ (^[Y0 : a]: ($false | (X0 = Y0)))) = X0) | ($true = ($false | (X0 = (sK4 @ (^[Y0 : a]: ($false | (X0 = Y0)))))))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f486])).
% 1.71/1.55 thf(f486,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (sP0 @ (^[Y0 : a]: ($false | (X0 = Y0))))) | ($true = ($false | (X0 = (sK4 @ (^[Y0 : a]: ($false | (X0 = Y0))))))) | ((sK4 @ (^[Y0 : a]: ($false | (X0 = Y0)))) = X0) | ($true = $false)) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f485])).
% 1.71/1.55 thf(f485,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (sP0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) | ($true = ((^[Y0 : a]: ($false)) @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true = ((^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))) @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ((sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))) = X0)) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f484])).
% 1.71/1.55 thf(f484,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != $true) | ((sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))) = X0) | ($true = ((^[Y0 : a]: ($false)) @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true = (sP0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) | ($true = ((^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))) @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(duplicate_literal_removal,[status(thm)],[f466])).
% 1.71/1.55 thf(f466,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = ((^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))) @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true = ((^[Y0 : a]: ($false)) @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ((sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))) = X0) | ($true != $true) | ($true = (sP0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) | ($true = (sP0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) ) | (~spl7_8 | ~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(superposition,[status(thm)],[f328,f73])).
% 1.71/1.55 thf(f73,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (($true = (sK3 @ X1 @ (^[Y0 : a]: ($false)))) | ($true = (sP0 @ X1)) | ($true = (X1 @ (sK4 @ X1)))) ) | ~spl7_8),
% 1.71/1.55 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.71/1.55 thf(f72,definition,(
% 1.71/1.55 spl7_8 <=> ! [X1 : a > $o] : (($true = (X1 @ (sK4 @ X1))) | ($true = (sK3 @ X1 @ (^[Y0 : a]: ($false)))) | ($true = (sP0 @ X1)))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_8])],[avatar_definition])).
% 1.71/1.55 thf(f328,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true = (X0 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ((sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))) = X1) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(equality_proxy_clausification,[status(thm)],[f327])).
% 1.71/1.55 thf(f327,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (((X1 = (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) = $true) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true = (X0 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))))) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(binary_proxy_clausification,[status(thm)],[f326])).
% 1.71/1.55 thf(f326,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true = ((X0 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | (X1 = (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))))) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f325])).
% 1.71/1.55 thf(f325,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true != $true) | ($true = ((X0 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | (X1 = (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))))) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f324])).
% 1.71/1.55 thf(f324,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true != ((X0 @ X1) | $true)) | ($true = ((X0 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | (X1 = (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))))) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f323])).
% 1.71/1.55 thf(f323,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true = ((X0 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | (X1 = (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))))) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != ((X0 @ X1) | (X1 = X1))) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0))) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f322])).
% 1.71/1.55 thf(f322,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true != ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X1)) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true = ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))))) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f321])).
% 1.71/1.55 thf(f321,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X1)) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true = ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ($true = $false)) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(duplicate_literal_removal,[status(thm)],[f275])).
% 1.71/1.55 thf(f275,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true = ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ($true = $false) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X1)) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true = ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))))) ) | (~spl7_9 | ~spl7_10)),
% 1.71/1.55 inference(superposition,[status(thm)],[f77,f121])).
% 1.71/1.55 thf(f121,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (((sK3 @ X1 @ X1) = $false) | ($true = (sP0 @ X1)) | ($true = (X1 @ (sK4 @ X1)))) ) | ~spl7_10),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.71/1.55 thf(f120,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (($true != $true) | ($true = (sP0 @ X1)) | ($true = (X1 @ (sK4 @ X1))) | ((sK3 @ X1 @ X1) = $false)) ) | ~spl7_10),
% 1.71/1.55 inference(fool_paramodulation,[status(thm)],[f81])).
% 1.71/1.55 thf(f81,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (((sK3 @ X1 @ X1) != $true) | ($true = (sP0 @ X1)) | ($true = (X1 @ (sK4 @ X1)))) ) | ~spl7_10),
% 1.71/1.55 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.71/1.55 thf(f80,definition,(
% 1.71/1.55 spl7_10 <=> ! [X1 : a > $o] : (($true = (sP0 @ X1)) | ($true = (X1 @ (sK4 @ X1))) | ((sK3 @ X1 @ X1) != $true))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_10])],[avatar_definition])).
% 1.71/1.55 thf(f77,plain,(
% 1.71/1.55 ( ! [X3 : a > $o,X1 : a > $o,X4 : a] : (($true = (sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0))))) | ((X1 @ X4) != $true) | ($true = (sP0 @ X1)) | ($true != (sK3 @ X1 @ X3)) | ($true = (X1 @ (sK4 @ X1)))) ) | ~spl7_9),
% 1.71/1.55 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.71/1.55 thf(f76,definition,(
% 1.71/1.55 spl7_9 <=> ! [X4 : a,X1 : a > $o,X3 : a > $o] : (($true = (sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0))))) | ($true = (sP0 @ X1)) | ($true != (sK3 @ X1 @ X3)) | ($true = (X1 @ (sK4 @ X1))) | ((X1 @ X4) != $true))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_9])],[avatar_definition])).
% 1.71/1.55 thf(f373,plain,(
% 1.71/1.55 ( ! [X0 : a] : (((sK2 @ (sK4 @ (= @ X0))) = $false) | ($true = (sP0 @ (= @ X0)))) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f372])).
% 1.71/1.55 thf(f372,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != $true) | ((sK2 @ (sK4 @ (= @ X0))) = $false) | ($true = (sP0 @ (= @ X0)))) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(fool_paramodulation,[status(thm)],[f363])).
% 1.71/1.55 thf(f363,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (sK2 @ (sK4 @ (= @ X0)))) | ($true = (sP0 @ (= @ X0)))) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f362])).
% 1.71/1.55 thf(f362,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (sK2 @ (sK4 @ (= @ X0)))) | ($true = (sP0 @ (^[Y0 : a]: (X0 = Y0))))) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f361])).
% 1.71/1.55 thf(f361,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (sP0 @ (^[Y0 : a]: ($false | (X0 = Y0))))) | ($true != (sK2 @ (sK4 @ (= @ X0))))) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f360])).
% 1.71/1.55 thf(f360,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (sK2 @ (sK4 @ (^[Y0 : a]: (X0 = Y0))))) | ($true = (sP0 @ (^[Y0 : a]: ($false | (X0 = Y0)))))) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f359])).
% 1.71/1.55 thf(f359,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (sK2 @ (sK4 @ (^[Y0 : a]: ($false | (X0 = Y0)))))) | ($true = (sP0 @ (^[Y0 : a]: ($false | (X0 = Y0)))))) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f358])).
% 1.71/1.55 thf(f358,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (sP0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))))) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f357])).
% 1.71/1.55 thf(f357,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true != (sK2 @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true = (sP0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) | ($true != $true)) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(duplicate_literal_removal,[status(thm)],[f333])).
% 1.71/1.55 thf(f333,plain,(
% 1.71/1.55 ( ! [X0 : a] : (($true = (sP0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true = (sP0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true != $true)) ) | (~spl7_3 | ~spl7_7 | ~spl7_11)),
% 1.71/1.55 inference(superposition,[status(thm)],[f272,f85])).
% 1.71/1.55 thf(f85,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (($true = (sK3 @ X1 @ (^[Y0 : a]: ($false)))) | ($true = (sP0 @ X1)) | ($true != (sK2 @ (sK4 @ X1)))) ) | ~spl7_11),
% 1.71/1.55 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.71/1.55 thf(f84,definition,(
% 1.71/1.55 spl7_11 <=> ! [X1 : a > $o] : (($true = (sK3 @ X1 @ (^[Y0 : a]: ($false)))) | ($true = (sP0 @ X1)) | ($true != (sK2 @ (sK4 @ X1))))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_11])],[avatar_definition])).
% 1.71/1.55 thf(f272,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))))) ) | (~spl7_3 | ~spl7_7)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f271])).
% 1.71/1.55 thf(f271,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ($true != $true)) ) | (~spl7_3 | ~spl7_7)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f270])).
% 1.71/1.55 thf(f270,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true != ((X0 @ X1) | $true)) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))))) ) | (~spl7_3 | ~spl7_7)),
% 1.71/1.55 inference(boolean_simplification,[status(thm)],[f269])).
% 1.71/1.55 thf(f269,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true != ((X0 @ X1) | (X1 = X1)))) ) | (~spl7_3 | ~spl7_7)),
% 1.71/1.55 inference(beta_eta_normalization,[status(thm)],[f268])).
% 1.71/1.55 thf(f268,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true != ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X1)) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0))) ) | (~spl7_3 | ~spl7_7)),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f267])).
% 1.71/1.55 thf(f267,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ($true = $false) | ($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true != ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X1))) ) | (~spl7_3 | ~spl7_7)),
% 1.71/1.55 inference(duplicate_literal_removal,[status(thm)],[f228])).
% 1.71/1.55 thf(f228,plain,(
% 1.71/1.55 ( ! [X0 : a > $o,X1 : a] : (($true != (sK3 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X0)) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ($true != ((^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))) @ X1)) | ($true = $false) | ($true != (sK2 @ (sK4 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0))))) | ($true = (sP0 @ (^[Y0 : a]: ((X0 @ Y0) | (X1 = Y0)))))) ) | (~spl7_3 | ~spl7_7)),
% 1.71/1.55 inference(superposition,[status(thm)],[f119,f50])).
% 1.71/1.55 thf(f50,plain,(
% 1.71/1.55 ( ! [X3 : a > $o,X1 : a > $o,X4 : a] : (($true = (sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0))))) | ($true = (sP0 @ X1)) | ($true != (sK2 @ (sK4 @ X1))) | ((X1 @ X4) != $true) | ($true != (sK3 @ X1 @ X3))) ) | ~spl7_3),
% 1.71/1.55 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.71/1.55 thf(f49,definition,(
% 1.71/1.55 spl7_3 <=> ! [X4 : a,X1 : a > $o,X3 : a > $o] : (($true = (sP0 @ X1)) | ((X1 @ X4) != $true) | ($true = (sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0))))) | ($true != (sK2 @ (sK4 @ X1))) | ($true != (sK3 @ X1 @ X3)))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition])).
% 1.71/1.55 thf(f119,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (((sK3 @ X1 @ X1) = $false) | ($true = (sP0 @ X1)) | ($true != (sK2 @ (sK4 @ X1)))) ) | ~spl7_7),
% 1.71/1.55 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.71/1.55 thf(f118,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (($true != (sK2 @ (sK4 @ X1))) | ($true = (sP0 @ X1)) | ($true != $true) | ((sK3 @ X1 @ X1) = $false)) ) | ~spl7_7),
% 1.71/1.55 inference(fool_paramodulation,[status(thm)],[f69])).
% 1.71/1.55 thf(f69,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (((sK3 @ X1 @ X1) != $true) | ($true != (sK2 @ (sK4 @ X1))) | ($true = (sP0 @ X1))) ) | ~spl7_7),
% 1.71/1.55 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.71/1.55 thf(f68,definition,(
% 1.71/1.55 spl7_7 <=> ! [X1 : a > $o] : (($true = (sP0 @ X1)) | ((sK3 @ X1 @ X1) != $true) | ($true != (sK2 @ (sK4 @ X1))))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_7])],[avatar_definition])).
% 1.71/1.55 thf(f65,plain,(
% 1.71/1.55 ($true = (sK2 @ t)) | ~spl7_6),
% 1.71/1.55 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.71/1.55 thf(f63,definition,(
% 1.71/1.55 spl7_6 <=> ($true = (sK2 @ t))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition])).
% 1.71/1.55 thf(f86,plain,(
% 1.71/1.55 spl7_11 | ~spl7_2),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f29,f43,f84])).
% 1.71/1.55 thf(f43,definition,(
% 1.71/1.55 spl7_2 <=> ($true = sP1)),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 1.71/1.55 thf(f29,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (($true = (sK3 @ X1 @ (^[Y0 : a]: ($false)))) | ($true != (sK2 @ (sK4 @ X1))) | ($true = (sP0 @ X1)) | ($true != sP1)) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.55 thf(f17,plain,(
% 1.71/1.55 (! [X1 : a > $o] : ((((sK3 @ X1 @ X1) != $true) & ($true = (sK3 @ X1 @ (^[Y0 : a]: ($false)))) & ! [X3 : a > $o] : (($true != (sK3 @ X1 @ X3)) | ! [X4 : a] : (((X1 @ X4) != $true) | ($true = (sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))))) | (($true != (sK2 @ (sK4 @ X1))) & ($true = (X1 @ (sK4 @ X1)))) | ($true = (sP0 @ X1))) & ($true = (cA @ sK2)) & ($true = (sK2 @ t))) | ($true != sP1)),
% 1.71/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f13,f16,f15,f14])).
% 1.71/1.55 thf(f14,plain,(
% 1.71/1.55 ? [X0 : a > $o] : (! [X1 : a > $o] : (? [X2 : (a > $o) > $o] : (((X2 @ X1) != $true) & ($true = (X2 @ (^[Y0 : a]: ($false)))) & ! [X3 : a > $o] : (($true != (X2 @ X3)) | ! [X4 : a] : (((X1 @ X4) != $true) | ($true = (X2 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))))) | ? [X5 : a] : (($true != (X0 @ X5)) & ((X1 @ X5) = $true)) | ($true = (sP0 @ X1))) & ((cA @ X0) = $true) & ((X0 @ t) = $true)) => (! [X1 : a > $o] : (? [X2 : (a > $o) > $o] : (((X2 @ X1) != $true) & ($true = (X2 @ (^[Y0 : a]: ($false)))) & ! [X3 : a > $o] : (($true != (X2 @ X3)) | ! [X4 : a] : (((X1 @ X4) != $true) | ($true = (X2 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))))) | ? [X5 : a] : (($true != (sK2 @ X5)) & ((X1 @ X5) = $true)) | ($true = (sP0 @ X1))) & ($true = (cA @ sK2)) & ($true = (sK2 @ t)))),
% 1.71/1.55 introduced(definition,[],[choice_axiom])).
% 1.71/1.55 thf(f15,plain,(
% 1.71/1.55 ! [X1 : a > $o] : (? [X2 : (a > $o) > $o] : (((X2 @ X1) != $true) & ($true = (X2 @ (^[Y0 : a]: ($false)))) & ! [X3 : a > $o] : (($true != (X2 @ X3)) | ! [X4 : a] : (((X1 @ X4) != $true) | ($true = (X2 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))))) => (((sK3 @ X1 @ X1) != $true) & ($true = (sK3 @ X1 @ (^[Y0 : a]: ($false)))) & ! [X3 : a > $o] : (($true != (sK3 @ X1 @ X3)) | ! [X4 : a] : (((X1 @ X4) != $true) | ($true = (sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))))))),
% 1.71/1.55 introduced(definition,[],[choice_axiom])).
% 1.71/1.55 thf(f16,plain,(
% 1.71/1.55 ! [X1 : a > $o] : (? [X5 : a] : (($true != (sK2 @ X5)) & ((X1 @ X5) = $true)) => (($true != (sK2 @ (sK4 @ X1))) & ($true = (X1 @ (sK4 @ X1)))))),
% 1.71/1.55 introduced(definition,[],[choice_axiom])).
% 1.71/1.55 thf(f13,plain,(
% 1.71/1.55 ? [X0 : a > $o] : (! [X1 : a > $o] : (? [X2 : (a > $o) > $o] : (((X2 @ X1) != $true) & ($true = (X2 @ (^[Y0 : a]: ($false)))) & ! [X3 : a > $o] : (($true != (X2 @ X3)) | ! [X4 : a] : (((X1 @ X4) != $true) | ($true = (X2 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))))) | ? [X5 : a] : (($true != (X0 @ X5)) & ((X1 @ X5) = $true)) | ($true = (sP0 @ X1))) & ((cA @ X0) = $true) & ((X0 @ t) = $true)) | ($true != sP1)),
% 1.71/1.55 inference(rectify,[status(thm)],[f12])).
% 1.71/1.55 thf(f12,plain,(
% 1.71/1.55 ? [X1 : a > $o] : (! [X2 : a > $o] : (? [X3 : (a > $o) > $o] : (($true != (X3 @ X2)) & ($true = (X3 @ (^[Y0 : a]: ($false)))) & ! [X4 : a > $o] : (($true != (X3 @ X4)) | ! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X3 @ (^[Y0 : a]: ((X4 @ Y0) | (X5 = Y0)))))))) | ? [X8 : a] : (($true != (X1 @ X8)) & ($true = (X2 @ X8))) | ($true = (sP0 @ X2))) & ((cA @ X1) = $true) & ($true = (X1 @ t))) | ($true != sP1)),
% 1.71/1.55 inference(nnf_transformation,[status(thm)],[f10])).
% 1.71/1.55 thf(f10,plain,(
% 1.71/1.55 ? [X1 : a > $o] : (! [X2 : a > $o] : (? [X3 : (a > $o) > $o] : (($true != (X3 @ X2)) & ($true = (X3 @ (^[Y0 : a]: ($false)))) & ! [X4 : a > $o] : (($true != (X3 @ X4)) | ! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X3 @ (^[Y0 : a]: ((X4 @ Y0) | (X5 = Y0)))))))) | ? [X8 : a] : (($true != (X1 @ X8)) & ($true = (X2 @ X8))) | ($true = (sP0 @ X2))) & ((cA @ X1) = $true) & ($true = (X1 @ t))) | ~($true = sP1)),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.71/1.55 thf(f82,plain,(
% 1.71/1.55 ~spl7_2 | spl7_10),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f30,f80,f43])).
% 1.71/1.55 thf(f30,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (($true = (sP0 @ X1)) | ($true != sP1) | ((sK3 @ X1 @ X1) != $true) | ($true = (X1 @ (sK4 @ X1)))) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.55 thf(f78,plain,(
% 1.71/1.55 spl7_9 | ~spl7_2),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f26,f43,f76])).
% 1.71/1.55 thf(f26,plain,(
% 1.71/1.55 ( ! [X3 : a > $o,X1 : a > $o,X4 : a] : (($true = (sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0))))) | ((X1 @ X4) != $true) | ($true = (X1 @ (sK4 @ X1))) | ($true != sP1) | ($true != (sK3 @ X1 @ X3)) | ($true = (sP0 @ X1))) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.55 thf(f74,plain,(
% 1.71/1.55 ~spl7_2 | spl7_8),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f28,f72,f43])).
% 1.71/1.55 thf(f28,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (($true != sP1) | ($true = (X1 @ (sK4 @ X1))) | ($true = (sP0 @ X1)) | ($true = (sK3 @ X1 @ (^[Y0 : a]: ($false))))) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.55 thf(f70,plain,(
% 1.71/1.55 spl7_7 | ~spl7_2),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f31,f43,f68])).
% 1.71/1.55 thf(f31,plain,(
% 1.71/1.55 ( ! [X1 : a > $o] : (($true = (sP0 @ X1)) | ($true != sP1) | ($true != (sK2 @ (sK4 @ X1))) | ((sK3 @ X1 @ X1) != $true)) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.55 thf(f66,plain,(
% 1.71/1.55 ~spl7_2 | spl7_6),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f24,f63,f43])).
% 1.71/1.55 thf(f24,plain,(
% 1.71/1.55 ($true != sP1) | ($true = (sK2 @ t))),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.55 thf(f51,plain,(
% 1.71/1.55 ~spl7_2 | spl7_3),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f27,f49,f43])).
% 1.71/1.55 thf(f27,plain,(
% 1.71/1.55 ( ! [X3 : a > $o,X1 : a > $o,X4 : a] : (($true = (sP0 @ X1)) | ($true != (sK3 @ X1 @ X3)) | ($true != (sK2 @ (sK4 @ X1))) | ($true = (sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0))))) | ((X1 @ X4) != $true) | ($true != sP1)) )),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.55 thf(f47,plain,(
% 1.71/1.55 spl7_2 | spl7_1),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f35,f39,f43])).
% 1.71/1.55 thf(f39,definition,(
% 1.71/1.55 spl7_1 <=> ($true = (cA @ sK6))),
% 1.71/1.55 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 1.71/1.55 thf(f35,plain,(
% 1.71/1.55 ($true = sP1) | ($true = (cA @ sK6))),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f23])).
% 1.71/1.55 thf(f23,plain,(
% 1.71/1.55 ($true = sP1) | (($true != (cA @ sK6)) & ($true = (sK6 @ t)) & ($true = (cA @ sK6)))),
% 1.71/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f11,f22])).
% 1.71/1.55 thf(f22,plain,(
% 1.71/1.55 ? [X0 : a > $o] : (((cA @ X0) != $true) & ((X0 @ t) = $true) & ((cA @ X0) = $true)) => (($true != (cA @ sK6)) & ($true = (sK6 @ t)) & ($true = (cA @ sK6)))),
% 1.71/1.55 introduced(definition,[],[choice_axiom])).
% 1.71/1.55 thf(f11,plain,(
% 1.71/1.55 ($true = sP1) | ? [X0 : a > $o] : (((cA @ X0) != $true) & ((X0 @ t) = $true) & ((cA @ X0) = $true))),
% 1.71/1.55 inference(definition_folding,[status(thm)],[f8,f10,f9])).
% 1.71/1.55 thf(f8,plain,(
% 1.71/1.55 ? [X1 : a > $o] : (! [X2 : a > $o] : (? [X3 : (a > $o) > $o] : (($true != (X3 @ X2)) & ($true = (X3 @ (^[Y0 : a]: ($false)))) & ! [X4 : a > $o] : (($true != (X3 @ X4)) | ! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X3 @ (^[Y0 : a]: ((X4 @ Y0) | (X5 = Y0)))))))) | ? [X8 : a] : (($true != (X1 @ X8)) & ($true = (X2 @ X8))) | ? [X6 : a > $o] : (($true = (cA @ X6)) & (($true != (X6 @ t)) | ($true != (cA @ X6))) & ! [X7 : a] : (($true = (X6 @ X7)) | ($true != (X2 @ X7))))) & ((cA @ X1) = $true) & ($true = (X1 @ t))) | ? [X0 : a > $o] : (((cA @ X0) != $true) & ((X0 @ t) = $true) & ((cA @ X0) = $true))),
% 1.71/1.55 inference(flattening,[status(thm)],[f7])).
% 1.71/1.55 thf(f7,plain,(
% 1.71/1.55 ? [X1 : a > $o] : (! [X2 : a > $o] : (? [X6 : a > $o] : ((($true != (X6 @ t)) | ($true != (cA @ X6))) & (($true = (cA @ X6)) & ! [X7 : a] : (($true = (X6 @ X7)) | ($true != (X2 @ X7))))) | ? [X8 : a] : (($true != (X1 @ X8)) & ($true = (X2 @ X8))) | ? [X3 : (a > $o) > $o] : (($true != (X3 @ X2)) & (($true = (X3 @ (^[Y0 : a]: ($false)))) & ! [X4 : a > $o] : (($true != (X3 @ X4)) | ! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X3 @ (^[Y0 : a]: ((X4 @ Y0) | (X5 = Y0)))))))))) & (($true = (X1 @ t)) & ((cA @ X1) = $true))) | ? [X0 : a > $o] : (((cA @ X0) != $true) & (((cA @ X0) = $true) & ((X0 @ t) = $true)))),
% 1.71/1.55 inference(ennf_transformation,[status(thm)],[f6])).
% 1.71/1.55 thf(f6,plain,(
% 1.71/1.55 ~(! [X1 : a > $o] : ((($true = (X1 @ t)) & ((cA @ X1) = $true)) => ? [X2 : a > $o] : (! [X6 : a > $o] : ((($true = (cA @ X6)) & ! [X7 : a] : (($true = (X2 @ X7)) => ($true = (X6 @ X7)))) => (($true = (X6 @ t)) & ($true = (cA @ X6)))) & ! [X8 : a] : (($true = (X2 @ X8)) => ($true = (X1 @ X8))) & ! [X3 : (a > $o) > $o] : ((($true = (X3 @ (^[Y0 : a]: ($false)))) & ! [X4 : a > $o] : (($true = (X3 @ X4)) => ! [X5 : a] : (($true = (X2 @ X5)) => ($true = (X3 @ (^[Y0 : a]: ((X4 @ Y0) | (X5 = Y0)))))))) => ($true = (X3 @ X2))))) & ! [X0 : a > $o] : ((((cA @ X0) = $true) & ((X0 @ t) = $true)) => ((cA @ X0) = $true)))),
% 1.71/1.55 inference(rectify,[status(thm)],[f5])).
% 1.71/1.55 thf(f5,plain,(
% 1.71/1.55 ~(! [X0 : a > $o] : ((((cA @ X0) = $true) & ((X0 @ t) = $true)) => ((cA @ X0) = $true)) & ! [X1 : a > $o] : ((($true = (X1 @ t)) & ((cA @ X1) = $true)) => ? [X2 : a > $o] : (! [X3 : (a > $o) > $o] : ((($true = (X3 @ (^[Y0 : a]: ($false)))) & ! [X5 : a > $o] : (((X3 @ X5) = $true) => ! [X6 : a] : (($true = (X2 @ X6)) => ($true = (X3 @ (^[Y0 : a]: ((X5 @ Y0) | (X6 = Y0)))))))) => ($true = (X3 @ X2))) & ! [X8 : a > $o] : ((($true = (cA @ X8)) & ! [X9 : a] : (($true = (X2 @ X9)) => ($true = (X8 @ X9)))) => (($true = (cA @ X8)) & ($true = (X8 @ t)))) & ! [X10 : a] : (($true = (X2 @ X10)) => ($true = (X1 @ X10))))))),
% 1.71/1.55 inference(fool_elimination,[status(thm)],[f4])).
% 1.71/1.55 thf(f4,plain,(
% 1.71/1.55 ~(! [X0 : a > $o] : (((X0 @ t) & (cA @ X0)) => (cA @ X0)) & ! [X1 : a > $o] : (((cA @ X1) & (X1 @ t)) => ? [X2 : a > $o] : (! [X3 : (a > $o) > $o] : (((X3 @ (^[X4 : a] : ($false))) & ! [X5 : a > $o] : ((X3 @ X5) => ! [X6 : a] : ((X2 @ X6) => (X3 @ (^[X7 : a] : ((X6 = X7) | (X5 @ X7))))))) => (X3 @ X2)) & ! [X8 : a > $o] : (((cA @ X8) & ! [X9 : a] : ((X2 @ X9) => (X8 @ X9))) => ((cA @ X8) & (X8 @ t))) & ! [X10 : a] : ((X2 @ X10) => (X1 @ X10)))))),
% 1.71/1.55 inference(rectify,[status(thm)],[f2])).
% 1.71/1.55 thf(f2,negated_conjecture,(
% 1.71/1.55 ~(! [X0 : a > $o] : (((X0 @ t) & (cA @ X0)) => (cA @ X0)) & ! [X0 : a > $o] : (((cA @ X0) & (X0 @ t)) => ? [X1 : a > $o] : (! [X2 : (a > $o) > $o] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : a > $o] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X5 = X6) | (X4 @ X6))))))) => (X2 @ X1)) & ! [X3 : a > $o] : (((cA @ X3) & ! [X4 : a] : ((X1 @ X4) => (X3 @ X4))) => ((cA @ X3) & (X3 @ t))) & ! [X4 : a] : ((X1 @ X4) => (X0 @ X4)))))),
% 1.71/1.55 inference(negated_conjecture,[status(cth)],[f1])).
% 1.71/1.55 thf(f1,conjecture,(
% 1.71/1.55 ! [X0 : a > $o] : (((X0 @ t) & (cA @ X0)) => (cA @ X0)) & ! [X0 : a > $o] : (((cA @ X0) & (X0 @ t)) => ? [X1 : a > $o] : (! [X2 : (a > $o) > $o] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : a > $o] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X5 = X6) | (X4 @ X6))))))) => (X2 @ X1)) & ! [X3 : a > $o] : (((cA @ X3) & ! [X4 : a] : ((X1 @ X4) => (X3 @ X4))) => ((cA @ X3) & (X3 @ t))) & ! [X4 : a] : ((X1 @ X4) => (X0 @ X4))))),
% 1.71/1.55 file('/export/starexec/sandbox/tmp/tmp.BIG0Vhr8BN/DTF2THF_30984.p',cDOMLEMMA5_pme)).
% 1.71/1.55 thf(f46,plain,(
% 1.71/1.55 ~spl7_1 | spl7_2),
% 1.71/1.55 inference(avatar_split_clause,[status(thm)],[f37,f43,f39])).
% 1.71/1.55 thf(f37,plain,(
% 1.71/1.55 ($true != (cA @ sK6)) | ($true = sP1)),
% 1.71/1.55 inference(cnf_transformation,[status(thm)],[f23])).
% 1.71/1.55 % SZS output end Proof for DTF2THF_30984
% 1.71/1.55 % (31107)------------------------------
% 1.71/1.55 % (31107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.55 % (31107)Termination reason: Refutation
% 1.71/1.55
% 1.71/1.55 % (31107)Memory used [KB]: 5756
% 1.71/1.55 % (31107)Time elapsed: 0.032 s
% 1.71/1.55 % (31107)Instructions burned: 52 (million)
% 1.71/1.55 % (31107)------------------------------
% 1.71/1.55 % (31107)------------------------------
% 1.71/1.55 % (31080)Success in time 0.121 s
%------------------------------------------------------------------------------