%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV095^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:16 AM UTC 2026
% Result : Theorem 1.69s 1.59s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 2 unt; 0 typ; 2 def)
% Number of atoms : 934 ( 381 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 1318 ( 109 ~; 149 |; 61 &; 980 @)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 806 ( 806 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 866 ( 666 ^; 139 !; 61 ?; 866 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sP0: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $o ).
thf(func_def_4,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_5,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_6,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_8,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_9,type,
sK6: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_10,type,
sK7: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_11,type,
sK8: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
sK9: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_15,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f988,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f186,f601,f987]) ).
thf(f987,plain,
~ spl10_2,
inference(avatar_contradiction_clause,[status(thm)],[f986]) ).
thf(f986,plain,
( $false
| ~ spl10_2 ),
inference(subsumption_resolution,[status(thm)],[f974,f673]) ).
thf(f673,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_2 ),
inference(subsumption_resolution,[status(thm)],[f672,f185]) ).
thf(f185,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[status(thm)],[f183]) ).
thf(f183,definition,
( spl10_2
<=> ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition]) ).
thf(f672,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( $true
!= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_2 ),
inference(equality_proxy_clausification,[status(thm)],[f671]) ).
thf(f671,plain,
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
!= $true )
| ( $true
!= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_2 ),
inference(beta_eta_normalization,[status(thm)],[f666]) ).
thf(f666,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) )
| ( $true
!= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f22,f614]) ).
thf(f614,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_2 ),
inference(equality_proxy_clausification,[status(thm)],[f613]) ).
thf(f613,plain,
( ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f612]) ).
thf(f612,plain,
( ( $true = $false )
| ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) )
| ~ spl10_2 ),
inference(beta_eta_normalization,[status(thm)],[f611]) ).
thf(f611,plain,
( ! [X0: $i] :
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X0 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X0 ) ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f610]) ).
thf(f610,plain,
( ! [X0: $i] :
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X0 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X0 ) )
| ( $true != $true ) )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f20,f185]) ).
thf(f20,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i] :
( ( $true
!= ( sP0 @ X1 @ X0 ) )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
= $true )
| ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
& ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 )
= $true ) )
& ! [X7: $i] :
( ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 ) )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
= $true ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f11,f13,f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ? [X5: $i] :
( ( $true
!= ( X0 @ X2 @ X4 @ X5 ) )
& ( $true
!= ( X1 @ X2 @ X4 @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ X2 @ X3 @ X6 ) )
| ( $true
= ( X1 @ X2 @ X3 @ X6 ) ) )
& ! [X7: $i] :
( ( ( X1 @ X3 @ X4 @ X7 )
= $true )
| ( $true
= ( X0 @ X3 @ X4 @ X7 ) ) ) )
=> ( ? [X5: $i] :
( ( $true
!= ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X5 ) )
& ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 )
= $true ) )
& ! [X7: $i] :
( ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 ) )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X5: $i] :
( ( $true
!= ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X5 ) )
& ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X5 ) ) )
=> ( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
& ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ? [X5: $i] :
( ( $true
!= ( X0 @ X2 @ X4 @ X5 ) )
& ( $true
!= ( X1 @ X2 @ X4 @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ X2 @ X3 @ X6 ) )
| ( $true
= ( X1 @ X2 @ X3 @ X6 ) ) )
& ! [X7: $i] :
( ( ( X1 @ X3 @ X4 @ X7 )
= $true )
| ( $true
= ( X0 @ X3 @ X4 @ X7 ) ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X3: $i > $o,X2: $i > $o,X4: $i > $o] :
( ? [X7: $i] :
( ( ( X1 @ X3 @ X4 @ X7 )
!= $true )
& ( $true
!= ( X0 @ X3 @ X4 @ X7 ) ) )
& ! [X5: $i] :
( ( $true
= ( X1 @ X3 @ X2 @ X5 ) )
| ( $true
= ( X0 @ X3 @ X2 @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ X2 @ X4 @ X6 ) )
| ( $true
= ( X1 @ X2 @ X4 @ X6 ) ) ) )
| ( $true
!= ( sP0 @ X0 @ X1 ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X3: $i > $o,X2: $i > $o,X4: $i > $o] :
( ? [X7: $i] :
( ( ( X1 @ X3 @ X4 @ X7 )
!= $true )
& ( $true
!= ( X0 @ X3 @ X4 @ X7 ) ) )
& ! [X5: $i] :
( ( $true
= ( X1 @ X3 @ X2 @ X5 ) )
| ( $true
= ( X0 @ X3 @ X2 @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ X2 @ X4 @ X6 ) )
| ( $true
= ( X1 @ X2 @ X4 @ X6 ) ) ) )
| ( $true
!= ( sP0 @ X0 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f974,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_2 ),
inference(equality_proxy_clausification,[status(thm)],[f973]) ).
thf(f973,plain,
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
= $true )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f972]) ).
thf(f972,plain,
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
= $true )
| ( $true = $false )
| ~ spl10_2 ),
inference(beta_eta_normalization,[status(thm)],[f971]) ).
thf(f971,plain,
( ! [X0: $i] :
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X0 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X0 ) ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f968]) ).
thf(f968,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X0 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X0 ) ) )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f21,f185]) ).
thf(f21,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
!= ( sP0 @ X1 @ X0 ) )
| ( $true
= ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f601,plain,
( ~ spl10_1
| spl10_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f600]) ).
thf(f600,plain,
( $false
| ~ spl10_1
| spl10_2 ),
inference(subsumption_resolution,[status(thm)],[f595,f184]) ).
thf(f184,plain,
( ( $true
!= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| spl10_2 ),
inference(avatar_component_clause,[status(thm)],[f183]) ).
thf(f595,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_1
| spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f592]) ).
thf(f592,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( $true = $false )
| ~ spl10_1
| spl10_2 ),
inference(superposition,[status(thm)],[f37,f540]) ).
thf(f540,plain,
( ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $false )
| ~ spl10_1
| spl10_2 ),
inference(subsumption_resolution,[status(thm)],[f539,f184]) ).
thf(f539,plain,
( ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $false )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ~ spl10_1 ),
inference(trivial_inequality_removal,[status(thm)],[f538]) ).
thf(f538,plain,
( ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
= $false )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( $true != $true )
| ~ spl10_1 ),
inference(superposition,[status(thm)],[f61,f432]) ).
thf(f432,plain,
( ! [X1: $i] :
( ( $true
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 )
= $false ) )
| ~ spl10_1 ),
inference(binary_proxy_clausification,[status(thm)],[f429]) ).
thf(f429,plain,
( ! [X1: $i] :
( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ~ spl10_1 ),
inference(argument_congruence,[status(thm)],[f181]) ).
thf(f181,plain,
( ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[status(thm)],[f179]) ).
thf(f179,definition,
( spl10_1
<=> ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition]) ).
thf(f61,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true != $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ( $true
!= ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK6 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK6 @ X1 @ X0 ) ) )
| ( $true
!= ( sK7 @ X1 @ X0 @ ( sK9 @ X1 @ X0 ) ) )
| ( $true
= ( sP0 @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK6 @ X1 @ X0 ) )
!= $true )
& ( $true
!= ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK6 @ X1 @ X0 ) ) ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ( ! [X6: $i] :
( ( ( X1 @ ( sK8 @ X1 @ X0 ) @ ( sK7 @ X1 @ X0 ) @ X6 )
= $true )
| ( $true
= ( X0 @ ( sK8 @ X1 @ X0 ) @ ( sK7 @ X1 @ X0 ) @ X6 ) ) )
& ( $true
!= ( sK7 @ X1 @ X0 @ ( sK9 @ X1 @ X0 ) ) )
& ( $true
= ( sK8 @ X1 @ X0 @ ( sK9 @ X1 @ X0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f15,f18,f17,f16]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X2: $i > $o,X3: $i] :
( ( $true
!= ( X1 @ X2 @ X2 @ X3 ) )
& ( $true
!= ( X0 @ X2 @ X2 @ X3 ) ) )
=> ( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK6 @ X1 @ X0 ) )
!= $true )
& ( $true
!= ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK6 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X4: $i > $o,X5: $i > $o] :
( ! [X6: $i] :
( ( $true
= ( X1 @ X5 @ X4 @ X6 ) )
| ( $true
= ( X0 @ X5 @ X4 @ X6 ) ) )
& ? [X7: $i] :
( ( $true
!= ( X4 @ X7 ) )
& ( $true
= ( X5 @ X7 ) ) ) )
=> ( ! [X6: $i] :
( ( ( X1 @ ( sK8 @ X1 @ X0 ) @ ( sK7 @ X1 @ X0 ) @ X6 )
= $true )
| ( $true
= ( X0 @ ( sK8 @ X1 @ X0 ) @ ( sK7 @ X1 @ X0 ) @ X6 ) ) )
& ? [X7: $i] :
( ( $true
!= ( sK7 @ X1 @ X0 @ X7 ) )
& ( ( sK8 @ X1 @ X0 @ X7 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X7: $i] :
( ( $true
!= ( sK7 @ X1 @ X0 @ X7 ) )
& ( ( sK8 @ X1 @ X0 @ X7 )
= $true ) )
=> ( ( $true
!= ( sK7 @ X1 @ X0 @ ( sK9 @ X1 @ X0 ) ) )
& ( $true
= ( sK8 @ X1 @ X0 @ ( sK9 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X2: $i > $o,X3: $i] :
( ( $true
!= ( X1 @ X2 @ X2 @ X3 ) )
& ( $true
!= ( X0 @ X2 @ X2 @ X3 ) ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ? [X4: $i > $o,X5: $i > $o] :
( ! [X6: $i] :
( ( $true
= ( X1 @ X5 @ X4 @ X6 ) )
| ( $true
= ( X0 @ X5 @ X4 @ X6 ) ) )
& ? [X7: $i] :
( ( $true
!= ( X4 @ X7 ) )
& ( $true
= ( X5 @ X7 ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X8: $i > $o,X9: $i] :
( ( $true
!= ( X1 @ X8 @ X8 @ X9 ) )
& ( $true
!= ( X0 @ X8 @ X8 @ X9 ) ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ? [X11: $i > $o,X10: $i > $o] :
( ! [X12: $i] :
( ( $true
= ( X1 @ X10 @ X11 @ X12 ) )
| ( $true
= ( X0 @ X10 @ X11 @ X12 ) ) )
& ? [X13: $i] :
( ( $true
!= ( X11 @ X13 ) )
& ( $true
= ( X10 @ X13 ) ) ) ) ),
inference(definition_folding,[status(thm)],[f7,f8]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X8: $i > $o,X9: $i] :
( ( $true
!= ( X1 @ X8 @ X8 @ X9 ) )
& ( $true
!= ( X0 @ X8 @ X8 @ X9 ) ) )
| ? [X3: $i > $o,X2: $i > $o,X4: $i > $o] :
( ? [X7: $i] :
( ( ( X1 @ X3 @ X4 @ X7 )
!= $true )
& ( $true
!= ( X0 @ X3 @ X4 @ X7 ) ) )
& ! [X5: $i] :
( ( $true
= ( X1 @ X3 @ X2 @ X5 ) )
| ( $true
= ( X0 @ X3 @ X2 @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ X2 @ X4 @ X6 ) )
| ( $true
= ( X1 @ X2 @ X4 @ X6 ) ) ) )
| ? [X11: $i > $o,X10: $i > $o] :
( ! [X12: $i] :
( ( $true
= ( X1 @ X10 @ X11 @ X12 ) )
| ( $true
= ( X0 @ X10 @ X11 @ X12 ) ) )
& ? [X13: $i] :
( ( $true
!= ( X11 @ X13 ) )
& ( $true
= ( X10 @ X13 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X11: $i > $o,X10: $i > $o] :
( ! [X12: $i] :
( ( $true
= ( X1 @ X10 @ X11 @ X12 ) )
| ( $true
= ( X0 @ X10 @ X11 @ X12 ) ) )
& ? [X13: $i] :
( ( $true
!= ( X11 @ X13 ) )
& ( $true
= ( X10 @ X13 ) ) ) )
| ? [X3: $i > $o,X4: $i > $o,X2: $i > $o] :
( ? [X7: $i] :
( ( ( X1 @ X3 @ X4 @ X7 )
!= $true )
& ( $true
!= ( X0 @ X3 @ X4 @ X7 ) ) )
& ! [X5: $i] :
( ( $true
= ( X1 @ X3 @ X2 @ X5 ) )
| ( $true
= ( X0 @ X3 @ X2 @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ X2 @ X4 @ X6 ) )
| ( $true
= ( X1 @ X2 @ X4 @ X6 ) ) ) )
| ? [X8: $i > $o,X9: $i] :
( ( $true
!= ( X1 @ X8 @ X8 @ X9 ) )
& ( $true
!= ( X0 @ X8 @ X8 @ X9 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X10: $i > $o,X11: $i > $o] :
( ! [X12: $i] :
( ( $true
= ( X1 @ X10 @ X11 @ X12 ) )
| ( $true
= ( X0 @ X10 @ X11 @ X12 ) ) )
=> ! [X13: $i] :
( ( $true
= ( X10 @ X13 ) )
=> ( $true
= ( X11 @ X13 ) ) ) )
& ! [X3: $i > $o,X4: $i > $o,X2: $i > $o] :
( ( ! [X5: $i] :
( ( $true
= ( X1 @ X3 @ X2 @ X5 ) )
| ( $true
= ( X0 @ X3 @ X2 @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( X0 @ X2 @ X4 @ X6 ) )
| ( $true
= ( X1 @ X2 @ X4 @ X6 ) ) ) )
=> ! [X7: $i] :
( ( $true
= ( X0 @ X3 @ X4 @ X7 ) )
| ( ( X1 @ X3 @ X4 @ X7 )
= $true ) ) )
& ! [X8: $i > $o,X9: $i] :
( ( $true
= ( X0 @ X8 @ X8 @ X9 ) )
| ( $true
= ( X1 @ X8 @ X8 @ X9 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ! [X5: $i] :
( ( X1 @ X3 @ X2 @ X5 )
| ( X0 @ X3 @ X2 @ X5 ) )
& ! [X6: $i] :
( ( X1 @ X2 @ X4 @ X6 )
| ( X0 @ X2 @ X4 @ X6 ) ) )
=> ! [X7: $i] :
( ( X1 @ X3 @ X4 @ X7 )
| ( X0 @ X3 @ X4 @ X7 ) ) )
& ! [X8: $i > $o,X9: $i] :
( ( X1 @ X8 @ X8 @ X9 )
| ( X0 @ X8 @ X8 @ X9 ) )
& ! [X10: $i > $o,X11: $i > $o] :
( ! [X12: $i] :
( ( X0 @ X10 @ X11 @ X12 )
| ( X1 @ X10 @ X11 @ X12 ) )
=> ! [X13: $i] :
( ( X10 @ X13 )
=> ( X11 @ X13 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X7: $i > $o,X6: $i > $o,X5: $i > $o] :
( ( ! [X4: $i] :
( ( X0 @ X6 @ X7 @ X4 )
| ( X1 @ X6 @ X7 @ X4 ) )
& ! [X4: $i] :
( ( X0 @ X7 @ X5 @ X4 )
| ( X1 @ X7 @ X5 @ X4 ) ) )
=> ! [X4: $i] :
( ( X0 @ X6 @ X5 @ X4 )
| ( X1 @ X6 @ X5 @ X4 ) ) )
& ! [X6: $i > $o,X4: $i] :
( ( X0 @ X6 @ X6 @ X4 )
| ( X1 @ X6 @ X6 @ X4 ) )
& ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X3 @ X4 )
| ( X0 @ X2 @ X3 @ X4 ) )
=> ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X7: $i > $o,X6: $i > $o,X5: $i > $o] :
( ( ! [X4: $i] :
( ( X0 @ X6 @ X7 @ X4 )
| ( X1 @ X6 @ X7 @ X4 ) )
& ! [X4: $i] :
( ( X0 @ X7 @ X5 @ X4 )
| ( X1 @ X7 @ X5 @ X4 ) ) )
=> ! [X4: $i] :
( ( X0 @ X6 @ X5 @ X4 )
| ( X1 @ X6 @ X5 @ X4 ) ) )
& ! [X6: $i > $o,X4: $i] :
( ( X0 @ X6 @ X6 @ X4 )
| ( X1 @ X6 @ X6 @ X4 ) )
& ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X3 @ X4 )
| ( X0 @ X2 @ X3 @ X4 ) )
=> ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.chEsFjBzWu/DTF2THF_4648.p',cTHM122C_pme) ).
thf(f37,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ( $true
= ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK9 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK6 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) ) ),
inference(primitive_instantiation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK6 @ X1 @ X0 ) ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ( $true
= ( sK8 @ X1 @ X0 @ ( sK9 @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f186,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[status(thm)],[f171,f183,f179]) ).
thf(f171,plain,
( ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) )
| ( $true = $false )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) ),
inference(beta_eta_normalization,[status(thm)],[f165]) ).
thf(f165,plain,
! [X6: $i] :
( ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X6 )
= $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f107]) ).
thf(f107,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
= ( X1
@ ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X6 ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ( ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ( $true
= ( X1
@ ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X6 ) )
| ( $true
= ( ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true != $true )
| ( $true
= ( X1
@ ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X6 ) )
| ( $true
= ( ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ( $true
!= ( ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( X1
@ ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X6 ) )
| ( $true
= ( ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
= ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
= ( X1
@ ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X6 ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK6 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK8 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ ( sK7 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 ) )
@ X6 ) ) ),
inference(primitive_instantiation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
!= ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK6 @ X1 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK8 @ X1 @ X0 ) @ ( sK7 @ X1 @ X0 ) @ X6 ) )
| ( ( X1 @ ( sK8 @ X1 @ X0 ) @ ( sK7 @ X1 @ X0 ) @ X6 )
= $true )
| ( $true
= ( sP0 @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV095^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n002.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 12:40:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.48 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : SEV095^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.48 % Domain : Set Theory (Relations)
% 0.31/0.48 % Problem : TPS problem from RELN-THMS
% 0.31/0.48 % Version : Especial.
% 0.31/0.48 % English :
% 0.31/0.48
% 0.31/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.48 % Source : [Bro09]
% 0.31/0.48 % Names : tps_1064 [Bro09]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.25 v8.2.0, 0.36 v8.1.0, 0.50 v7.4.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.38 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.50 v5.2.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.31/0.48 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.31/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.48 % Number of connectives : 43 ( 0 ~; 5 |; 3 &; 32 @)
% 0.31/0.48 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 15 ( 15 avg)
% 0.31/0.48 % Number of types : 2 ( 0 usr)
% 0.31/0.48 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.48 % Number of variables : 14 ( 0 ^; 12 !; 2 ?; 14 :)
% 0.31/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.48
% 0.31/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 thf(cTHM122C_pme,conjecture,
% 0.31/0.48 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 0.31/0.48 ( ! [Xu: $i > $o,Xv: $i > $o] :
% 0.31/0.48 ( ! [Xw_2: $i] :
% 0.31/0.48 ( ( Xr_27 @ Xu @ Xv @ Xw_2 )
% 0.31/0.48 | ( Xr_28 @ Xu @ Xv @ Xw_2 ) )
% 0.31/0.48 => ! [Xz: $i] :
% 0.31/0.48 ( ( Xu @ Xz )
% 0.31/0.48 => ( Xv @ Xz ) ) )
% 0.31/0.48 & ! [Xx: $i > $o,Xw_2: $i] :
% 0.31/0.48 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 0.31/0.48 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
% 0.31/0.48 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.31/0.48 ( ( ! [Xw_2: $i] :
% 0.31/0.48 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 0.31/0.48 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 0.31/0.48 & ! [Xw_2: $i] :
% 0.31/0.48 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 0.31/0.48 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 0.31/0.48 => ! [Xw_2: $i] :
% 0.31/0.48 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 0.31/0.48 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 1.46/1.29 ---- Embedded in THF ---
% 1.46/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.29 %%% Generated on Tue Feb 24 12:40:19 EST 2026
% 1.46/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.29 %%% Logic specification used:
% 1.46/1.29 %%% thf(spec, logic, $$dhol).
% 1.46/1.29
% 1.46/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.chEsFjBzWu/DTF2DTF4648.p
% See solution above
% 1.46/1.29 ------------------------
% 1.68/1.30 ---- Cleaned THF ---
% 1.68/1.30 thf(cTHM122C_pme,conjecture,
% 1.68/1.30 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 1.68/1.30 ( ! [Xu: $i > $o,Xv: $i > $o] :
% 1.68/1.30 ( ! [Xw_2: $i] :
% 1.68/1.30 ( ( Xr_27 @ Xu @ Xv @ Xw_2 )
% 1.68/1.30 | ( Xr_28 @ Xu @ Xv @ Xw_2 ) )
% 1.68/1.30 => ! [Xz: $i] :
% 1.68/1.30 ( ( Xu @ Xz )
% 1.68/1.30 => ( Xv @ Xz ) ) )
% 1.68/1.30 & ! [Xx: $i > $o,Xw_2: $i] :
% 1.68/1.30 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 1.68/1.30 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
% 1.68/1.30 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.68/1.30 ( ( ! [Xw_2: $i] :
% 1.68/1.30 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 1.68/1.30 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 1.68/1.30 & ! [Xw_2: $i] :
% 1.68/1.30 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 1.68/1.30 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 1.68/1.30 => ! [Xw_2: $i] :
% 1.68/1.30 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 1.68/1.30 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ) ).
% 1.68/1.30 ------------------------
% 1.68/1.32 % (4823)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/183Mi)
% 1.68/1.32 % (4824)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_4648 for (2999ds/4Mi)
% 1.68/1.32 % (4827)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_4648 for (2999ds/2Mi)
% 1.68/1.32 % (4826)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/2Mi)
% 1.68/1.32 % (4828)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_4648 for (2999ds/275Mi)
% 1.68/1.32 % (4824)Instruction limit reached!
% 1.68/1.32 % (4824)------------------------------
% 1.68/1.32 % (4824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (4824)Termination reason: Unknown
% 1.68/1.32 % (4824)Termination phase: Saturation
% 1.68/1.32
% 1.68/1.32 % (4824)Memory used [KB]: 5500
% 1.68/1.32 % (4824)Time elapsed: 0.004 s
% 1.68/1.32 % (4824)Instructions burned: 5 (million)
% 1.68/1.33 % (4824)------------------------------
% 1.68/1.33 % (4824)------------------------------
% 1.68/1.33 % (4826)Instruction limit reached!
% 1.68/1.33 % (4826)------------------------------
% 1.68/1.33 % (4826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (4826)Termination reason: Unknown
% 1.68/1.33 % (4826)Termination phase: Preprocessing 3
% 1.68/1.33 % (4827)Instruction limit reached!
% 1.68/1.33 % (4827)------------------------------
% 1.68/1.33 % (4827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33
% 1.68/1.33 % (4826)Memory used [KB]: 1023
% 1.68/1.33 % (4826)Time elapsed: 0.003 s
% 1.68/1.33 % (4826)Instructions burned: 2 (million)
% 1.68/1.33 % (4826)------------------------------
% 1.68/1.33 % (4826)------------------------------
% 1.68/1.33 % (4827)Termination reason: Unknown
% 1.68/1.33 % (4827)Termination phase: Property scanning
% 1.68/1.33
% 1.68/1.33 % (4827)Memory used [KB]: 1023
% 1.68/1.33 % (4827)Time elapsed: 0.003 s
% 1.68/1.33 % (4827)Instructions burned: 3 (million)
% 1.68/1.33 % (4827)------------------------------
% 1.68/1.33 % (4827)------------------------------
% 1.68/1.33 % (4829)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/18Mi)
% 1.68/1.33 % (4825)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_4648 for (2999ds/27Mi)
% 1.68/1.34 % (4825)Refutation not found, incomplete strategy
% 1.68/1.34 % (4825)------------------------------
% 1.68/1.34 % (4825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (4825)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.34
% 1.68/1.34
% 1.68/1.34 % (4825)Memory used [KB]: 5500
% 1.68/1.34 % (4825)Time elapsed: 0.008 s
% 1.68/1.34 % (4825)Instructions burned: 18 (million)
% 1.68/1.34 % (4825)------------------------------
% 1.68/1.34 % (4825)------------------------------
% 1.68/1.34 % (4829)Instruction limit reached!
% 1.68/1.34 % (4829)------------------------------
% 1.68/1.34 % (4829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (4829)Termination reason: Unknown
% 1.68/1.34 % (4829)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (4829)Memory used [KB]: 5628
% 1.68/1.34 % (4829)Time elapsed: 0.011 s
% 1.68/1.34 % (4832)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_4648 for (2999ds/15Mi)
% 1.68/1.34 % (4829)Instructions burned: 18 (million)
% 1.68/1.34 % (4829)------------------------------
% 1.68/1.34 % (4829)------------------------------
% 1.68/1.34 % (4830)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/3Mi)
% 1.68/1.34 % (4831)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_4648 for (2999ds/37Mi)
% 1.68/1.34 % (4830)Instruction limit reached!
% 1.68/1.34 % (4830)------------------------------
% 1.68/1.34 % (4830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (4830)Termination reason: Unknown
% 1.68/1.34 % (4830)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (4830)Memory used [KB]: 5500
% 1.68/1.34 % (4830)Time elapsed: 0.004 s
% 1.68/1.34 % (4830)Instructions burned: 4 (million)
% 1.68/1.34 % (4830)------------------------------
% 1.68/1.34 % (4830)------------------------------
% 1.68/1.35 % (4832)Instruction limit reached!
% 1.68/1.35 % (4832)------------------------------
% 1.68/1.35 % (4832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.35 % (4832)Termination reason: Unknown
% 1.68/1.35 % (4832)Termination phase: Saturation
% 1.68/1.35
% 1.68/1.35 % (4832)Memory used [KB]: 5628
% 1.68/1.35 % (4832)Time elapsed: 0.009 s
% 1.68/1.35 % (4832)Instructions burned: 16 (million)
% 1.68/1.35 % (4832)------------------------------
% 1.68/1.35 % (4832)------------------------------
% 1.68/1.35 % (4834)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_4648 for (2999ds/3Mi)
% 1.68/1.35 % (4834)Instruction limit reached!
% 1.68/1.35 % (4834)------------------------------
% 1.68/1.35 % (4834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.35 % (4834)Termination reason: Unknown
% 1.68/1.35 % (4834)Termination phase: Saturation
% 1.68/1.35
% 1.68/1.35 % (4834)Memory used [KB]: 5500
% 1.68/1.35 % (4834)Time elapsed: 0.003 s
% 1.68/1.35 % (4834)Instructions burned: 4 (million)
% 1.68/1.35 % (4834)------------------------------
% 1.68/1.35 % (4834)------------------------------
% 1.68/1.36 % (4836)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/7Mi)
% 1.68/1.36 % (4835)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_4648 for (2999ds/1041Mi)
% 1.68/1.36 % (4836)Instruction limit reached!
% 1.68/1.36 % (4836)------------------------------
% 1.68/1.36 % (4836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (4836)Termination reason: Unknown
% 1.68/1.36 % (4836)Termination phase: Saturation
% 1.68/1.36
% 1.68/1.36 % (4836)Memory used [KB]: 1023
% 1.68/1.36 % (4836)Time elapsed: 0.004 s
% 1.68/1.36 % (4836)Instructions burned: 8 (million)
% 1.68/1.36 % (4836)------------------------------
% 1.68/1.36 % (4836)------------------------------
% 1.68/1.36 % (4831)Instruction limit reached!
% 1.68/1.36 % (4831)------------------------------
% 1.68/1.36 % (4831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (4831)Termination reason: Unknown
% 1.68/1.36 % (4831)Termination phase: Saturation
% 1.68/1.36
% 1.68/1.36 % (4831)Memory used [KB]: 5628
% 1.68/1.36 % (4831)Time elapsed: 0.020 s
% 1.68/1.36 % (4831)Instructions burned: 37 (million)
% 1.68/1.36 % (4831)------------------------------
% 1.68/1.36 % (4831)------------------------------
% 1.68/1.37 % (4838)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/16Mi)
% 1.68/1.37 % (4839)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_4648 for (2999ds/3Mi)
% 1.68/1.37 % (4840)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_4648 for (2999ds/3Mi)
% 1.68/1.37 % (4839)Instruction limit reached!
% 1.68/1.37 % (4839)------------------------------
% 1.68/1.37 % (4839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (4839)Termination reason: Unknown
% 1.68/1.37 % (4839)Termination phase: Twee Goal Transformation
% 1.68/1.37
% 1.68/1.37 % (4839)Memory used [KB]: 1023
% 1.68/1.37 % (4839)Time elapsed: 0.004 s
% 1.68/1.37 % (4839)Instructions burned: 4 (million)
% 1.68/1.37 % (4839)------------------------------
% 1.68/1.37 % (4839)------------------------------
% 1.68/1.37 % (4840)Instruction limit reached!
% 1.68/1.37 % (4840)------------------------------
% 1.68/1.37 % (4840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (4840)Termination reason: Unknown
% 1.68/1.37 % (4840)Termination phase: Property scanning
% 1.68/1.37
% 1.68/1.37 % (4840)Memory used [KB]: 1023
% 1.68/1.37 % (4840)Time elapsed: 0.003 s
% 1.68/1.37 % (4840)Instructions burned: 5 (million)
% 1.68/1.37 % (4840)------------------------------
% 1.68/1.37 % (4840)------------------------------
% 1.68/1.38 % (4838)Instruction limit reached!
% 1.68/1.38 % (4838)------------------------------
% 1.68/1.38 % (4838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (4838)Termination reason: Unknown
% 1.68/1.38 % (4838)Termination phase: Saturation
% 1.68/1.38
% 1.68/1.38 % (4838)Memory used [KB]: 5628
% 1.68/1.38 % (4838)Time elapsed: 0.010 s
% 1.68/1.38 % (4838)Instructions burned: 16 (million)
% 1.68/1.38 % (4838)------------------------------
% 1.68/1.38 % (4838)------------------------------
% 1.68/1.38 % (4841)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/7Mi)
% 1.68/1.38 % (4841)Instruction limit reached!
% 1.68/1.38 % (4841)------------------------------
% 1.68/1.38 % (4841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (4841)Termination reason: Unknown
% 1.68/1.38 % (4841)Termination phase: Saturation
% 1.68/1.38
% 1.68/1.38 % (4841)Memory used [KB]: 5500
% 1.68/1.38 % (4841)Time elapsed: 0.005 s
% 1.68/1.38 % (4841)Instructions burned: 7 (million)
% 1.68/1.38 % (4841)------------------------------
% 1.68/1.38 % (4841)------------------------------
% 1.68/1.38 % (4844)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/4Mi)
% 1.68/1.38 % (4844)Instruction limit reached!
% 1.68/1.38 % (4844)------------------------------
% 1.68/1.38 % (4844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (4844)Termination reason: Unknown
% 1.68/1.38 % (4844)Termination phase: Saturation
% 1.68/1.38
% 1.68/1.38 % (4844)Memory used [KB]: 5500
% 1.68/1.38 % (4844)Time elapsed: 0.003 s
% 1.68/1.38 % (4844)Instructions burned: 4 (million)
% 1.68/1.38 % (4844)------------------------------
% 1.68/1.38 % (4844)------------------------------
% 1.68/1.39 % (4843)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/3Mi)
% 1.68/1.39 % (4843)Instruction limit reached!
% 1.68/1.39 % (4843)------------------------------
% 1.68/1.39 % (4843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (4843)Termination reason: Unknown
% 1.68/1.39 % (4843)Termination phase: Saturation
% 1.68/1.39
% 1.68/1.39 % (4843)Memory used [KB]: 1023
% 1.68/1.39 % (4843)Time elapsed: 0.003 s
% 1.68/1.39 % (4843)Instructions burned: 3 (million)
% 1.68/1.39 % (4843)------------------------------
% 1.68/1.39 % (4843)------------------------------
% 1.68/1.39 % (4847)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/6Mi)
% 1.68/1.39 % (4845)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/18Mi)
% 1.68/1.39 % (4847)Instruction limit reached!
% 1.68/1.39 % (4847)------------------------------
% 1.68/1.39 % (4847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (4847)Termination reason: Unknown
% 1.68/1.39 % (4847)Termination phase: Saturation
% 1.68/1.39
% 1.68/1.39 % (4847)Memory used [KB]: 5500
% 1.68/1.39 % (4847)Time elapsed: 0.004 s
% 1.68/1.39 % (4847)Instructions burned: 7 (million)
% 1.68/1.39 % (4847)------------------------------
% 1.68/1.39 % (4847)------------------------------
% 1.69/1.40 % (4846)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/710Mi)
% 1.69/1.40 % (4845)Refutation not found, incomplete strategy
% 1.69/1.40 % (4845)------------------------------
% 1.69/1.40 % (4845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (4845)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.40
% 1.69/1.40
% 1.69/1.40 % (4845)Memory used [KB]: 5500
% 1.69/1.40 % (4845)Time elapsed: 0.007 s
% 1.69/1.40 % (4845)Instructions burned: 10 (million)
% 1.69/1.40 % (4845)------------------------------
% 1.69/1.40 % (4845)------------------------------
% 1.69/1.41 % (4848)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_4648 for (2999ds/902Mi)
% 1.69/1.41 % (4823)Instruction limit reached!
% 1.69/1.41 % (4823)------------------------------
% 1.69/1.41 % (4823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (4823)Termination reason: Unknown
% 1.69/1.41 % (4823)Termination phase: Saturation
% 1.69/1.41
% 1.69/1.41 % (4823)Memory used [KB]: 6780
% 1.69/1.41 % (4823)Time elapsed: 0.089 s
% 1.69/1.41 % (4823)Instructions burned: 186 (million)
% 1.69/1.41 % (4823)------------------------------
% 1.69/1.41 % (4823)------------------------------
% 1.69/1.41 % (4849)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_4648 for (2999ds/21Mi)
% 1.69/1.42 % (4852)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4648 for (2999ds/5Mi)
% 1.69/1.42 % (4849)Instruction limit reached!
% 1.69/1.42 % (4849)------------------------------
% 1.69/1.42 % (4849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.42 % (4849)Termination reason: Unknown
% 1.69/1.42 % (4849)Termination phase: Saturation
% 1.69/1.42
% 1.69/1.42 % (4849)Memory used [KB]: 5628
% 1.69/1.42 % (4849)Time elapsed: 0.014 s
% 1.69/1.42 % (4849)Instructions burned: 21 (million)
% 1.69/1.42 % (4849)------------------------------
% 1.69/1.42 % (4849)------------------------------
% 1.69/1.42 % (4852)Instruction limit reached!
% 1.69/1.42 % (4852)------------------------------
% 1.69/1.42 % (4852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.42 % (4852)Termination reason: Unknown
% 1.69/1.42 % (4852)Termination phase: Saturation
% 1.69/1.42
% 1.69/1.42 % (4852)Memory used [KB]: 5500
% 1.69/1.42 % (4852)Time elapsed: 0.003 s
% 1.69/1.42 % (4852)Instructions burned: 6 (million)
% 1.69/1.42 % (4852)------------------------------
% 1.69/1.42 % (4852)------------------------------
% 1.69/1.43 % (4853)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_4648 for (2999ds/6Mi)
% 1.69/1.43 % (4853)Instruction limit reached!
% 1.69/1.43 % (4853)------------------------------
% 1.69/1.43 % (4853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.43 % (4853)Termination reason: Unknown
% 1.69/1.43 % (4853)Termination phase: Saturation
% 1.69/1.43
% 1.69/1.43 % (4853)Memory used [KB]: 5500
% 1.69/1.43 % (4853)Time elapsed: 0.003 s
% 1.69/1.43 % (4853)Instructions burned: 7 (million)
% 1.69/1.43 % (4853)------------------------------
% 1.69/1.43 % (4853)------------------------------
% 1.69/1.44 % (4855)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4648 for (2998ds/377Mi)
% 1.69/1.44 % (4856)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_4648 for (2998ds/779Mi)
% 1.69/1.44 % (4858)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_4648 for (2998ds/19Mi)
% 1.69/1.45 % (4858)Instruction limit reached!
% 1.69/1.45 % (4858)------------------------------
% 1.69/1.45 % (4858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.45 % (4858)Termination reason: Unknown
% 1.69/1.45 % (4858)Termination phase: Saturation
% 1.69/1.45
% 1.69/1.45 % (4858)Memory used [KB]: 5628
% 1.69/1.45 % (4858)Time elapsed: 0.008 s
% 1.69/1.45 % (4858)Instructions burned: 20 (million)
% 1.69/1.45 % (4858)------------------------------
% 1.69/1.45 % (4858)------------------------------
% 1.69/1.46 % (4828)Instruction limit reached!
% 1.69/1.46 % (4828)------------------------------
% 1.69/1.46 % (4828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.46 % (4828)Termination reason: Unknown
% 1.69/1.46 % (4828)Termination phase: Saturation
% 1.69/1.46
% 1.69/1.46 % (4828)Memory used [KB]: 6012
% 1.69/1.46 % (4828)Time elapsed: 0.136 s
% 1.69/1.46 % (4828)Instructions burned: 276 (million)
% 1.69/1.46 % (4828)------------------------------
% 1.69/1.46 % (4828)------------------------------
% 1.69/1.46 % (4859)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4648 for (2998ds/879Mi)
% 1.69/1.48 % (4860)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4648 for (2998ds/17Mi)
% 1.69/1.48 % (4860)Instruction limit reached!
% 1.69/1.48 % (4860)------------------------------
% 1.69/1.48 % (4860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.48 % (4860)Termination reason: Unknown
% 1.69/1.48 % (4860)Termination phase: Saturation
% 1.69/1.48
% 1.69/1.48 % (4860)Memory used [KB]: 5628
% 1.69/1.48 % (4860)Time elapsed: 0.011 s
% 1.69/1.48 % (4860)Instructions burned: 18 (million)
% 1.69/1.48 % (4860)------------------------------
% 1.69/1.48 % (4860)------------------------------
% 1.69/1.50 % (4863)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4648 for (2998ds/3Mi)
% 1.69/1.50 % (4863)Instruction limit reached!
% 1.69/1.50 % (4863)------------------------------
% 1.69/1.50 % (4863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.50 % (4863)Termination reason: Unknown
% 1.69/1.50 % (4863)Termination phase: Preprocessing 3
% 1.69/1.50
% 1.69/1.50 % (4863)Memory used [KB]: 1023
% 1.69/1.50 % (4863)Time elapsed: 0.003 s
% 1.69/1.50 % (4863)Instructions burned: 3 (million)
% 1.69/1.50 % (4863)------------------------------
% 1.69/1.50 % (4863)------------------------------
% 1.69/1.52 % (4866)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_4648 for (2998ds/30Mi)
% 1.69/1.54 % (4866)Instruction limit reached!
% 1.69/1.54 % (4866)------------------------------
% 1.69/1.54 % (4866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.54 % (4866)Termination reason: Unknown
% 1.69/1.54 % (4866)Termination phase: Saturation
% 1.69/1.54
% 1.69/1.54 % (4866)Memory used [KB]: 5756
% 1.69/1.54 % (4866)Time elapsed: 0.018 s
% 1.69/1.54 % (4866)Instructions burned: 32 (million)
% 1.69/1.54 % (4866)------------------------------
% 1.69/1.54 % (4866)------------------------------
% 1.69/1.56 % (4870)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_4648 for (2997ds/127Mi)
% 1.69/1.58 % (4859)First to succeed.
% 1.69/1.59 % (4859)Refutation found. Thanks to Tanya!
% 1.69/1.59 % SZS status Theorem for DTF2THF_4648
% 1.69/1.59 % SZS output start Proof for DTF2THF_4648
% 1.69/1.59 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $o).
% 1.69/1.59 thf(func_def_4, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.69/1.59 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.69/1.59 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.69/1.59 thf(func_def_7, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.69/1.59 thf(func_def_8, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.69/1.59 thf(func_def_9, type, sK6: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.69/1.59 thf(func_def_10, type, sK7: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.69/1.59 thf(func_def_11, type, sK8: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.69/1.59 thf(func_def_12, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.69/1.59 thf(func_def_15, type, ph11: !>[X0: $tType]:(X0)).
% 1.69/1.59 thf(f988,plain,(
% 1.69/1.59 $false),
% 1.69/1.59 inference(avatar_sat_refutation,[status(thm)],[f186,f601,f987])).
% 1.69/1.59 thf(f987,plain,(
% 1.69/1.59 ~spl10_2),
% 1.69/1.59 inference(avatar_contradiction_clause,[status(thm)],[f986])).
% 1.69/1.59 thf(f986,plain,(
% 1.69/1.59 $false | ~spl10_2),
% 1.69/1.59 inference(subsumption_resolution,[status(thm)],[f974,f673])).
% 1.69/1.59 thf(f673,plain,(
% 1.69/1.59 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl10_2),
% 1.69/1.59 inference(subsumption_resolution,[status(thm)],[f672,f185])).
% 1.69/1.59 thf(f185,plain,(
% 1.69/1.59 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl10_2),
% 1.69/1.59 inference(avatar_component_clause,[status(thm)],[f183])).
% 1.69/1.59 thf(f183,definition,(
% 1.69/1.59 spl10_2 <=> ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))),
% 1.69/1.59 introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition])).
% 1.69/1.59 thf(f672,plain,(
% 1.69/1.59 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl10_2),
% 1.69/1.59 inference(equality_proxy_clausification,[status(thm)],[f671])).
% 1.69/1.59 thf(f671,plain,(
% 1.69/1.59 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != $true) | ($true != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl10_2),
% 1.69/1.59 inference(beta_eta_normalization,[status(thm)],[f666])).
% 1.69/1.59 thf(f666,plain,(
% 1.69/1.59 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl10_2),
% 1.69/1.59 inference(superposition,[status(thm)],[f22,f614])).
% 1.69/1.59 thf(f614,plain,(
% 1.69/1.59 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl10_2),
% 1.69/1.59 inference(equality_proxy_clausification,[status(thm)],[f613])).
% 1.69/1.59 thf(f613,plain,(
% 1.69/1.59 ($true = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f612])).
% 1.69/1.59 thf(f612,plain,(
% 1.69/1.59 ($true = $false) | ($true = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ~spl10_2),
% 1.69/1.59 inference(beta_eta_normalization,[status(thm)],[f611])).
% 1.69/1.59 thf(f611,plain,(
% 1.69/1.59 ( ! [X0 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0))) ) | ~spl10_2),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f610])).
% 1.69/1.59 thf(f610,plain,(
% 1.69/1.59 ( ! [X0 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0)) | ($true != $true)) ) | ~spl10_2),
% 1.69/1.59 inference(superposition,[status(thm)],[f20,f185])).
% 1.69/1.59 thf(f20,plain,(
% 1.69/1.59 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true != (sP0 @ X1 @ X0)) | ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) = $true) | ($true = (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7))) )),
% 1.69/1.59 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.59 thf(f14,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (((((X0 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) & ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) & ! [X6 : $i] : (($true = (X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true)) & ! [X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7)) | ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) = $true))) | ($true != (sP0 @ X1 @ X0)))),
% 1.69/1.59 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f11,f13,f12])).
% 1.69/1.59 thf(f12,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (? [X5 : $i] : (($true != (X0 @ X2 @ X4 @ X5)) & ($true != (X1 @ X2 @ X4 @ X5))) & ! [X6 : $i] : (($true = (X0 @ X2 @ X3 @ X6)) | ($true = (X1 @ X2 @ X3 @ X6))) & ! [X7 : $i] : (((X1 @ X3 @ X4 @ X7) = $true) | ($true = (X0 @ X3 @ X4 @ X7)))) => (? [X5 : $i] : (($true != (X0 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X5)) & ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X5))) & ! [X6 : $i] : (($true = (X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true)) & ! [X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7)) | ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) = $true))))),
% 1.69/1.59 introduced(definition,[],[choice_axiom])).
% 1.69/1.59 thf(f13,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X5 : $i] : (($true != (X0 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X5)) & ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X5))) => (((X0 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) & ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0)))))),
% 1.69/1.59 introduced(definition,[],[choice_axiom])).
% 1.69/1.59 thf(f11,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (? [X5 : $i] : (($true != (X0 @ X2 @ X4 @ X5)) & ($true != (X1 @ X2 @ X4 @ X5))) & ! [X6 : $i] : (($true = (X0 @ X2 @ X3 @ X6)) | ($true = (X1 @ X2 @ X3 @ X6))) & ! [X7 : $i] : (((X1 @ X3 @ X4 @ X7) = $true) | ($true = (X0 @ X3 @ X4 @ X7)))) | ($true != (sP0 @ X1 @ X0)))),
% 1.69/1.59 inference(rectify,[status(thm)],[f10])).
% 1.69/1.59 thf(f10,plain,(
% 1.69/1.59 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X2 : $i > $o,X4 : $i > $o] : (? [X7 : $i] : (((X1 @ X3 @ X4 @ X7) != $true) & ($true != (X0 @ X3 @ X4 @ X7))) & ! [X5 : $i] : (($true = (X1 @ X3 @ X2 @ X5)) | ($true = (X0 @ X3 @ X2 @ X5))) & ! [X6 : $i] : (($true = (X0 @ X2 @ X4 @ X6)) | ($true = (X1 @ X2 @ X4 @ X6)))) | ($true != (sP0 @ X0 @ X1)))),
% 1.69/1.59 inference(nnf_transformation,[status(thm)],[f8])).
% 1.69/1.59 thf(f8,plain,(
% 1.69/1.59 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X2 : $i > $o,X4 : $i > $o] : (? [X7 : $i] : (((X1 @ X3 @ X4 @ X7) != $true) & ($true != (X0 @ X3 @ X4 @ X7))) & ! [X5 : $i] : (($true = (X1 @ X3 @ X2 @ X5)) | ($true = (X0 @ X3 @ X2 @ X5))) & ! [X6 : $i] : (($true = (X0 @ X2 @ X4 @ X6)) | ($true = (X1 @ X2 @ X4 @ X6)))) | ~($true = (sP0 @ X0 @ X1)))),
% 1.69/1.59 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.69/1.59 thf(f22,plain,(
% 1.69/1.59 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X1 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0))) | ($true != (sP0 @ X1 @ X0))) )),
% 1.69/1.59 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.59 thf(f974,plain,(
% 1.69/1.59 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl10_2),
% 1.69/1.59 inference(equality_proxy_clausification,[status(thm)],[f973])).
% 1.69/1.59 thf(f973,plain,(
% 1.69/1.59 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = $true) | ~spl10_2),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f972])).
% 1.69/1.59 thf(f972,plain,(
% 1.69/1.59 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = $true) | ($true = $false) | ~spl10_2),
% 1.69/1.59 inference(beta_eta_normalization,[status(thm)],[f971])).
% 1.69/1.59 thf(f971,plain,(
% 1.69/1.59 ( ! [X0 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0))) ) | ~spl10_2),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f968])).
% 1.69/1.59 thf(f968,plain,(
% 1.69/1.59 ( ! [X0 : $i] : (($true != $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0))) ) | ~spl10_2),
% 1.69/1.59 inference(superposition,[status(thm)],[f21,f185])).
% 1.69/1.59 thf(f21,plain,(
% 1.69/1.59 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true != (sP0 @ X1 @ X0)) | ($true = (X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true)) )),
% 1.69/1.59 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.59 thf(f601,plain,(
% 1.69/1.59 ~spl10_1 | spl10_2),
% 1.69/1.59 inference(avatar_contradiction_clause,[status(thm)],[f600])).
% 1.69/1.59 thf(f600,plain,(
% 1.69/1.59 $false | (~spl10_1 | spl10_2)),
% 1.69/1.59 inference(subsumption_resolution,[status(thm)],[f595,f184])).
% 1.69/1.59 thf(f184,plain,(
% 1.69/1.59 ($true != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl10_2),
% 1.69/1.59 inference(avatar_component_clause,[status(thm)],[f183])).
% 1.69/1.59 thf(f595,plain,(
% 1.69/1.59 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | (~spl10_1 | spl10_2)),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f592])).
% 1.69/1.59 thf(f592,plain,(
% 1.69/1.59 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true = $false) | (~spl10_1 | spl10_2)),
% 1.69/1.59 inference(superposition,[status(thm)],[f37,f540])).
% 1.69/1.59 thf(f540,plain,(
% 1.69/1.59 ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $false) | (~spl10_1 | spl10_2)),
% 1.69/1.59 inference(subsumption_resolution,[status(thm)],[f539,f184])).
% 1.69/1.59 thf(f539,plain,(
% 1.69/1.59 ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $false) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl10_1),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f538])).
% 1.69/1.59 thf(f538,plain,(
% 1.69/1.59 ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $false) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true != $true) | ~spl10_1),
% 1.69/1.59 inference(superposition,[status(thm)],[f61,f432])).
% 1.69/1.59 thf(f432,plain,(
% 1.69/1.59 ( ! [X1 : $i] : (($true = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1)) | ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1) = $false)) ) | ~spl10_1),
% 1.69/1.59 inference(binary_proxy_clausification,[status(thm)],[f429])).
% 1.69/1.59 thf(f429,plain,(
% 1.69/1.59 ( ! [X1 : $i] : (((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1))) ) | ~spl10_1),
% 1.69/1.59 inference(argument_congruence,[status(thm)],[f181])).
% 1.69/1.59 thf(f181,plain,(
% 1.69/1.59 ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ~spl10_1),
% 1.69/1.59 inference(avatar_component_clause,[status(thm)],[f179])).
% 1.69/1.59 thf(f179,definition,(
% 1.69/1.59 spl10_1 <=> ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))),
% 1.69/1.59 introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition])).
% 1.69/1.59 thf(f61,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1))) )),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.69/1.59 thf(f60,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1)) | ($true != (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 1.69/1.59 inference(boolean_simplification,[status(thm)],[f59])).
% 1.69/1.59 thf(f59,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != ((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true != (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1))) )),
% 1.69/1.59 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.69/1.59 thf(f46,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK6 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true != (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 1.69/1.59 inference(primitive_instantiation,[status(thm)],[f25])).
% 1.69/1.59 thf(f25,plain,(
% 1.69/1.59 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0))) | ($true != (sK7 @ X1 @ X0 @ (sK9 @ X1 @ X0))) | ($true = (sP0 @ X0 @ X1))) )),
% 1.69/1.59 inference(cnf_transformation,[status(thm)],[f19])).
% 1.69/1.59 thf(f19,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : ((((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)) != $true) & ($true != (X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)))) | ($true = (sP0 @ X0 @ X1)) | (! [X6 : $i] : (((X1 @ (sK8 @ X1 @ X0) @ (sK7 @ X1 @ X0) @ X6) = $true) | ($true = (X0 @ (sK8 @ X1 @ X0) @ (sK7 @ X1 @ X0) @ X6))) & (($true != (sK7 @ X1 @ X0 @ (sK9 @ X1 @ X0))) & ($true = (sK8 @ X1 @ X0 @ (sK9 @ X1 @ X0))))))),
% 1.69/1.59 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f15,f18,f17,f16])).
% 1.69/1.59 thf(f16,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i] : (($true != (X1 @ X2 @ X2 @ X3)) & ($true != (X0 @ X2 @ X2 @ X3))) => (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)) != $true) & ($true != (X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0)))))),
% 1.69/1.59 introduced(definition,[],[choice_axiom])).
% 1.69/1.59 thf(f17,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X4 : $i > $o,X5 : $i > $o] : (! [X6 : $i] : (($true = (X1 @ X5 @ X4 @ X6)) | ($true = (X0 @ X5 @ X4 @ X6))) & ? [X7 : $i] : (($true != (X4 @ X7)) & ($true = (X5 @ X7)))) => (! [X6 : $i] : (((X1 @ (sK8 @ X1 @ X0) @ (sK7 @ X1 @ X0) @ X6) = $true) | ($true = (X0 @ (sK8 @ X1 @ X0) @ (sK7 @ X1 @ X0) @ X6))) & ? [X7 : $i] : (($true != (sK7 @ X1 @ X0 @ X7)) & ((sK8 @ X1 @ X0 @ X7) = $true))))),
% 1.69/1.59 introduced(definition,[],[choice_axiom])).
% 1.69/1.59 thf(f18,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X7 : $i] : (($true != (sK7 @ X1 @ X0 @ X7)) & ((sK8 @ X1 @ X0 @ X7) = $true)) => (($true != (sK7 @ X1 @ X0 @ (sK9 @ X1 @ X0))) & ($true = (sK8 @ X1 @ X0 @ (sK9 @ X1 @ X0)))))),
% 1.69/1.59 introduced(definition,[],[choice_axiom])).
% 1.69/1.59 thf(f15,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i] : (($true != (X1 @ X2 @ X2 @ X3)) & ($true != (X0 @ X2 @ X2 @ X3))) | ($true = (sP0 @ X0 @ X1)) | ? [X4 : $i > $o,X5 : $i > $o] : (! [X6 : $i] : (($true = (X1 @ X5 @ X4 @ X6)) | ($true = (X0 @ X5 @ X4 @ X6))) & ? [X7 : $i] : (($true != (X4 @ X7)) & ($true = (X5 @ X7)))))),
% 1.69/1.59 inference(rectify,[status(thm)],[f9])).
% 1.69/1.59 thf(f9,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X8 : $i > $o,X9 : $i] : (($true != (X1 @ X8 @ X8 @ X9)) & ($true != (X0 @ X8 @ X8 @ X9))) | ($true = (sP0 @ X0 @ X1)) | ? [X11 : $i > $o,X10 : $i > $o] : (! [X12 : $i] : (($true = (X1 @ X10 @ X11 @ X12)) | ($true = (X0 @ X10 @ X11 @ X12))) & ? [X13 : $i] : (($true != (X11 @ X13)) & ($true = (X10 @ X13)))))),
% 1.69/1.59 inference(definition_folding,[status(thm)],[f7,f8])).
% 1.69/1.59 thf(f7,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X8 : $i > $o,X9 : $i] : (($true != (X1 @ X8 @ X8 @ X9)) & ($true != (X0 @ X8 @ X8 @ X9))) | ? [X3 : $i > $o,X2 : $i > $o,X4 : $i > $o] : (? [X7 : $i] : (((X1 @ X3 @ X4 @ X7) != $true) & ($true != (X0 @ X3 @ X4 @ X7))) & ! [X5 : $i] : (($true = (X1 @ X3 @ X2 @ X5)) | ($true = (X0 @ X3 @ X2 @ X5))) & ! [X6 : $i] : (($true = (X0 @ X2 @ X4 @ X6)) | ($true = (X1 @ X2 @ X4 @ X6)))) | ? [X11 : $i > $o,X10 : $i > $o] : (! [X12 : $i] : (($true = (X1 @ X10 @ X11 @ X12)) | ($true = (X0 @ X10 @ X11 @ X12))) & ? [X13 : $i] : (($true != (X11 @ X13)) & ($true = (X10 @ X13)))))),
% 1.69/1.59 inference(flattening,[status(thm)],[f6])).
% 1.69/1.59 thf(f6,plain,(
% 1.69/1.59 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X11 : $i > $o,X10 : $i > $o] : (! [X12 : $i] : (($true = (X1 @ X10 @ X11 @ X12)) | ($true = (X0 @ X10 @ X11 @ X12))) & ? [X13 : $i] : (($true != (X11 @ X13)) & ($true = (X10 @ X13)))) | ? [X3 : $i > $o,X4 : $i > $o,X2 : $i > $o] : (? [X7 : $i] : (((X1 @ X3 @ X4 @ X7) != $true) & ($true != (X0 @ X3 @ X4 @ X7))) & (! [X5 : $i] : (($true = (X1 @ X3 @ X2 @ X5)) | ($true = (X0 @ X3 @ X2 @ X5))) & ! [X6 : $i] : (($true = (X0 @ X2 @ X4 @ X6)) | ($true = (X1 @ X2 @ X4 @ X6))))) | ? [X8 : $i > $o,X9 : $i] : (($true != (X1 @ X8 @ X8 @ X9)) & ($true != (X0 @ X8 @ X8 @ X9))))),
% 1.69/1.59 inference(ennf_transformation,[status(thm)],[f5])).
% 1.69/1.59 thf(f5,plain,(
% 1.69/1.59 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X10 : $i > $o,X11 : $i > $o] : (! [X12 : $i] : (($true = (X1 @ X10 @ X11 @ X12)) | ($true = (X0 @ X10 @ X11 @ X12))) => ! [X13 : $i] : (($true = (X10 @ X13)) => ($true = (X11 @ X13)))) & ! [X3 : $i > $o,X4 : $i > $o,X2 : $i > $o] : ((! [X5 : $i] : (($true = (X1 @ X3 @ X2 @ X5)) | ($true = (X0 @ X3 @ X2 @ X5))) & ! [X6 : $i] : (($true = (X0 @ X2 @ X4 @ X6)) | ($true = (X1 @ X2 @ X4 @ X6)))) => ! [X7 : $i] : (($true = (X0 @ X3 @ X4 @ X7)) | ((X1 @ X3 @ X4 @ X7) = $true))) & ! [X8 : $i > $o,X9 : $i] : (($true = (X0 @ X8 @ X8 @ X9)) | ($true = (X1 @ X8 @ X8 @ X9))))),
% 1.69/1.59 inference(fool_elimination,[status(thm)],[f4])).
% 1.69/1.59 thf(f4,plain,(
% 1.69/1.59 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : ((! [X5 : $i] : ((X1 @ X3 @ X2 @ X5) | (X0 @ X3 @ X2 @ X5)) & ! [X6 : $i] : ((X1 @ X2 @ X4 @ X6) | (X0 @ X2 @ X4 @ X6))) => ! [X7 : $i] : ((X1 @ X3 @ X4 @ X7) | (X0 @ X3 @ X4 @ X7))) & ! [X8 : $i > $o,X9 : $i] : ((X1 @ X8 @ X8 @ X9) | (X0 @ X8 @ X8 @ X9)) & ! [X10 : $i > $o,X11 : $i > $o] : (! [X12 : $i] : ((X0 @ X10 @ X11 @ X12) | (X1 @ X10 @ X11 @ X12)) => ! [X13 : $i] : ((X10 @ X13) => (X11 @ X13))))),
% 1.69/1.59 inference(rectify,[status(thm)],[f2])).
% 1.69/1.59 thf(f2,negated_conjecture,(
% 1.69/1.59 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X7 : $i > $o,X6 : $i > $o,X5 : $i > $o] : ((! [X4 : $i] : ((X0 @ X6 @ X7 @ X4) | (X1 @ X6 @ X7 @ X4)) & ! [X4 : $i] : ((X0 @ X7 @ X5 @ X4) | (X1 @ X7 @ X5 @ X4))) => ! [X4 : $i] : ((X0 @ X6 @ X5 @ X4) | (X1 @ X6 @ X5 @ X4))) & ! [X6 : $i > $o,X4 : $i] : ((X0 @ X6 @ X6 @ X4) | (X1 @ X6 @ X6 @ X4)) & ! [X2 : $i > $o,X3 : $i > $o] : (! [X4 : $i] : ((X1 @ X2 @ X3 @ X4) | (X0 @ X2 @ X3 @ X4)) => ! [X5 : $i] : ((X2 @ X5) => (X3 @ X5))))),
% 1.69/1.59 inference(negated_conjecture,[status(cth)],[f1])).
% 1.69/1.59 thf(f1,conjecture,(
% 1.69/1.59 ? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X7 : $i > $o,X6 : $i > $o,X5 : $i > $o] : ((! [X4 : $i] : ((X0 @ X6 @ X7 @ X4) | (X1 @ X6 @ X7 @ X4)) & ! [X4 : $i] : ((X0 @ X7 @ X5 @ X4) | (X1 @ X7 @ X5 @ X4))) => ! [X4 : $i] : ((X0 @ X6 @ X5 @ X4) | (X1 @ X6 @ X5 @ X4))) & ! [X6 : $i > $o,X4 : $i] : ((X0 @ X6 @ X6 @ X4) | (X1 @ X6 @ X6 @ X4)) & ! [X2 : $i > $o,X3 : $i > $o] : (! [X4 : $i] : ((X1 @ X2 @ X3 @ X4) | (X0 @ X2 @ X3 @ X4)) => ! [X5 : $i] : ((X2 @ X5) => (X3 @ X5))))),
% 1.69/1.59 file('/export/starexec/sandbox2/tmp/tmp.chEsFjBzWu/DTF2THF_4648.p',cTHM122C_pme)).
% 1.69/1.59 thf(f37,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1))) )),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.69/1.59 thf(f36,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true != $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1))) )),
% 1.69/1.59 inference(boolean_simplification,[status(thm)],[f35])).
% 1.69/1.59 thf(f35,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1)) | ($true = (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true != ((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 1.69/1.59 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.69/1.59 thf(f30,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK9 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK6 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1))) )),
% 1.69/1.59 inference(primitive_instantiation,[status(thm)],[f24])).
% 1.69/1.59 thf(f24,plain,(
% 1.69/1.59 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0))) | ($true = (sP0 @ X0 @ X1)) | ($true = (sK8 @ X1 @ X0 @ (sK9 @ X1 @ X0)))) )),
% 1.69/1.59 inference(cnf_transformation,[status(thm)],[f19])).
% 1.69/1.59 thf(f186,plain,(
% 1.69/1.59 spl10_1 | spl10_2),
% 1.69/1.59 inference(avatar_split_clause,[status(thm)],[f171,f183,f179])).
% 1.69/1.59 thf(f171,plain,(
% 1.69/1.59 ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.69/1.59 thf(f170,plain,(
% 1.69/1.59 ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = $false) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))),
% 1.69/1.59 inference(beta_eta_normalization,[status(thm)],[f165])).
% 1.69/1.59 thf(f165,plain,(
% 1.69/1.59 ( ! [X6 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) )),
% 1.69/1.59 inference(primitive_instantiation,[status(thm)],[f107])).
% 1.69/1.59 thf(f107,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X1 @ (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6)) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1)) | ((sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) )),
% 1.69/1.59 inference(equality_proxy_clausification,[status(thm)],[f106])).
% 1.69/1.59 thf(f106,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1)) | ($true = (X1 @ (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6)) | ($true = ((sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 1.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.69/1.59 thf(f105,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true != $true) | ($true = (X1 @ (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6)) | ($true = ((sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1))) )),
% 1.69/1.59 inference(boolean_simplification,[status(thm)],[f104])).
% 1.69/1.59 thf(f104,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1)) | ($true != ((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (X1 @ (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6)) | ($true = ((sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 1.69/1.59 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.69/1.59 thf(f94,plain,(
% 1.69/1.59 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X1 @ (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK6 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X1)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK8 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK7 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6))) )),
% 1.69/1.59 inference(primitive_instantiation,[status(thm)],[f26])).
% 1.69/1.59 thf(f26,plain,(
% 1.69/1.59 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true != (X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK6 @ X1 @ X0))) | ($true = (X0 @ (sK8 @ X1 @ X0) @ (sK7 @ X1 @ X0) @ X6)) | ((X1 @ (sK8 @ X1 @ X0) @ (sK7 @ X1 @ X0) @ X6) = $true) | ($true = (sP0 @ X0 @ X1))) )),
% 1.69/1.59 inference(cnf_transformation,[status(thm)],[f19])).
% 1.69/1.59 % SZS output end Proof for DTF2THF_4648
% 1.69/1.59 % (4859)------------------------------
% 1.69/1.59 % (4859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.59 % (4859)Termination reason: Refutation
% 1.69/1.59
% 1.69/1.59 % (4859)Memory used [KB]: 6396
% 1.69/1.59 % (4859)Time elapsed: 0.130 s
% 1.69/1.59 % (4859)Instructions burned: 307 (million)
% 1.69/1.59 % (4859)------------------------------
% 1.69/1.59 % (4859)------------------------------
% 1.69/1.59 % (4822)Success in time 0.268 s
%------------------------------------------------------------------------------