%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA075^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 08:38:48 AM UTC 2026
% Result : Theorem 4.92s 2.35s
% Output : Refutation 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 103 ( 12 unt; 0 typ; 5 def)
% Number of atoms : 878 ( 257 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 1096 ( 135 ~; 134 |; 59 &; 724 @)
% ( 7 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 12 con; 0-3 aty)
% Number of variables : 195 ( 0 ^; 164 !; 31 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/trivia/I':
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_2,type,
'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_3,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_10,type,
sP0: ( 'type/realax/real' > $o ) > $o ).
thf(func_def_11,type,
sP1: ( 'type/realax/real' > $o ) > $o ).
thf(func_def_12,type,
sK2: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_13,type,
sK3: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_14,type,
sK4: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_15,type,
sK5:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_16,type,
sK6:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK7: 'type/realax/real' > $o ).
thf(func_def_18,type,
sK8: 'type/realax/real' > $o ).
thf(func_def_19,type,
sK9: 'type/realax/real' ).
thf(func_def_21,type,
ph11:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK12: 'type/realax/real' ).
thf(func_def_24,type,
sK13: 'type/realax/real' ).
thf(func_def_25,type,
sK14: 'type/realax/real' ).
thf(func_def_26,type,
sK15: 'type/realax/real' ).
thf(f655,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f278,f295,f314,f491,f576,f647]) ).
thf(f647,plain,
( ~ spl10_7
| ~ spl10_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f646]) ).
thf(f646,plain,
( $false
| ~ spl10_7
| ~ spl10_23 ),
inference(trivial_inequality_removal,[status(thm)],[f643]) ).
thf(f643,plain,
( ( $false = $true )
| ~ spl10_7
| ~ spl10_23 ),
inference(backward_demodulation,[status(thm)],[f277,f631]) ).
thf(f631,plain,
( ! [X0: 'type/realax/real'] :
( $false
= ( sK8 @ X0 ) )
| ~ spl10_7 ),
inference(trivial_inequality_removal,[status(thm)],[f627]) ).
thf(f627,plain,
( ! [X0: 'type/realax/real'] :
( ( $false
= ( sK8 @ X0 ) )
| ( $true != $true ) )
| ~ spl10_7 ),
inference(superposition,[status(thm)],[f522,f76]) ).
thf(f76,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( $false
= ( X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X3: X0 > $o,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= ( X3 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/IN_') ).
thf(f522,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK8 ) )
| ~ spl10_7 ),
inference(superposition,[status(thm)],[f70,f120]) ).
thf(f120,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK8 ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f119,definition,
( spl10_7
<=> ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl10_7])],[avatar_definition]) ).
thf(f70,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/NOT_IN_EMPTY_') ).
thf(f277,plain,
( ( $true
= ( sK8 @ sK14 ) )
| ~ spl10_23 ),
inference(avatar_component_clause,[status(thm)],[f276]) ).
thf(f276,definition,
( spl10_23
<=> ( $true
= ( sK8 @ sK14 ) ) ),
introduced(definition,[new_symbols(naming,[spl10_23])],[avatar_definition]) ).
thf(f576,plain,
( spl10_23
| ~ spl10_22 ),
inference(avatar_split_clause,[status(thm)],[f573,f273,f276]) ).
thf(f273,definition,
( spl10_22
<=> ( ( sK7 @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_22])],[avatar_definition]) ).
thf(f573,plain,
( ( $true
= ( sK8 @ sK14 ) )
| ~ spl10_22 ),
inference(trivial_inequality_removal,[status(thm)],[f572]) ).
thf(f572,plain,
( ( $false = $true )
| ( $true
= ( sK8 @ sK14 ) )
| ~ spl10_22 ),
inference(superposition,[status(thm)],[f409,f274]) ).
thf(f274,plain,
( ( ( sK7 @ sK14 )
= $true )
| ~ spl10_22 ),
inference(avatar_component_clause,[status(thm)],[f273]) ).
thf(f409,plain,
! [X0: 'type/realax/real'] :
( ( $false
= ( sK7 @ X0 ) )
| ( ( sK8 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f404]) ).
thf(f404,plain,
! [X0: 'type/realax/real'] :
( ( $false
= ( sK7 @ X0 ) )
| ( ( sK8 @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f361,f76]) ).
thf(f361,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK7 ) )
| ( ( sK8 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f348]) ).
thf(f348,plain,
! [X0: 'type/realax/real'] :
( ( ( sK8 @ X0 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK7 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f147,f77]) ).
thf(f77,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $false
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) )
| ( $true
= ( X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f147,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK8 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK7 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f146]) ).
thf(f146,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK7 ) )
| ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK8 ) ) ),
inference(superposition,[status(thm)],[f67,f72]) ).
thf(f72,plain,
( ( 'const/sets/SUBSET' @ 'type/realax/real' @ sK7 @ sK8 )
= $true ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK7 ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK7 ) @ ( 'const/sets/sup' @ sK8 ) )
!= $true )
& ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ sK7 @ sK8 )
= $true )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK8 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ sK9 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f27,f54,f53]) ).
thf(f53,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ X1 ) )
!= $true )
& ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1 )
= $true )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ X2 ) ) ) )
=> ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK7 ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK7 ) @ ( 'const/sets/sup' @ sK8 ) )
!= $true )
& ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ sK7 @ sK8 )
= $true )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK8 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK8 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ X2 ) ) )
=> ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK8 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ X1 ) )
!= $true )
& ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1 )
= $true )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ X1 ) )
!= $true )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ X2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 ) )
=> ( $true
= ( 'const/realax/real_le' @ X3 @ X2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
=> ( 'const/realax/real_le' @ X3 @ X2 ) )
& ( 'const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ X1 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X2: 'type/realax/real'] :
! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 )
=> ( 'const/realax/real_le' @ X4 @ X2 ) )
& ( 'const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X2: 'type/realax/real'] :
! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 )
=> ( 'const/realax/real_le' @ X4 @ X2 ) )
& ( 'const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/REAL_SUP_LE_SUBSET_') ).
thf(f67,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X2 @ X1 ) @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X2 @ X1 ) @ X1 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f46,f47]) ).
thf(f47,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true ) )
=> ( ( ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X2 @ X1 ) @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X2 @ X1 ) @ X1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f46,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ? [X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ! [X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) )
<=> ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
<=> ! [X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
=> ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X4 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/SUBSET_') ).
thf(f491,plain,
~ spl10_5,
inference(avatar_contradiction_clause,[status(thm)],[f490]) ).
thf(f490,plain,
( $false
| ~ spl10_5 ),
inference(subsumption_resolution,[status(thm)],[f489,f74]) ).
thf(f74,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK7 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f489,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK7 ) )
| ~ spl10_5 ),
inference(subsumption_resolution,[status(thm)],[f487,f73]) ).
thf(f73,plain,
( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK7 ) @ ( 'const/sets/sup' @ sK8 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f487,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK7 ) @ ( 'const/sets/sup' @ sK8 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK7 ) )
| ~ spl10_5 ),
inference(trivial_inequality_removal,[status(thm)],[f486]) ).
thf(f486,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK7 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK7 ) @ ( 'const/sets/sup' @ sK8 ) )
= $true )
| ( $true != $true )
| ~ spl10_5 ),
inference(duplicate_literal_removal,[status(thm)],[f483]) ).
thf(f483,plain,
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK7 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK7 ) @ ( 'const/sets/sup' @ sK8 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK7 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK7 ) @ ( 'const/sets/sup' @ sK8 ) )
= $true )
| ~ spl10_5 ),
inference(superposition,[status(thm)],[f460,f63]) ).
thf(f63,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f29,f43]) ).
thf(f43,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
=> ( ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/REAL_SUP_LE_') ).
thf(f460,plain,
( ! [X0: 'type/realax/real' > $o] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ ( 'const/sets/sup' @ sK8 ) @ X0 ) @ sK7 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ sK8 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) )
| ~ spl10_5 ),
inference(subsumption_resolution,[status(thm)],[f456,f125]) ).
thf(f125,plain,
( ( ( sP1 @ sK8 )
= $true )
| ~ spl10_5 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl10_5
<=> ( ( sP1 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_5])],[avatar_definition]) ).
thf(f456,plain,
! [X0: 'type/realax/real' > $o] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ ( 'const/sets/sup' @ sK8 ) @ X0 ) @ sK7 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ sK8 ) ) )
| ( ( sP1 @ sK8 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f452]) ).
thf(f452,plain,
! [X0: 'type/realax/real' > $o] :
( ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ ( 'const/sets/sup' @ sK8 ) @ X0 ) @ sK7 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ ( 'const/sets/sup' @ sK8 ) ) )
| ( ( sP1 @ sK8 )
!= $true ) ),
inference(superposition,[status(thm)],[f129,f147]) ).
thf(f129,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ ( 'const/sets/sup' @ X0 ) @ X1 ) @ X0 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X1 ) @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ ( 'const/sets/sup' @ X0 ) @ X1 ) @ X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X1 ) @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X1 ) )
| ( $true != $true )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f64,f56]) ).
thf(f56,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( $true
= ( sP0 @ X0 ) )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( $true
= ( sP0 @ X0 ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) ) ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( $true
= ( sP0 @ X0 ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) ) ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f314,plain,
( spl10_7
| spl10_5
| ~ spl10_8 ),
inference(avatar_split_clause,[status(thm)],[f311,f122,f108,f119]) ).
thf(f122,definition,
( spl10_8
<=> ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ ( sK3 @ X0 @ sK8 ) @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl10_8])],[avatar_definition]) ).
thf(f311,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK8 ) )
| ( ( sP1 @ sK8 )
= $true )
| ~ spl10_8 ),
inference(trivial_inequality_removal,[status(thm)],[f310]) ).
thf(f310,plain,
( ( ( sP1 @ sK8 )
= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK8 ) )
| ~ spl10_8 ),
inference(superposition,[status(thm)],[f60,f123]) ).
thf(f123,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ ( sK3 @ X0 @ sK8 ) @ sK9 ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f60,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK3 @ X1 @ X0 ) @ X1 ) )
| ( $true
= ( sP1 @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK3 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( sK3 @ X1 @ X0 ) @ X1 ) ) )
| ( $true
= ( sP1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f34,f41]) ).
thf(f41,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK3 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( sK3 @ X1 @ X0 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
| ( $true
= ( sP1 @ X0 ) ) ),
inference(definition_folding,[status(thm)],[f31,f33,f32]) ).
thf(f32,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
| ( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X5 @ X4 )
= $true ) )
=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X5 @ X4 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
& ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/SUP_') ).
thf(f295,plain,
( spl10_7
| spl10_8
| spl10_5 ),
inference(avatar_split_clause,[status(thm)],[f294,f108,f122,f119]) ).
thf(f294,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK8 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK3 @ X0 @ sK8 ) @ sK9 ) )
| ( ( sP1 @ sK8 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f291]) ).
thf(f291,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( sP1 @ sK8 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK3 @ X0 @ sK8 ) @ sK9 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK8 ) ) ),
inference(superposition,[status(thm)],[f71,f61]) ).
thf(f61,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK3 @ X1 @ X0 ) @ X0 ) )
| ( $true
= ( sP1 @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f71,plain,
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK8 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f278,plain,
( spl10_22
| spl10_23
| ~ spl10_7 ),
inference(avatar_split_clause,[status(thm)],[f270,f119,f276,f273]) ).
thf(f270,plain,
( ( $true
= ( sK8 @ sK14 ) )
| ( ( sK7 @ sK14 )
= $true )
| ~ spl10_7 ),
inference(binary_proxy_clausification,[status(thm)],[f269]) ).
thf(f269,plain,
( ( ( sK7 @ sK14 )
!= ( sK8 @ sK14 ) )
| ~ spl10_7 ),
inference(negative_extensionality,[status(thm)],[f265]) ).
thf(f265,plain,
( ( sK7 != sK8 )
| ~ spl10_7 ),
inference(superposition,[status(thm)],[f74,f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA075^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n025.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 03:49:57 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : ANA075^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.38 % Domain : Analysis
% 0.18/0.38 % Problem : REAL_SUP_LE_SUBSET
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English :
% 0.18/0.38
% 0.18/0.38 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.38 % Source : [Kal16]
% 0.18/0.38 % Names : REAL_SUP_LE_SUBSET_.p [Kal16]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.18/0.38 % Syntax : Number of formulae : 15 ( 4 unt; 7 typ; 0 def)
% 0.18/0.38 % Number of atoms : 34 ( 9 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 8 ( 4 avg)
% 0.18/0.38 % Number of connectives : 86 ( 4 ~; 0 |; 5 &; 67 @)
% 0.18/0.38 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 12 ( 7 avg)
% 0.18/0.38 % Number of types : 2 ( 1 usr)
% 0.18/0.38 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.18/0.38 % Number of variables : 32 ( 0 ^; 26 !; 2 ?; 32 :)
% 0.18/0.38 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.38 % SPC : TH1_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : Exported from core HOL Light.
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf('thf_type_type/realax/real',type,
% 0.18/0.38 'type/realax/real': $tType ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/trivia/I',type,
% 0.18/0.38 'const/trivia/I':
% 0.18/0.38 !>[A: $tType] : ( A > A ) ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/sets/sup',type,
% 0.18/0.38 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/sets/SUBSET',type,
% 0.18/0.38 'const/sets/SUBSET':
% 0.18/0.38 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/sets/IN',type,
% 0.18/0.38 'const/sets/IN':
% 0.18/0.38 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/sets/EMPTY',type,
% 0.18/0.38 'const/sets/EMPTY':
% 0.18/0.38 !>[A: $tType] : ( A > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/realax/real_le',type,
% 0.18/0.38 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/REAL_SUP_LE_',axiom,
% 0.18/0.38 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.18/0.38 ( ( ( A
% 0.18/0.38 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.18/0.38 & ! [A1: 'type/realax/real'] :
% 0.18/0.38 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.18/0.38 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 0.18/0.38 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/trivia/I_THM_',axiom,
% 0.18/0.38 ! [A: $tType,A0: A] :
% 0.18/0.38 ( ( 'const/trivia/I' @ A @ A0 )
% 0.18/0.38 = A0 ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/IN_',axiom,
% 0.18/0.38 ! [A: $tType,P: A > $o,A0: A] :
% 0.18/0.38 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.18/0.38 = ( P @ A0 ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 0.18/0.38 ! [A: $tType,A0: A] :
% 0.18/0.38 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/EXTENSION_',axiom,
% 0.18/0.38 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.38 ( ( A0 = A1 )
% 0.18/0.38 = ( ! [A2: A] :
% 0.18/0.38 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.18/0.38 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/SUBSET_',axiom,
% 0.18/0.38 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.38 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 0.18/0.38 = ( ! [A2: A] :
% 0.18/0.38 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.18/0.38 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/SUP_',axiom,
% 0.18/0.38 ! [A: 'type/realax/real' > $o] :
% 0.18/0.38 ( ( ( A
% 0.18/0.38 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.18/0.38 & ? [A0: 'type/realax/real'] :
% 0.18/0.38 ! [A1: 'type/realax/real'] :
% 0.18/0.38 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.18/0.38 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 0.18/0.38 => ( ! [A0: 'type/realax/real'] :
% 0.18/0.38 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.18/0.38 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
% 0.18/0.38 & ! [A0: 'type/realax/real'] :
% 0.18/0.38 ( ! [A1: 'type/realax/real'] :
% 0.18/0.38 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.18/0.38 => ( 'const/realax/real_le' @ A1 @ A0 ) )
% 0.18/0.38 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/REAL_SUP_LE_SUBSET_',conjecture,
% 0.18/0.38 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real' > $o] :
% 0.18/0.38 ( ( ( A
% 0.18/0.38 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.18/0.38 & ( 'const/sets/SUBSET' @ 'type/realax/real' @ A @ A0 )
% 0.18/0.38 & ? [A1: 'type/realax/real'] :
% 0.18/0.38 ! [A2: 'type/realax/real'] :
% 0.18/0.38 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A0 )
% 0.18/0.38 => ( 'const/realax/real_le' @ A2 @ A1 ) ) )
% 0.18/0.38 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ ( 'const/sets/sup' @ A0 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.52/1.76 ---- Embedded in THF ---
% 1.52/1.77 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.77 %%% Generated on Tue Feb 24 03:49:59 EST 2026
% 1.52/1.77 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.77 %%% Logic specification used:
% 1.52/1.77 %%% thf(spec, logic, $$dhol).
% 1.52/1.77
% 1.52/1.77 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2DTF19883.p
% See solution above
% 1.52/1.77 ------------------------
% 1.52/1.77 ---- Cleaned THF ---
% 1.52/1.78 thf('thf_type_type/realax/real',type,
% 1.52/1.78 'type/realax/real': $tType ).
% 1.52/1.78
% 1.52/1.78 thf('thf_const_const/trivia/I',type,
% 1.52/1.78 'const/trivia/I':
% 1.52/1.78 !>[A: $tType] : ( A > A ) ).
% 1.52/1.78
% 1.52/1.78 thf('thf_const_const/sets/sup',type,
% 1.52/1.78 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.52/1.78
% 1.52/1.78 thf('thf_const_const/sets/SUBSET',type,
% 1.52/1.78 'const/sets/SUBSET':
% 1.52/1.78 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.52/1.78
% 1.52/1.78 thf('thf_const_const/sets/IN',type,
% 1.52/1.78 'const/sets/IN':
% 1.52/1.78 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.52/1.78
% 1.52/1.78 thf('thf_const_const/sets/EMPTY',type,
% 1.52/1.78 'const/sets/EMPTY':
% 1.52/1.78 !>[A: $tType] : ( A > $o ) ).
% 1.52/1.78
% 1.52/1.78 thf('thf_const_const/realax/real_le',type,
% 1.52/1.78 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.52/1.78
% 1.52/1.78 thf('thm/sets/REAL_SUP_LE_',axiom,
% 1.52/1.78 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.52/1.78 ( ( ( A
% 1.52/1.78 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.52/1.78 & ! [A1: 'type/realax/real'] :
% 1.52/1.78 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.52/1.78 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 1.52/1.78 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ).
% 1.52/1.78
% 1.52/1.78 thf('thm/trivia/I_THM_',axiom,
% 1.52/1.78 ! [A: $tType,A0: A] :
% 1.52/1.78 ( ( 'const/trivia/I' @ A @ A0 )
% 1.52/1.78 = A0 ) ).
% 1.52/1.78
% 1.52/1.78 thf('thm/sets/IN_',axiom,
% 1.52/1.78 ! [A: $tType,P: A > $o,A0: A] :
% 1.52/1.78 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 1.52/1.78 = ( P @ A0 ) ) ).
% 1.52/1.78
% 1.52/1.78 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 1.52/1.78 ! [A: $tType,A0: A] :
% 1.52/1.78 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 1.52/1.78
% 1.52/1.78 thf('thm/sets/EXTENSION_',axiom,
% 1.52/1.78 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.52/1.78 ( ( A0 = A1 )
% 1.52/1.78 = ( ! [A2: A] :
% 1.52/1.78 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.52/1.78 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.52/1.78
% 1.52/1.78 thf('thm/sets/SUBSET_',axiom,
% 1.52/1.78 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.52/1.78 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 1.52/1.78 = ( ! [A2: A] :
% 1.52/1.78 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.52/1.78 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.52/1.78
% 1.52/1.78 thf('thm/sets/SUP_',axiom,
% 1.52/1.78 ! [A: 'type/realax/real' > $o] :
% 1.52/1.78 ( ( ( A
% 1.52/1.78 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.52/1.78 & ? [A0: 'type/realax/real'] :
% 1.52/1.78 ! [A1: 'type/realax/real'] :
% 1.52/1.78 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.52/1.78 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 1.52/1.78 => ( ! [A0: 'type/realax/real'] :
% 1.52/1.78 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.52/1.78 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
% 1.52/1.78 & ! [A0: 'type/realax/real'] :
% 1.52/1.78 ( ! [A1: 'type/realax/real'] :
% 1.52/1.78 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.52/1.78 => ( 'const/realax/real_le' @ A1 @ A0 ) )
% 1.52/1.78 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
% 1.52/1.78
% 1.52/1.78 thf('thm/sets/REAL_SUP_LE_SUBSET_',conjecture,
% 1.52/1.78 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real' > $o] :
% 1.52/1.78 ( ( ( A
% 1.52/1.78 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.52/1.78 & ( 'const/sets/SUBSET' @ 'type/realax/real' @ A @ A0 )
% 1.52/1.78 & ? [A1: 'type/realax/real'] :
% 1.52/1.78 ! [A2: 'type/realax/real'] :
% 1.52/1.78 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A0 )
% 1.52/1.78 => ( 'const/realax/real_le' @ A2 @ A1 ) ) )
% 1.52/1.78 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ ( 'const/sets/sup' @ A0 ) ) ) ).
% 1.52/1.78 ------------------------
% 1.52/1.80 % (19980)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/183Mi)
% 1.52/1.80 % (19985)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_19883 for (2999ds/275Mi)
% 1.52/1.80 % (19983)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/2Mi)
% 1.52/1.80 % (19982)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_19883 for (2999ds/27Mi)
% 1.52/1.80 % (19981)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_19883 for (2999ds/4Mi)
% 1.52/1.80 % (19986)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/18Mi)
% 1.52/1.80 % (19984)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_19883 for (2999ds/2Mi)
% 1.70/1.80 % (19983)Instruction limit reached!
% 1.70/1.80 % (19983)------------------------------
% 1.70/1.80 % (19983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.80 % (19983)Termination reason: Unknown
% 1.70/1.80 % (19983)Termination phase: Preprocessing 3
% 1.70/1.80
% 1.70/1.80 % (19983)Memory used [KB]: 1023
% 1.70/1.80 % (19983)Time elapsed: 0.003 s
% 1.70/1.80 % (19983)Instructions burned: 3 (million)
% 1.70/1.80 % (19983)------------------------------
% 1.70/1.80 % (19983)------------------------------
% 1.70/1.80 % (19981)Instruction limit reached!
% 1.70/1.80 % (19981)------------------------------
% 1.70/1.80 % (19981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.80 % (19981)Termination reason: Unknown
% 1.70/1.80 % (19981)Termination phase: Saturation
% 1.70/1.80
% 1.70/1.80 % (19981)Memory used [KB]: 1023
% 1.70/1.80 % (19981)Time elapsed: 0.004 s
% 1.70/1.80 % (19981)Instructions burned: 4 (million)
% 1.70/1.80 % (19981)------------------------------
% 1.70/1.80 % (19981)------------------------------
% 1.70/1.80 % (19984)Instruction limit reached!
% 1.70/1.80 % (19984)------------------------------
% 1.70/1.80 % (19984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.80 % (19984)Termination reason: Unknown
% 1.70/1.80 % (19984)Termination phase: Property scanning
% 1.70/1.80
% 1.70/1.80 % (19984)Memory used [KB]: 1023
% 1.70/1.80 % (19984)Time elapsed: 0.003 s
% 1.70/1.80 % (19984)Instructions burned: 3 (million)
% 1.70/1.80 % (19984)------------------------------
% 1.70/1.80 % (19984)------------------------------
% 1.70/1.81 % (19986)Instruction limit reached!
% 1.70/1.81 % (19986)------------------------------
% 1.70/1.81 % (19986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.81 % (19986)Termination reason: Unknown
% 1.70/1.81 % (19986)Termination phase: Saturation
% 1.70/1.81
% 1.70/1.81 % (19986)Memory used [KB]: 5628
% 1.70/1.81 % (19986)Time elapsed: 0.012 s
% 1.70/1.81 % (19986)Instructions burned: 19 (million)
% 1.70/1.81 % (19986)------------------------------
% 1.70/1.81 % (19986)------------------------------
% 1.70/1.81 % (19982)Instruction limit reached!
% 1.70/1.81 % (19982)------------------------------
% 1.70/1.81 % (19982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.81 % (19982)Termination reason: Unknown
% 1.70/1.81 % (19982)Termination phase: Saturation
% 1.70/1.81
% 1.70/1.81 % (19982)Memory used [KB]: 5628
% 1.70/1.81 % (19982)Time elapsed: 0.017 s
% 1.70/1.81 % (19982)Instructions burned: 27 (million)
% 1.70/1.81 % (19982)------------------------------
% 1.70/1.81 % (19982)------------------------------
% 1.70/1.81 % (19987)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/3Mi)
% 1.70/1.81 % (19988)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_19883 for (2999ds/37Mi)
% 1.70/1.81 % (19989)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_19883 for (2999ds/15Mi)
% 1.70/1.82 % (19987)Instruction limit reached!
% 1.70/1.82 % (19987)------------------------------
% 1.70/1.82 % (19987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.82 % (19987)Termination reason: Unknown
% 1.70/1.82 % (19987)Termination phase: Saturation
% 1.70/1.82
% 1.70/1.82 % (19987)Memory used [KB]: 1023
% 1.70/1.82 % (19987)Time elapsed: 0.003 s
% 1.70/1.82 % (19987)Instructions burned: 3 (million)
% 1.70/1.82 % (19987)------------------------------
% 1.70/1.82 % (19987)------------------------------
% 1.70/1.82 % (19990)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_19883 for (2999ds/3Mi)
% 1.70/1.82 % (19989)Instruction limit reached!
% 1.70/1.82 % (19989)------------------------------
% 1.70/1.82 % (19989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.82 % (19989)Termination reason: Unknown
% 1.70/1.82 % (19989)Termination phase: Saturation
% 1.70/1.82
% 1.70/1.82 % (19989)Memory used [KB]: 5628
% 1.70/1.82 % (19989)Time elapsed: 0.010 s
% 1.70/1.82 % (19989)Instructions burned: 16 (million)
% 1.70/1.82 % (19989)------------------------------
% 1.70/1.82 % (19989)------------------------------
% 1.70/1.82 % (19990)Instruction limit reached!
% 1.70/1.82 % (19990)------------------------------
% 1.70/1.82 % (19990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.82 % (19990)Termination reason: Unknown
% 1.70/1.82 % (19990)Termination phase: Saturation
% 1.70/1.82
% 1.70/1.82 % (19990)Memory used [KB]: 1023
% 1.70/1.82 % (19990)Time elapsed: 0.003 s
% 1.70/1.82 % (19990)Instructions burned: 3 (million)
% 1.70/1.82 % (19990)------------------------------
% 1.70/1.82 % (19990)------------------------------
% 1.70/1.83 % (19991)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_19883 for (2999ds/1041Mi)
% 1.70/1.83 % (19992)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/7Mi)
% 1.70/1.83 % (19988)Instruction limit reached!
% 1.70/1.83 % (19988)------------------------------
% 1.70/1.83 % (19988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.83 % (19988)Termination reason: Unknown
% 1.70/1.83 % (19988)Termination phase: Saturation
% 1.70/1.83
% 1.70/1.83 % (19988)Memory used [KB]: 5756
% 1.70/1.83 % (19988)Time elapsed: 0.021 s
% 1.70/1.83 % (19988)Instructions burned: 38 (million)
% 1.70/1.83 % (19988)------------------------------
% 1.70/1.83 % (19988)------------------------------
% 1.70/1.83 % (19992)Instruction limit reached!
% 1.70/1.83 % (19992)------------------------------
% 1.70/1.83 % (19992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.83 % (19992)Termination reason: Unknown
% 1.70/1.83 % (19992)Termination phase: Saturation
% 1.70/1.83
% 1.70/1.83 % (19992)Memory used [KB]: 1023
% 1.70/1.83 % (19992)Time elapsed: 0.005 s
% 1.70/1.83 % (19992)Instructions burned: 7 (million)
% 1.70/1.83 % (19992)------------------------------
% 1.70/1.83 % (19992)------------------------------
% 1.70/1.84 % (19993)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/16Mi)
% 1.70/1.84 % (19994)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_19883 for (2999ds/3Mi)
% 1.70/1.84 % (19994)Instruction limit reached!
% 1.70/1.84 % (19994)------------------------------
% 1.70/1.84 % (19994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.84 % (19994)Termination reason: Unknown
% 1.70/1.84 % (19994)Termination phase: Property scanning
% 1.70/1.84
% 1.70/1.84 % (19994)Memory used [KB]: 1023
% 1.70/1.84 % (19994)Time elapsed: 0.003 s
% 1.70/1.84 % (19994)Instructions burned: 3 (million)
% 1.70/1.84 % (19994)------------------------------
% 1.70/1.84 % (19994)------------------------------
% 1.70/1.85 % (19993)Instruction limit reached!
% 1.70/1.85 % (19993)------------------------------
% 1.70/1.85 % (19993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.85 % (19993)Termination reason: Unknown
% 1.70/1.85 % (19993)Termination phase: Saturation
% 1.70/1.85
% 1.70/1.85 % (19993)Memory used [KB]: 5628
% 1.70/1.85 % (19993)Time elapsed: 0.010 s
% 1.70/1.85 % (19993)Instructions burned: 17 (million)
% 1.70/1.85 % (19993)------------------------------
% 1.70/1.85 % (19993)------------------------------
% 1.70/1.85 % (19995)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_19883 for (2999ds/3Mi)
% 1.70/1.85 % (19996)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/7Mi)
% 1.70/1.85 % (19995)Instruction limit reached!
% 1.70/1.85 % (19995)------------------------------
% 1.70/1.85 % (19995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.85 % (19995)Termination reason: Unknown
% 1.70/1.85 % (19995)Termination phase: Property scanning
% 1.70/1.85
% 1.70/1.85 % (19995)Memory used [KB]: 1023
% 1.70/1.85 % (19995)Time elapsed: 0.003 s
% 1.70/1.85 % (19995)Instructions burned: 3 (million)
% 1.70/1.85 % (19995)------------------------------
% 1.70/1.85 % (19995)------------------------------
% 1.70/1.85 % (19996)Instruction limit reached!
% 1.70/1.85 % (19996)------------------------------
% 1.70/1.85 % (19996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.85 % (19996)Termination reason: Unknown
% 1.70/1.85 % (19996)Termination phase: Saturation
% 1.70/1.85
% 1.70/1.85 % (19996)Memory used [KB]: 5500
% 1.70/1.85 % (19996)Time elapsed: 0.005 s
% 1.70/1.85 % (19996)Instructions burned: 7 (million)
% 1.70/1.85 % (19996)------------------------------
% 1.70/1.85 % (19996)------------------------------
% 1.70/1.86 % (19997)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/3Mi)
% 1.70/1.86 % (19997)Instruction limit reached!
% 1.70/1.86 % (19997)------------------------------
% 1.70/1.86 % (19997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.86 % (19997)Termination reason: Unknown
% 1.70/1.86 % (19997)Termination phase: Property scanning
% 1.70/1.86
% 1.70/1.86 % (19997)Memory used [KB]: 1023
% 1.70/1.86 % (19997)Time elapsed: 0.003 s
% 1.70/1.86 % (19997)Instructions burned: 4 (million)
% 1.70/1.86 % (19997)------------------------------
% 1.70/1.86 % (19997)------------------------------
% 1.70/1.86 % (19998)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/4Mi)
% 1.70/1.87 % (19998)Instruction limit reached!
% 1.70/1.87 % (19998)------------------------------
% 1.70/1.87 % (19998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.87 % (19998)Termination reason: Unknown
% 1.70/1.87 % (19998)Termination phase: Saturation
% 1.70/1.87
% 1.70/1.87 % (19998)Memory used [KB]: 5500
% 1.70/1.87 % (19998)Time elapsed: 0.004 s
% 1.70/1.87 % (19998)Instructions burned: 5 (million)
% 1.70/1.87 % (19998)------------------------------
% 1.70/1.87 % (19998)------------------------------
% 1.70/1.87 % (19999)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/18Mi)
% 1.70/1.87 % (20000)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/710Mi)
% 1.70/1.87 % (20001)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/6Mi)
% 1.70/1.88 % (19999)Instruction limit reached!
% 1.70/1.88 % (19999)------------------------------
% 1.70/1.88 % (19999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.88 % (19999)Termination reason: Unknown
% 1.70/1.88 % (19999)Termination phase: Saturation
% 1.70/1.88
% 1.70/1.88 % (19999)Memory used [KB]: 5628
% 1.70/1.88 % (19999)Time elapsed: 0.011 s
% 1.70/1.88 % (19999)Instructions burned: 18 (million)
% 1.70/1.88 % (19999)------------------------------
% 1.70/1.88 % (19999)------------------------------
% 1.70/1.88 % (20001)Instruction limit reached!
% 1.70/1.88 % (20001)------------------------------
% 1.70/1.88 % (20001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.88 % (20001)Termination reason: Unknown
% 1.70/1.88 % (20001)Termination phase: Saturation
% 1.70/1.88
% 1.70/1.88 % (20001)Memory used [KB]: 5500
% 1.70/1.88 % (20001)Time elapsed: 0.005 s
% 1.70/1.88 % (20001)Instructions burned: 7 (million)
% 1.70/1.88 % (20001)------------------------------
% 1.70/1.88 % (20001)------------------------------
% 1.70/1.88 % (20002)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_19883 for (2999ds/902Mi)
% 1.70/1.89 % (19980)Instruction limit reached!
% 1.70/1.89 % (19980)------------------------------
% 1.70/1.89 % (19980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.89 % (19980)Termination reason: Unknown
% 1.70/1.89 % (19980)Termination phase: Saturation
% 1.70/1.89
% 1.70/1.89 % (19980)Memory used [KB]: 6780
% 1.70/1.89 % (19980)Time elapsed: 0.092 s
% 1.70/1.89 % (19980)Instructions burned: 183 (million)
% 1.70/1.89 % (19980)------------------------------
% 1.70/1.89 % (19980)------------------------------
% 1.70/1.89 % (20003)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_19883 for (2999ds/21Mi)
% 1.70/1.89 % (20004)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19883 for (2999ds/5Mi)
% 1.70/1.90 % (20004)Instruction limit reached!
% 1.70/1.90 % (20004)------------------------------
% 1.70/1.90 % (20004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.90 % (20004)Termination reason: Unknown
% 1.70/1.90 % (20004)Termination phase: Saturation
% 1.70/1.90
% 1.70/1.90 % (20004)Memory used [KB]: 5500
% 1.70/1.90 % (20004)Time elapsed: 0.004 s
% 1.70/1.90 % (20004)Instructions burned: 5 (million)
% 1.70/1.90 % (20004)------------------------------
% 1.70/1.90 % (20004)------------------------------
% 1.70/1.90 % (20005)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_19883 for (2999ds/6Mi)
% 1.70/1.90 % (20003)Instruction limit reached!
% 1.70/1.90 % (20003)------------------------------
% 1.70/1.90 % (20003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.90 % (20003)Termination reason: Unknown
% 1.70/1.90 % (20003)Termination phase: Saturation
% 1.70/1.90
% 1.70/1.90 % (20003)Memory used [KB]: 5628
% 1.70/1.90 % (20003)Time elapsed: 0.013 s
% 1.70/1.90 % (20003)Instructions burned: 21 (million)
% 1.70/1.90 % (20003)------------------------------
% 1.70/1.90 % (20003)------------------------------
% 1.70/1.91 % (20005)Instruction limit reached!
% 1.70/1.91 % (20005)------------------------------
% 1.70/1.91 % (20005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.91 % (20005)Termination reason: Unknown
% 1.70/1.91 % (20005)Termination phase: Saturation
% 1.70/1.91
% 1.70/1.91 % (20005)Memory used [KB]: 5500
% 1.70/1.91 % (20005)Time elapsed: 0.005 s
% 1.70/1.91 % (20005)Instructions burned: 7 (million)
% 1.70/1.91 % (20005)------------------------------
% 1.70/1.91 % (20005)------------------------------
% 1.70/1.91 % (20002)Refutation not found, incomplete strategy
% 1.70/1.91 % (20002)------------------------------
% 1.70/1.91 % (20002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.91 % (20002)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.91
% 1.70/1.91
% 1.70/1.91 % (20002)Memory used [KB]: 5756
% 1.70/1.91 % (20002)Time elapsed: 0.029 s
% 1.70/1.91 % (20002)Instructions burned: 52 (million)
% 1.70/1.91 % (20002)------------------------------
% 1.70/1.91 % (20002)------------------------------
% 1.70/1.91 % (20006)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19883 for (2998ds/377Mi)
% 1.70/1.92 % (20007)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_19883 for (2998ds/779Mi)
% 1.70/1.92 % (20008)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_19883 for (2998ds/19Mi)
% 1.70/1.93 % (20009)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19883 for (2998ds/879Mi)
% 1.70/1.93 % (20008)Instruction limit reached!
% 1.70/1.93 % (20008)------------------------------
% 1.70/1.93 % (20008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.93 % (20008)Termination reason: Unknown
% 1.70/1.93 % (20008)Termination phase: Saturation
% 1.70/1.93
% 1.70/1.93 % (20008)Memory used [KB]: 5628
% 1.70/1.93 % (20008)Time elapsed: 0.011 s
% 1.70/1.93 % (20008)Instructions burned: 19 (million)
% 1.70/1.93 % (20008)------------------------------
% 1.70/1.93 % (20008)------------------------------
% 1.70/1.94 % (19985)Instruction limit reached!
% 1.70/1.94 % (19985)------------------------------
% 1.70/1.94 % (19985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.94 % (19985)Termination reason: Unknown
% 1.70/1.94 % (19985)Termination phase: Saturation
% 1.70/1.94
% 1.70/1.94 % (19985)Memory used [KB]: 7419
% 1.70/1.94 % (19985)Time elapsed: 0.147 s
% 1.70/1.94 % (19985)Instructions burned: 276 (million)
% 1.70/1.94 % (19985)------------------------------
% 1.70/1.94 % (19985)------------------------------
% 1.70/1.95 % (20010)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19883 for (2998ds/17Mi)
% 1.70/1.96 % (20010)Instruction limit reached!
% 1.70/1.96 % (20010)------------------------------
% 1.70/1.96 % (20010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.96 % (20010)Termination reason: Unknown
% 1.70/1.96 % (20010)Termination phase: Saturation
% 1.70/1.96
% 1.70/1.96 % (20010)Memory used [KB]: 5628
% 1.70/1.96 % (20010)Time elapsed: 0.011 s
% 1.70/1.96 % (20010)Instructions burned: 17 (million)
% 1.70/1.96 % (20010)------------------------------
% 1.70/1.96 % (20010)------------------------------
% 1.70/1.96 % (20011)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19883 for (2998ds/3Mi)
% 1.70/1.96 % (20011)Instruction limit reached!
% 1.70/1.96 % (20011)------------------------------
% 1.70/1.96 % (20011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.96 % (20011)Termination reason: Unknown
% 1.70/1.96 % (20011)Termination phase: Property scanning
% 1.70/1.96
% 1.70/1.96 % (20011)Memory used [KB]: 1023
% 1.70/1.96 % (20011)Time elapsed: 0.003 s
% 1.70/1.96 % (20011)Instructions burned: 3 (million)
% 1.70/1.96 % (20011)------------------------------
% 1.70/1.96 % (20011)------------------------------
% 1.70/1.97 % (20012)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19883 for (2998ds/30Mi)
% 1.70/1.98 % (20013)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19883 for (2998ds/127Mi)
% 1.70/1.99 % (20012)Instruction limit reached!
% 1.70/1.99 % (20012)------------------------------
% 1.70/1.99 % (20012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.99 % (20012)Termination reason: Unknown
% 1.70/1.99 % (20012)Termination phase: Saturation
% 1.70/1.99
% 1.70/1.99 % (20012)Memory used [KB]: 5628
% 1.70/1.99 % (20012)Time elapsed: 0.017 s
% 1.70/1.99 % (20012)Instructions burned: 30 (million)
% 1.70/1.99 % (20012)------------------------------
% 1.70/1.99 % (20012)------------------------------
% 1.70/2.00 % (20014)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19883 for (2997ds/100Mi)
% 3.34/2.04 % (20013)Instruction limit reached!
% 3.34/2.04 % (20013)------------------------------
% 3.34/2.04 % (20013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/2.04 % (20013)Termination reason: Unknown
% 3.34/2.04 % (20013)Termination phase: Saturation
% 3.34/2.04
% 3.34/2.04 % (20013)Memory used [KB]: 5756
% 3.34/2.04 % (20013)Time elapsed: 0.065 s
% 3.34/2.04 % (20013)Instructions burned: 127 (million)
% 3.34/2.04 % (20013)------------------------------
% 3.34/2.04 % (20013)------------------------------
% 3.34/2.06 % (20015)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_19883 for (2997ds/3Mi)
% 3.34/2.06 % (20014)Instruction limit reached!
% 3.34/2.06 % (20014)------------------------------
% 3.34/2.06 % (20014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/2.06 % (20014)Termination reason: Unknown
% 3.34/2.06 % (20014)Termination phase: Saturation
% 3.34/2.06
% 3.34/2.06 % (20014)Memory used [KB]: 5884
% 3.34/2.06 % (20014)Time elapsed: 0.053 s
% 3.34/2.06 % (20014)Instructions burned: 100 (million)
% 3.34/2.06 % (20014)------------------------------
% 3.34/2.06 % (20014)------------------------------
% 3.34/2.06 % (20015)Instruction limit reached!
% 3.34/2.06 % (20015)------------------------------
% 3.34/2.06 % (20015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/2.06 % (20015)Termination reason: Unknown
% 3.34/2.06 % (20015)Termination phase: Property scanning
% 3.34/2.06
% 3.34/2.06 % (20015)Memory used [KB]: 1023
% 3.34/2.06 % (20015)Time elapsed: 0.003 s
% 3.34/2.06 % (20015)Instructions burned: 3 (million)
% 3.34/2.06 % (20015)------------------------------
% 3.34/2.06 % (20015)------------------------------
% 3.34/2.07 % (20016)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_19883 for (2997ds/20Mi)
% 3.34/2.07 % (20017)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_19883 for (2997ds/86Mi)
% 3.34/2.08 % (20016)Instruction limit reached!
% 3.34/2.08 % (20016)------------------------------
% 3.34/2.08 % (20016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/2.08 % (20016)Termination reason: Unknown
% 3.34/2.08 % (20016)Termination phase: Saturation
% 3.34/2.08
% 3.34/2.08 % (20016)Memory used [KB]: 5628
% 3.34/2.08 % (20016)Time elapsed: 0.012 s
% 3.34/2.08 % (20016)Instructions burned: 20 (million)
% 3.34/2.08 % (20016)------------------------------
% 3.34/2.08 % (20016)------------------------------
% 3.34/2.10 % (20018)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_19883 for (2997ds/107Mi)
% 3.34/2.11 % (20006)Instruction limit reached!
% 3.34/2.11 % (20006)------------------------------
% 3.34/2.11 % (20006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/2.11 % (20006)Termination reason: Unknown
% 3.34/2.11 % (20006)Termination phase: Saturation
% 3.34/2.11
% 3.34/2.11 % (20006)Memory used [KB]: 6268
% 3.34/2.11 % (20006)Time elapsed: 0.200 s
% 3.34/2.11 % (20006)Instructions burned: 378 (million)
% 3.34/2.11 % (20006)------------------------------
% 3.34/2.11 % (20006)------------------------------
% 3.34/2.11 % (20017)Instruction limit reached!
% 3.34/2.11 % (20017)------------------------------
% 3.34/2.11 % (20017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.34/2.11 % (20017)Termination reason: Unknown
% 3.34/2.11 % (20017)Termination phase: Saturation
% 3.34/2.11
% 3.34/2.11 % (20017)Memory used [KB]: 5756
% 3.34/2.11 % (20017)Time elapsed: 0.043 s
% 3.34/2.11 % (20017)Instructions burned: 87 (million)
% 3.34/2.11 % (20017)------------------------------
% 3.34/2.11 % (20017)------------------------------
% 4.00/2.13 % (20019)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_19883 for (2996ds/39Mi)
% 4.00/2.13 % (20020)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_19883 for (2996ds/448Mi)
% 4.00/2.15 % (20019)Instruction limit reached!
% 4.00/2.15 % (20019)------------------------------
% 4.00/2.15 % (20019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.00/2.15 % (20019)Termination reason: Unknown
% 4.00/2.15 % (20019)Termination phase: Saturation
% 4.00/2.15
% 4.00/2.15 % (20019)Memory used [KB]: 5884
% 4.00/2.15 % (20019)Time elapsed: 0.022 s
% 4.00/2.15 % (20019)Instructions burned: 40 (million)
% 4.00/2.15 % (20019)------------------------------
% 4.00/2.15 % (20019)------------------------------
% 4.00/2.15 % (20018)Instruction limit reached!
% 4.00/2.15 % (20018)------------------------------
% 4.00/2.15 % (20018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.00/2.15 % (20018)Termination reason: Unknown
% 4.00/2.15 % (20018)Termination phase: Saturation
% 4.00/2.15
% 4.00/2.15 % (20018)Memory used [KB]: 5884
% 4.00/2.15 % (20018)Time elapsed: 0.058 s
% 4.00/2.15 % (20018)Instructions burned: 107 (million)
% 4.00/2.15 % (20018)------------------------------
% 4.00/2.15 % (20018)------------------------------
% 4.00/2.16 % (20021)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_19883 for (2996ds/46Mi)
% 4.00/2.17 % (20022)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_19883 for (2996ds/98Mi)
% 4.00/2.19 % (20021)Instruction limit reached!
% 4.00/2.19 % (20021)------------------------------
% 4.00/2.19 % (20021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.00/2.19 % (20021)Termination reason: Unknown
% 4.00/2.19 % (20021)Termination phase: Saturation
% 4.00/2.19
% 4.00/2.19 % (20021)Memory used [KB]: 5756
% 4.00/2.19 % (20021)Time elapsed: 0.027 s
% 4.00/2.19 % (20021)Instructions burned: 47 (million)
% 4.00/2.19 % (20021)------------------------------
% 4.00/2.19 % (20021)------------------------------
% 4.43/2.21 % (20023)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_19883 for (2995ds/507Mi)
% 4.43/2.22 % (20022)Instruction limit reached!
% 4.43/2.22 % (20022)------------------------------
% 4.43/2.22 % (20022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.22 % (20022)Termination reason: Unknown
% 4.43/2.22 % (20022)Termination phase: Saturation
% 4.43/2.22
% 4.43/2.22 % (20022)Memory used [KB]: 1407
% 4.43/2.22 % (20022)Time elapsed: 0.048 s
% 4.43/2.22 % (20022)Instructions burned: 98 (million)
% 4.43/2.22 % (20022)------------------------------
% 4.43/2.22 % (20022)------------------------------
% 4.43/2.22 % (20023)Refutation not found, incomplete strategy
% 4.43/2.22 % (20023)------------------------------
% 4.43/2.22 % (20023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.22 % (20023)Termination reason: Refutation not found, incomplete strategy
% 4.43/2.22
% 4.43/2.22
% 4.43/2.22 % (20023)Memory used [KB]: 5628
% 4.43/2.22 % (20023)Time elapsed: 0.016 s
% 4.43/2.22 % (20023)Instructions burned: 26 (million)
% 4.43/2.22 % (20023)------------------------------
% 4.43/2.22 % (20023)------------------------------
% 4.43/2.23 % (20000)Instruction limit reached!
% 4.43/2.23 % (20000)------------------------------
% 4.43/2.23 % (20000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.23 % (20000)Termination reason: Unknown
% 4.43/2.23 % (20000)Termination phase: Saturation
% 4.43/2.23
% 4.43/2.23 % (20000)Memory used [KB]: 6908
% 4.43/2.23 % (20000)Time elapsed: 0.366 s
% 4.43/2.23 % (20000)Instructions burned: 710 (million)
% 4.43/2.23 % (20000)------------------------------
% 4.43/2.23 % (20000)------------------------------
% 4.43/2.24 % (20025)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_19883 for (2995ds/39Mi)
% 4.43/2.24 % (20024)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_19883 for (2995ds/149Mi)
% 4.43/2.25 % (20026)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_19883 for (2995ds/6Mi)
% 4.43/2.26 % (20026)Instruction limit reached!
% 4.43/2.26 % (20026)------------------------------
% 4.43/2.26 % (20026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.26 % (20026)Termination reason: Unknown
% 4.43/2.26 % (20026)Termination phase: Saturation
% 4.43/2.26
% 4.43/2.26 % (20026)Memory used [KB]: 9978
% 4.43/2.26 % (20026)Time elapsed: 0.005 s
% 4.43/2.26 % (20026)Instructions burned: 6 (million)
% 4.43/2.26 % (20026)------------------------------
% 4.43/2.26 % (20026)------------------------------
% 4.43/2.26 % (20025)Instruction limit reached!
% 4.43/2.26 % (20025)------------------------------
% 4.43/2.26 % (20025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.26 % (20025)Termination reason: Unknown
% 4.43/2.26 % (20025)Termination phase: Saturation
% 4.43/2.26
% 4.43/2.26 % (20025)Memory used [KB]: 5628
% 4.43/2.26 % (20025)Time elapsed: 0.022 s
% 4.43/2.26 % (20025)Instructions burned: 39 (million)
% 4.43/2.26 % (20025)------------------------------
% 4.43/2.26 % (20025)------------------------------
% 4.43/2.27 % (19991)Instruction limit reached!
% 4.43/2.27 % (19991)------------------------------
% 4.43/2.27 % (19991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.27 % (19991)Termination reason: Unknown
% 4.43/2.27 % (19991)Termination phase: Saturation
% 4.43/2.27
% 4.43/2.27 % (19991)Memory used [KB]: 7164
% 4.43/2.27 % (19991)Time elapsed: 0.446 s
% 4.43/2.27 % (19991)Instructions burned: 1041 (million)
% 4.43/2.27 % (19991)------------------------------
% 4.43/2.27 % (19991)------------------------------
% 4.43/2.27 % (20028)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_19883 for (2995ds/47Mi)
% 4.43/2.28 % (20027)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_19883 for (2995ds/1087Mi)
% 4.43/2.29 % (20029)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_19883 for (2995ds/44Mi)
% 4.92/2.30 % (20028)Instruction limit reached!
% 4.92/2.30 % (20028)------------------------------
% 4.92/2.30 % (20028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.30 % (20028)Termination reason: Unknown
% 4.92/2.30 % (20028)Termination phase: Saturation
% 4.92/2.30
% 4.92/2.30 % (20028)Memory used [KB]: 5756
% 4.92/2.30 % (20028)Time elapsed: 0.027 s
% 4.92/2.30 % (20028)Instructions burned: 47 (million)
% 4.92/2.30 % (20028)------------------------------
% 4.92/2.30 % (20028)------------------------------
% 4.92/2.30 % (20007)Instruction limit reached!
% 4.92/2.30 % (20007)------------------------------
% 4.92/2.30 % (20007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.30 % (20007)Termination reason: Unknown
% 4.92/2.30 % (20007)Termination phase: Saturation
% 4.92/2.30
% 4.92/2.30 % (20007)Memory used [KB]: 6908
% 4.92/2.30 % (20007)Time elapsed: 0.405 s
% 4.92/2.30 % (20007)Instructions burned: 779 (million)
% 4.92/2.30 % (20007)------------------------------
% 4.92/2.30 % (20007)------------------------------
% 4.92/2.30 % (20024)Instruction limit reached!
% 4.92/2.30 % (20024)------------------------------
% 4.92/2.30 % (20024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.30 % (20024)Termination reason: Unknown
% 4.92/2.30 % (20024)Termination phase: Saturation
% 4.92/2.30
% 4.92/2.30 % (20024)Memory used [KB]: 6012
% 4.92/2.30 % (20024)Time elapsed: 0.085 s
% 4.92/2.30 % (20024)Instructions burned: 150 (million)
% 4.92/2.30 % (20024)------------------------------
% 4.92/2.30 % (20024)------------------------------
% 4.92/2.31 % (20029)Instruction limit reached!
% 4.92/2.31 % (20029)------------------------------
% 4.92/2.31 % (20029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.31 % (20029)Termination reason: Unknown
% 4.92/2.31 % (20029)Termination phase: Saturation
% 4.92/2.31
% 4.92/2.31 % (20029)Memory used [KB]: 1279
% 4.92/2.31 % (20029)Time elapsed: 0.024 s
% 4.92/2.31 % (20029)Instructions burned: 44 (million)
% 4.92/2.31 % (20029)------------------------------
% 4.92/2.31 % (20029)------------------------------
% 4.92/2.31 % (20030)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_19883 for (2994ds/432Mi)
% 4.92/2.32 % (20031)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_19883 for (2994ds/62Mi)
% 4.92/2.32 % (20032)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_19883 for (2994ds/31Mi)
% 4.92/2.33 % (20033)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_19883 for (2994ds/96Mi)
% 4.92/2.34 % (20032)Instruction limit reached!
% 4.92/2.34 % (20032)------------------------------
% 4.92/2.34 % (20032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.34 % (20032)Termination reason: Unknown
% 4.92/2.34 % (20032)Termination phase: Saturation
% 4.92/2.34
% 4.92/2.34 % (20032)Memory used [KB]: 5756
% 4.92/2.34 % (20032)Time elapsed: 0.018 s
% 4.92/2.34 % (20032)Instructions burned: 31 (million)
% 4.92/2.34 % (20032)------------------------------
% 4.92/2.34 % (20032)------------------------------
% 4.92/2.35 % (20027)First to succeed.
% 4.92/2.35 % (20031)Instruction limit reached!
% 4.92/2.35 % (20031)------------------------------
% 4.92/2.35 % (20031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.35 % (20031)Termination reason: Unknown
% 4.92/2.35 % (20031)Termination phase: Saturation
% 4.92/2.35
% 4.92/2.35 % (20031)Memory used [KB]: 5884
% 4.92/2.35 % (20031)Time elapsed: 0.033 s
% 4.92/2.35 % (20031)Instructions burned: 62 (million)
% 4.92/2.35 % (20031)------------------------------
% 4.92/2.35 % (20031)------------------------------
% 4.92/2.35 % (20027)Refutation found. Thanks to Tanya!
% 4.92/2.35 % SZS status Theorem for DTF2THF_19883
% 4.92/2.35 % SZS output start Proof for DTF2THF_19883
% 4.92/2.35 thf(type_def_6, type, 'type/realax/real': $tType).
% 4.92/2.35 thf(func_def_0, type, 'type/realax/real': $tType).
% 4.92/2.35 thf(func_def_1, type, 'const/trivia/I': !>[X0: $tType]:(X0 > X0)).
% 4.92/2.35 thf(func_def_2, type, 'const/sets/sup': ('type/realax/real' > $o) > 'type/realax/real').
% 4.92/2.35 thf(func_def_3, type, 'const/sets/SUBSET': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 4.92/2.35 thf(func_def_4, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 4.92/2.35 thf(func_def_5, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 4.92/2.35 thf(func_def_6, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 4.92/2.35 thf(func_def_10, type, sP0: ('type/realax/real' > $o) > $o).
% 4.92/2.35 thf(func_def_11, type, sP1: ('type/realax/real' > $o) > $o).
% 4.92/2.35 thf(func_def_12, type, sK2: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 4.92/2.35 thf(func_def_13, type, sK3: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 4.92/2.35 thf(func_def_14, type, sK4: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 4.92/2.35 thf(func_def_15, type, sK5: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 4.92/2.35 thf(func_def_16, type, sK6: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 4.92/2.35 thf(func_def_17, type, sK7: 'type/realax/real' > $o).
% 4.92/2.35 thf(func_def_18, type, sK8: 'type/realax/real' > $o).
% 4.92/2.35 thf(func_def_19, type, sK9: 'type/realax/real').
% 4.92/2.35 thf(func_def_21, type, ph11: !>[X0: $tType]:(X0)).
% 4.92/2.35 thf(func_def_23, type, sK12: 'type/realax/real').
% 4.92/2.35 thf(func_def_24, type, sK13: 'type/realax/real').
% 4.92/2.35 thf(func_def_25, type, sK14: 'type/realax/real').
% 4.92/2.35 thf(func_def_26, type, sK15: 'type/realax/real').
% 4.92/2.35 thf(f655,plain,(
% 4.92/2.35 $false),
% 4.92/2.35 inference(avatar_sat_refutation,[status(thm)],[f278,f295,f314,f491,f576,f647])).
% 4.92/2.35 thf(f647,plain,(
% 4.92/2.35 ~spl10_7 | ~spl10_23),
% 4.92/2.35 inference(avatar_contradiction_clause,[status(thm)],[f646])).
% 4.92/2.35 thf(f646,plain,(
% 4.92/2.35 $false | (~spl10_7 | ~spl10_23)),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f643])).
% 4.92/2.35 thf(f643,plain,(
% 4.92/2.35 ($false = $true) | (~spl10_7 | ~spl10_23)),
% 4.92/2.35 inference(backward_demodulation,[status(thm)],[f277,f631])).
% 4.92/2.35 thf(f631,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($false = (sK8 @ X0))) ) | ~spl10_7),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f627])).
% 4.92/2.35 thf(f627,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($false = (sK8 @ X0)) | ($true != $true)) ) | ~spl10_7),
% 4.92/2.35 inference(superposition,[status(thm)],[f522,f76])).
% 4.92/2.35 thf(f76,plain,(
% 4.92/2.35 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = $true) | ($false = (X1 @ X2))) )),
% 4.92/2.35 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 4.92/2.35 thf(f62,plain,(
% 4.92/2.35 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f24])).
% 4.92/2.35 thf(f24,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))),
% 4.92/2.35 inference(rectify,[status(thm)],[f3])).
% 4.92/2.35 thf(f3,axiom,(
% 4.92/2.35 ! [X0 : $tType,X3 : X0 > $o,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ X3) = (X3 @ X1))),
% 4.92/2.35 file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/IN_')).
% 4.92/2.35 thf(f522,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK8))) ) | ~spl10_7),
% 4.92/2.35 inference(superposition,[status(thm)],[f70,f120])).
% 4.92/2.35 thf(f120,plain,(
% 4.92/2.35 ('const/sets/EMPTY' @ 'type/realax/real' = sK8) | ~spl10_7),
% 4.92/2.35 inference(avatar_component_clause,[status(thm)],[f119])).
% 4.92/2.35 thf(f119,definition,(
% 4.92/2.35 spl10_7 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK8)),
% 4.92/2.35 introduced(definition,[new_symbols(naming,[spl10_7])],[avatar_definition])).
% 4.92/2.35 thf(f70,plain,(
% 4.92/2.35 ( ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f23])).
% 4.92/2.35 thf(f23,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)),
% 4.92/2.35 inference(flattening,[status(thm)],[f18])).
% 4.92/2.35 thf(f18,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0] : ~(('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)),
% 4.92/2.35 inference(fool_elimination,[status(thm)],[f17])).
% 4.92/2.35 thf(f17,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 4.92/2.35 inference(rectify,[status(thm)],[f4])).
% 4.92/2.35 thf(f4,axiom,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 4.92/2.35 file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/NOT_IN_EMPTY_')).
% 4.92/2.35 thf(f277,plain,(
% 4.92/2.35 ($true = (sK8 @ sK14)) | ~spl10_23),
% 4.92/2.35 inference(avatar_component_clause,[status(thm)],[f276])).
% 4.92/2.35 thf(f276,definition,(
% 4.92/2.35 spl10_23 <=> ($true = (sK8 @ sK14))),
% 4.92/2.35 introduced(definition,[new_symbols(naming,[spl10_23])],[avatar_definition])).
% 4.92/2.35 thf(f576,plain,(
% 4.92/2.35 spl10_23 | ~spl10_22),
% 4.92/2.35 inference(avatar_split_clause,[status(thm)],[f573,f273,f276])).
% 4.92/2.35 thf(f273,definition,(
% 4.92/2.35 spl10_22 <=> ((sK7 @ sK14) = $true)),
% 4.92/2.35 introduced(definition,[new_symbols(naming,[spl10_22])],[avatar_definition])).
% 4.92/2.35 thf(f573,plain,(
% 4.92/2.35 ($true = (sK8 @ sK14)) | ~spl10_22),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f572])).
% 4.92/2.35 thf(f572,plain,(
% 4.92/2.35 ($false = $true) | ($true = (sK8 @ sK14)) | ~spl10_22),
% 4.92/2.35 inference(superposition,[status(thm)],[f409,f274])).
% 4.92/2.35 thf(f274,plain,(
% 4.92/2.35 ((sK7 @ sK14) = $true) | ~spl10_22),
% 4.92/2.35 inference(avatar_component_clause,[status(thm)],[f273])).
% 4.92/2.35 thf(f409,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($false = (sK7 @ X0)) | ((sK8 @ X0) = $true)) )),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f404])).
% 4.92/2.35 thf(f404,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($false = (sK7 @ X0)) | ((sK8 @ X0) = $true) | ($true != $true)) )),
% 4.92/2.35 inference(superposition,[status(thm)],[f361,f76])).
% 4.92/2.35 thf(f361,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK7)) | ((sK8 @ X0) = $true)) )),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f348])).
% 4.92/2.35 thf(f348,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (((sK8 @ X0) = $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK7)) | ($false = $true)) )),
% 4.92/2.35 inference(superposition,[status(thm)],[f147,f77])).
% 4.92/2.35 thf(f77,plain,(
% 4.92/2.35 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = ('const/sets/IN' @ X0 @ X2 @ X1)) | ($true = (X1 @ X2))) )),
% 4.92/2.35 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 4.92/2.35 thf(f147,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK8)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK7))) )),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 4.92/2.35 thf(f146,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK7)) | ($true != $true) | ($true = ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK8))) )),
% 4.92/2.35 inference(superposition,[status(thm)],[f67,f72])).
% 4.92/2.35 thf(f72,plain,(
% 4.92/2.35 (('const/sets/SUBSET' @ 'type/realax/real' @ sK7 @ sK8) = $true)),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f55])).
% 4.92/2.35 thf(f55,plain,(
% 4.92/2.35 ('const/sets/EMPTY' @ 'type/realax/real' != sK7) & (('const/realax/real_le' @ ('const/sets/sup' @ sK7) @ ('const/sets/sup' @ sK8)) != $true) & (('const/sets/SUBSET' @ 'type/realax/real' @ sK7 @ sK8) = $true) & ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK8) != $true) | ($true = ('const/realax/real_le' @ X3 @ sK9)))),
% 4.92/2.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f27,f54,f53])).
% 4.92/2.35 thf(f53,plain,(
% 4.92/2.35 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)) != $true) & (('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1) = $true) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) | ($true = ('const/realax/real_le' @ X3 @ X2)))) => (('const/sets/EMPTY' @ 'type/realax/real' != sK7) & (('const/realax/real_le' @ ('const/sets/sup' @ sK7) @ ('const/sets/sup' @ sK8)) != $true) & (('const/sets/SUBSET' @ 'type/realax/real' @ sK7 @ sK8) = $true) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK8) != $true) | ($true = ('const/realax/real_le' @ X3 @ X2))))),
% 4.92/2.35 introduced(definition,[],[choice_axiom])).
% 4.92/2.35 thf(f54,plain,(
% 4.92/2.35 ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK8) != $true) | ($true = ('const/realax/real_le' @ X3 @ X2))) => ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK8) != $true) | ($true = ('const/realax/real_le' @ X3 @ sK9)))),
% 4.92/2.35 introduced(definition,[],[choice_axiom])).
% 4.92/2.35 thf(f27,plain,(
% 4.92/2.35 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)) != $true) & (('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1) = $true) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) | ($true = ('const/realax/real_le' @ X3 @ X2))))),
% 4.92/2.35 inference(flattening,[status(thm)],[f26])).
% 4.92/2.35 thf(f26,plain,(
% 4.92/2.35 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)) != $true) & (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) | ($true = ('const/realax/real_le' @ X3 @ X2))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1) = $true)))),
% 4.92/2.35 inference(ennf_transformation,[status(thm)],[f20])).
% 4.92/2.35 thf(f20,plain,(
% 4.92/2.35 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) => ($true = ('const/realax/real_le' @ X3 @ X2))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1) = $true)) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)) = $true))),
% 4.92/2.35 inference(fool_elimination,[status(thm)],[f19])).
% 4.92/2.35 thf(f19,plain,(
% 4.92/2.35 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) => ('const/realax/real_le' @ X3 @ X2)) & ('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)))),
% 4.92/2.35 inference(rectify,[status(thm)],[f9])).
% 4.92/2.35 thf(f9,negated_conjecture,(
% 4.92/2.35 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X1) => ('const/realax/real_le' @ X4 @ X2)) & ('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)))),
% 4.92/2.35 inference(negated_conjecture,[status(cth)],[f8])).
% 4.92/2.35 thf(f8,conjecture,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X1) => ('const/realax/real_le' @ X4 @ X2)) & ('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)))),
% 4.92/2.35 file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/REAL_SUP_LE_SUBSET_')).
% 4.92/2.35 thf(f67,plain,(
% 4.92/2.35 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/IN' @ X0 @ X3 @ X1) != $true) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f48])).
% 4.92/2.35 thf(f48,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X2) = $true) | (('const/sets/IN' @ X0 @ X3 @ X1) != $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ((('const/sets/IN' @ X0 @ (sK5 @ X0 @ X2 @ X1) @ X2) != $true) & (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X2 @ X1) @ X1) = $true))))),
% 4.92/2.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f46,f47])).
% 4.92/2.35 thf(f47,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X2) != $true) & (('const/sets/IN' @ X0 @ X4 @ X1) = $true)) => ((('const/sets/IN' @ X0 @ (sK5 @ X0 @ X2 @ X1) @ X2) != $true) & (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X2 @ X1) @ X1) = $true)))),
% 4.92/2.35 introduced(definition,[],[choice_axiom])).
% 4.92/2.35 thf(f46,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X2) = $true) | (('const/sets/IN' @ X0 @ X3 @ X1) != $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X2) != $true) & (('const/sets/IN' @ X0 @ X4 @ X1) = $true))))),
% 4.92/2.35 inference(rectify,[status(thm)],[f45])).
% 4.92/2.35 thf(f45,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X2) = $true) | (('const/sets/IN' @ X0 @ X3 @ X1) != $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ? [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X2) != $true) & (('const/sets/IN' @ X0 @ X3 @ X1) = $true))))),
% 4.92/2.35 inference(nnf_transformation,[status(thm)],[f25])).
% 4.92/2.35 thf(f25,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X2) = $true) | (('const/sets/IN' @ X0 @ X3 @ X1) != $true)) <=> (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true))),
% 4.92/2.35 inference(ennf_transformation,[status(thm)],[f12])).
% 4.92/2.35 thf(f12,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) <=> ! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1) = $true) => (('const/sets/IN' @ X0 @ X3 @ X2) = $true)))),
% 4.92/2.35 inference(fool_elimination,[status(thm)],[f11])).
% 4.92/2.35 thf(f11,plain,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ X2) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 4.92/2.35 inference(rectify,[status(thm)],[f6])).
% 4.92/2.35 thf(f6,axiom,(
% 4.92/2.35 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ X2) = ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/sets/IN' @ X0 @ X4 @ X2)))),
% 4.92/2.35 file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/SUBSET_')).
% 4.92/2.35 thf(f491,plain,(
% 4.92/2.35 ~spl10_5),
% 4.92/2.35 inference(avatar_contradiction_clause,[status(thm)],[f490])).
% 4.92/2.35 thf(f490,plain,(
% 4.92/2.35 $false | ~spl10_5),
% 4.92/2.35 inference(subsumption_resolution,[status(thm)],[f489,f74])).
% 4.92/2.35 thf(f74,plain,(
% 4.92/2.35 ('const/sets/EMPTY' @ 'type/realax/real' != sK7)),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f55])).
% 4.92/2.35 thf(f489,plain,(
% 4.92/2.35 ('const/sets/EMPTY' @ 'type/realax/real' = sK7) | ~spl10_5),
% 4.92/2.35 inference(subsumption_resolution,[status(thm)],[f487,f73])).
% 4.92/2.35 thf(f73,plain,(
% 4.92/2.35 (('const/realax/real_le' @ ('const/sets/sup' @ sK7) @ ('const/sets/sup' @ sK8)) != $true)),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f55])).
% 4.92/2.35 thf(f487,plain,(
% 4.92/2.35 (('const/realax/real_le' @ ('const/sets/sup' @ sK7) @ ('const/sets/sup' @ sK8)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK7) | ~spl10_5),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f486])).
% 4.92/2.35 thf(f486,plain,(
% 4.92/2.35 ('const/sets/EMPTY' @ 'type/realax/real' = sK7) | (('const/realax/real_le' @ ('const/sets/sup' @ sK7) @ ('const/sets/sup' @ sK8)) = $true) | ($true != $true) | ~spl10_5),
% 4.92/2.35 inference(duplicate_literal_removal,[status(thm)],[f483])).
% 4.92/2.35 thf(f483,plain,(
% 4.92/2.35 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK7) | (('const/realax/real_le' @ ('const/sets/sup' @ sK7) @ ('const/sets/sup' @ sK8)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK7) | (('const/realax/real_le' @ ('const/sets/sup' @ sK7) @ ('const/sets/sup' @ sK8)) = $true) | ~spl10_5),
% 4.92/2.35 inference(superposition,[status(thm)],[f460,f63])).
% 4.92/2.35 thf(f63,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f44])).
% 4.92/2.35 thf(f44,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true))),
% 4.92/2.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f29,f43])).
% 4.92/2.35 thf(f43,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) => ((('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true)))),
% 4.92/2.35 introduced(definition,[],[choice_axiom])).
% 4.92/2.35 thf(f29,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true))),
% 4.92/2.35 inference(flattening,[status(thm)],[f28])).
% 4.92/2.35 thf(f28,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) | (? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 4.92/2.35 inference(ennf_transformation,[status(thm)],[f22])).
% 4.92/2.35 thf(f22,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X2 @ X1) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true))),
% 4.92/2.35 inference(fool_elimination,[status(thm)],[f21])).
% 4.92/2.35 thf(f21,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))),
% 4.92/2.35 inference(rectify,[status(thm)],[f1])).
% 4.92/2.35 thf(f1,axiom,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))),
% 4.92/2.35 file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/REAL_SUP_LE_')).
% 4.92/2.35 thf(f460,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o] : (($true != ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ ('const/sets/sup' @ sK8) @ X0) @ sK7)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ sK8))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) ) | ~spl10_5),
% 4.92/2.35 inference(subsumption_resolution,[status(thm)],[f456,f125])).
% 4.92/2.35 thf(f125,plain,(
% 4.92/2.35 ((sP1 @ sK8) = $true) | ~spl10_5),
% 4.92/2.35 inference(avatar_component_clause,[status(thm)],[f108])).
% 4.92/2.35 thf(f108,definition,(
% 4.92/2.35 spl10_5 <=> ((sP1 @ sK8) = $true)),
% 4.92/2.35 introduced(definition,[new_symbols(naming,[spl10_5])],[avatar_definition])).
% 4.92/2.35 thf(f456,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o] : (($true != ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ ('const/sets/sup' @ sK8) @ X0) @ sK7)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ sK8))) | ((sP1 @ sK8) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f452])).
% 4.92/2.35 thf(f452,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o] : (($true != $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ ('const/sets/sup' @ sK8) @ X0) @ sK7)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ sK8))) | ((sP1 @ sK8) != $true)) )),
% 4.92/2.35 inference(superposition,[status(thm)],[f129,f147])).
% 4.92/2.35 thf(f129,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : (($true != ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ ('const/sets/sup' @ X0) @ X1) @ X0)) | ($true != (sP1 @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ ('const/sets/sup' @ X0)) = $true)) )),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 4.92/2.35 thf(f128,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : (($true != ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ ('const/sets/sup' @ X0) @ X1) @ X0)) | (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ ('const/sets/sup' @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true != $true) | ($true != (sP1 @ X0))) )),
% 4.92/2.35 inference(superposition,[status(thm)],[f64,f56])).
% 4.92/2.35 thf(f56,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | ($true != (sP1 @ X0))) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f36])).
% 4.92/2.35 thf(f36,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : ((($true = (sP0 @ X0)) & ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true))) | ($true != (sP1 @ X0)))),
% 4.92/2.35 inference(rectify,[status(thm)],[f35])).
% 4.92/2.35 thf(f35,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : ((($true = (sP0 @ X0)) & ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))))) | ($true != (sP1 @ X0)))),
% 4.92/2.35 inference(nnf_transformation,[status(thm)],[f33])).
% 4.92/2.35 thf(f33,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : ((($true = (sP0 @ X0)) & ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))))) | ~($true = (sP1 @ X0)))),
% 4.92/2.35 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 4.92/2.35 thf(f64,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true)) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f44])).
% 4.92/2.35 thf(f314,plain,(
% 4.92/2.35 spl10_7 | spl10_5 | ~spl10_8),
% 4.92/2.35 inference(avatar_split_clause,[status(thm)],[f311,f122,f108,f119])).
% 4.92/2.35 thf(f122,definition,(
% 4.92/2.35 spl10_8 <=> ! [X0 : 'type/realax/real'] : ($true = ('const/realax/real_le' @ (sK3 @ X0 @ sK8) @ sK9))),
% 4.92/2.35 introduced(definition,[new_symbols(naming,[spl10_8])],[avatar_definition])).
% 4.92/2.35 thf(f311,plain,(
% 4.92/2.35 ('const/sets/EMPTY' @ 'type/realax/real' = sK8) | ((sP1 @ sK8) = $true) | ~spl10_8),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f310])).
% 4.92/2.35 thf(f310,plain,(
% 4.92/2.35 ((sP1 @ sK8) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK8) | ~spl10_8),
% 4.92/2.35 inference(superposition,[status(thm)],[f60,f123])).
% 4.92/2.35 thf(f123,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK3 @ X0 @ sK8) @ sK9))) ) | ~spl10_8),
% 4.92/2.35 inference(avatar_component_clause,[status(thm)],[f122])).
% 4.92/2.35 thf(f60,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK3 @ X1 @ X0) @ X1)) | ($true = (sP1 @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f42])).
% 4.92/2.35 thf(f42,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ (sK3 @ X1 @ X0) @ X1))) | ($true = (sP1 @ X0)))),
% 4.92/2.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f34,f41])).
% 4.92/2.35 thf(f41,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X1) != $true)) => (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ (sK3 @ X1 @ X0) @ X1))))),
% 4.92/2.35 introduced(definition,[],[choice_axiom])).
% 4.92/2.35 thf(f34,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X1) != $true)) | ($true = (sP1 @ X0)))),
% 4.92/2.35 inference(definition_folding,[status(thm)],[f31,f33,f32])).
% 4.92/2.35 thf(f32,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : (! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)) | ? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X5 @ X4) != $true))) | ~($true = (sP0 @ X0)))),
% 4.92/2.35 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 4.92/2.35 thf(f31,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X1) != $true)) | (! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)) | ? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X5 @ X4) != $true))) & ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))))))),
% 4.92/2.35 inference(flattening,[status(thm)],[f30])).
% 4.92/2.35 thf(f30,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : ((! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)) | ? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X5 @ X4) != $true))) & ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X1) != $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 4.92/2.35 inference(ennf_transformation,[status(thm)],[f16])).
% 4.92/2.35 thf(f16,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X2 @ X1) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) => ($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) => (('const/realax/real_le' @ X5 @ X4) = $true)) => ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)))))),
% 4.92/2.35 inference(fool_elimination,[status(thm)],[f15])).
% 4.92/2.35 thf(f15,plain,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => (! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X5 @ X4)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4))))),
% 4.92/2.35 inference(rectify,[status(thm)],[f7])).
% 4.92/2.35 thf(f7,axiom,(
% 4.92/2.35 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) & ! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))))),
% 4.92/2.35 file('/export/starexec/sandbox/tmp/tmp.gKRN8dUoXe/DTF2THF_19883.p','thm/sets/SUP_')).
% 4.92/2.35 thf(f295,plain,(
% 4.92/2.35 spl10_7 | spl10_8 | spl10_5),
% 4.92/2.35 inference(avatar_split_clause,[status(thm)],[f294,f108,f122,f119])).
% 4.92/2.35 thf(f294,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK8) | ($true = ('const/realax/real_le' @ (sK3 @ X0 @ sK8) @ sK9)) | ((sP1 @ sK8) = $true)) )),
% 4.92/2.35 inference(trivial_inequality_removal,[status(thm)],[f291])).
% 4.92/2.35 thf(f291,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((sP1 @ sK8) = $true) | ($true = ('const/realax/real_le' @ (sK3 @ X0 @ sK8) @ sK9)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK8)) )),
% 4.92/2.35 inference(superposition,[status(thm)],[f71,f61])).
% 4.92/2.35 thf(f61,plain,(
% 4.92/2.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X1 @ X0) @ X0)) | ($true = (sP1 @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f42])).
% 4.92/2.35 thf(f71,plain,(
% 4.92/2.35 ( ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK8) != $true) | ($true = ('const/realax/real_le' @ X3 @ sK9))) )),
% 4.92/2.35 inference(cnf_transformation,[status(thm)],[f55])).
% 4.92/2.35 thf(f278,plain,(
% 4.92/2.35 spl10_22 | spl10_23 | ~spl10_7),
% 4.92/2.35 inference(avatar_split_clause,[status(thm)],[f270,f119,f276,f273])).
% 4.92/2.35 thf(f270,plain,(
% 4.92/2.35 ($true = (sK8 @ sK14)) | ((sK7 @ sK14) = $true) | ~spl10_7),
% 4.92/2.35 inference(binary_proxy_clausification,[status(thm)],[f269])).
% 4.92/2.35 thf(f269,plain,(
% 4.92/2.35 ((sK7 @ sK14) != (sK8 @ sK14)) | ~spl10_7),
% 4.92/2.35 inference(negative_extensionality,[status(thm)],[f265])).
% 4.92/2.35 thf(f265,plain,(
% 4.92/2.35 (sK7 != sK8) | ~spl10_7),
% 4.92/2.35 inference(superposition,[status(thm)],[f74,f120])).
% 4.92/2.35 % SZS output end Proof for DTF2THF_19883
% 4.92/2.35 % (20027)------------------------------
% 4.92/2.35 % (20027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.35 % (20027)Termination reason: Refutation
% 4.92/2.35
% 4.92/2.35 % (20027)Memory used [KB]: 6012
% 4.92/2.35 % (20027)Time elapsed: 0.075 s
% 4.92/2.35 % (20027)Instructions burned: 134 (million)
% 4.92/2.35 % (20027)------------------------------
% 4.92/2.35 % (20027)------------------------------
% 4.92/2.35 % (19979)Success in time 0.556 s
%------------------------------------------------------------------------------