%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU876^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:38 AM UTC 2026
% Result : Theorem 2.98s 1.27s
% Output : Refutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 25
% Syntax : Number of formulae : 121 ( 3 unt; 0 typ; 9 def)
% Number of atoms : 1478 ( 478 equ; 0 cnn)
% Maximal formula atoms : 25 ( 12 avg)
% Number of connectives : 1418 ( 264 ~; 263 |; 143 &; 656 @)
% ( 9 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 182 ( 182 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 13 con; 0-2 aty)
% Number of variables : 300 ( 58 ^; 191 !; 51 ?; 300 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cE: a > $o ).
thf(func_def_2,type,
cA: ( a > $o ) > $o ).
thf(func_def_10,type,
sP0: ( a > $o ) > $o ).
thf(func_def_11,type,
sP1: ( a > $o ) > $o ).
thf(func_def_12,type,
sP2: ( a > $o ) > $o ).
thf(func_def_13,type,
sP3: ( a > $o ) > $o ).
thf(func_def_16,type,
sP6: ( ( a > $o ) > $o ) > ( a > $o ) > $o ).
thf(func_def_17,type,
sK7: ( ( a > $o ) > $o ) > ( a > $o ) > a ).
thf(func_def_18,type,
sK8: a > $o ).
thf(func_def_19,type,
sK9: a > $o ).
thf(func_def_20,type,
sK10: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_21,type,
sK11: ( a > $o ) > a > $o ).
thf(func_def_22,type,
sK12: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_23,type,
sK13: ( a > $o ) > a ).
thf(func_def_24,type,
sK14: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_27,type,
ph16:
!>[X0: $tType] : X0 ).
thf(f803,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f74,f81,f93,f96,f98,f490,f570,f759,f767,f802]) ).
thf(f802,plain,
( ~ spl15_29
| ~ spl15_46 ),
inference(avatar_contradiction_clause,[status(thm)],[f801]) ).
thf(f801,plain,
( $false
| ~ spl15_29
| ~ spl15_46 ),
inference(subsumption_resolution,[status(thm)],[f800,f489]) ).
thf(f489,plain,
( ( ( sP1 @ cE )
= $true )
| ~ spl15_29 ),
inference(avatar_component_clause,[status(thm)],[f488]) ).
thf(f488,definition,
( spl15_29
<=> ( ( sP1 @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl15_29])],[avatar_definition]) ).
thf(f800,plain,
( ( ( sP1 @ cE )
!= $true )
| ~ spl15_46 ),
inference(trivial_inequality_removal,[status(thm)],[f799]) ).
thf(f799,plain,
( ( $true != $true )
| ( ( sP1 @ cE )
!= $true )
| ~ spl15_46 ),
inference(superposition,[status(thm)],[f62,f758]) ).
thf(f758,plain,
( ( ( sK12 @ cE @ cE )
= $true )
| ~ spl15_46 ),
inference(avatar_component_clause,[status(thm)],[f757]) ).
thf(f757,definition,
( spl15_46
<=> ( ( sK12 @ cE @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl15_46])],[avatar_definition]) ).
thf(f62,plain,
! [X0: a > $o] :
( ( $true
!= ( sK12 @ X0 @ X0 ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: a > $o] :
( ( ( $true
!= ( sK12 @ X0 @ X0 ) )
& ( ( sK12 @ X0
@ ^ [Y0: a] : $false )
= $true )
& ! [X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( sK12 @ X0
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) )
= $true ) )
| ( ( sK12 @ X0 @ X2 )
!= $true ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f38,f39]) ).
thf(f39,plain,
! [X0: a > $o] :
( ? [X1: ( a > $o ) > $o] :
( ( ( X1 @ X0 )
!= $true )
& ( $true
= ( X1
@ ^ [Y0: a] : $false ) )
& ! [X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) )
= $true ) )
| ( ( X1 @ X2 )
!= $true ) ) )
=> ( ( $true
!= ( sK12 @ X0 @ X0 ) )
& ( ( sK12 @ X0
@ ^ [Y0: a] : $false )
= $true )
& ! [X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( sK12 @ X0
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) )
= $true ) )
| ( ( sK12 @ X0 @ X2 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
! [X0: a > $o] :
( ? [X1: ( a > $o ) > $o] :
( ( ( X1 @ X0 )
!= $true )
& ( $true
= ( X1
@ ^ [Y0: a] : $false ) )
& ! [X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) )
= $true ) )
| ( ( X1 @ X2 )
!= $true ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
! [X5: a > $o] :
( ? [X6: ( a > $o ) > $o] :
( ( ( X6 @ X5 )
!= $true )
& ( ( X6
@ ^ [Y0: a] : $false )
= $true )
& ! [X7: a > $o] :
( ! [X8: a] :
( ( ( X5 @ X8 )
!= $true )
| ( ( X6
@ ^ [Y0: a] :
( ( X8 = Y0 )
| ( X7 @ Y0 ) ) )
= $true ) )
| ( ( X6 @ X7 )
!= $true ) ) )
| ( ( sP1 @ X5 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X5: a > $o] :
( ? [X6: ( a > $o ) > $o] :
( ( ( X6 @ X5 )
!= $true )
& ( ( X6
@ ^ [Y0: a] : $false )
= $true )
& ! [X7: a > $o] :
( ! [X8: a] :
( ( ( X5 @ X8 )
!= $true )
| ( ( X6
@ ^ [Y0: a] :
( ( X8 = Y0 )
| ( X7 @ Y0 ) ) )
= $true ) )
| ( ( X6 @ X7 )
!= $true ) ) )
| ( ( sP1 @ X5 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f767,plain,
( ~ spl15_29
| spl15_45 ),
inference(avatar_contradiction_clause,[status(thm)],[f766]) ).
thf(f766,plain,
( $false
| ~ spl15_29
| spl15_45 ),
inference(subsumption_resolution,[status(thm)],[f765,f489]) ).
thf(f765,plain,
( ( ( sP1 @ cE )
!= $true )
| spl15_45 ),
inference(trivial_inequality_removal,[status(thm)],[f764]) ).
thf(f764,plain,
( ( $true != $true )
| ( ( sP1 @ cE )
!= $true )
| spl15_45 ),
inference(superposition,[status(thm)],[f755,f61]) ).
thf(f61,plain,
! [X0: a > $o] :
( ( ( sK12 @ X0
@ ^ [Y0: a] : $false )
= $true )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f755,plain,
( ( ( sK12 @ cE
@ ^ [Y0: a] : $false )
!= $true )
| spl15_45 ),
inference(avatar_component_clause,[status(thm)],[f754]) ).
thf(f754,definition,
( spl15_45
<=> ( ( sK12 @ cE
@ ^ [Y0: a] : $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl15_45])],[avatar_definition]) ).
thf(f759,plain,
( ~ spl15_45
| spl15_46
| ~ spl15_29 ),
inference(avatar_split_clause,[status(thm)],[f752,f488,f757,f754]) ).
thf(f752,plain,
( ( ( sK12 @ cE @ cE )
= $true )
| ( ( sK12 @ cE
@ ^ [Y0: a] : $false )
!= $true )
| ~ spl15_29 ),
inference(subsumption_resolution,[status(thm)],[f739,f67]) ).
thf(f67,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK14 @ X0 ) )
= $true )
| ( ( X0
@ ^ [Y0: a] : $false )
!= $true )
| ( ( X0 @ cE )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ! [X0: ( a > $o ) > $o] :
( ( ( ( X0 @ ( sK14 @ X0 ) )
= $true )
& ( ( sP6 @ X0 @ ( sK14 @ X0 ) )
= $true ) )
| ( ( X0
@ ^ [Y0: a] : $false )
!= $true )
| ( ( X0 @ cE )
= $true ) )
& ( ( sP5 = $true )
| ( sP4 = $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f16,f45]) ).
thf(f45,plain,
! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
& ( ( sP6 @ X0 @ X1 )
= $true ) )
=> ( ( ( X0 @ ( sK14 @ X0 ) )
= $true )
& ( ( sP6 @ X0 @ ( sK14 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
& ( ( sP6 @ X0 @ X1 )
= $true ) )
| ( ( X0
@ ^ [Y0: a] : $false )
!= $true )
| ( ( X0 @ cE )
= $true ) )
& ( ( sP5 = $true )
| ( sP4 = $true ) ) ),
inference(definition_folding,[status(thm)],[f8,f15,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X10: a > $o] :
( ? [X12: a] :
( ( ( cE @ X12 )
= $true )
& ( ( X10 @ X12 )
!= $true ) )
| ( $true
!= ( cA @ X10 ) )
| ( ( sP0 @ X10 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f11,plain,
! [X5: a > $o] :
( ? [X10: a > $o] :
( ( $true
= ( cA @ X10 ) )
& ! [X11: a] :
( ( ( X5 @ X11 )
!= $true )
| ( ( X10 @ X11 )
= $true ) )
& ( ( sP0 @ X10 )
= $true ) )
| ( ( sP2 @ X5 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f12,plain,
! [X3: a > $o] :
( ! [X5: a > $o] :
( ? [X9: a] :
( ( ( X3 @ X9 )
!= $true )
& ( ( X5 @ X9 )
= $true ) )
| ( ( sP2 @ X5 )
= $true )
| ( ( sP1 @ X5 )
= $true ) )
| ( ( sP3 @ X3 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f13,plain,
( ? [X13: a > $o] :
( ( ( cA @ X13 )
!= $true )
& ( ( cA @ X13 )
= $true )
& ! [X14: a] :
( ( ( X13 @ X14 )
= $true )
| ( ( cE @ X14 )
!= $true ) ) )
| ( sP4 != $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f14,plain,
( ? [X3: a > $o] :
( ! [X4: a] :
( ( ( X3 @ X4 )
= $true )
| ( ( cE @ X4 )
!= $true ) )
& ( ( sP3 @ X3 )
= $true )
& ( ( cA @ X3 )
= $true ) )
| ( sP5 != $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
! [X1: a > $o,X0: ( a > $o ) > $o] :
( ? [X2: a] :
( ( ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) )
!= $true )
& ( ( cE @ X2 )
= $true ) )
| ( ( sP6 @ X0 @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
( ! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
& ? [X2: a] :
( ( ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) )
!= $true )
& ( ( cE @ X2 )
= $true ) ) )
| ( ( X0
@ ^ [Y0: a] : $false )
!= $true )
| ( ( X0 @ cE )
= $true ) )
& ( ? [X3: a > $o] :
( ! [X4: a] :
( ( ( X3 @ X4 )
= $true )
| ( ( cE @ X4 )
!= $true ) )
& ! [X5: a > $o] :
( ? [X9: a] :
( ( ( X3 @ X9 )
!= $true )
& ( ( X5 @ X9 )
= $true ) )
| ? [X10: a > $o] :
( ( $true
= ( cA @ X10 ) )
& ! [X11: a] :
( ( ( X5 @ X11 )
!= $true )
| ( ( X10 @ X11 )
= $true ) )
& ( ? [X12: a] :
( ( ( cE @ X12 )
= $true )
& ( ( X10 @ X12 )
!= $true ) )
| ( $true
!= ( cA @ X10 ) ) ) )
| ? [X6: ( a > $o ) > $o] :
( ( ( X6 @ X5 )
!= $true )
& ( ( X6
@ ^ [Y0: a] : $false )
= $true )
& ! [X7: a > $o] :
( ! [X8: a] :
( ( ( X5 @ X8 )
!= $true )
| ( ( X6
@ ^ [Y0: a] :
( ( X8 = Y0 )
| ( X7 @ Y0 ) ) )
= $true ) )
| ( ( X6 @ X7 )
!= $true ) ) ) )
& ( ( cA @ X3 )
= $true ) )
| ? [X13: a > $o] :
( ( ( cA @ X13 )
!= $true )
& ( ( cA @ X13 )
= $true )
& ! [X14: a] :
( ( ( X13 @ X14 )
= $true )
| ( ( cE @ X14 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ? [X3: a > $o] :
( ! [X5: a > $o] :
( ? [X9: a] :
( ( ( X3 @ X9 )
!= $true )
& ( ( X5 @ X9 )
= $true ) )
| ? [X10: a > $o] :
( ( ? [X12: a] :
( ( ( cE @ X12 )
= $true )
& ( ( X10 @ X12 )
!= $true ) )
| ( $true
!= ( cA @ X10 ) ) )
& ! [X11: a] :
( ( ( X5 @ X11 )
!= $true )
| ( ( X10 @ X11 )
= $true ) )
& ( $true
= ( cA @ X10 ) ) )
| ? [X6: ( a > $o ) > $o] :
( ( ( X6 @ X5 )
!= $true )
& ! [X7: a > $o] :
( ! [X8: a] :
( ( ( X5 @ X8 )
!= $true )
| ( ( X6
@ ^ [Y0: a] :
( ( X8 = Y0 )
| ( X7 @ Y0 ) ) )
= $true ) )
| ( ( X6 @ X7 )
!= $true ) )
& ( ( X6
@ ^ [Y0: a] : $false )
= $true ) ) )
& ( ( cA @ X3 )
= $true )
& ! [X4: a] :
( ( ( X3 @ X4 )
= $true )
| ( ( cE @ X4 )
!= $true ) ) )
| ? [X13: a > $o] :
( ( ( cA @ X13 )
!= $true )
& ! [X14: a] :
( ( ( X13 @ X14 )
= $true )
| ( ( cE @ X14 )
!= $true ) )
& ( ( cA @ X13 )
= $true ) ) )
& ! [X0: ( a > $o ) > $o] :
( ( ( X0 @ cE )
= $true )
| ? [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
& ? [X2: a] :
( ( ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) )
!= $true )
& ( ( cE @ X2 )
= $true ) ) )
| ( ( X0
@ ^ [Y0: a] : $false )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
=> ! [X2: a] :
( ( ( cE @ X2 )
= $true )
=> ( ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ( X0
@ ^ [Y0: a] : $false )
= $true ) )
=> ( ( X0 @ cE )
= $true ) )
=> ( ! [X3: a > $o] :
( ( ( ( cA @ X3 )
= $true )
& ! [X4: a] :
( ( ( cE @ X4 )
= $true )
=> ( ( X3 @ X4 )
= $true ) ) )
=> ? [X5: a > $o] :
( ! [X9: a] :
( ( ( X5 @ X9 )
= $true )
=> ( ( X3 @ X9 )
= $true ) )
& ! [X10: a > $o] :
( ( ! [X11: a] :
( ( ( X5 @ X11 )
= $true )
=> ( ( X10 @ X11 )
= $true ) )
& ( $true
= ( cA @ X10 ) ) )
=> ( ! [X12: a] :
( ( ( cE @ X12 )
= $true )
=> ( ( X10 @ X12 )
= $true ) )
& ( $true
= ( cA @ X10 ) ) ) )
& ! [X6: ( a > $o ) > $o] :
( ( ! [X7: a > $o] :
( ( ( X6 @ X7 )
= $true )
=> ! [X8: a] :
( ( ( X5 @ X8 )
= $true )
=> ( ( X6
@ ^ [Y0: a] :
( ( X8 = Y0 )
| ( X7 @ Y0 ) ) )
= $true ) ) )
& ( ( X6
@ ^ [Y0: a] : $false )
= $true ) )
=> ( ( X6 @ X5 )
= $true ) ) ) )
& ! [X13: a > $o] :
( ( ! [X14: a] :
( ( ( cE @ X14 )
= $true )
=> ( ( X13 @ X14 )
= $true ) )
& ( ( cA @ X13 )
= $true ) )
=> ( ( cA @ X13 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
=> ! [X2: a] :
( ( ( cE @ X2 )
= $true )
=> ( ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ( X0
@ ^ [Y0: a] : $false )
= $true ) )
=> ( ( X0 @ cE )
= $true ) )
=> ( ! [X5: a > $o] :
( ( ( ( cA @ X5 )
= $true )
& ! [X6: a] :
( ( ( cE @ X6 )
= $true )
=> ( ( X5 @ X6 )
= $true ) ) )
=> ? [X7: a > $o] :
( ! [X8: ( a > $o ) > $o] :
( ( ( ( X8
@ ^ [Y0: a] : $false )
= $true )
& ! [X10: a > $o] :
( ( ( X8 @ X10 )
= $true )
=> ! [X11: a] :
( ( ( X7 @ X11 )
= $true )
=> ( ( X8
@ ^ [Y0: a] :
( ( X11 = Y0 )
| ( X10 @ Y0 ) ) )
= $true ) ) ) )
=> ( ( X8 @ X7 )
= $true ) )
& ! [X13: a] :
( ( ( X7 @ X13 )
= $true )
=> ( ( X5 @ X13 )
= $true ) )
& ! [X14: a > $o] :
( ( ( ( cA @ X14 )
= $true )
& ! [X15: a] :
( ( ( X7 @ X15 )
= $true )
=> ( $true
= ( X14 @ X15 ) ) ) )
=> ( ( ( cA @ X14 )
= $true )
& ! [X16: a] :
( ( ( cE @ X16 )
= $true )
=> ( ( X14 @ X16 )
= $true ) ) ) ) ) )
& ! [X17: a > $o] :
( ( ( ( cA @ X17 )
= $true )
& ! [X18: a] :
( ( ( cE @ X18 )
= $true )
=> ( ( X17 @ X18 )
= $true ) ) )
=> ( ( cA @ X17 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ! [X2: a] :
( ( cE @ X2 )
=> ( X0
@ ^ [X3: a] :
( ( X1 @ X3 )
| ( X2 = X3 ) ) ) ) )
& ( X0
@ ^ [X4: a] : $false ) )
=> ( X0 @ cE ) )
=> ( ! [X5: a > $o] :
( ( ( cA @ X5 )
& ! [X6: a] :
( ( cE @ X6 )
=> ( X5 @ X6 ) ) )
=> ? [X7: a > $o] :
( ! [X8: ( a > $o ) > $o] :
( ( ( X8
@ ^ [X9: a] : $false )
& ! [X10: a > $o] :
( ( X8 @ X10 )
=> ! [X11: a] :
( ( X7 @ X11 )
=> ( X8
@ ^ [X12: a] :
( ( X10 @ X12 )
| ( X11 = X12 ) ) ) ) ) )
=> ( X8 @ X7 ) )
& ! [X13: a] :
( ( X7 @ X13 )
=> ( X5 @ X13 ) )
& ! [X14: a > $o] :
( ( ( cA @ X14 )
& ! [X15: a] :
( ( X7 @ X15 )
=> ( X14 @ X15 ) ) )
=> ( ( cA @ X14 )
& ! [X16: a] :
( ( cE @ X16 )
=> ( X14 @ X16 ) ) ) ) ) )
& ! [X17: a > $o] :
( ( ( cA @ X17 )
& ! [X18: a] :
( ( cE @ X18 )
=> ( X17 @ X18 ) ) )
=> ( cA @ X17 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X0 @ X2 )
=> ! [X3: a] :
( ( cE @ X3 )
=> ( X0
@ ^ [X4: a] :
( ( X2 @ X4 )
| ( X3 = X4 ) ) ) ) )
& ( X0
@ ^ [X1: a] : $false ) )
=> ( X0 @ cE ) )
=> ( ! [X2: a > $o] :
( ( ( cA @ X2 )
& ! [X5: a] :
( ( cE @ X5 )
=> ( X2 @ X5 ) ) )
=> ? [X6: a > $o] :
( ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X5: a > $o] :
( ( X0 @ X5 )
=> ! [X3: a] :
( ( X6 @ X3 )
=> ( X0
@ ^ [X4: a] :
( ( X5 @ X4 )
| ( X3 = X4 ) ) ) ) ) )
=> ( X0 @ X6 ) )
& ! [X5: a] :
( ( X6 @ X5 )
=> ( X2 @ X5 ) )
& ! [X1: a > $o] :
( ( ( cA @ X1 )
& ! [X5: a] :
( ( X6 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( cA @ X1 )
& ! [X5: a] :
( ( cE @ X5 )
=> ( X1 @ X5 ) ) ) ) ) )
& ! [X2: a > $o] :
( ( ( cA @ X2 )
& ! [X5: a] :
( ( cE @ X5 )
=> ( X2 @ X5 ) ) )
=> ( cA @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X0 @ X2 )
=> ! [X3: a] :
( ( cE @ X3 )
=> ( X0
@ ^ [X4: a] :
( ( X2 @ X4 )
| ( X3 = X4 ) ) ) ) )
& ( X0
@ ^ [X1: a] : $false ) )
=> ( X0 @ cE ) )
=> ( ! [X2: a > $o] :
( ( ( cA @ X2 )
& ! [X5: a] :
( ( cE @ X5 )
=> ( X2 @ X5 ) ) )
=> ? [X6: a > $o] :
( ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X5: a > $o] :
( ( X0 @ X5 )
=> ! [X3: a] :
( ( X6 @ X3 )
=> ( X0
@ ^ [X4: a] :
( ( X5 @ X4 )
| ( X3 = X4 ) ) ) ) ) )
=> ( X0 @ X6 ) )
& ! [X5: a] :
( ( X6 @ X5 )
=> ( X2 @ X5 ) )
& ! [X1: a > $o] :
( ( ( cA @ X1 )
& ! [X5: a] :
( ( X6 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( cA @ X1 )
& ! [X5: a] :
( ( cE @ X5 )
=> ( X1 @ X5 ) ) ) ) ) )
& ! [X2: a > $o] :
( ( ( cA @ X2 )
& ! [X5: a] :
( ( cE @ X5 )
=> ( X2 @ X5 ) ) )
=> ( cA @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aZAifMX8r9/DTF2THF_29381.p',cDOMLEMMA4_pme) ).
thf(f739,plain,
( ( ( sK12 @ cE
@ ^ [Y0: a] : $false )
!= $true )
| ( ( sK12 @ cE @ cE )
= $true )
| ( ( sK12 @ cE @ ( sK14 @ ( sK12 @ cE ) ) )
!= $true )
| ~ spl15_29 ),
inference(trivial_inequality_removal,[status(thm)],[f733]) ).
thf(f733,plain,
( ( ( sK12 @ cE @ cE )
= $true )
| ( ( sK12 @ cE @ ( sK14 @ ( sK12 @ cE ) ) )
!= $true )
| ( $true != $true )
| ( ( sK12 @ cE
@ ^ [Y0: a] : $false )
!= $true )
| ~ spl15_29 ),
inference(superposition,[status(thm)],[f648,f66]) ).
thf(f66,plain,
! [X0: ( a > $o ) > $o] :
( ( ( sP6 @ X0 @ ( sK14 @ X0 ) )
= $true )
| ( ( X0 @ cE )
= $true )
| ( ( X0
@ ^ [Y0: a] : $false )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f648,plain,
( ! [X0: a > $o] :
( ( ( sP6 @ ( sK12 @ cE ) @ X0 )
!= $true )
| ( $true
!= ( sK12 @ cE @ X0 ) ) )
| ~ spl15_29 ),
inference(subsumption_resolution,[status(thm)],[f647,f489]) ).
thf(f647,plain,
! [X0: a > $o] :
( ( $true
!= ( sK12 @ cE @ X0 ) )
| ( ( sP6 @ ( sK12 @ cE ) @ X0 )
!= $true )
| ( ( sP1 @ cE )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f646]) ).
thf(f646,plain,
! [X0: a > $o] :
( ( $true
!= ( sK12 @ cE @ X0 ) )
| ( $true != $true )
| ( ( sP1 @ cE )
!= $true )
| ( ( sP6 @ ( sK12 @ cE ) @ X0 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f638]) ).
thf(f638,plain,
! [X0: a > $o] :
( ( $true
!= ( sK12 @ cE @ X0 ) )
| ( ( sP6 @ ( sK12 @ cE ) @ X0 )
!= $true )
| ( ( sP1 @ cE )
!= $true )
| ( $true != $true )
| ( ( sP6 @ ( sK12 @ cE ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f424,f47]) ).
thf(f47,plain,
! [X0: a > $o,X1: ( a > $o ) > $o] :
( ( ( cE @ ( sK7 @ X1 @ X0 ) )
= $true )
| ( ( sP6 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: a > $o,X1: ( a > $o ) > $o] :
( ( ( ( X1
@ ^ [Y0: a] :
( ( ( sK7 @ X1 @ X0 )
= Y0 )
| ( X0 @ Y0 ) ) )
!= $true )
& ( ( cE @ ( sK7 @ X1 @ X0 ) )
= $true ) )
| ( ( sP6 @ X1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f18,f19]) ).
thf(f19,plain,
! [X0: a > $o,X1: ( a > $o ) > $o] :
( ? [X2: a] :
( ( $true
!= ( X1
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X0 @ Y0 ) ) ) )
& ( ( cE @ X2 )
= $true ) )
=> ( ( ( X1
@ ^ [Y0: a] :
( ( ( sK7 @ X1 @ X0 )
= Y0 )
| ( X0 @ Y0 ) ) )
!= $true )
& ( ( cE @ ( sK7 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
! [X0: a > $o,X1: ( a > $o ) > $o] :
( ? [X2: a] :
( ( $true
!= ( X1
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X0 @ Y0 ) ) ) )
& ( ( cE @ X2 )
= $true ) )
| ( ( sP6 @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: a > $o,X0: ( a > $o ) > $o] :
( ? [X2: a] :
( ( ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) )
!= $true )
& ( ( cE @ X2 )
= $true ) )
| ( ( sP6 @ X0 @ X1 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f424,plain,
! [X0: a > $o,X1: a > $o] :
( ( ( X0 @ ( sK7 @ ( sK12 @ X0 ) @ X1 ) )
!= $true )
| ( ( sP6 @ ( sK12 @ X0 ) @ X1 )
!= $true )
| ( ( sP1 @ X0 )
!= $true )
| ( ( sK12 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f423]) ).
thf(f423,plain,
! [X0: a > $o,X1: a > $o] :
( ( ( X0 @ ( sK7 @ ( sK12 @ X0 ) @ X1 ) )
!= $true )
| ( $true != $true )
| ( ( sP1 @ X0 )
!= $true )
| ( ( sK12 @ X0 @ X1 )
!= $true )
| ( ( sP6 @ ( sK12 @ X0 ) @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f48,f60]) ).
thf(f60,plain,
! [X2: a > $o,X3: a,X0: a > $o] :
( ( ( sK12 @ X0
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) )
= $true )
| ( ( X0 @ X3 )
!= $true )
| ( ( sK12 @ X0 @ X2 )
!= $true )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f48,plain,
! [X0: a > $o,X1: ( a > $o ) > $o] :
( ( ( X1
@ ^ [Y0: a] :
( ( ( sK7 @ X1 @ X0 )
= Y0 )
| ( X0 @ Y0 ) ) )
!= $true )
| ( ( sP6 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f570,plain,
~ spl15_28,
inference(avatar_contradiction_clause,[status(thm)],[f569]) ).
thf(f569,plain,
( $false
| ~ spl15_28 ),
inference(subsumption_resolution,[status(thm)],[f486,f476]) ).
thf(f476,plain,
( ( sP2 @ cE )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f475,f59]) ).
thf(f59,plain,
! [X0: a > $o] :
( ( ( cA @ ( sK11 @ X0 ) )
= $true )
| ( ( sP2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: a > $o] :
( ( ( ( cA @ ( sK11 @ X0 ) )
= $true )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( sK11 @ X0 @ X2 )
= $true ) )
& ( $true
= ( sP0 @ ( sK11 @ X0 ) ) ) )
| ( ( sP2 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f34,f35]) ).
thf(f35,plain,
! [X0: a > $o] :
( ? [X1: a > $o] :
( ( ( cA @ X1 )
= $true )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
& ( ( sP0 @ X1 )
= $true ) )
=> ( ( ( cA @ ( sK11 @ X0 ) )
= $true )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( sK11 @ X0 @ X2 )
= $true ) )
& ( $true
= ( sP0 @ ( sK11 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
! [X0: a > $o] :
( ? [X1: a > $o] :
( ( ( cA @ X1 )
= $true )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
& ( ( sP0 @ X1 )
= $true ) )
| ( ( sP2 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
! [X5: a > $o] :
( ? [X10: a > $o] :
( ( $true
= ( cA @ X10 ) )
& ! [X11: a] :
( ( ( X5 @ X11 )
!= $true )
| ( ( X10 @ X11 )
= $true ) )
& ( ( sP0 @ X10 )
= $true ) )
| ( ( sP2 @ X5 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f475,plain,
( ( ( cA @ ( sK11 @ cE ) )
!= $true )
| ( ( sP2 @ cE )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f466,f57]) ).
thf(f57,plain,
! [X0: a > $o] :
( ( $true
= ( sP0 @ ( sK11 @ X0 ) ) )
| ( ( sP2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f466,plain,
( ( ( sP0 @ ( sK11 @ cE ) )
!= $true )
| ( ( cA @ ( sK11 @ cE ) )
!= $true )
| ( ( sP2 @ cE )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f459]) ).
thf(f459,plain,
( ( ( sP2 @ cE )
!= $true )
| ( ( sP0 @ ( sK11 @ cE ) )
!= $true )
| ( ( cA @ ( sK11 @ cE ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f212,f64]) ).
thf(f64,plain,
! [X0: a > $o] :
( ( ( cE @ ( sK13 @ X0 ) )
= $true )
| ( ( cA @ X0 )
!= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: a > $o] :
( ( ( ( cE @ ( sK13 @ X0 ) )
= $true )
& ( ( X0 @ ( sK13 @ X0 ) )
!= $true ) )
| ( ( cA @ X0 )
!= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f42,f43]) ).
thf(f43,plain,
! [X0: a > $o] :
( ? [X1: a] :
( ( ( cE @ X1 )
= $true )
& ( ( X0 @ X1 )
!= $true ) )
=> ( ( ( cE @ ( sK13 @ X0 ) )
= $true )
& ( ( X0 @ ( sK13 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
! [X0: a > $o] :
( ? [X1: a] :
( ( ( cE @ X1 )
= $true )
& ( ( X0 @ X1 )
!= $true ) )
| ( ( cA @ X0 )
!= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,plain,
! [X10: a > $o] :
( ? [X12: a] :
( ( ( cE @ X12 )
= $true )
& ( ( X10 @ X12 )
!= $true ) )
| ( $true
!= ( cA @ X10 ) )
| ( ( sP0 @ X10 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f212,plain,
! [X0: a > $o] :
( ( ( X0 @ ( sK13 @ ( sK11 @ X0 ) ) )
!= $true )
| ( ( sP2 @ X0 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f211,f57]) ).
thf(f211,plain,
! [X0: a > $o] :
( ( ( sP2 @ X0 )
!= $true )
| ( $true
!= ( sP0 @ ( sK11 @ X0 ) ) )
| ( ( X0 @ ( sK13 @ ( sK11 @ X0 ) ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f201,f59]) ).
thf(f201,plain,
! [X0: a > $o] :
( ( ( X0 @ ( sK13 @ ( sK11 @ X0 ) ) )
!= $true )
| ( ( sP2 @ X0 )
!= $true )
| ( ( cA @ ( sK11 @ X0 ) )
!= $true )
| ( $true
!= ( sP0 @ ( sK11 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f197]) ).
thf(f197,plain,
! [X0: a > $o] :
( ( ( X0 @ ( sK13 @ ( sK11 @ X0 ) ) )
!= $true )
| ( ( cA @ ( sK11 @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( sP0 @ ( sK11 @ X0 ) ) )
| ( ( sP2 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f63,f58]) ).
thf(f58,plain,
! [X2: a,X0: a > $o] :
( ( ( sK11 @ X0 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( sP2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f63,plain,
! [X0: a > $o] :
( ( ( X0 @ ( sK13 @ X0 ) )
!= $true )
| ( ( cA @ X0 )
!= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f486,plain,
( ( ( sP2 @ cE )
= $true )
| ~ spl15_28 ),
inference(avatar_component_clause,[status(thm)],[f485]) ).
thf(f485,definition,
( spl15_28
<=> ( ( sP2 @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl15_28])],[avatar_definition]) ).
thf(f490,plain,
( spl15_28
| spl15_29
| ~ spl15_1
| ~ spl15_7 ),
inference(avatar_split_clause,[status(thm)],[f483,f91,f69,f488,f485]) ).
thf(f69,definition,
( spl15_1
<=> ( $true
= ( sP3 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl15_1])],[avatar_definition]) ).
thf(f91,definition,
( spl15_7
<=> ! [X1: a] :
( ( ( cE @ X1 )
!= $true )
| ( $true
= ( sK8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl15_7])],[avatar_definition]) ).
thf(f483,plain,
( ( ( sP1 @ cE )
= $true )
| ( ( sP2 @ cE )
= $true )
| ~ spl15_1
| ~ spl15_7 ),
inference(subsumption_resolution,[status(thm)],[f482,f70]) ).
thf(f70,plain,
( ( $true
= ( sP3 @ sK8 ) )
| ~ spl15_1 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f482,plain,
( ( ( sP2 @ cE )
= $true )
| ( $true
!= ( sP3 @ sK8 ) )
| ( ( sP1 @ cE )
= $true )
| ~ spl15_1
| ~ spl15_7 ),
inference(trivial_inequality_removal,[status(thm)],[f481]) ).
thf(f481,plain,
( ( ( sP1 @ cE )
= $true )
| ( $true
!= ( sP3 @ sK8 ) )
| ( $true != $true )
| ( ( sP2 @ cE )
= $true )
| ~ spl15_1
| ~ spl15_7 ),
inference(duplicate_literal_removal,[status(thm)],[f480]) ).
thf(f480,plain,
( ( ( sP2 @ cE )
= $true )
| ( ( sP1 @ cE )
= $true )
| ( $true != $true )
| ( ( sP1 @ cE )
= $true )
| ( ( sP2 @ cE )
= $true )
| ( $true
!= ( sP3 @ sK8 ) )
| ~ spl15_1
| ~ spl15_7 ),
inference(superposition,[status(thm)],[f405,f55]) ).
thf(f55,plain,
! [X0: a > $o,X1: a > $o] :
( ( ( X1 @ ( sK10 @ X1 @ X0 ) )
= $true )
| ( ( sP2 @ X1 )
= $true )
| ( ( sP3 @ X0 )
!= $true )
| ( ( sP1 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: a > $o] :
( ! [X1: a > $o] :
( ( ( ( X0 @ ( sK10 @ X1 @ X0 ) )
!= $true )
& ( ( X1 @ ( sK10 @ X1 @ X0 ) )
= $true ) )
| ( ( sP2 @ X1 )
= $true )
| ( ( sP1 @ X1 )
= $true ) )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f30,f31]) ).
thf(f31,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
=> ( ( ( X0 @ ( sK10 @ X1 @ X0 ) )
!= $true )
& ( ( X1 @ ( sK10 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
! [X0: a > $o] :
( ! [X1: a > $o] :
( ? [X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
| ( ( sP2 @ X1 )
= $true )
| ( ( sP1 @ X1 )
= $true ) )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
! [X3: a > $o] :
( ! [X5: a > $o] :
( ? [X9: a] :
( ( ( X3 @ X9 )
!= $true )
& ( ( X5 @ X9 )
= $true ) )
| ( ( sP2 @ X5 )
= $true )
| ( ( sP1 @ X5 )
= $true ) )
| ( ( sP3 @ X3 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f405,plain,
( ! [X0: a > $o] :
( ( ( cE @ ( sK10 @ X0 @ sK8 ) )
!= $true )
| ( ( sP2 @ X0 )
= $true )
| ( ( sP1 @ X0 )
= $true ) )
| ~ spl15_1
| ~ spl15_7 ),
inference(subsumption_resolution,[status(thm)],[f402,f70]) ).
thf(f402,plain,
( ! [X0: a > $o] :
( ( $true
!= ( sP3 @ sK8 ) )
| ( ( sP2 @ X0 )
= $true )
| ( ( sP1 @ X0 )
= $true )
| ( ( cE @ ( sK10 @ X0 @ sK8 ) )
!= $true ) )
| ~ spl15_7 ),
inference(trivial_inequality_removal,[status(thm)],[f394]) ).
thf(f394,plain,
( ! [X0: a > $o] :
( ( $true != $true )
| ( ( sP1 @ X0 )
= $true )
| ( $true
!= ( sP3 @ sK8 ) )
| ( ( cE @ ( sK10 @ X0 @ sK8 ) )
!= $true )
| ( ( sP2 @ X0 )
= $true ) )
| ~ spl15_7 ),
inference(superposition,[status(thm)],[f56,f92]) ).
thf(f92,plain,
( ! [X1: a] :
( ( $true
= ( sK8 @ X1 ) )
| ( ( cE @ X1 )
!= $true ) )
| ~ spl15_7 ),
inference(avatar_component_clause,[status(thm)],[f91]) ).
thf(f56,plain,
! [X0: a > $o,X1: a > $o] :
( ( ( X0 @ ( sK10 @ X1 @ X0 ) )
!= $true )
| ( ( sP1 @ X1 )
= $true )
| ( ( sP2 @ X1 )
= $true )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f98,plain,
( ~ spl15_4
| ~ spl15_3 ),
inference(avatar_split_clause,[status(thm)],[f54,f76,f79]) ).
thf(f79,definition,
( spl15_4
<=> ( ( cA @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl15_4])],[avatar_definition]) ).
thf(f76,definition,
( spl15_3
<=> ( sP4 = $true ) ),
introduced(definition,[new_symbols(naming,[spl15_3])],[avatar_definition]) ).
thf(f54,plain,
( ( ( cA @ sK9 )
!= $true )
| ( sP4 != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( ( cA @ sK9 )
!= $true )
& ( ( cA @ sK9 )
= $true )
& ! [X1: a] :
( ( ( sK9 @ X1 )
= $true )
| ( ( cE @ X1 )
!= $true ) ) )
| ( sP4 != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f26,f27]) ).
thf(f27,plain,
( ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true )
& ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
| ( ( cE @ X1 )
!= $true ) ) )
=> ( ( ( cA @ sK9 )
!= $true )
& ( ( cA @ sK9 )
= $true )
& ! [X1: a] :
( ( ( sK9 @ X1 )
= $true )
| ( ( cE @ X1 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true )
& ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
| ( ( cE @ X1 )
!= $true ) ) )
| ( sP4 != $true ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ? [X13: a > $o] :
( ( ( cA @ X13 )
!= $true )
& ( ( cA @ X13 )
= $true )
& ! [X14: a] :
( ( ( X13 @ X14 )
= $true )
| ( ( cE @ X14 )
!= $true ) ) )
| ( sP4 != $true ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f96,plain,
( spl15_2
| spl15_3 ),
inference(avatar_split_clause,[status(thm)],[f65,f76,f72]) ).
thf(f72,definition,
( spl15_2
<=> ( sP5 = $true ) ),
introduced(definition,[new_symbols(naming,[spl15_2])],[avatar_definition]) ).
thf(f65,plain,
( ( sP4 = $true )
| ( sP5 = $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f93,plain,
( spl15_7
| ~ spl15_2 ),
inference(avatar_split_clause,[status(thm)],[f51,f72,f91]) ).
thf(f51,plain,
! [X1: a] :
( ( sP5 != $true )
| ( ( cE @ X1 )
!= $true )
| ( $true
= ( sK8 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X1: a] :
( ( $true
= ( sK8 @ X1 ) )
| ( ( cE @ X1 )
!= $true ) )
& ( $true
= ( sP3 @ sK8 ) )
& ( ( cA @ sK8 )
= $true ) )
| ( sP5 != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f22,f23]) ).
thf(f23,plain,
( ? [X0: a > $o] :
( ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
| ( ( cE @ X1 )
!= $true ) )
& ( ( sP3 @ X0 )
= $true )
& ( ( cA @ X0 )
= $true ) )
=> ( ! [X1: a] :
( ( $true
= ( sK8 @ X1 ) )
| ( ( cE @ X1 )
!= $true ) )
& ( $true
= ( sP3 @ sK8 ) )
& ( ( cA @ sK8 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X0: a > $o] :
( ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
| ( ( cE @ X1 )
!= $true ) )
& ( ( sP3 @ X0 )
= $true )
& ( ( cA @ X0 )
= $true ) )
| ( sP5 != $true ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ? [X3: a > $o] :
( ! [X4: a] :
( ( ( X3 @ X4 )
= $true )
| ( ( cE @ X4 )
!= $true ) )
& ( ( sP3 @ X3 )
= $true )
& ( ( cA @ X3 )
= $true ) )
| ( sP5 != $true ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f81,plain,
( ~ spl15_3
| spl15_4 ),
inference(avatar_split_clause,[status(thm)],[f53,f79,f76]) ).
thf(f53,plain,
( ( sP4 != $true )
| ( ( cA @ sK9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f74,plain,
( spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[status(thm)],[f50,f72,f69]) ).
thf(f50,plain,
( ( $true
= ( sP3 @ sK8 ) )
| ( sP5 != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU876^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:35:45 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU876^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Set Theory (Finite sets)
% 0.07/0.32 % Problem : TPS problem from SET-TOPOLOGY-THMS
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_1126 [Bro09]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.45 v7.5.0, 0.57 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.07/0.32 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.07/0.32 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 14 ( 14 avg)
% 0.07/0.32 % Number of connectives : 53 ( 0 ~; 2 |; 9 &; 27 @)
% 0.07/0.32 % ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 18 ( 18 avg)
% 0.07/0.32 % Number of types : 2 ( 1 usr)
% 0.07/0.32 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% 0.07/0.32 % Number of variables : 19 ( 4 ^; 14 !; 1 ?; 19 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(a_type,type,
% 0.07/0.32 a: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(cE,type,
% 0.07/0.32 cE: a > $o ).
% 0.07/0.32
% 0.07/0.32 thf(cA,type,
% 0.07/0.32 cA: ( a > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(cDOMLEMMA4_pme,conjecture,
% 0.07/0.32 ( ! [X: ( a > $o ) > $o] :
% 0.07/0.32 ( ( ( X
% 0.07/0.32 @ ^ [Xy: a] : $false )
% 0.07/0.32 & ! [Xx: a > $o] :
% 0.07/0.32 ( ( X @ Xx )
% 0.07/0.32 => ! [Xt: a] :
% 0.07/0.32 ( ( cE @ Xt )
% 0.07/0.32 => ( X
% 0.07/0.32 @ ^ [Xz: a] :
% 0.07/0.32 ( ( Xx @ Xz )
% 0.07/0.32 | ( Xt = Xz ) ) ) ) ) )
% 0.07/0.32 => ( X @ cE ) )
% 0.07/0.32 => ( ! [Xx: a > $o] :
% 0.07/0.32 ( ( ( cA @ Xx )
% 0.07/0.32 & ! [Xx0: a] :
% 0.07/0.32 ( ( cE @ Xx0 )
% 0.07/0.32 => ( Xx @ Xx0 ) ) )
% 0.07/0.32 => ( cA @ Xx ) )
% 0.07/0.32 & ! [Xx: a > $o] :
% 0.07/0.32 ( ( ( cA @ Xx )
% 0.07/0.32 & ! [Xx0: a] :
% 0.07/0.32 ( ( cE @ Xx0 )
% 0.07/0.32 => ( Xx @ Xx0 ) ) )
% 0.07/0.32 => ? [Xe: a > $o] :
% 0.07/0.32 ( ! [X: ( a > $o ) > $o] :
% 0.07/0.32 ( ( ( X
% 0.07/0.32 @ ^ [Xy: a] : $false )
% 0.07/0.32 & ! [Xx0: a > $o] :
% 0.07/0.32 ( ( X @ Xx0 )
% 0.07/0.32 => ! [Xt: a] :
% 0.07/0.32 ( ( Xe @ Xt )
% 0.07/0.32 => ( X
% 0.07/0.32 @ ^ [Xz: a] :
% 0.07/0.32 ( ( Xx0 @ Xz )
% 0.07/0.32 | ( Xt = Xz ) ) ) ) ) )
% 0.07/0.32 => ( X @ Xe ) )
% 0.07/0.32 & ! [Xx0: a] :
% 0.07/0.32 ( ( Xe @ Xx0 )
% 0.07/0.32 => ( Xx @ Xx0 ) )
% 0.07/0.32 & ! [Xy: a > $o] :
% 0.07/0.32 ( ( ( cA @ Xy )
% 0.07/0.32 & ! [Xx0: a] :
% 0.07/0.32 ( ( Xe @ Xx0 )
% 0.07/0.32 => ( Xy @ Xx0 ) ) )
% 0.07/0.32 => ( ( cA @ Xy )
% 0.07/0.32 & ! [Xx0: a] :
% 0.07/0.32 ( ( cE @ Xx0 )
% 0.07/0.32 => ( Xy @ Xx0 ) ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.84/0.89 ---- Embedded in THF ---
% 0.84/0.89 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.89 %%% Generated on Tue Feb 24 12:35:46 EST 2026
% 0.84/0.89 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.89 %%% Logic specification used:
% 0.84/0.89 %%% thf(spec, logic, $$dhol).
% 0.84/0.89
% 0.84/0.89 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aZAifMX8r9/DTF2DTF29381.p
% See solution above
% 0.84/0.89 ------------------------
% 1.02/0.90 ---- Cleaned THF ---
% 1.02/0.90 thf(a_type,type,
% 1.02/0.90 a: $tType ).
% 1.02/0.90
% 1.02/0.90 thf(cE,type,
% 1.02/0.90 cE: a > $o ).
% 1.02/0.90
% 1.02/0.90 thf(cA,type,
% 1.02/0.90 cA: ( a > $o ) > $o ).
% 1.02/0.90
% 1.02/0.90 thf(cDOMLEMMA4_pme,conjecture,
% 1.02/0.90 ( ! [X: ( a > $o ) > $o] :
% 1.02/0.90 ( ( ( X
% 1.02/0.90 @ ^ [Xy: a] : $false )
% 1.02/0.90 & ! [Xx: a > $o] :
% 1.02/0.90 ( ( X @ Xx )
% 1.02/0.90 => ! [Xt: a] :
% 1.02/0.90 ( ( cE @ Xt )
% 1.02/0.90 => ( X
% 1.02/0.90 @ ^ [Xz: a] :
% 1.02/0.90 ( ( Xx @ Xz )
% 1.02/0.90 | ( Xt = Xz ) ) ) ) ) )
% 1.02/0.90 => ( X @ cE ) )
% 1.02/0.90 => ( ! [Xx: a > $o] :
% 1.02/0.90 ( ( ( cA @ Xx )
% 1.02/0.90 & ! [Xx0: a] :
% 1.02/0.90 ( ( cE @ Xx0 )
% 1.02/0.90 => ( Xx @ Xx0 ) ) )
% 1.02/0.90 => ( cA @ Xx ) )
% 1.02/0.90 & ! [Xx: a > $o] :
% 1.02/0.90 ( ( ( cA @ Xx )
% 1.02/0.90 & ! [Xx0: a] :
% 1.02/0.90 ( ( cE @ Xx0 )
% 1.02/0.90 => ( Xx @ Xx0 ) ) )
% 1.02/0.90 => ? [Xe: a > $o] :
% 1.02/0.90 ( ! [X: ( a > $o ) > $o] :
% 1.02/0.90 ( ( ( X
% 1.02/0.90 @ ^ [Xy: a] : $false )
% 1.02/0.90 & ! [Xx0: a > $o] :
% 1.02/0.90 ( ( X @ Xx0 )
% 1.02/0.90 => ! [Xt: a] :
% 1.02/0.90 ( ( Xe @ Xt )
% 1.02/0.90 => ( X
% 1.02/0.90 @ ^ [Xz: a] :
% 1.02/0.90 ( ( Xx0 @ Xz )
% 1.02/0.90 | ( Xt = Xz ) ) ) ) ) )
% 1.02/0.90 => ( X @ Xe ) )
% 1.02/0.90 & ! [Xx0: a] :
% 1.02/0.90 ( ( Xe @ Xx0 )
% 1.02/0.90 => ( Xx @ Xx0 ) )
% 1.02/0.90 & ! [Xy: a > $o] :
% 1.02/0.90 ( ( ( cA @ Xy )
% 1.02/0.90 & ! [Xx0: a] :
% 1.02/0.90 ( ( Xe @ Xx0 )
% 1.02/0.90 => ( Xy @ Xx0 ) ) )
% 1.02/0.90 => ( ( cA @ Xy )
% 1.02/0.90 & ! [Xx0: a] :
% 1.02/0.90 ( ( cE @ Xx0 )
% 1.02/0.90 => ( Xy @ Xx0 ) ) ) ) ) ) ) ) ).
% 1.02/0.90 ------------------------
% 1.02/0.91 % (29643)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_29381 for (3000ds/4Mi)
% 1.02/0.91 % (29644)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_29381 for (3000ds/27Mi)
% 1.02/0.91 % (29645)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29381 for (3000ds/2Mi)
% 1.02/0.91 % (29642)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29381 for (3000ds/183Mi)
% 1.02/0.91 % (29646)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_29381 for (3000ds/2Mi)
% 1.02/0.91 % (29648)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29381 for (3000ds/18Mi)
% 1.02/0.91 % (29647)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_29381 for (3000ds/275Mi)
% 1.02/0.91 % (29645)Instruction limit reached!
% 1.02/0.91 % (29645)------------------------------
% 1.02/0.91 % (29645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.91 % (29645)Termination reason: Unknown
% 1.02/0.91 % (29645)Termination phase: Preprocessing 3
% 1.02/0.91
% 1.02/0.91 % (29645)Memory used [KB]: 1023
% 1.02/0.91 % (29645)Time elapsed: 0.002 s
% 1.02/0.91 % (29645)Instructions burned: 3 (million)
% 1.02/0.91 % (29645)------------------------------
% 1.02/0.91 % (29645)------------------------------
% 1.02/0.91 % (29646)Instruction limit reached!
% 1.02/0.91 % (29646)------------------------------
% 1.02/0.91 % (29646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.91 % (29646)Termination reason: Unknown
% 1.02/0.91 % (29646)Termination phase: Saturation
% 1.02/0.91
% 1.02/0.91 % (29646)Memory used [KB]: 1023
% 1.02/0.91 % (29646)Time elapsed: 0.002 s
% 1.02/0.91 % (29646)Instructions burned: 3 (million)
% 1.02/0.91 % (29646)------------------------------
% 1.02/0.91 % (29646)------------------------------
% 1.02/0.91 % (29643)Instruction limit reached!
% 1.02/0.91 % (29643)------------------------------
% 1.02/0.91 % (29643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.91 % (29643)Termination reason: Unknown
% 1.02/0.91 % (29643)Termination phase: Saturation
% 1.02/0.91
% 1.02/0.91 % (29643)Memory used [KB]: 5500
% 1.02/0.91 % (29643)Time elapsed: 0.003 s
% 1.02/0.91 % (29643)Instructions burned: 5 (million)
% 1.02/0.91 % (29643)------------------------------
% 1.02/0.91 % (29643)------------------------------
% 1.02/0.92 % (29647)Refutation not found, incomplete strategy
% 1.02/0.92 % (29647)------------------------------
% 1.02/0.92 % (29647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.92 % (29647)Termination reason: Refutation not found, incomplete strategy
% 1.02/0.92
% 1.02/0.92
% 1.02/0.92 % (29647)Memory used [KB]: 5628
% 1.02/0.92 % (29647)Time elapsed: 0.007 s
% 1.02/0.92 % (29647)Instructions burned: 17 (million)
% 1.02/0.92 % (29647)------------------------------
% 1.02/0.92 % (29647)------------------------------
% 1.02/0.92 % (29648)Instruction limit reached!
% 1.02/0.92 % (29648)------------------------------
% 1.02/0.92 % (29648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.92 % (29648)Termination reason: Unknown
% 1.02/0.92 % (29648)Termination phase: Saturation
% 1.02/0.92
% 1.02/0.92 % (29648)Memory used [KB]: 5628
% 1.02/0.92 % (29648)Time elapsed: 0.008 s
% 1.02/0.92 % (29648)Instructions burned: 20 (million)
% 1.02/0.92 % (29648)------------------------------
% 1.02/0.92 % (29648)------------------------------
% 1.02/0.92 % (29644)Instruction limit reached!
% 1.02/0.92 % (29644)------------------------------
% 1.02/0.92 % (29644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.92 % (29644)Termination reason: Unknown
% 1.02/0.92 % (29644)Termination phase: Saturation
% 1.02/0.92
% 1.02/0.92 % (29644)Memory used [KB]: 5756
% 1.02/0.92 % (29644)Time elapsed: 0.011 s
% 1.02/0.92 % (29644)Instructions burned: 28 (million)
% 1.02/0.92 % (29644)------------------------------
% 1.02/0.92 % (29644)------------------------------
% 1.02/0.92 % (29649)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/3Mi)
% 1.02/0.92 % (29650)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_29381 for (2999ds/37Mi)
% 1.02/0.92 % (29651)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_29381 for (2999ds/15Mi)
% 1.02/0.92 % (29649)Instruction limit reached!
% 1.02/0.92 % (29649)------------------------------
% 1.02/0.92 % (29649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.92 % (29649)Termination reason: Unknown
% 1.02/0.92 % (29649)Termination phase: Property scanning
% 1.02/0.92
% 1.02/0.92 % (29649)Memory used [KB]: 1023
% 1.02/0.92 % (29649)Time elapsed: 0.002 s
% 1.02/0.92 % (29649)Instructions burned: 3 (million)
% 1.02/0.92 % (29649)------------------------------
% 1.02/0.92 % (29649)------------------------------
% 1.02/0.93 % (29652)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_29381 for (2999ds/3Mi)
% 1.02/0.93 % (29653)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_29381 for (2999ds/1041Mi)
% 1.02/0.93 % (29651)Instruction limit reached!
% 1.02/0.93 % (29651)------------------------------
% 1.02/0.93 % (29651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.93 % (29651)Termination reason: Unknown
% 1.02/0.93 % (29651)Termination phase: Saturation
% 1.02/0.93
% 1.02/0.93 % (29651)Memory used [KB]: 5756
% 1.02/0.93 % (29651)Time elapsed: 0.007 s
% 1.02/0.93 % (29651)Instructions burned: 17 (million)
% 1.02/0.93 % (29651)------------------------------
% 1.02/0.93 % (29651)------------------------------
% 1.02/0.93 % (29652)Instruction limit reached!
% 1.02/0.93 % (29652)------------------------------
% 1.02/0.93 % (29652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.93 % (29652)Termination reason: Unknown
% 1.02/0.93 % (29652)Termination phase: Saturation
% 1.02/0.93
% 1.02/0.93 % (29652)Memory used [KB]: 5500
% 1.02/0.93 % (29652)Time elapsed: 0.003 s
% 1.02/0.93 % (29652)Instructions burned: 5 (million)
% 1.02/0.93 % (29652)------------------------------
% 1.02/0.93 % (29652)------------------------------
% 1.02/0.93 % (29654)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/7Mi)
% 1.02/0.93 % (29655)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/16Mi)
% 1.02/0.93 % (29654)Instruction limit reached!
% 1.02/0.93 % (29654)------------------------------
% 1.02/0.93 % (29654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.93 % (29654)Termination reason: Unknown
% 1.02/0.93 % (29654)Termination phase: Saturation
% 1.02/0.93
% 1.02/0.93 % (29654)Memory used [KB]: 1023
% 1.02/0.93 % (29654)Time elapsed: 0.004 s
% 1.02/0.93 % (29654)Instructions burned: 8 (million)
% 1.02/0.93 % (29654)------------------------------
% 1.02/0.93 % (29654)------------------------------
% 1.02/0.93 % (29650)Instruction limit reached!
% 1.02/0.93 % (29650)------------------------------
% 1.02/0.93 % (29650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.93 % (29650)Termination reason: Unknown
% 1.02/0.93 % (29650)Termination phase: Saturation
% 1.02/0.93
% 1.02/0.93 % (29650)Memory used [KB]: 5628
% 1.02/0.93 % (29650)Time elapsed: 0.013 s
% 1.02/0.93 % (29650)Instructions burned: 38 (million)
% 1.02/0.93 % (29650)------------------------------
% 1.02/0.93 % (29650)------------------------------
% 1.02/0.94 % (29655)Instruction limit reached!
% 1.02/0.94 % (29655)------------------------------
% 1.02/0.94 % (29655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.94 % (29655)Termination reason: Unknown
% 1.02/0.94 % (29655)Termination phase: Saturation
% 1.02/0.94
% 1.02/0.94 % (29655)Memory used [KB]: 5628
% 1.02/0.94 % (29655)Time elapsed: 0.007 s
% 1.02/0.94 % (29655)Instructions burned: 17 (million)
% 1.02/0.94 % (29655)------------------------------
% 1.02/0.94 % (29655)------------------------------
% 1.02/0.94 % (29656)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_29381 for (2999ds/3Mi)
% 1.02/0.94 % (29656)Instruction limit reached!
% 1.02/0.94 % (29656)------------------------------
% 1.02/0.94 % (29656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.94 % (29656)Termination reason: Unknown
% 1.02/0.94 % (29656)Termination phase: Preprocessing 3
% 1.02/0.94
% 1.02/0.94 % (29656)Memory used [KB]: 1023
% 1.02/0.94 % (29656)Time elapsed: 0.002 s
% 1.02/0.94 % (29656)Instructions burned: 3 (million)
% 1.02/0.94 % (29656)------------------------------
% 1.02/0.94 % (29656)------------------------------
% 1.02/0.94 % (29657)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_29381 for (2999ds/3Mi)
% 1.02/0.94 % (29657)Instruction limit reached!
% 1.02/0.94 % (29657)------------------------------
% 1.02/0.94 % (29657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.94 % (29657)Termination reason: Unknown
% 1.02/0.94 % (29657)Termination phase: Preprocessing 3
% 1.02/0.94
% 1.02/0.94 % (29657)Memory used [KB]: 1023
% 1.02/0.94 % (29657)Time elapsed: 0.002 s
% 1.02/0.94 % (29657)Instructions burned: 3 (million)
% 1.02/0.94 % (29657)------------------------------
% 1.02/0.94 % (29657)------------------------------
% 1.02/0.94 % (29658)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/7Mi)
% 1.02/0.94 % (29659)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/3Mi)
% 1.02/0.94 % (29659)Instruction limit reached!
% 1.02/0.94 % (29659)------------------------------
% 1.02/0.94 % (29659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.94 % (29659)Termination reason: Unknown
% 1.02/0.94 % (29659)Termination phase: Saturation
% 1.02/0.94
% 1.02/0.94 % (29659)Memory used [KB]: 5500
% 1.02/0.94 % (29659)Time elapsed: 0.002 s
% 1.02/0.94 % (29659)Instructions burned: 3 (million)
% 1.02/0.94 % (29659)------------------------------
% 1.02/0.94 % (29659)------------------------------
% 1.02/0.94 % (29658)Instruction limit reached!
% 1.02/0.94 % (29658)------------------------------
% 1.02/0.94 % (29658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.94 % (29658)Termination reason: Unknown
% 1.02/0.94 % (29658)Termination phase: Saturation
% 1.02/0.94
% 1.02/0.94 % (29658)Memory used [KB]: 5628
% 1.02/0.94 % (29658)Time elapsed: 0.004 s
% 1.02/0.94 % (29658)Instructions burned: 8 (million)
% 1.02/0.94 % (29658)------------------------------
% 1.02/0.94 % (29658)------------------------------
% 1.02/0.94 % (29660)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/4Mi)
% 1.02/0.95 % (29661)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/18Mi)
% 1.02/0.95 % (29662)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/710Mi)
% 1.02/0.95 % (29660)Instruction limit reached!
% 1.02/0.95 % (29660)------------------------------
% 1.02/0.95 % (29660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.95 % (29660)Termination reason: Unknown
% 1.02/0.95 % (29660)Termination phase: Saturation
% 1.02/0.95
% 1.02/0.95 % (29660)Memory used [KB]: 5500
% 1.02/0.95 % (29660)Time elapsed: 0.003 s
% 1.02/0.95 % (29660)Instructions burned: 6 (million)
% 1.02/0.95 % (29660)------------------------------
% 1.02/0.95 % (29660)------------------------------
% 1.02/0.95 % (29663)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/6Mi)
% 1.02/0.95 % (29661)Instruction limit reached!
% 1.02/0.95 % (29661)------------------------------
% 1.02/0.95 % (29661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.95 % (29661)Termination reason: Unknown
% 1.02/0.95 % (29661)Termination phase: Saturation
% 1.02/0.95
% 1.02/0.95 % (29661)Memory used [KB]: 5628
% 1.02/0.95 % (29661)Time elapsed: 0.007 s
% 1.02/0.95 % (29661)Instructions burned: 18 (million)
% 1.02/0.95 % (29661)------------------------------
% 1.02/0.95 % (29661)------------------------------
% 1.02/0.95 % (29664)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_29381 for (2999ds/902Mi)
% 1.02/0.95 % (29663)Instruction limit reached!
% 1.02/0.95 % (29663)------------------------------
% 1.02/0.95 % (29663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.95 % (29663)Termination reason: Unknown
% 1.02/0.95 % (29663)Termination phase: Saturation
% 1.02/0.95
% 1.02/0.95 % (29663)Memory used [KB]: 5500
% 1.02/0.95 % (29663)Time elapsed: 0.003 s
% 1.02/0.95 % (29663)Instructions burned: 6 (million)
% 1.02/0.95 % (29663)------------------------------
% 1.02/0.95 % (29663)------------------------------
% 1.02/0.96 % (29665)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_29381 for (2999ds/21Mi)
% 1.02/0.96 % (29666)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/5Mi)
% 1.02/0.96 % (29667)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_29381 for (2999ds/6Mi)
% 1.02/0.96 % (29666)Instruction limit reached!
% 1.02/0.96 % (29666)------------------------------
% 1.02/0.96 % (29666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.96 % (29666)Termination reason: Unknown
% 1.02/0.96 % (29666)Termination phase: Saturation
% 1.02/0.96
% 1.02/0.96 % (29666)Memory used [KB]: 5500
% 1.02/0.96 % (29666)Time elapsed: 0.003 s
% 1.02/0.96 % (29666)Instructions burned: 7 (million)
% 1.02/0.96 % (29666)------------------------------
% 1.02/0.96 % (29666)------------------------------
% 1.02/0.96 % (29665)Instruction limit reached!
% 1.02/0.96 % (29665)------------------------------
% 1.02/0.96 % (29665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.96 % (29665)Termination reason: Unknown
% 1.02/0.96 % (29665)Termination phase: Saturation
% 1.02/0.96
% 1.02/0.96 % (29665)Memory used [KB]: 5756
% 1.02/0.96 % (29665)Time elapsed: 0.008 s
% 1.02/0.96 % (29665)Instructions burned: 21 (million)
% 1.02/0.96 % (29665)------------------------------
% 1.02/0.96 % (29665)------------------------------
% 1.02/0.96 % (29642)Instruction limit reached!
% 1.02/0.96 % (29642)------------------------------
% 1.02/0.96 % (29642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.96 % (29642)Termination reason: Unknown
% 1.02/0.96 % (29642)Termination phase: Saturation
% 1.02/0.96
% 1.02/0.96 % (29642)Memory used [KB]: 6908
% 1.02/0.96 % (29642)Time elapsed: 0.056 s
% 1.02/0.96 % (29642)Instructions burned: 184 (million)
% 1.02/0.96 % (29642)------------------------------
% 1.02/0.96 % (29642)------------------------------
% 1.02/0.96 % (29667)Instruction limit reached!
% 1.02/0.96 % (29667)------------------------------
% 1.02/0.96 % (29667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.96 % (29667)Termination reason: Unknown
% 1.02/0.96 % (29667)Termination phase: Saturation
% 1.02/0.96
% 1.02/0.96 % (29667)Memory used [KB]: 5500
% 1.02/0.96 % (29667)Time elapsed: 0.003 s
% 1.02/0.96 % (29667)Instructions burned: 7 (million)
% 1.02/0.96 % (29667)------------------------------
% 1.02/0.96 % (29667)------------------------------
% 1.02/0.97 % (29668)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/377Mi)
% 1.02/0.97 % (29669)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_29381 for (2999ds/779Mi)
% 1.02/0.97 % (29670)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_29381 for (2999ds/19Mi)
% 1.02/0.97 % (29671)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/879Mi)
% 1.02/0.98 % (29670)Instruction limit reached!
% 1.02/0.98 % (29670)------------------------------
% 1.02/0.98 % (29670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.98 % (29670)Termination reason: Unknown
% 1.02/0.98 % (29670)Termination phase: Saturation
% 1.02/0.98
% 1.02/0.98 % (29670)Memory used [KB]: 5500
% 1.02/0.98 % (29670)Time elapsed: 0.007 s
% 1.02/0.98 % (29670)Instructions burned: 21 (million)
% 1.02/0.98 % (29670)------------------------------
% 1.02/0.98 % (29670)------------------------------
% 1.02/0.99 % (29672)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/17Mi)
% 1.02/0.99 % (29672)Instruction limit reached!
% 1.02/0.99 % (29672)------------------------------
% 1.02/0.99 % (29672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.99 % (29672)Termination reason: Unknown
% 1.02/0.99 % (29672)Termination phase: Saturation
% 1.02/0.99
% 1.02/0.99 % (29672)Memory used [KB]: 5756
% 1.02/0.99 % (29672)Time elapsed: 0.029 s
% 1.02/0.99 % (29672)Instructions burned: 18 (million)
% 1.02/0.99 % (29672)------------------------------
% 1.02/0.99 % (29672)------------------------------
% 1.02/1.00 % (29673)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29381 for (2999ds/3Mi)
% 1.02/1.00 % (29673)Instruction limit reached!
% 1.02/1.00 % (29673)------------------------------
% 1.02/1.00 % (29673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/1.00 % (29673)Termination reason: Unknown
% 1.02/1.00 % (29673)Termination phase: Property scanning
% 1.02/1.00
% 1.02/1.00 % (29673)Memory used [KB]: 1023
% 1.02/1.00 % (29673)Time elapsed: 0.002 s
% 1.02/1.00 % (29673)Instructions burned: 4 (million)
% 1.02/1.00 % (29673)------------------------------
% 1.02/1.00 % (29673)------------------------------
% 1.74/1.01 % (29674)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29381 for (2998ds/30Mi)
% 1.74/1.02 % (29674)Instruction limit reached!
% 1.74/1.02 % (29674)------------------------------
% 1.74/1.02 % (29674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.02 % (29674)Termination reason: Unknown
% 1.74/1.02 % (29674)Termination phase: Saturation
% 1.74/1.02
% 1.74/1.02 % (29674)Memory used [KB]: 5756
% 1.74/1.02 % (29674)Time elapsed: 0.011 s
% 1.74/1.02 % (29674)Instructions burned: 30 (million)
% 1.74/1.02 % (29674)------------------------------
% 1.74/1.02 % (29674)------------------------------
% 1.74/1.03 % (29675)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29381 for (2998ds/127Mi)
% 1.74/1.07 % (29675)Instruction limit reached!
% 1.74/1.07 % (29675)------------------------------
% 1.74/1.07 % (29675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.07 % (29675)Termination reason: Unknown
% 1.74/1.07 % (29675)Termination phase: Saturation
% 1.74/1.07
% 1.74/1.07 % (29675)Memory used [KB]: 6012
% 1.74/1.07 % (29675)Time elapsed: 0.040 s
% 1.74/1.07 % (29675)Instructions burned: 128 (million)
% 1.74/1.07 % (29675)------------------------------
% 1.74/1.07 % (29675)------------------------------
% 1.74/1.08 % (29676)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29381 for (2998ds/100Mi)
% 1.74/1.08 % (29668)Instruction limit reached!
% 1.74/1.08 % (29668)------------------------------
% 1.74/1.08 % (29668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.08 % (29668)Termination reason: Unknown
% 1.74/1.08 % (29668)Termination phase: Saturation
% 1.74/1.08
% 1.74/1.08 % (29668)Memory used [KB]: 6524
% 1.74/1.08 % (29668)Time elapsed: 0.112 s
% 1.74/1.08 % (29668)Instructions burned: 378 (million)
% 1.74/1.08 % (29668)------------------------------
% 1.74/1.08 % (29668)------------------------------
% 1.74/1.09 % (29677)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_29381 for (2998ds/3Mi)
% 1.74/1.09 % (29677)Instruction limit reached!
% 1.74/1.09 % (29677)------------------------------
% 1.74/1.09 % (29677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.09 % (29677)Termination reason: Unknown
% 1.74/1.09 % (29677)Termination phase: shuffling
% 1.74/1.09
% 1.74/1.09 % (29677)Memory used [KB]: 1023
% 1.74/1.09 % (29677)Time elapsed: 0.002 s
% 1.74/1.09 % (29677)Instructions burned: 3 (million)
% 1.74/1.09 % (29677)------------------------------
% 1.74/1.09 % (29677)------------------------------
% 1.74/1.10 % (29678)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_29381 for (2998ds/20Mi)
% 1.74/1.11 % (29678)Instruction limit reached!
% 1.74/1.11 % (29678)------------------------------
% 1.74/1.11 % (29678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.11 % (29678)Termination reason: Unknown
% 1.74/1.11 % (29678)Termination phase: Saturation
% 1.74/1.11
% 1.74/1.11 % (29678)Memory used [KB]: 5628
% 1.74/1.11 % (29678)Time elapsed: 0.008 s
% 1.74/1.11 % (29678)Instructions burned: 21 (million)
% 1.74/1.11 % (29678)------------------------------
% 1.74/1.11 % (29678)------------------------------
% 2.42/1.11 % (29676)Instruction limit reached!
% 2.42/1.11 % (29676)------------------------------
% 2.42/1.11 % (29676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.11 % (29676)Termination reason: Unknown
% 2.42/1.11 % (29676)Termination phase: Saturation
% 2.42/1.11
% 2.42/1.11 % (29676)Memory used [KB]: 5756
% 2.42/1.11 % (29676)Time elapsed: 0.032 s
% 2.42/1.11 % (29676)Instructions burned: 102 (million)
% 2.42/1.11 % (29676)------------------------------
% 2.42/1.11 % (29676)------------------------------
% 2.42/1.12 % (29679)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/86Mi)
% 2.42/1.12 % (29680)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/107Mi)
% 2.42/1.15 % (29679)Instruction limit reached!
% 2.42/1.15 % (29679)------------------------------
% 2.42/1.15 % (29679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.15 % (29679)Termination reason: Unknown
% 2.42/1.15 % (29679)Termination phase: Saturation
% 2.42/1.15
% 2.42/1.15 % (29679)Memory used [KB]: 6140
% 2.42/1.15 % (29679)Time elapsed: 0.028 s
% 2.42/1.15 % (29679)Instructions burned: 86 (million)
% 2.42/1.15 % (29679)------------------------------
% 2.42/1.15 % (29679)------------------------------
% 2.42/1.16 % (29681)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/39Mi)
% 2.42/1.16 % (29680)Instruction limit reached!
% 2.42/1.16 % (29680)------------------------------
% 2.42/1.16 % (29680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.16 % (29680)Termination reason: Unknown
% 2.42/1.16 % (29680)Termination phase: Saturation
% 2.42/1.16
% 2.42/1.16 % (29680)Memory used [KB]: 6012
% 2.42/1.16 % (29680)Time elapsed: 0.036 s
% 2.42/1.16 % (29680)Instructions burned: 109 (million)
% 2.42/1.16 % (29680)------------------------------
% 2.42/1.16 % (29680)------------------------------
% 2.42/1.16 % (29662)Instruction limit reached!
% 2.42/1.16 % (29662)------------------------------
% 2.42/1.16 % (29662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.16 % (29662)Termination reason: Unknown
% 2.42/1.16 % (29662)Termination phase: Saturation
% 2.42/1.16
% 2.42/1.16 % (29662)Memory used [KB]: 7291
% 2.42/1.16 % (29662)Time elapsed: 0.219 s
% 2.42/1.16 % (29662)Instructions burned: 711 (million)
% 2.42/1.16 % (29662)------------------------------
% 2.42/1.16 % (29662)------------------------------
% 2.42/1.17 % (29682)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/448Mi)
% 2.42/1.17 % (29681)Instruction limit reached!
% 2.42/1.17 % (29681)------------------------------
% 2.42/1.17 % (29681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.17 % (29681)Termination reason: Unknown
% 2.42/1.17 % (29681)Termination phase: Saturation
% 2.42/1.17
% 2.42/1.17 % (29681)Memory used [KB]: 5884
% 2.42/1.17 % (29681)Time elapsed: 0.013 s
% 2.42/1.17 % (29681)Instructions burned: 42 (million)
% 2.42/1.17 % (29681)------------------------------
% 2.42/1.17 % (29681)------------------------------
% 2.42/1.17 % (29683)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/46Mi)
% 2.42/1.18 % (29684)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/98Mi)
% 2.42/1.18 % (29653)Instruction limit reached!
% 2.42/1.18 % (29653)------------------------------
% 2.42/1.18 % (29653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.18 % (29653)Termination reason: Unknown
% 2.42/1.18 % (29653)Termination phase: Saturation
% 2.42/1.18
% 2.42/1.18 % (29653)Memory used [KB]: 6396
% 2.42/1.18 % (29653)Time elapsed: 0.258 s
% 2.42/1.18 % (29653)Instructions burned: 1041 (million)
% 2.42/1.18 % (29653)------------------------------
% 2.42/1.18 % (29653)------------------------------
% 2.42/1.19 % (29683)Instruction limit reached!
% 2.42/1.19 % (29683)------------------------------
% 2.42/1.19 % (29683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.19 % (29683)Termination reason: Unknown
% 2.42/1.19 % (29683)Termination phase: Saturation
% 2.42/1.19
% 2.42/1.19 % (29683)Memory used [KB]: 5756
% 2.42/1.19 % (29683)Time elapsed: 0.016 s
% 2.42/1.19 % (29683)Instructions burned: 46 (million)
% 2.42/1.19 % (29683)------------------------------
% 2.42/1.19 % (29683)------------------------------
% 2.42/1.19 % (29685)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/507Mi)
% 2.98/1.20 % (29686)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/149Mi)
% 2.98/1.20 % (29669)Instruction limit reached!
% 2.98/1.20 % (29669)------------------------------
% 2.98/1.20 % (29669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.20 % (29669)Termination reason: Unknown
% 2.98/1.20 % (29669)Termination phase: Saturation
% 2.98/1.20
% 2.98/1.20 % (29669)Memory used [KB]: 6780
% 2.98/1.20 % (29669)Time elapsed: 0.231 s
% 2.98/1.20 % (29669)Instructions burned: 781 (million)
% 2.98/1.20 % (29669)------------------------------
% 2.98/1.20 % (29669)------------------------------
% 2.98/1.21 % (29684)Instruction limit reached!
% 2.98/1.21 % (29684)------------------------------
% 2.98/1.21 % (29684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.21 % (29684)Termination reason: Unknown
% 2.98/1.21 % (29684)Termination phase: Saturation
% 2.98/1.21
% 2.98/1.21 % (29684)Memory used [KB]: 1279
% 2.98/1.21 % (29684)Time elapsed: 0.031 s
% 2.98/1.21 % (29684)Instructions burned: 98 (million)
% 2.98/1.21 % (29684)------------------------------
% 2.98/1.21 % (29684)------------------------------
% 2.98/1.21 % (29687)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_29381 for (2997ds/39Mi)
% 2.98/1.22 % (29688)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_29381 for (2996ds/6Mi)
% 2.98/1.22 % (29688)Instruction limit reached!
% 2.98/1.22 % (29688)------------------------------
% 2.98/1.22 % (29688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.22 % (29688)Termination reason: Unknown
% 2.98/1.22 % (29688)Termination phase: Saturation
% 2.98/1.22
% 2.98/1.22 % (29688)Memory used [KB]: 9978
% 2.98/1.22 % (29688)Time elapsed: 0.004 s
% 2.98/1.22 % (29688)Instructions burned: 8 (million)
% 2.98/1.22 % (29688)------------------------------
% 2.98/1.22 % (29688)------------------------------
% 2.98/1.22 % (29664)Instruction limit reached!
% 2.98/1.22 % (29664)------------------------------
% 2.98/1.22 % (29664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.22 % (29664)Termination reason: Unknown
% 2.98/1.22 % (29664)Termination phase: Saturation
% 2.98/1.22
% 2.98/1.22 % (29664)Memory used [KB]: 8315
% 2.98/1.22 % (29664)Time elapsed: 0.271 s
% 2.98/1.22 % (29664)Instructions burned: 903 (million)
% 2.98/1.22 % (29664)------------------------------
% 2.98/1.22 % (29664)------------------------------
% 2.98/1.22 % (29687)Instruction limit reached!
% 2.98/1.22 % (29687)------------------------------
% 2.98/1.22 % (29687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.22 % (29687)Termination reason: Unknown
% 2.98/1.22 % (29687)Termination phase: Saturation
% 2.98/1.22
% 2.98/1.22 % (29687)Memory used [KB]: 5756
% 2.98/1.22 % (29687)Time elapsed: 0.014 s
% 2.98/1.22 % (29687)Instructions burned: 40 (million)
% 2.98/1.22 % (29687)------------------------------
% 2.98/1.22 % (29687)------------------------------
% 2.98/1.23 % (29689)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_29381 for (2996ds/1087Mi)
% 2.98/1.23 % (29690)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_29381 for (2996ds/47Mi)
% 2.98/1.23 % (29691)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_29381 for (2996ds/44Mi)
% 2.98/1.24 % (29671)Instruction limit reached!
% 2.98/1.24 % (29671)------------------------------
% 2.98/1.24 % (29671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.24 % (29671)Termination reason: Unknown
% 2.98/1.24 % (29671)Termination phase: Saturation
% 2.98/1.24
% 2.98/1.24 % (29671)Memory used [KB]: 7547
% 2.98/1.24 % (29671)Time elapsed: 0.289 s
% 2.98/1.24 % (29671)Instructions burned: 881 (million)
% 2.98/1.24 % (29671)------------------------------
% 2.98/1.24 % (29671)------------------------------
% 2.98/1.25 % (29691)Instruction limit reached!
% 2.98/1.25 % (29691)------------------------------
% 2.98/1.25 % (29691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.25 % (29691)Termination reason: Unknown
% 2.98/1.25 % (29691)Termination phase: Saturation
% 2.98/1.25
% 2.98/1.25 % (29691)Memory used [KB]: 1151
% 2.98/1.25 % (29691)Time elapsed: 0.014 s
% 2.98/1.25 % (29691)Instructions burned: 44 (million)
% 2.98/1.25 % (29691)------------------------------
% 2.98/1.25 % (29691)------------------------------
% 2.98/1.25 % (29686)Instruction limit reached!
% 2.98/1.25 % (29686)------------------------------
% 2.98/1.25 % (29686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.25 % (29686)Termination reason: Unknown
% 2.98/1.25 % (29686)Termination phase: Saturation
% 2.98/1.25
% 2.98/1.25 % (29686)Memory used [KB]: 6012
% 2.98/1.25 % (29686)Time elapsed: 0.050 s
% 2.98/1.25 % (29686)Instructions burned: 151 (million)
% 2.98/1.25 % (29686)------------------------------
% 2.98/1.25 % (29686)------------------------------
% 2.98/1.25 % (29690)Instruction limit reached!
% 2.98/1.25 % (29690)------------------------------
% 2.98/1.25 % (29690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.25 % (29690)Termination reason: Unknown
% 2.98/1.25 % (29690)Termination phase: Saturation
% 2.98/1.25
% 2.98/1.25 % (29690)Memory used [KB]: 5756
% 2.98/1.25 % (29690)Time elapsed: 0.017 s
% 2.98/1.25 % (29690)Instructions burned: 49 (million)
% 2.98/1.25 % (29690)------------------------------
% 2.98/1.25 % (29690)------------------------------
% 2.98/1.25 % (29692)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_29381 for (2996ds/432Mi)
% 2.98/1.26 % (29693)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_29381 for (2996ds/62Mi)
% 2.98/1.26 % (29694)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_29381 for (2996ds/31Mi)
% 2.98/1.26 % (29695)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_29381 for (2996ds/96Mi)
% 2.98/1.27 % (29689)First to succeed.
% 2.98/1.27 % (29694)Instruction limit reached!
% 2.98/1.27 % (29694)------------------------------
% 2.98/1.27 % (29694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.27 % (29694)Termination reason: Unknown
% 2.98/1.27 % (29694)Termination phase: Saturation
% 2.98/1.27
% 2.98/1.27 % (29694)Memory used [KB]: 5756
% 2.98/1.27 % (29694)Time elapsed: 0.012 s
% 2.98/1.27 % (29694)Instructions burned: 31 (million)
% 2.98/1.27 % (29694)------------------------------
% 2.98/1.27 % (29694)------------------------------
% 2.98/1.27 % (29689)Refutation found. Thanks to Tanya!
% 2.98/1.27 % SZS status Theorem for DTF2THF_29381
% 2.98/1.27 % SZS output start Proof for DTF2THF_29381
% 2.98/1.27 thf(type_def_5, type, a: $tType).
% 2.98/1.27 thf(func_def_0, type, a: $tType).
% 2.98/1.27 thf(func_def_1, type, cE: a > $o).
% 2.98/1.27 thf(func_def_2, type, cA: (a > $o) > $o).
% 2.98/1.27 thf(func_def_10, type, sP0: (a > $o) > $o).
% 2.98/1.27 thf(func_def_11, type, sP1: (a > $o) > $o).
% 2.98/1.27 thf(func_def_12, type, sP2: (a > $o) > $o).
% 2.98/1.27 thf(func_def_13, type, sP3: (a > $o) > $o).
% 2.98/1.27 thf(func_def_16, type, sP6: ((a > $o) > $o) > (a > $o) > $o).
% 2.98/1.27 thf(func_def_17, type, sK7: ((a > $o) > $o) > (a > $o) > a).
% 2.98/1.27 thf(func_def_18, type, sK8: a > $o).
% 2.98/1.27 thf(func_def_19, type, sK9: a > $o).
% 2.98/1.27 thf(func_def_20, type, sK10: (a > $o) > (a > $o) > a).
% 2.98/1.27 thf(func_def_21, type, sK11: (a > $o) > a > $o).
% 2.98/1.27 thf(func_def_22, type, sK12: (a > $o) > (a > $o) > $o).
% 2.98/1.27 thf(func_def_23, type, sK13: (a > $o) > a).
% 2.98/1.27 thf(func_def_24, type, sK14: ((a > $o) > $o) > a > $o).
% 2.98/1.27 thf(func_def_27, type, ph16: !>[X0: $tType]:(X0)).
% 2.98/1.27 thf(f803,plain,(
% 2.98/1.27 $false),
% 2.98/1.27 inference(avatar_sat_refutation,[status(thm)],[f74,f81,f93,f96,f98,f490,f570,f759,f767,f802])).
% 2.98/1.27 thf(f802,plain,(
% 2.98/1.27 ~spl15_29 | ~spl15_46),
% 2.98/1.27 inference(avatar_contradiction_clause,[status(thm)],[f801])).
% 2.98/1.27 thf(f801,plain,(
% 2.98/1.27 $false | (~spl15_29 | ~spl15_46)),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f800,f489])).
% 2.98/1.27 thf(f489,plain,(
% 2.98/1.27 ((sP1 @ cE) = $true) | ~spl15_29),
% 2.98/1.27 inference(avatar_component_clause,[status(thm)],[f488])).
% 2.98/1.27 thf(f488,definition,(
% 2.98/1.27 spl15_29 <=> ((sP1 @ cE) = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_29])],[avatar_definition])).
% 2.98/1.27 thf(f800,plain,(
% 2.98/1.27 ((sP1 @ cE) != $true) | ~spl15_46),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f799])).
% 2.98/1.27 thf(f799,plain,(
% 2.98/1.27 ($true != $true) | ((sP1 @ cE) != $true) | ~spl15_46),
% 2.98/1.27 inference(superposition,[status(thm)],[f62,f758])).
% 2.98/1.27 thf(f758,plain,(
% 2.98/1.27 ((sK12 @ cE @ cE) = $true) | ~spl15_46),
% 2.98/1.27 inference(avatar_component_clause,[status(thm)],[f757])).
% 2.98/1.27 thf(f757,definition,(
% 2.98/1.27 spl15_46 <=> ((sK12 @ cE @ cE) = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_46])],[avatar_definition])).
% 2.98/1.27 thf(f62,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (($true != (sK12 @ X0 @ X0)) | ((sP1 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f40])).
% 2.98/1.27 thf(f40,plain,(
% 2.98/1.27 ! [X0 : a > $o] : ((($true != (sK12 @ X0 @ X0)) & ((sK12 @ X0 @ (^[Y0 : a]: ($false))) = $true) & ! [X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) != $true) | ((sK12 @ X0 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))) = $true)) | ((sK12 @ X0 @ X2) != $true))) | ((sP1 @ X0) != $true))),
% 2.98/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f38,f39])).
% 2.98/1.27 thf(f39,plain,(
% 2.98/1.27 ! [X0 : a > $o] : (? [X1 : (a > $o) > $o] : (((X1 @ X0) != $true) & ($true = (X1 @ (^[Y0 : a]: ($false)))) & ! [X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) != $true) | ((X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))) = $true)) | ((X1 @ X2) != $true))) => (($true != (sK12 @ X0 @ X0)) & ((sK12 @ X0 @ (^[Y0 : a]: ($false))) = $true) & ! [X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) != $true) | ((sK12 @ X0 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))) = $true)) | ((sK12 @ X0 @ X2) != $true))))),
% 2.98/1.27 introduced(definition,[],[choice_axiom])).
% 2.98/1.27 thf(f38,plain,(
% 2.98/1.27 ! [X0 : a > $o] : (? [X1 : (a > $o) > $o] : (((X1 @ X0) != $true) & ($true = (X1 @ (^[Y0 : a]: ($false)))) & ! [X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) != $true) | ((X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))) = $true)) | ((X1 @ X2) != $true))) | ((sP1 @ X0) != $true))),
% 2.98/1.27 inference(rectify,[status(thm)],[f37])).
% 2.98/1.27 thf(f37,plain,(
% 2.98/1.27 ! [X5 : a > $o] : (? [X6 : (a > $o) > $o] : (((X6 @ X5) != $true) & ((X6 @ (^[Y0 : a]: ($false))) = $true) & ! [X7 : a > $o] : (! [X8 : a] : (((X5 @ X8) != $true) | ((X6 @ (^[Y0 : a]: ((X8 = Y0) | (X7 @ Y0)))) = $true)) | ((X6 @ X7) != $true))) | ((sP1 @ X5) != $true))),
% 2.98/1.27 inference(nnf_transformation,[status(thm)],[f10])).
% 2.98/1.27 thf(f10,plain,(
% 2.98/1.27 ! [X5 : a > $o] : (? [X6 : (a > $o) > $o] : (((X6 @ X5) != $true) & ((X6 @ (^[Y0 : a]: ($false))) = $true) & ! [X7 : a > $o] : (! [X8 : a] : (((X5 @ X8) != $true) | ((X6 @ (^[Y0 : a]: ((X8 = Y0) | (X7 @ Y0)))) = $true)) | ((X6 @ X7) != $true))) | ~((sP1 @ X5) = $true))),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.98/1.27 thf(f767,plain,(
% 2.98/1.27 ~spl15_29 | spl15_45),
% 2.98/1.27 inference(avatar_contradiction_clause,[status(thm)],[f766])).
% 2.98/1.27 thf(f766,plain,(
% 2.98/1.27 $false | (~spl15_29 | spl15_45)),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f765,f489])).
% 2.98/1.27 thf(f765,plain,(
% 2.98/1.27 ((sP1 @ cE) != $true) | spl15_45),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f764])).
% 2.98/1.27 thf(f764,plain,(
% 2.98/1.27 ($true != $true) | ((sP1 @ cE) != $true) | spl15_45),
% 2.98/1.27 inference(superposition,[status(thm)],[f755,f61])).
% 2.98/1.27 thf(f61,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((sK12 @ X0 @ (^[Y0 : a]: ($false))) = $true) | ((sP1 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f40])).
% 2.98/1.27 thf(f755,plain,(
% 2.98/1.27 ((sK12 @ cE @ (^[Y0 : a]: ($false))) != $true) | spl15_45),
% 2.98/1.27 inference(avatar_component_clause,[status(thm)],[f754])).
% 2.98/1.27 thf(f754,definition,(
% 2.98/1.27 spl15_45 <=> ((sK12 @ cE @ (^[Y0 : a]: ($false))) = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_45])],[avatar_definition])).
% 2.98/1.27 thf(f759,plain,(
% 2.98/1.27 ~spl15_45 | spl15_46 | ~spl15_29),
% 2.98/1.27 inference(avatar_split_clause,[status(thm)],[f752,f488,f757,f754])).
% 2.98/1.27 thf(f752,plain,(
% 2.98/1.27 ((sK12 @ cE @ cE) = $true) | ((sK12 @ cE @ (^[Y0 : a]: ($false))) != $true) | ~spl15_29),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f739,f67])).
% 2.98/1.27 thf(f67,plain,(
% 2.98/1.27 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK14 @ X0)) = $true) | ((X0 @ (^[Y0 : a]: ($false))) != $true) | ((X0 @ cE) = $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f46])).
% 2.98/1.27 thf(f46,plain,(
% 2.98/1.27 ! [X0 : (a > $o) > $o] : ((((X0 @ (sK14 @ X0)) = $true) & ((sP6 @ X0 @ (sK14 @ X0)) = $true)) | ((X0 @ (^[Y0 : a]: ($false))) != $true) | ((X0 @ cE) = $true)) & ((sP5 = $true) | (sP4 = $true))),
% 2.98/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f16,f45])).
% 2.98/1.27 thf(f45,plain,(
% 2.98/1.27 ! [X0 : (a > $o) > $o] : (? [X1 : a > $o] : (((X0 @ X1) = $true) & ((sP6 @ X0 @ X1) = $true)) => (((X0 @ (sK14 @ X0)) = $true) & ((sP6 @ X0 @ (sK14 @ X0)) = $true)))),
% 2.98/1.27 introduced(definition,[],[choice_axiom])).
% 2.98/1.27 thf(f16,plain,(
% 2.98/1.27 ! [X0 : (a > $o) > $o] : (? [X1 : a > $o] : (((X0 @ X1) = $true) & ((sP6 @ X0 @ X1) = $true)) | ((X0 @ (^[Y0 : a]: ($false))) != $true) | ((X0 @ cE) = $true)) & ((sP5 = $true) | (sP4 = $true))),
% 2.98/1.27 inference(definition_folding,[status(thm)],[f8,f15,f14,f13,f12,f11,f10,f9])).
% 2.98/1.27 thf(f9,plain,(
% 2.98/1.27 ! [X10 : a > $o] : (? [X12 : a] : (((cE @ X12) = $true) & ((X10 @ X12) != $true)) | ($true != (cA @ X10)) | ~((sP0 @ X10) = $true))),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.98/1.27 thf(f11,plain,(
% 2.98/1.27 ! [X5 : a > $o] : (? [X10 : a > $o] : (($true = (cA @ X10)) & ! [X11 : a] : (((X5 @ X11) != $true) | ((X10 @ X11) = $true)) & ((sP0 @ X10) = $true)) | ~((sP2 @ X5) = $true))),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.98/1.27 thf(f12,plain,(
% 2.98/1.27 ! [X3 : a > $o] : (! [X5 : a > $o] : (? [X9 : a] : (((X3 @ X9) != $true) & ((X5 @ X9) = $true)) | ((sP2 @ X5) = $true) | ((sP1 @ X5) = $true)) | ~((sP3 @ X3) = $true))),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.98/1.27 thf(f13,plain,(
% 2.98/1.27 ? [X13 : a > $o] : (((cA @ X13) != $true) & ((cA @ X13) = $true) & ! [X14 : a] : (((X13 @ X14) = $true) | ((cE @ X14) != $true))) | ~(sP4 = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.98/1.27 thf(f14,plain,(
% 2.98/1.27 ? [X3 : a > $o] : (! [X4 : a] : (((X3 @ X4) = $true) | ((cE @ X4) != $true)) & ((sP3 @ X3) = $true) & ((cA @ X3) = $true)) | ~(sP5 = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.98/1.27 thf(f15,plain,(
% 2.98/1.27 ! [X1 : a > $o,X0 : (a > $o) > $o] : (? [X2 : a] : (((X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))) != $true) & ((cE @ X2) = $true)) | ~((sP6 @ X0 @ X1) = $true))),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.98/1.27 thf(f8,plain,(
% 2.98/1.27 ! [X0 : (a > $o) > $o] : (? [X1 : a > $o] : (((X0 @ X1) = $true) & ? [X2 : a] : (((X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))) != $true) & ((cE @ X2) = $true))) | ((X0 @ (^[Y0 : a]: ($false))) != $true) | ((X0 @ cE) = $true)) & (? [X3 : a > $o] : (! [X4 : a] : (((X3 @ X4) = $true) | ((cE @ X4) != $true)) & ! [X5 : a > $o] : (? [X9 : a] : (((X3 @ X9) != $true) & ((X5 @ X9) = $true)) | ? [X10 : a > $o] : (($true = (cA @ X10)) & ! [X11 : a] : (((X5 @ X11) != $true) | ((X10 @ X11) = $true)) & (? [X12 : a] : (((cE @ X12) = $true) & ((X10 @ X12) != $true)) | ($true != (cA @ X10)))) | ? [X6 : (a > $o) > $o] : (((X6 @ X5) != $true) & ((X6 @ (^[Y0 : a]: ($false))) = $true) & ! [X7 : a > $o] : (! [X8 : a] : (((X5 @ X8) != $true) | ((X6 @ (^[Y0 : a]: ((X8 = Y0) | (X7 @ Y0)))) = $true)) | ((X6 @ X7) != $true)))) & ((cA @ X3) = $true)) | ? [X13 : a > $o] : (((cA @ X13) != $true) & ((cA @ X13) = $true) & ! [X14 : a] : (((X13 @ X14) = $true) | ((cE @ X14) != $true))))),
% 2.98/1.27 inference(flattening,[status(thm)],[f7])).
% 2.98/1.27 thf(f7,plain,(
% 2.98/1.27 (? [X3 : a > $o] : (! [X5 : a > $o] : (? [X9 : a] : (((X3 @ X9) != $true) & ((X5 @ X9) = $true)) | ? [X10 : a > $o] : ((? [X12 : a] : (((cE @ X12) = $true) & ((X10 @ X12) != $true)) | ($true != (cA @ X10))) & (! [X11 : a] : (((X5 @ X11) != $true) | ((X10 @ X11) = $true)) & ($true = (cA @ X10)))) | ? [X6 : (a > $o) > $o] : (((X6 @ X5) != $true) & (! [X7 : a > $o] : (! [X8 : a] : (((X5 @ X8) != $true) | ((X6 @ (^[Y0 : a]: ((X8 = Y0) | (X7 @ Y0)))) = $true)) | ((X6 @ X7) != $true)) & ((X6 @ (^[Y0 : a]: ($false))) = $true)))) & (((cA @ X3) = $true) & ! [X4 : a] : (((X3 @ X4) = $true) | ((cE @ X4) != $true)))) | ? [X13 : a > $o] : (((cA @ X13) != $true) & (! [X14 : a] : (((X13 @ X14) = $true) | ((cE @ X14) != $true)) & ((cA @ X13) = $true)))) & ! [X0 : (a > $o) > $o] : (((X0 @ cE) = $true) | (? [X1 : a > $o] : (((X0 @ X1) = $true) & ? [X2 : a] : (((X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))) != $true) & ((cE @ X2) = $true))) | ((X0 @ (^[Y0 : a]: ($false))) != $true)))),
% 2.98/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 2.98/1.27 thf(f6,plain,(
% 2.98/1.27 ~(! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : (((X0 @ X1) = $true) => ! [X2 : a] : (((cE @ X2) = $true) => ((X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))) = $true))) & ((X0 @ (^[Y0 : a]: ($false))) = $true)) => ((X0 @ cE) = $true)) => (! [X3 : a > $o] : ((((cA @ X3) = $true) & ! [X4 : a] : (((cE @ X4) = $true) => ((X3 @ X4) = $true))) => ? [X5 : a > $o] : (! [X9 : a] : (((X5 @ X9) = $true) => ((X3 @ X9) = $true)) & ! [X10 : a > $o] : ((! [X11 : a] : (((X5 @ X11) = $true) => ((X10 @ X11) = $true)) & ($true = (cA @ X10))) => (! [X12 : a] : (((cE @ X12) = $true) => ((X10 @ X12) = $true)) & ($true = (cA @ X10)))) & ! [X6 : (a > $o) > $o] : ((! [X7 : a > $o] : (((X6 @ X7) = $true) => ! [X8 : a] : (((X5 @ X8) = $true) => ((X6 @ (^[Y0 : a]: ((X8 = Y0) | (X7 @ Y0)))) = $true))) & ((X6 @ (^[Y0 : a]: ($false))) = $true)) => ((X6 @ X5) = $true)))) & ! [X13 : a > $o] : ((! [X14 : a] : (((cE @ X14) = $true) => ((X13 @ X14) = $true)) & ((cA @ X13) = $true)) => ((cA @ X13) = $true))))),
% 2.98/1.27 inference(rectify,[status(thm)],[f5])).
% 2.98/1.27 thf(f5,plain,(
% 2.98/1.27 ~(! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : (((X0 @ X1) = $true) => ! [X2 : a] : (((cE @ X2) = $true) => ((X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))) = $true))) & ((X0 @ (^[Y0 : a]: ($false))) = $true)) => ((X0 @ cE) = $true)) => (! [X5 : a > $o] : ((((cA @ X5) = $true) & ! [X6 : a] : (((cE @ X6) = $true) => ((X5 @ X6) = $true))) => ? [X7 : a > $o] : (! [X8 : (a > $o) > $o] : ((((X8 @ (^[Y0 : a]: ($false))) = $true) & ! [X10 : a > $o] : (((X8 @ X10) = $true) => ! [X11 : a] : (((X7 @ X11) = $true) => ((X8 @ (^[Y0 : a]: ((X11 = Y0) | (X10 @ Y0)))) = $true)))) => ((X8 @ X7) = $true)) & ! [X13 : a] : (((X7 @ X13) = $true) => ((X5 @ X13) = $true)) & ! [X14 : a > $o] : ((((cA @ X14) = $true) & ! [X15 : a] : (((X7 @ X15) = $true) => ($true = (X14 @ X15)))) => (((cA @ X14) = $true) & ! [X16 : a] : (((cE @ X16) = $true) => ((X14 @ X16) = $true)))))) & ! [X17 : a > $o] : ((((cA @ X17) = $true) & ! [X18 : a] : (((cE @ X18) = $true) => ((X17 @ X18) = $true))) => ((cA @ X17) = $true))))),
% 2.98/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 2.98/1.27 thf(f4,plain,(
% 2.98/1.27 ~(! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : ((X0 @ X1) => ! [X2 : a] : ((cE @ X2) => (X0 @ (^[X3 : a] : ((X1 @ X3) | (X2 = X3)))))) & (X0 @ (^[X4 : a] : ($false)))) => (X0 @ cE)) => (! [X5 : a > $o] : (((cA @ X5) & ! [X6 : a] : ((cE @ X6) => (X5 @ X6))) => ? [X7 : a > $o] : (! [X8 : (a > $o) > $o] : (((X8 @ (^[X9 : a] : ($false))) & ! [X10 : a > $o] : ((X8 @ X10) => ! [X11 : a] : ((X7 @ X11) => (X8 @ (^[X12 : a] : ((X10 @ X12) | (X11 = X12))))))) => (X8 @ X7)) & ! [X13 : a] : ((X7 @ X13) => (X5 @ X13)) & ! [X14 : a > $o] : (((cA @ X14) & ! [X15 : a] : ((X7 @ X15) => (X14 @ X15))) => ((cA @ X14) & ! [X16 : a] : ((cE @ X16) => (X14 @ X16)))))) & ! [X17 : a > $o] : (((cA @ X17) & ! [X18 : a] : ((cE @ X18) => (X17 @ X18))) => (cA @ X17))))),
% 2.98/1.27 inference(rectify,[status(thm)],[f2])).
% 2.98/1.27 thf(f2,negated_conjecture,(
% 2.98/1.27 ~(! [X0 : (a > $o) > $o] : ((! [X2 : a > $o] : ((X0 @ X2) => ! [X3 : a] : ((cE @ X3) => (X0 @ (^[X4 : a] : ((X2 @ X4) | (X3 = X4)))))) & (X0 @ (^[X1 : a] : ($false)))) => (X0 @ cE)) => (! [X2 : a > $o] : (((cA @ X2) & ! [X5 : a] : ((cE @ X5) => (X2 @ X5))) => ? [X6 : a > $o] : (! [X0 : (a > $o) > $o] : (((X0 @ (^[X1 : a] : ($false))) & ! [X5 : a > $o] : ((X0 @ X5) => ! [X3 : a] : ((X6 @ X3) => (X0 @ (^[X4 : a] : ((X5 @ X4) | (X3 = X4))))))) => (X0 @ X6)) & ! [X5 : a] : ((X6 @ X5) => (X2 @ X5)) & ! [X1 : a > $o] : (((cA @ X1) & ! [X5 : a] : ((X6 @ X5) => (X1 @ X5))) => ((cA @ X1) & ! [X5 : a] : ((cE @ X5) => (X1 @ X5)))))) & ! [X2 : a > $o] : (((cA @ X2) & ! [X5 : a] : ((cE @ X5) => (X2 @ X5))) => (cA @ X2))))),
% 2.98/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 2.98/1.27 thf(f1,conjecture,(
% 2.98/1.27 ! [X0 : (a > $o) > $o] : ((! [X2 : a > $o] : ((X0 @ X2) => ! [X3 : a] : ((cE @ X3) => (X0 @ (^[X4 : a] : ((X2 @ X4) | (X3 = X4)))))) & (X0 @ (^[X1 : a] : ($false)))) => (X0 @ cE)) => (! [X2 : a > $o] : (((cA @ X2) & ! [X5 : a] : ((cE @ X5) => (X2 @ X5))) => ? [X6 : a > $o] : (! [X0 : (a > $o) > $o] : (((X0 @ (^[X1 : a] : ($false))) & ! [X5 : a > $o] : ((X0 @ X5) => ! [X3 : a] : ((X6 @ X3) => (X0 @ (^[X4 : a] : ((X5 @ X4) | (X3 = X4))))))) => (X0 @ X6)) & ! [X5 : a] : ((X6 @ X5) => (X2 @ X5)) & ! [X1 : a > $o] : (((cA @ X1) & ! [X5 : a] : ((X6 @ X5) => (X1 @ X5))) => ((cA @ X1) & ! [X5 : a] : ((cE @ X5) => (X1 @ X5)))))) & ! [X2 : a > $o] : (((cA @ X2) & ! [X5 : a] : ((cE @ X5) => (X2 @ X5))) => (cA @ X2)))),
% 2.98/1.27 file('/export/starexec/sandbox/tmp/tmp.aZAifMX8r9/DTF2THF_29381.p',cDOMLEMMA4_pme)).
% 2.98/1.27 thf(f739,plain,(
% 2.98/1.27 ((sK12 @ cE @ (^[Y0 : a]: ($false))) != $true) | ((sK12 @ cE @ cE) = $true) | ((sK12 @ cE @ (sK14 @ (sK12 @ cE))) != $true) | ~spl15_29),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f733])).
% 2.98/1.27 thf(f733,plain,(
% 2.98/1.27 ((sK12 @ cE @ cE) = $true) | ((sK12 @ cE @ (sK14 @ (sK12 @ cE))) != $true) | ($true != $true) | ((sK12 @ cE @ (^[Y0 : a]: ($false))) != $true) | ~spl15_29),
% 2.98/1.27 inference(superposition,[status(thm)],[f648,f66])).
% 2.98/1.27 thf(f66,plain,(
% 2.98/1.27 ( ! [X0 : (a > $o) > $o] : (((sP6 @ X0 @ (sK14 @ X0)) = $true) | ((X0 @ cE) = $true) | ((X0 @ (^[Y0 : a]: ($false))) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f46])).
% 2.98/1.27 thf(f648,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((sP6 @ (sK12 @ cE) @ X0) != $true) | ($true != (sK12 @ cE @ X0))) ) | ~spl15_29),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f647,f489])).
% 2.98/1.27 thf(f647,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (($true != (sK12 @ cE @ X0)) | ((sP6 @ (sK12 @ cE) @ X0) != $true) | ((sP1 @ cE) != $true)) )),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f646])).
% 2.98/1.27 thf(f646,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (($true != (sK12 @ cE @ X0)) | ($true != $true) | ((sP1 @ cE) != $true) | ((sP6 @ (sK12 @ cE) @ X0) != $true)) )),
% 2.98/1.27 inference(duplicate_literal_removal,[status(thm)],[f638])).
% 2.98/1.27 thf(f638,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (($true != (sK12 @ cE @ X0)) | ((sP6 @ (sK12 @ cE) @ X0) != $true) | ((sP1 @ cE) != $true) | ($true != $true) | ((sP6 @ (sK12 @ cE) @ X0) != $true)) )),
% 2.98/1.27 inference(superposition,[status(thm)],[f424,f47])).
% 2.98/1.27 thf(f47,plain,(
% 2.98/1.27 ( ! [X0 : a > $o,X1 : (a > $o) > $o] : (((cE @ (sK7 @ X1 @ X0)) = $true) | ((sP6 @ X1 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f20])).
% 2.98/1.27 thf(f20,plain,(
% 2.98/1.27 ! [X0 : a > $o,X1 : (a > $o) > $o] : ((((X1 @ (^[Y0 : a]: (((sK7 @ X1 @ X0) = Y0) | (X0 @ Y0)))) != $true) & ((cE @ (sK7 @ X1 @ X0)) = $true)) | ((sP6 @ X1 @ X0) != $true))),
% 2.98/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f18,f19])).
% 2.98/1.27 thf(f19,plain,(
% 2.98/1.27 ! [X0 : a > $o,X1 : (a > $o) > $o] : (? [X2 : a] : (($true != (X1 @ (^[Y0 : a]: ((X2 = Y0) | (X0 @ Y0))))) & ((cE @ X2) = $true)) => (((X1 @ (^[Y0 : a]: (((sK7 @ X1 @ X0) = Y0) | (X0 @ Y0)))) != $true) & ((cE @ (sK7 @ X1 @ X0)) = $true)))),
% 2.98/1.27 introduced(definition,[],[choice_axiom])).
% 2.98/1.27 thf(f18,plain,(
% 2.98/1.27 ! [X0 : a > $o,X1 : (a > $o) > $o] : (? [X2 : a] : (($true != (X1 @ (^[Y0 : a]: ((X2 = Y0) | (X0 @ Y0))))) & ((cE @ X2) = $true)) | ((sP6 @ X1 @ X0) != $true))),
% 2.98/1.27 inference(rectify,[status(thm)],[f17])).
% 2.98/1.27 thf(f17,plain,(
% 2.98/1.27 ! [X1 : a > $o,X0 : (a > $o) > $o] : (? [X2 : a] : (((X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))) != $true) & ((cE @ X2) = $true)) | ((sP6 @ X0 @ X1) != $true))),
% 2.98/1.27 inference(nnf_transformation,[status(thm)],[f15])).
% 2.98/1.27 thf(f424,plain,(
% 2.98/1.27 ( ! [X0 : a > $o,X1 : a > $o] : (((X0 @ (sK7 @ (sK12 @ X0) @ X1)) != $true) | ((sP6 @ (sK12 @ X0) @ X1) != $true) | ((sP1 @ X0) != $true) | ((sK12 @ X0 @ X1) != $true)) )),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f423])).
% 2.98/1.27 thf(f423,plain,(
% 2.98/1.27 ( ! [X0 : a > $o,X1 : a > $o] : (((X0 @ (sK7 @ (sK12 @ X0) @ X1)) != $true) | ($true != $true) | ((sP1 @ X0) != $true) | ((sK12 @ X0 @ X1) != $true) | ((sP6 @ (sK12 @ X0) @ X1) != $true)) )),
% 2.98/1.27 inference(superposition,[status(thm)],[f48,f60])).
% 2.98/1.27 thf(f60,plain,(
% 2.98/1.27 ( ! [X2 : a > $o,X3 : a,X0 : a > $o] : (((sK12 @ X0 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))) = $true) | ((X0 @ X3) != $true) | ((sK12 @ X0 @ X2) != $true) | ((sP1 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f40])).
% 2.98/1.27 thf(f48,plain,(
% 2.98/1.27 ( ! [X0 : a > $o,X1 : (a > $o) > $o] : (((X1 @ (^[Y0 : a]: (((sK7 @ X1 @ X0) = Y0) | (X0 @ Y0)))) != $true) | ((sP6 @ X1 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f20])).
% 2.98/1.27 thf(f570,plain,(
% 2.98/1.27 ~spl15_28),
% 2.98/1.27 inference(avatar_contradiction_clause,[status(thm)],[f569])).
% 2.98/1.27 thf(f569,plain,(
% 2.98/1.27 $false | ~spl15_28),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f486,f476])).
% 2.98/1.27 thf(f476,plain,(
% 2.98/1.27 ((sP2 @ cE) != $true)),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f475,f59])).
% 2.98/1.27 thf(f59,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((cA @ (sK11 @ X0)) = $true) | ((sP2 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f36])).
% 2.98/1.27 thf(f36,plain,(
% 2.98/1.27 ! [X0 : a > $o] : ((((cA @ (sK11 @ X0)) = $true) & ! [X2 : a] : (((X0 @ X2) != $true) | ((sK11 @ X0 @ X2) = $true)) & ($true = (sP0 @ (sK11 @ X0)))) | ((sP2 @ X0) != $true))),
% 2.98/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f34,f35])).
% 2.98/1.27 thf(f35,plain,(
% 2.98/1.27 ! [X0 : a > $o] : (? [X1 : a > $o] : (((cA @ X1) = $true) & ! [X2 : a] : (((X0 @ X2) != $true) | ((X1 @ X2) = $true)) & ((sP0 @ X1) = $true)) => (((cA @ (sK11 @ X0)) = $true) & ! [X2 : a] : (((X0 @ X2) != $true) | ((sK11 @ X0 @ X2) = $true)) & ($true = (sP0 @ (sK11 @ X0)))))),
% 2.98/1.27 introduced(definition,[],[choice_axiom])).
% 2.98/1.27 thf(f34,plain,(
% 2.98/1.27 ! [X0 : a > $o] : (? [X1 : a > $o] : (((cA @ X1) = $true) & ! [X2 : a] : (((X0 @ X2) != $true) | ((X1 @ X2) = $true)) & ((sP0 @ X1) = $true)) | ((sP2 @ X0) != $true))),
% 2.98/1.27 inference(rectify,[status(thm)],[f33])).
% 2.98/1.27 thf(f33,plain,(
% 2.98/1.27 ! [X5 : a > $o] : (? [X10 : a > $o] : (($true = (cA @ X10)) & ! [X11 : a] : (((X5 @ X11) != $true) | ((X10 @ X11) = $true)) & ((sP0 @ X10) = $true)) | ((sP2 @ X5) != $true))),
% 2.98/1.27 inference(nnf_transformation,[status(thm)],[f11])).
% 2.98/1.27 thf(f475,plain,(
% 2.98/1.27 ((cA @ (sK11 @ cE)) != $true) | ((sP2 @ cE) != $true)),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f466,f57])).
% 2.98/1.27 thf(f57,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (($true = (sP0 @ (sK11 @ X0))) | ((sP2 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f36])).
% 2.98/1.27 thf(f466,plain,(
% 2.98/1.27 ((sP0 @ (sK11 @ cE)) != $true) | ((cA @ (sK11 @ cE)) != $true) | ((sP2 @ cE) != $true)),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f459])).
% 2.98/1.27 thf(f459,plain,(
% 2.98/1.27 ((sP2 @ cE) != $true) | ((sP0 @ (sK11 @ cE)) != $true) | ((cA @ (sK11 @ cE)) != $true) | ($true != $true)),
% 2.98/1.27 inference(superposition,[status(thm)],[f212,f64])).
% 2.98/1.27 thf(f64,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((cE @ (sK13 @ X0)) = $true) | ((cA @ X0) != $true) | ((sP0 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f44])).
% 2.98/1.27 thf(f44,plain,(
% 2.98/1.27 ! [X0 : a > $o] : ((((cE @ (sK13 @ X0)) = $true) & ((X0 @ (sK13 @ X0)) != $true)) | ((cA @ X0) != $true) | ((sP0 @ X0) != $true))),
% 2.98/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f42,f43])).
% 2.98/1.27 thf(f43,plain,(
% 2.98/1.27 ! [X0 : a > $o] : (? [X1 : a] : (((cE @ X1) = $true) & ((X0 @ X1) != $true)) => (((cE @ (sK13 @ X0)) = $true) & ((X0 @ (sK13 @ X0)) != $true)))),
% 2.98/1.27 introduced(definition,[],[choice_axiom])).
% 2.98/1.27 thf(f42,plain,(
% 2.98/1.27 ! [X0 : a > $o] : (? [X1 : a] : (((cE @ X1) = $true) & ((X0 @ X1) != $true)) | ((cA @ X0) != $true) | ((sP0 @ X0) != $true))),
% 2.98/1.27 inference(rectify,[status(thm)],[f41])).
% 2.98/1.27 thf(f41,plain,(
% 2.98/1.27 ! [X10 : a > $o] : (? [X12 : a] : (((cE @ X12) = $true) & ((X10 @ X12) != $true)) | ($true != (cA @ X10)) | ((sP0 @ X10) != $true))),
% 2.98/1.27 inference(nnf_transformation,[status(thm)],[f9])).
% 2.98/1.27 thf(f212,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((X0 @ (sK13 @ (sK11 @ X0))) != $true) | ((sP2 @ X0) != $true)) )),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f211,f57])).
% 2.98/1.27 thf(f211,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((sP2 @ X0) != $true) | ($true != (sP0 @ (sK11 @ X0))) | ((X0 @ (sK13 @ (sK11 @ X0))) != $true)) )),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f201,f59])).
% 2.98/1.27 thf(f201,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((X0 @ (sK13 @ (sK11 @ X0))) != $true) | ((sP2 @ X0) != $true) | ((cA @ (sK11 @ X0)) != $true) | ($true != (sP0 @ (sK11 @ X0)))) )),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f197])).
% 2.98/1.27 thf(f197,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((X0 @ (sK13 @ (sK11 @ X0))) != $true) | ((cA @ (sK11 @ X0)) != $true) | ($true != $true) | ($true != (sP0 @ (sK11 @ X0))) | ((sP2 @ X0) != $true)) )),
% 2.98/1.27 inference(superposition,[status(thm)],[f63,f58])).
% 2.98/1.27 thf(f58,plain,(
% 2.98/1.27 ( ! [X2 : a,X0 : a > $o] : (((sK11 @ X0 @ X2) = $true) | ((X0 @ X2) != $true) | ((sP2 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f36])).
% 2.98/1.27 thf(f63,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((X0 @ (sK13 @ X0)) != $true) | ((cA @ X0) != $true) | ((sP0 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f44])).
% 2.98/1.27 thf(f486,plain,(
% 2.98/1.27 ((sP2 @ cE) = $true) | ~spl15_28),
% 2.98/1.27 inference(avatar_component_clause,[status(thm)],[f485])).
% 2.98/1.27 thf(f485,definition,(
% 2.98/1.27 spl15_28 <=> ((sP2 @ cE) = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_28])],[avatar_definition])).
% 2.98/1.27 thf(f490,plain,(
% 2.98/1.27 spl15_28 | spl15_29 | ~spl15_1 | ~spl15_7),
% 2.98/1.27 inference(avatar_split_clause,[status(thm)],[f483,f91,f69,f488,f485])).
% 2.98/1.27 thf(f69,definition,(
% 2.98/1.27 spl15_1 <=> ($true = (sP3 @ sK8))),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_1])],[avatar_definition])).
% 2.98/1.27 thf(f91,definition,(
% 2.98/1.27 spl15_7 <=> ! [X1 : a] : (((cE @ X1) != $true) | ($true = (sK8 @ X1)))),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_7])],[avatar_definition])).
% 2.98/1.27 thf(f483,plain,(
% 2.98/1.27 ((sP1 @ cE) = $true) | ((sP2 @ cE) = $true) | (~spl15_1 | ~spl15_7)),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f482,f70])).
% 2.98/1.27 thf(f70,plain,(
% 2.98/1.27 ($true = (sP3 @ sK8)) | ~spl15_1),
% 2.98/1.27 inference(avatar_component_clause,[status(thm)],[f69])).
% 2.98/1.27 thf(f482,plain,(
% 2.98/1.27 ((sP2 @ cE) = $true) | ($true != (sP3 @ sK8)) | ((sP1 @ cE) = $true) | (~spl15_1 | ~spl15_7)),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f481])).
% 2.98/1.27 thf(f481,plain,(
% 2.98/1.27 ((sP1 @ cE) = $true) | ($true != (sP3 @ sK8)) | ($true != $true) | ((sP2 @ cE) = $true) | (~spl15_1 | ~spl15_7)),
% 2.98/1.27 inference(duplicate_literal_removal,[status(thm)],[f480])).
% 2.98/1.27 thf(f480,plain,(
% 2.98/1.27 ((sP2 @ cE) = $true) | ((sP1 @ cE) = $true) | ($true != $true) | ((sP1 @ cE) = $true) | ((sP2 @ cE) = $true) | ($true != (sP3 @ sK8)) | (~spl15_1 | ~spl15_7)),
% 2.98/1.27 inference(superposition,[status(thm)],[f405,f55])).
% 2.98/1.27 thf(f55,plain,(
% 2.98/1.27 ( ! [X0 : a > $o,X1 : a > $o] : (((X1 @ (sK10 @ X1 @ X0)) = $true) | ((sP2 @ X1) = $true) | ((sP3 @ X0) != $true) | ((sP1 @ X1) = $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f32])).
% 2.98/1.27 thf(f32,plain,(
% 2.98/1.27 ! [X0 : a > $o] : (! [X1 : a > $o] : ((((X0 @ (sK10 @ X1 @ X0)) != $true) & ((X1 @ (sK10 @ X1 @ X0)) = $true)) | ((sP2 @ X1) = $true) | ((sP1 @ X1) = $true)) | ((sP3 @ X0) != $true))),
% 2.98/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f30,f31])).
% 2.98/1.27 thf(f31,plain,(
% 2.98/1.27 ! [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : (((X0 @ X2) != $true) & ((X1 @ X2) = $true)) => (((X0 @ (sK10 @ X1 @ X0)) != $true) & ((X1 @ (sK10 @ X1 @ X0)) = $true)))),
% 2.98/1.27 introduced(definition,[],[choice_axiom])).
% 2.98/1.27 thf(f30,plain,(
% 2.98/1.27 ! [X0 : a > $o] : (! [X1 : a > $o] : (? [X2 : a] : (((X0 @ X2) != $true) & ((X1 @ X2) = $true)) | ((sP2 @ X1) = $true) | ((sP1 @ X1) = $true)) | ((sP3 @ X0) != $true))),
% 2.98/1.27 inference(rectify,[status(thm)],[f29])).
% 2.98/1.27 thf(f29,plain,(
% 2.98/1.27 ! [X3 : a > $o] : (! [X5 : a > $o] : (? [X9 : a] : (((X3 @ X9) != $true) & ((X5 @ X9) = $true)) | ((sP2 @ X5) = $true) | ((sP1 @ X5) = $true)) | ((sP3 @ X3) != $true))),
% 2.98/1.27 inference(nnf_transformation,[status(thm)],[f12])).
% 2.98/1.27 thf(f405,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (((cE @ (sK10 @ X0 @ sK8)) != $true) | ((sP2 @ X0) = $true) | ((sP1 @ X0) = $true)) ) | (~spl15_1 | ~spl15_7)),
% 2.98/1.27 inference(subsumption_resolution,[status(thm)],[f402,f70])).
% 2.98/1.27 thf(f402,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (($true != (sP3 @ sK8)) | ((sP2 @ X0) = $true) | ((sP1 @ X0) = $true) | ((cE @ (sK10 @ X0 @ sK8)) != $true)) ) | ~spl15_7),
% 2.98/1.27 inference(trivial_inequality_removal,[status(thm)],[f394])).
% 2.98/1.27 thf(f394,plain,(
% 2.98/1.27 ( ! [X0 : a > $o] : (($true != $true) | ((sP1 @ X0) = $true) | ($true != (sP3 @ sK8)) | ((cE @ (sK10 @ X0 @ sK8)) != $true) | ((sP2 @ X0) = $true)) ) | ~spl15_7),
% 2.98/1.27 inference(superposition,[status(thm)],[f56,f92])).
% 2.98/1.27 thf(f92,plain,(
% 2.98/1.27 ( ! [X1 : a] : (($true = (sK8 @ X1)) | ((cE @ X1) != $true)) ) | ~spl15_7),
% 2.98/1.27 inference(avatar_component_clause,[status(thm)],[f91])).
% 2.98/1.27 thf(f56,plain,(
% 2.98/1.27 ( ! [X0 : a > $o,X1 : a > $o] : (((X0 @ (sK10 @ X1 @ X0)) != $true) | ((sP1 @ X1) = $true) | ((sP2 @ X1) = $true) | ((sP3 @ X0) != $true)) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f32])).
% 2.98/1.27 thf(f98,plain,(
% 2.98/1.27 ~spl15_4 | ~spl15_3),
% 2.98/1.27 inference(avatar_split_clause,[status(thm)],[f54,f76,f79])).
% 2.98/1.27 thf(f79,definition,(
% 2.98/1.27 spl15_4 <=> ((cA @ sK9) = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_4])],[avatar_definition])).
% 2.98/1.27 thf(f76,definition,(
% 2.98/1.27 spl15_3 <=> (sP4 = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_3])],[avatar_definition])).
% 2.98/1.27 thf(f54,plain,(
% 2.98/1.27 ((cA @ sK9) != $true) | (sP4 != $true)),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f28])).
% 2.98/1.27 thf(f28,plain,(
% 2.98/1.27 (((cA @ sK9) != $true) & ((cA @ sK9) = $true) & ! [X1 : a] : (((sK9 @ X1) = $true) | ((cE @ X1) != $true))) | (sP4 != $true)),
% 2.98/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f26,f27])).
% 2.98/1.27 thf(f27,plain,(
% 2.98/1.27 ? [X0 : a > $o] : (((cA @ X0) != $true) & ((cA @ X0) = $true) & ! [X1 : a] : (((X0 @ X1) = $true) | ((cE @ X1) != $true))) => (((cA @ sK9) != $true) & ((cA @ sK9) = $true) & ! [X1 : a] : (((sK9 @ X1) = $true) | ((cE @ X1) != $true)))),
% 2.98/1.27 introduced(definition,[],[choice_axiom])).
% 2.98/1.27 thf(f26,plain,(
% 2.98/1.27 ? [X0 : a > $o] : (((cA @ X0) != $true) & ((cA @ X0) = $true) & ! [X1 : a] : (((X0 @ X1) = $true) | ((cE @ X1) != $true))) | (sP4 != $true)),
% 2.98/1.27 inference(rectify,[status(thm)],[f25])).
% 2.98/1.27 thf(f25,plain,(
% 2.98/1.27 ? [X13 : a > $o] : (((cA @ X13) != $true) & ((cA @ X13) = $true) & ! [X14 : a] : (((X13 @ X14) = $true) | ((cE @ X14) != $true))) | (sP4 != $true)),
% 2.98/1.27 inference(nnf_transformation,[status(thm)],[f13])).
% 2.98/1.27 thf(f96,plain,(
% 2.98/1.27 spl15_2 | spl15_3),
% 2.98/1.27 inference(avatar_split_clause,[status(thm)],[f65,f76,f72])).
% 2.98/1.27 thf(f72,definition,(
% 2.98/1.27 spl15_2 <=> (sP5 = $true)),
% 2.98/1.27 introduced(definition,[new_symbols(naming,[spl15_2])],[avatar_definition])).
% 2.98/1.27 thf(f65,plain,(
% 2.98/1.27 (sP4 = $true) | (sP5 = $true)),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f46])).
% 2.98/1.27 thf(f93,plain,(
% 2.98/1.27 spl15_7 | ~spl15_2),
% 2.98/1.27 inference(avatar_split_clause,[status(thm)],[f51,f72,f91])).
% 2.98/1.27 thf(f51,plain,(
% 2.98/1.27 ( ! [X1 : a] : ((sP5 != $true) | ((cE @ X1) != $true) | ($true = (sK8 @ X1))) )),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f24])).
% 2.98/1.27 thf(f24,plain,(
% 2.98/1.27 (! [X1 : a] : (($true = (sK8 @ X1)) | ((cE @ X1) != $true)) & ($true = (sP3 @ sK8)) & ((cA @ sK8) = $true)) | (sP5 != $true)),
% 2.98/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f22,f23])).
% 2.98/1.27 thf(f23,plain,(
% 2.98/1.27 ? [X0 : a > $o] : (! [X1 : a] : (((X0 @ X1) = $true) | ((cE @ X1) != $true)) & ((sP3 @ X0) = $true) & ((cA @ X0) = $true)) => (! [X1 : a] : (($true = (sK8 @ X1)) | ((cE @ X1) != $true)) & ($true = (sP3 @ sK8)) & ((cA @ sK8) = $true))),
% 2.98/1.27 introduced(definition,[],[choice_axiom])).
% 2.98/1.27 thf(f22,plain,(
% 2.98/1.27 ? [X0 : a > $o] : (! [X1 : a] : (((X0 @ X1) = $true) | ((cE @ X1) != $true)) & ((sP3 @ X0) = $true) & ((cA @ X0) = $true)) | (sP5 != $true)),
% 2.98/1.27 inference(rectify,[status(thm)],[f21])).
% 2.98/1.27 thf(f21,plain,(
% 2.98/1.27 ? [X3 : a > $o] : (! [X4 : a] : (((X3 @ X4) = $true) | ((cE @ X4) != $true)) & ((sP3 @ X3) = $true) & ((cA @ X3) = $true)) | (sP5 != $true)),
% 2.98/1.27 inference(nnf_transformation,[status(thm)],[f14])).
% 2.98/1.27 thf(f81,plain,(
% 2.98/1.27 ~spl15_3 | spl15_4),
% 2.98/1.27 inference(avatar_split_clause,[status(thm)],[f53,f79,f76])).
% 2.98/1.27 thf(f53,plain,(
% 2.98/1.27 (sP4 != $true) | ((cA @ sK9) = $true)),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f28])).
% 2.98/1.27 thf(f74,plain,(
% 2.98/1.27 spl15_1 | ~spl15_2),
% 2.98/1.27 inference(avatar_split_clause,[status(thm)],[f50,f72,f69])).
% 2.98/1.27 thf(f50,plain,(
% 2.98/1.27 ($true = (sP3 @ sK8)) | (sP5 != $true)),
% 2.98/1.27 inference(cnf_transformation,[status(thm)],[f24])).
% 2.98/1.27 % SZS output end Proof for DTF2THF_29381
% 2.98/1.27 % (29689)------------------------------
% 2.98/1.27 % (29689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.27 % (29689)Termination reason: Refutation
% 2.98/1.27
% 2.98/1.27 % (29689)Memory used [KB]: 6268
% 2.98/1.27 % (29689)Time elapsed: 0.042 s
% 2.98/1.27 % (29689)Instructions burned: 114 (million)
% 2.98/1.27 % (29689)------------------------------
% 2.98/1.27 % (29689)------------------------------
% 2.98/1.27 % (29641)Success in time 0.362 s
%------------------------------------------------------------------------------