%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA087^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:38:50 AM UTC 2026
% Result : Theorem 1.69s 1.40s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 114 ( 13 unt; 0 typ; 10 def)
% Number of atoms : 918 ( 253 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 1157 ( 158 ~; 149 |; 58 &; 742 @)
% ( 12 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 22 con; 0-3 aty)
% Number of variables : 187 ( 0 ^; 157 !; 30 ?; 187 :)
% 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/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
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,
sK0: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_11,type,
sK1: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_12,type,
sK2: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_13,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK5: 'type/realax/real' > $o ).
thf(func_def_16,type,
sK6: 'type/realax/real' > $o ).
thf(func_def_17,type,
sK7: 'type/realax/real' ).
thf(func_def_19,type,
ph9:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK10: 'type/realax/real' ).
thf(func_def_22,type,
sK11: 'type/realax/real' ).
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(func_def_27,type,
sK16: 'type/realax/real' ).
thf(func_def_28,type,
sK17: 'type/realax/real' ).
thf(func_def_29,type,
sK18: 'type/realax/real' ).
thf(f711,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f132,f163,f172,f256,f362,f560,f591,f599,f669,f701,f707]) ).
thf(f707,plain,
~ spl8_29,
inference(avatar_contradiction_clause,[status(thm)],[f706]) ).
thf(f706,plain,
( $false
| ~ spl8_29 ),
inference(trivial_inequality_removal,[status(thm)],[f703]) ).
thf(f703,plain,
( ( sK6 != sK6 )
| ~ spl8_29 ),
inference(superposition,[status(thm)],[f66,f251]) ).
thf(f251,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK6 ) )
| ~ spl8_29 ),
inference(avatar_component_clause,[status(thm)],[f249]) ).
thf(f249,definition,
( spl8_29
<=> ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_29])],[avatar_definition]) ).
thf(f66,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK6 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true
= ( 'const/sets/SUBSET' @ 'type/realax/real' @ sK6 @ sK5 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK6 ) )
& ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK5 ) )
| ( $true
= ( 'const/realax/real_le' @ sK7 @ X3 ) ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f26,f46,f45]) ).
thf(f45,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ ( 'const/sets/inf' @ X1 ) )
!= $true ) )
=> ( ( $true
= ( 'const/sets/SUBSET' @ 'type/realax/real' @ sK6 @ sK5 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK6 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK5 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f46,plain,
( ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK5 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) )
=> ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK5 ) )
| ( $true
= ( 'const/realax/real_le' @ sK7 @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ ( 'const/sets/inf' @ X1 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ ( 'const/sets/inf' @ X1 ) )
!= $true )
& ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0 )
= $true )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0 )
= $true )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ ( 'const/sets/inf' @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ ( 'const/sets/inf' @ X1 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ? [X2: 'type/realax/real'] :
! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X4 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ ( 'const/sets/inf' @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ? [X2: 'type/realax/real'] :
! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X4 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ ( 'const/sets/inf' @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/REAL_LE_INF_SUBSET_') ).
thf(f701,plain,
~ spl8_61,
inference(avatar_contradiction_clause,[status(thm)],[f700]) ).
thf(f700,plain,
( $false
| ~ spl8_61 ),
inference(trivial_inequality_removal,[status(thm)],[f699]) ).
thf(f699,plain,
( ( $true != $true )
| ~ spl8_61 ),
inference(superposition,[status(thm)],[f64,f644]) ).
thf(f644,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
= $true )
| ~ spl8_61 ),
inference(avatar_component_clause,[status(thm)],[f642]) ).
thf(f642,definition,
( spl8_61
<=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_61])],[avatar_definition]) ).
thf(f64,plain,
( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f669,plain,
( spl8_61
| spl8_29
| ~ spl8_11
| ~ spl8_28 ),
inference(avatar_split_clause,[status(thm)],[f667,f245,f130,f249,f642]) ).
thf(f130,definition,
( spl8_11
<=> ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ X1 ) )
| ( $true
!= ( sK5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_11])],[avatar_definition]) ).
thf(f245,definition,
( spl8_28
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( sK5 @ ( sK2 @ X0 @ sK6 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK6 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_28])],[avatar_definition]) ).
thf(f667,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK6 ) )
| ~ spl8_11
| ~ spl8_28 ),
inference(trivial_inequality_removal,[status(thm)],[f666]) ).
thf(f666,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK6 ) )
| ~ spl8_11
| ~ spl8_28 ),
inference(duplicate_literal_removal,[status(thm)],[f664]) ).
thf(f664,plain,
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK6 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ sK6 ) )
= $true )
| ~ spl8_11
| ~ spl8_28 ),
inference(superposition,[status(thm)],[f637,f246]) ).
thf(f246,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( sK5 @ ( sK2 @ X0 @ sK6 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK6 ) ) ) )
| ~ spl8_28 ),
inference(avatar_component_clause,[status(thm)],[f245]) ).
thf(f637,plain,
( ! [X0: 'type/realax/real' > $o] :
( ( ( sK5 @ ( sK2 @ ( 'const/sets/inf' @ sK5 ) @ X0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) )
| ~ spl8_11 ),
inference(trivial_inequality_removal,[status(thm)],[f632]) ).
thf(f632,plain,
( ! [X0: 'type/realax/real' > $o] :
( ( ( sK5 @ ( sK2 @ ( 'const/sets/inf' @ sK5 ) @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl8_11 ),
inference(superposition,[status(thm)],[f56,f131]) ).
thf(f131,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ X1 ) )
| ( $true
!= ( sK5 @ X1 ) ) )
| ~ spl8_11 ),
inference(avatar_component_clause,[status(thm)],[f130]) ).
thf(f56,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK2 @ X1 @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( sK2 @ X1 @ X0 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f31,f35]) ).
thf(f35,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' @ X1 @ X2 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( sK2 @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $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' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
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' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/REAL_LE_INF_') ).
thf(f599,plain,
( ~ spl8_6
| ~ spl8_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f598]) ).
thf(f598,plain,
( $false
| ~ spl8_6
| ~ spl8_14 ),
inference(trivial_inequality_removal,[status(thm)],[f597]) ).
thf(f597,plain,
( ( $true != $true )
| ~ spl8_6
| ~ spl8_14 ),
inference(superposition,[status(thm)],[f402,f162]) ).
thf(f162,plain,
( ( ( sK5 @ sK11 )
= $true )
| ~ spl8_14 ),
inference(avatar_component_clause,[status(thm)],[f160]) ).
thf(f160,definition,
( spl8_14
<=> ( ( sK5 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_14])],[avatar_definition]) ).
thf(f402,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( sK5 @ X0 ) )
| ~ spl8_6 ),
inference(superposition,[status(thm)],[f371,f60]) ).
thf(f60,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( X1 @ X2 )
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( X1 @ X2 )
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ),
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/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/IN_') ).
thf(f371,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK5 ) )
| ~ spl8_6 ),
inference(superposition,[status(thm)],[f55,f112]) ).
thf(f112,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK5 ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[status(thm)],[f110]) ).
thf(f110,definition,
( spl8_6
<=> ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f55,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,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/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/NOT_IN_EMPTY_') ).
thf(f591,plain,
( ~ spl8_13
| ~ spl8_16 ),
inference(avatar_contradiction_clause,[status(thm)],[f590]) ).
thf(f590,plain,
( $false
| ~ spl8_13
| ~ spl8_16 ),
inference(trivial_inequality_removal,[status(thm)],[f586]) ).
thf(f586,plain,
( ( $true = $false )
| ~ spl8_13
| ~ spl8_16 ),
inference(superposition,[status(thm)],[f171,f158]) ).
thf(f158,plain,
( ( ( sK6 @ sK11 )
= $true )
| ~ spl8_13 ),
inference(avatar_component_clause,[status(thm)],[f156]) ).
thf(f156,definition,
( spl8_13
<=> ( ( sK6 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_13])],[avatar_definition]) ).
thf(f171,plain,
( ( ( sK6 @ sK11 )
= $false )
| ~ spl8_16 ),
inference(avatar_component_clause,[status(thm)],[f169]) ).
thf(f169,definition,
( spl8_16
<=> ( ( sK6 @ sK11 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl8_16])],[avatar_definition]) ).
thf(f560,plain,
( ~ spl8_13
| ~ spl8_15 ),
inference(avatar_split_clause,[status(thm)],[f556,f165,f156]) ).
thf(f165,definition,
( spl8_15
<=> ( ( sK5 @ sK11 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl8_15])],[avatar_definition]) ).
thf(f556,plain,
( ( ( sK6 @ sK11 )
!= $true )
| ~ spl8_15 ),
inference(trivial_inequality_removal,[status(thm)],[f553]) ).
thf(f553,plain,
( ( ( sK6 @ sK11 )
!= $true )
| ( $true = $false )
| ~ spl8_15 ),
inference(superposition,[status(thm)],[f167,f205]) ).
thf(f205,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( sK5 @ X0 ) )
| ( $true
!= ( sK6 @ X0 ) ) ),
inference(superposition,[status(thm)],[f92,f60]) ).
thf(f92,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK6 ) )
| ( $true
= ( sK5 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f91,f60]) ).
thf(f91,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK6 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK6 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK5 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f63,f67]) ).
thf(f67,plain,
( $true
= ( 'const/sets/SUBSET' @ 'type/realax/real' @ sK6 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f63,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X2 @ X1 ) @ X1 )
= $true )
& ( $true
!= ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X2 @ X1 ) @ X2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f42,f43]) ).
thf(f43,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X2 @ X1 ) @ X1 )
= $true )
& ( $true
!= ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X2 @ X1 ) @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ? [X3: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ! [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $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] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X4 @ X2 ) )
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/SUBSET_') ).
thf(f167,plain,
( ( ( sK5 @ sK11 )
= $false )
| ~ spl8_15 ),
inference(avatar_component_clause,[status(thm)],[f165]) ).
thf(f362,plain,
( spl8_6
| spl8_11
| ~ spl8_8 ),
inference(avatar_split_clause,[status(thm)],[f334,f118,f130,f110]) ).
thf(f118,definition,
( spl8_8
<=> ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK7 @ ( sK0 @ X0 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition]) ).
thf(f334,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( sK5 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK5 ) ) )
| ~ spl8_8 ),
inference(forward_demodulation,[status(thm)],[f333,f60]) ).
thf(f333,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK5 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK5 ) ) )
| ~ spl8_8 ),
inference(trivial_inequality_removal,[status(thm)],[f332]) ).
thf(f332,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK5 ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK5 ) ) )
| ~ spl8_8 ),
inference(superposition,[status(thm)],[f49,f119]) ).
thf(f119,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK7 @ ( sK0 @ X0 @ sK5 ) ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[status(thm)],[f118]) ).
thf(f49,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X5: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X3 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ ( sK1 @ X3 @ X0 ) ) ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) ) )
& ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f28,f33,f32]) ).
thf(f32,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' @ X1 @ X2 )
!= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
! [X0: 'type/realax/real' > $o,X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
=> ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X3 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ ( sK1 @ X3 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,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' @ X1 @ X2 )
!= $true ) )
| ( ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) ) )
& ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) ) )
& ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,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' @ X1 @ X2 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) )
& ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
=> ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,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' @ X1 @ X2 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ X4 ) )
=> ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) )
& ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) ) ),
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' @ X1 @ X2 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/INF_') ).
thf(f256,plain,
( spl8_28
| spl8_29 ),
inference(avatar_split_clause,[status(thm)],[f206,f249,f245]) ).
thf(f206,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( sK5 @ ( sK2 @ X0 @ sK6 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK6 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK6 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f199]) ).
thf(f199,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( sK5 @ ( sK2 @ X0 @ sK6 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK6 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK6 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f92,f57]) ).
thf(f57,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X1 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f172,plain,
( spl8_15
| spl8_16
| ~ spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f154,f110,f169,f165]) ).
thf(f154,plain,
( ( ( sK5 @ sK11 )
= $false )
| ( ( sK6 @ sK11 )
= $false )
| ~ spl8_6 ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f152,plain,
( ( ( sK6 @ sK11 )
!= ( sK5 @ sK11 ) )
| ~ spl8_6 ),
inference(negative_extensionality,[status(thm)],[f138]) ).
thf(f138,plain,
( ( sK6 != sK5 )
| ~ spl8_6 ),
inference(superposition,[status(thm)],[f66,f112]) ).
thf(f163,plain,
( spl8_13
| spl8_14
| ~ spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f153,f110,f160,f156]) ).
thf(f153,plain,
( ( ( sK6 @ sK11 )
= $true )
| ( ( sK5 @ sK11 )
= $true )
| ~ spl8_6 ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f132,plain,
( spl8_11
| spl8_8
| spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f128,f110,f118,f130]) ).
thf(f128,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK5 ) )
| ( $true
= ( 'const/realax/real_le' @ sK7 @ ( sK0 @ X0 @ sK5 ) ) )
| ( $true
!= ( sK5 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f102,f60]) ).
thf(f102,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK7 @ ( sK0 @ X0 @ sK5 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK5 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK5 )
!= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK5 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK5 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK7 @ ( sK0 @ X0 @ sK5 ) ) ) ),
inference(superposition,[status(thm)],[f65,f52]) ).
thf(f52,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f65,plain,
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK5 ) )
| ( $true
= ( 'const/realax/real_le' @ sK7 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA087^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 03:50:36 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : ANA087^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.45 % Domain : Analysis
% 0.30/0.45 % Problem : REAL_LE_INF_SUBSET
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Kal16]
% 0.30/0.45 % Names : REAL_LE_INF_SUBSET_.p [Kal16]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.30/0.45 % Syntax : Number of formulae : 15 ( 4 unt; 7 typ; 0 def)
% 0.30/0.45 % Number of atoms : 34 ( 9 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 8 ( 4 avg)
% 0.30/0.45 % Number of connectives : 86 ( 4 ~; 0 |; 5 &; 67 @)
% 0.30/0.45 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 12 ( 7 avg)
% 0.30/0.45 % Number of types : 2 ( 1 usr)
% 0.30/0.45 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.30/0.45 % Number of variables : 32 ( 0 ^; 26 !; 2 ?; 32 :)
% 0.30/0.45 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.45 % SPC : TH1_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : Exported from core HOL Light.
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf('thf_type_type/realax/real',type,
% 0.30/0.45 'type/realax/real': $tType ).
% 0.30/0.45
% 0.30/0.45 thf('thf_const_const/trivia/I',type,
% 0.30/0.45 'const/trivia/I':
% 0.30/0.45 !>[A: $tType] : ( A > A ) ).
% 0.30/0.45
% 0.30/0.45 thf('thf_const_const/sets/SUBSET',type,
% 0.30/0.45 'const/sets/SUBSET':
% 0.30/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf('thf_const_const/sets/inf',type,
% 0.30/0.45 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.30/0.45
% 0.30/0.45 thf('thf_const_const/sets/IN',type,
% 0.30/0.45 'const/sets/IN':
% 0.30/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf('thf_const_const/sets/EMPTY',type,
% 0.30/0.45 'const/sets/EMPTY':
% 0.30/0.45 !>[A: $tType] : ( A > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf('thf_const_const/realax/real_le',type,
% 0.30/0.45 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.30/0.45
% 0.30/0.45 thf('thm/sets/REAL_LE_INF_',axiom,
% 0.30/0.45 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.30/0.45 ( ( ( A
% 0.30/0.45 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.30/0.45 & ! [A1: 'type/realax/real'] :
% 0.30/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.30/0.45 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 0.30/0.45 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf('thm/trivia/I_THM_',axiom,
% 0.30/0.45 ! [A: $tType,A0: A] :
% 0.30/0.45 ( ( 'const/trivia/I' @ A @ A0 )
% 0.30/0.45 = A0 ) ).
% 0.30/0.45
% 0.30/0.45 thf('thm/sets/IN_',axiom,
% 0.30/0.45 ! [A: $tType,P: A > $o,A0: A] :
% 0.30/0.45 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.30/0.45 = ( P @ A0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 0.30/0.45 ! [A: $tType,A0: A] :
% 0.30/0.45 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 0.30/0.45
% 0.30/0.45 thf('thm/sets/EXTENSION_',axiom,
% 0.30/0.45 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.30/0.45 ( ( A0 = A1 )
% 0.30/0.45 = ( ! [A2: A] :
% 0.30/0.45 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.30/0.45 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf('thm/sets/SUBSET_',axiom,
% 0.30/0.45 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.30/0.45 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 0.30/0.45 = ( ! [A2: A] :
% 0.30/0.45 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.30/0.45 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf('thm/sets/INF_',axiom,
% 0.30/0.45 ! [A: 'type/realax/real' > $o] :
% 0.30/0.45 ( ( ( A
% 0.30/0.45 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.30/0.45 & ? [A0: 'type/realax/real'] :
% 0.30/0.45 ! [A1: 'type/realax/real'] :
% 0.30/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.30/0.45 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 0.30/0.45 => ( ! [A0: 'type/realax/real'] :
% 0.30/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.30/0.45 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 0.30/0.45 & ! [A0: 'type/realax/real'] :
% 0.30/0.45 ( ! [A1: 'type/realax/real'] :
% 0.30/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.30/0.45 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.30/0.45 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf('thm/sets/REAL_LE_INF_SUBSET_',conjecture,
% 0.30/0.45 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real' > $o] :
% 0.30/0.45 ( ( ( A0
% 0.30/0.45 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.30/0.45 & ( 'const/sets/SUBSET' @ 'type/realax/real' @ A0 @ A )
% 0.30/0.45 & ? [A1: 'type/realax/real'] :
% 0.30/0.45 ! [A2: 'type/realax/real'] :
% 0.30/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 0.30/0.45 => ( 'const/realax/real_le' @ A1 @ A2 ) ) )
% 0.30/0.45 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ ( 'const/sets/inf' @ A0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.51/1.27 ---- Embedded in THF ---
% 1.51/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.27 %%% Generated on Tue Feb 24 03:50:36 EST 2026
% 1.51/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.27 %%% Logic specification used:
% 1.51/1.27 %%% thf(spec, logic, $$dhol).
% 1.51/1.27
% 1.51/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2DTF9440.p
% See solution above
% 1.51/1.27 ------------------------
% 1.51/1.28 ---- Cleaned THF ---
% 1.51/1.28 thf('thf_type_type/realax/real',type,
% 1.51/1.28 'type/realax/real': $tType ).
% 1.51/1.28
% 1.51/1.28 thf('thf_const_const/trivia/I',type,
% 1.51/1.28 'const/trivia/I':
% 1.51/1.28 !>[A: $tType] : ( A > A ) ).
% 1.51/1.28
% 1.51/1.28 thf('thf_const_const/sets/SUBSET',type,
% 1.51/1.28 'const/sets/SUBSET':
% 1.51/1.28 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.51/1.28
% 1.51/1.28 thf('thf_const_const/sets/inf',type,
% 1.51/1.28 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.51/1.28
% 1.51/1.28 thf('thf_const_const/sets/IN',type,
% 1.51/1.28 'const/sets/IN':
% 1.51/1.28 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.51/1.28
% 1.51/1.28 thf('thf_const_const/sets/EMPTY',type,
% 1.51/1.28 'const/sets/EMPTY':
% 1.51/1.28 !>[A: $tType] : ( A > $o ) ).
% 1.51/1.28
% 1.51/1.28 thf('thf_const_const/realax/real_le',type,
% 1.51/1.28 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.51/1.28
% 1.51/1.28 thf('thm/sets/REAL_LE_INF_',axiom,
% 1.51/1.28 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.51/1.28 ( ( ( A
% 1.51/1.28 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.51/1.28 & ! [A1: 'type/realax/real'] :
% 1.51/1.28 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.51/1.28 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 1.51/1.28 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf('thm/trivia/I_THM_',axiom,
% 1.51/1.28 ! [A: $tType,A0: A] :
% 1.51/1.28 ( ( 'const/trivia/I' @ A @ A0 )
% 1.51/1.28 = A0 ) ).
% 1.51/1.28
% 1.51/1.28 thf('thm/sets/IN_',axiom,
% 1.51/1.28 ! [A: $tType,P: A > $o,A0: A] :
% 1.51/1.28 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 1.51/1.28 = ( P @ A0 ) ) ).
% 1.51/1.28
% 1.51/1.28 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 1.51/1.28 ! [A: $tType,A0: A] :
% 1.51/1.28 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 1.51/1.28
% 1.51/1.28 thf('thm/sets/EXTENSION_',axiom,
% 1.51/1.28 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.51/1.28 ( ( A0 = A1 )
% 1.51/1.28 = ( ! [A2: A] :
% 1.51/1.28 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.51/1.28 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf('thm/sets/SUBSET_',axiom,
% 1.51/1.28 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.51/1.28 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 1.51/1.28 = ( ! [A2: A] :
% 1.51/1.28 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.51/1.28 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf('thm/sets/INF_',axiom,
% 1.51/1.28 ! [A: 'type/realax/real' > $o] :
% 1.51/1.28 ( ( ( A
% 1.51/1.28 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.51/1.28 & ? [A0: 'type/realax/real'] :
% 1.51/1.28 ! [A1: 'type/realax/real'] :
% 1.51/1.28 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.51/1.28 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 1.51/1.28 => ( ! [A0: 'type/realax/real'] :
% 1.51/1.28 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.51/1.28 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 1.51/1.28 & ! [A0: 'type/realax/real'] :
% 1.51/1.28 ( ! [A1: 'type/realax/real'] :
% 1.51/1.28 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.51/1.28 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.51/1.28 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf('thm/sets/REAL_LE_INF_SUBSET_',conjecture,
% 1.51/1.28 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real' > $o] :
% 1.51/1.28 ( ( ( A0
% 1.51/1.28 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.51/1.28 & ( 'const/sets/SUBSET' @ 'type/realax/real' @ A0 @ A )
% 1.51/1.28 & ? [A1: 'type/realax/real'] :
% 1.51/1.28 ! [A2: 'type/realax/real'] :
% 1.51/1.28 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 1.51/1.28 => ( 'const/realax/real_le' @ A1 @ A2 ) ) )
% 1.51/1.28 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ ( 'const/sets/inf' @ A0 ) ) ) ).
% 1.51/1.28 ------------------------
% 1.69/1.30 % (9772)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_9440 for (2999ds/275Mi)
% 1.69/1.30 % (9771)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_9440 for (2999ds/2Mi)
% 1.69/1.30 % (9771)Instruction limit reached!
% 1.69/1.30 % (9771)------------------------------
% 1.69/1.30 % (9771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (9771)Termination reason: Unknown
% 1.69/1.30 % (9771)Termination phase: Property scanning
% 1.69/1.30
% 1.69/1.30 % (9771)Memory used [KB]: 1023
% 1.69/1.30 % (9771)Time elapsed: 0.002 s
% 1.69/1.30 % (9771)Instructions burned: 3 (million)
% 1.69/1.30 % (9771)------------------------------
% 1.69/1.30 % (9771)------------------------------
% 1.69/1.30 % (9767)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/183Mi)
% 1.69/1.30 % (9768)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_9440 for (2999ds/4Mi)
% 1.69/1.31 % (9769)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_9440 for (2999ds/27Mi)
% 1.69/1.31 % (9770)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/2Mi)
% 1.69/1.31 % (9773)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/18Mi)
% 1.69/1.31 % (9770)Instruction limit reached!
% 1.69/1.31 % (9770)------------------------------
% 1.69/1.31 % (9770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (9770)Termination reason: Unknown
% 1.69/1.31 % (9770)Termination phase: Property scanning
% 1.69/1.31
% 1.69/1.31 % (9770)Memory used [KB]: 895
% 1.69/1.31 % (9770)Time elapsed: 0.003 s
% 1.69/1.31 % (9770)Instructions burned: 2 (million)
% 1.69/1.31 % (9770)------------------------------
% 1.69/1.31 % (9770)------------------------------
% 1.69/1.31 % (9768)Instruction limit reached!
% 1.69/1.31 % (9768)------------------------------
% 1.69/1.31 % (9768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (9768)Termination reason: Unknown
% 1.69/1.31 % (9768)Termination phase: Property scanning
% 1.69/1.31
% 1.69/1.31 % (9768)Memory used [KB]: 1023
% 1.69/1.31 % (9768)Time elapsed: 0.004 s
% 1.69/1.31 % (9768)Instructions burned: 4 (million)
% 1.69/1.31 % (9768)------------------------------
% 1.69/1.31 % (9768)------------------------------
% 1.69/1.31 % (9774)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/3Mi)
% 1.69/1.31 % (9774)Instruction limit reached!
% 1.69/1.31 % (9774)------------------------------
% 1.69/1.31 % (9774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (9774)Termination reason: Unknown
% 1.69/1.31 % (9774)Termination phase: Saturation
% 1.69/1.31
% 1.69/1.31 % (9774)Memory used [KB]: 5500
% 1.69/1.31 % (9774)Time elapsed: 0.003 s
% 1.69/1.31 % (9774)Instructions burned: 4 (million)
% 1.69/1.31 % (9774)------------------------------
% 1.69/1.31 % (9774)------------------------------
% 1.69/1.32 % (9773)Instruction limit reached!
% 1.69/1.32 % (9773)------------------------------
% 1.69/1.32 % (9773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (9773)Termination reason: Unknown
% 1.69/1.32 % (9773)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (9773)Memory used [KB]: 5628
% 1.69/1.32 % (9773)Time elapsed: 0.013 s
% 1.69/1.32 % (9773)Instructions burned: 18 (million)
% 1.69/1.32 % (9773)------------------------------
% 1.69/1.32 % (9773)------------------------------
% 1.69/1.32 % (9777)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_9440 for (2999ds/3Mi)
% 1.69/1.32 % (9777)Instruction limit reached!
% 1.69/1.32 % (9777)------------------------------
% 1.69/1.32 % (9777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (9777)Termination reason: Unknown
% 1.69/1.32 % (9777)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (9777)Memory used [KB]: 5500
% 1.69/1.32 % (9777)Time elapsed: 0.003 s
% 1.69/1.32 % (9777)Instructions burned: 4 (million)
% 1.69/1.32 % (9777)------------------------------
% 1.69/1.32 % (9777)------------------------------
% 1.69/1.32 % (9769)Instruction limit reached!
% 1.69/1.32 % (9769)------------------------------
% 1.69/1.32 % (9769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (9769)Termination reason: Unknown
% 1.69/1.32 % (9769)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (9769)Memory used [KB]: 5628
% 1.69/1.32 % (9769)Time elapsed: 0.020 s
% 1.69/1.32 % (9769)Instructions burned: 27 (million)
% 1.69/1.32 % (9769)------------------------------
% 1.69/1.32 % (9769)------------------------------
% 1.69/1.32 % (9775)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_9440 for (2999ds/37Mi)
% 1.69/1.32 % (9776)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_9440 for (2999ds/15Mi)
% 1.69/1.33 % (9779)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/7Mi)
% 1.69/1.33 % (9776)Instruction limit reached!
% 1.69/1.33 % (9776)------------------------------
% 1.69/1.33 % (9776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (9776)Termination reason: Unknown
% 1.69/1.33 % (9776)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (9776)Memory used [KB]: 5628
% 1.69/1.33 % (9776)Time elapsed: 0.012 s
% 1.69/1.33 % (9776)Instructions burned: 15 (million)
% 1.69/1.33 % (9776)------------------------------
% 1.69/1.33 % (9776)------------------------------
% 1.69/1.33 % (9778)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_9440 for (2999ds/1041Mi)
% 1.69/1.34 % (9779)Instruction limit reached!
% 1.69/1.34 % (9779)------------------------------
% 1.69/1.34 % (9779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (9779)Termination reason: Unknown
% 1.69/1.34 % (9779)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (9779)Memory used [KB]: 1023
% 1.69/1.34 % (9779)Time elapsed: 0.005 s
% 1.69/1.34 % (9779)Instructions burned: 9 (million)
% 1.69/1.34 % (9779)------------------------------
% 1.69/1.34 % (9779)------------------------------
% 1.69/1.34 % (9775)Instruction limit reached!
% 1.69/1.34 % (9775)------------------------------
% 1.69/1.34 % (9775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (9775)Termination reason: Unknown
% 1.69/1.34 % (9775)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (9775)Memory used [KB]: 5756
% 1.69/1.34 % (9780)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/16Mi)
% 1.69/1.34 % (9775)Time elapsed: 0.019 s
% 1.69/1.34 % (9775)Instructions burned: 38 (million)
% 1.69/1.34 % (9775)------------------------------
% 1.69/1.34 % (9775)------------------------------
% 1.69/1.35 % (9782)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_9440 for (2999ds/3Mi)
% 1.69/1.35 % (9782)Instruction limit reached!
% 1.69/1.35 % (9782)------------------------------
% 1.69/1.35 % (9782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (9782)Termination reason: Unknown
% 1.69/1.35 % (9782)Termination phase: Property scanning
% 1.69/1.35
% 1.69/1.35 % (9782)Memory used [KB]: 1023
% 1.69/1.35 % (9782)Time elapsed: 0.003 s
% 1.69/1.35 % (9782)Instructions burned: 4 (million)
% 1.69/1.35 % (9782)------------------------------
% 1.69/1.35 % (9782)------------------------------
% 1.69/1.35 % (9780)Instruction limit reached!
% 1.69/1.35 % (9780)------------------------------
% 1.69/1.35 % (9780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (9780)Termination reason: Unknown
% 1.69/1.35 % (9780)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (9780)Memory used [KB]: 5628
% 1.69/1.35 % (9780)Time elapsed: 0.012 s
% 1.69/1.35 % (9780)Instructions burned: 17 (million)
% 1.69/1.35 % (9780)------------------------------
% 1.69/1.35 % (9780)------------------------------
% 1.69/1.35 % (9783)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/7Mi)
% 1.69/1.35 % (9781)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_9440 for (2999ds/3Mi)
% 1.69/1.35 % (9783)Instruction limit reached!
% 1.69/1.35 % (9783)------------------------------
% 1.69/1.35 % (9783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (9783)Termination reason: Unknown
% 1.69/1.35 % (9783)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (9783)Memory used [KB]: 5500
% 1.69/1.35 % (9783)Time elapsed: 0.004 s
% 1.69/1.35 % (9783)Instructions burned: 9 (million)
% 1.69/1.35 % (9783)------------------------------
% 1.69/1.35 % (9783)------------------------------
% 1.69/1.35 % (9781)Instruction limit reached!
% 1.69/1.35 % (9781)------------------------------
% 1.69/1.35 % (9781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (9781)Termination reason: Unknown
% 1.69/1.35 % (9781)Termination phase: Property scanning
% 1.69/1.35
% 1.69/1.35 % (9781)Memory used [KB]: 1023
% 1.69/1.35 % (9781)Time elapsed: 0.004 s
% 1.69/1.35 % (9781)Instructions burned: 3 (million)
% 1.69/1.35 % (9781)------------------------------
% 1.69/1.35 % (9781)------------------------------
% 1.69/1.36 % (9784)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/3Mi)
% 1.69/1.36 % (9784)Instruction limit reached!
% 1.69/1.36 % (9784)------------------------------
% 1.69/1.36 % (9784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (9784)Termination reason: Unknown
% 1.69/1.36 % (9784)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (9784)Memory used [KB]: 5500
% 1.69/1.36 % (9784)Time elapsed: 0.003 s
% 1.69/1.36 % (9784)Instructions burned: 4 (million)
% 1.69/1.36 % (9784)------------------------------
% 1.69/1.36 % (9784)------------------------------
% 1.69/1.36 % (9786)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/18Mi)
% 1.69/1.37 % (9785)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/4Mi)
% 1.69/1.37 % (9785)Instruction limit reached!
% 1.69/1.37 % (9785)------------------------------
% 1.69/1.37 % (9785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (9785)Termination reason: Unknown
% 1.69/1.37 % (9785)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (9785)Memory used [KB]: 5500
% 1.69/1.37 % (9785)Time elapsed: 0.003 s
% 1.69/1.37 % (9785)Instructions burned: 4 (million)
% 1.69/1.37 % (9785)------------------------------
% 1.69/1.37 % (9785)------------------------------
% 1.69/1.37 % (9788)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/6Mi)
% 1.69/1.37 % (9788)Instruction limit reached!
% 1.69/1.37 % (9788)------------------------------
% 1.69/1.37 % (9788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (9788)Termination reason: Unknown
% 1.69/1.37 % (9788)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (9788)Memory used [KB]: 5500
% 1.69/1.37 % (9788)Time elapsed: 0.004 s
% 1.69/1.37 % (9788)Instructions burned: 7 (million)
% 1.69/1.37 % (9788)------------------------------
% 1.69/1.37 % (9788)------------------------------
% 1.69/1.37 % (9786)Instruction limit reached!
% 1.69/1.37 % (9786)------------------------------
% 1.69/1.37 % (9786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (9786)Termination reason: Unknown
% 1.69/1.37 % (9786)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (9786)Memory used [KB]: 5628
% 1.69/1.37 % (9786)Time elapsed: 0.009 s
% 1.69/1.37 % (9786)Instructions burned: 20 (million)
% 1.69/1.37 % (9786)------------------------------
% 1.69/1.37 % (9786)------------------------------
% 1.69/1.37 % (9787)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/710Mi)
% 1.69/1.38 % (9789)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_9440 for (2999ds/902Mi)
% 1.69/1.38 % (9790)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_9440 for (2999ds/21Mi)
% 1.69/1.39 % (9790)Instruction limit reached!
% 1.69/1.39 % (9790)------------------------------
% 1.69/1.39 % (9790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (9790)Termination reason: Unknown
% 1.69/1.39 % (9790)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (9790)Memory used [KB]: 5628
% 1.69/1.39 % (9790)Time elapsed: 0.010 s
% 1.69/1.39 % (9790)Instructions burned: 22 (million)
% 1.69/1.39 % (9790)------------------------------
% 1.69/1.39 % (9790)------------------------------
% 1.69/1.39 % (9791)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9440 for (2999ds/5Mi)
% 1.69/1.39 % (9772)Instruction limit reached!
% 1.69/1.39 % (9772)------------------------------
% 1.69/1.39 % (9772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (9772)Termination reason: Unknown
% 1.69/1.39 % (9772)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (9772)Memory used [KB]: 7419
% 1.69/1.39 % (9772)Time elapsed: 0.094 s
% 1.69/1.39 % (9772)Instructions burned: 277 (million)
% 1.69/1.39 % (9772)------------------------------
% 1.69/1.39 % (9772)------------------------------
% 1.69/1.39 % (9791)Instruction limit reached!
% 1.69/1.39 % (9791)------------------------------
% 1.69/1.39 % (9791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (9791)Termination reason: Unknown
% 1.69/1.39 % (9791)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (9791)Memory used [KB]: 5500
% 1.69/1.39 % (9791)Time elapsed: 0.005 s
% 1.69/1.39 % (9791)Instructions burned: 5 (million)
% 1.69/1.39 % (9791)------------------------------
% 1.69/1.39 % (9791)------------------------------
% 1.69/1.40 % (9789)First to succeed.
% 1.69/1.40 % (9789)Refutation found. Thanks to Tanya!
% 1.69/1.40 % SZS status Theorem for DTF2THF_9440
% 1.69/1.40 % SZS output start Proof for DTF2THF_9440
% 1.69/1.40 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.69/1.40 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.69/1.40 thf(func_def_1, type, 'const/trivia/I': !>[X0: $tType]:(X0 > X0)).
% 1.69/1.40 thf(func_def_2, type, 'const/sets/SUBSET': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.69/1.40 thf(func_def_3, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 1.69/1.40 thf(func_def_4, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.69/1.40 thf(func_def_5, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.69/1.40 thf(func_def_6, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.69/1.40 thf(func_def_10, type, sK0: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.69/1.40 thf(func_def_11, type, sK1: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.69/1.40 thf(func_def_12, type, sK2: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.69/1.40 thf(func_def_13, type, sK3: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.69/1.40 thf(func_def_14, type, sK4: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.69/1.40 thf(func_def_15, type, sK5: 'type/realax/real' > $o).
% 1.69/1.40 thf(func_def_16, type, sK6: 'type/realax/real' > $o).
% 1.69/1.40 thf(func_def_17, type, sK7: 'type/realax/real').
% 1.69/1.40 thf(func_def_19, type, ph9: !>[X0: $tType]:(X0)).
% 1.69/1.40 thf(func_def_21, type, sK10: 'type/realax/real').
% 1.69/1.40 thf(func_def_22, type, sK11: 'type/realax/real').
% 1.69/1.40 thf(func_def_23, type, sK12: 'type/realax/real').
% 1.69/1.40 thf(func_def_24, type, sK13: 'type/realax/real').
% 1.69/1.40 thf(func_def_25, type, sK14: 'type/realax/real').
% 1.69/1.40 thf(func_def_26, type, sK15: 'type/realax/real').
% 1.69/1.40 thf(func_def_27, type, sK16: 'type/realax/real').
% 1.69/1.40 thf(func_def_28, type, sK17: 'type/realax/real').
% 1.69/1.40 thf(func_def_29, type, sK18: 'type/realax/real').
% 1.69/1.40 thf(f711,plain,(
% 1.69/1.40 $false),
% 1.69/1.40 inference(avatar_sat_refutation,[status(thm)],[f132,f163,f172,f256,f362,f560,f591,f599,f669,f701,f707])).
% 1.69/1.40 thf(f707,plain,(
% 1.69/1.40 ~spl8_29),
% 1.69/1.40 inference(avatar_contradiction_clause,[status(thm)],[f706])).
% 1.69/1.40 thf(f706,plain,(
% 1.69/1.40 $false | ~spl8_29),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f703])).
% 1.69/1.40 thf(f703,plain,(
% 1.69/1.40 (sK6 != sK6) | ~spl8_29),
% 1.69/1.40 inference(superposition,[status(thm)],[f66,f251])).
% 1.69/1.40 thf(f251,plain,(
% 1.69/1.40 ('const/sets/EMPTY' @ 'type/realax/real' = sK6) | ~spl8_29),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f249])).
% 1.69/1.40 thf(f249,definition,(
% 1.69/1.40 spl8_29 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK6)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_29])],[avatar_definition])).
% 1.69/1.40 thf(f66,plain,(
% 1.69/1.40 ('const/sets/EMPTY' @ 'type/realax/real' != sK6)),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f47])).
% 1.69/1.40 thf(f47,plain,(
% 1.69/1.40 ($true = ('const/sets/SUBSET' @ 'type/realax/real' @ sK6 @ sK5)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK6) & ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK5)) | ($true = ('const/realax/real_le' @ sK7 @ X3))) & (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) != $true)),
% 1.69/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f26,f46,f45])).
% 1.69/1.40 thf(f45,plain,(
% 1.69/1.40 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ X2 @ X3))) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)) != $true)) => (($true = ('const/sets/SUBSET' @ 'type/realax/real' @ sK6 @ sK5)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK6) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK5)) | ($true = ('const/realax/real_le' @ X2 @ X3))) & (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) != $true))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f46,plain,(
% 1.69/1.40 ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK5)) | ($true = ('const/realax/real_le' @ X2 @ X3))) => ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK5)) | ($true = ('const/realax/real_le' @ sK7 @ X3)))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f26,plain,(
% 1.69/1.40 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ X2 @ X3))) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)) != $true))),
% 1.69/1.40 inference(flattening,[status(thm)],[f25])).
% 1.69/1.40 thf(f25,plain,(
% 1.69/1.40 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)) != $true) & ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) = $true) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ X2 @ X3))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1)))),
% 1.69/1.40 inference(ennf_transformation,[status(thm)],[f14])).
% 1.69/1.40 thf(f14,plain,(
% 1.69/1.40 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : (((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) = $true) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) => ($true = ('const/realax/real_le' @ X2 @ X3))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1)) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)) = $true))),
% 1.69/1.40 inference(fool_elimination,[status(thm)],[f13])).
% 1.69/1.40 thf(f13,plain,(
% 1.69/1.40 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X2 @ X3))) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)))),
% 1.69/1.40 inference(rectify,[status(thm)],[f9])).
% 1.69/1.40 thf(f9,negated_conjecture,(
% 1.69/1.40 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X2 @ X4))) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)))),
% 1.69/1.40 inference(negated_conjecture,[status(cth)],[f8])).
% 1.69/1.40 thf(f8,conjecture,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real' > $o] : ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X2 @ X4))) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)))),
% 1.69/1.40 file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/REAL_LE_INF_SUBSET_')).
% 1.69/1.40 thf(f701,plain,(
% 1.69/1.40 ~spl8_61),
% 1.69/1.40 inference(avatar_contradiction_clause,[status(thm)],[f700])).
% 1.69/1.40 thf(f700,plain,(
% 1.69/1.40 $false | ~spl8_61),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f699])).
% 1.69/1.40 thf(f699,plain,(
% 1.69/1.40 ($true != $true) | ~spl8_61),
% 1.69/1.40 inference(superposition,[status(thm)],[f64,f644])).
% 1.69/1.40 thf(f644,plain,(
% 1.69/1.40 (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) = $true) | ~spl8_61),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f642])).
% 1.69/1.40 thf(f642,definition,(
% 1.69/1.40 spl8_61 <=> (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) = $true)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_61])],[avatar_definition])).
% 1.69/1.40 thf(f64,plain,(
% 1.69/1.40 (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) != $true)),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f47])).
% 1.69/1.40 thf(f669,plain,(
% 1.69/1.40 spl8_61 | spl8_29 | ~spl8_11 | ~spl8_28),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f667,f245,f130,f249,f642])).
% 1.69/1.40 thf(f130,definition,(
% 1.69/1.40 spl8_11 <=> ! [X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ X1)) | ($true != (sK5 @ X1)))),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_11])],[avatar_definition])).
% 1.69/1.40 thf(f245,definition,(
% 1.69/1.40 spl8_28 <=> ! [X0 : 'type/realax/real'] : (($true = (sK5 @ (sK2 @ X0 @ sK6))) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK6))))),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_28])],[avatar_definition])).
% 1.69/1.40 thf(f667,plain,(
% 1.69/1.40 (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK6) | (~spl8_11 | ~spl8_28)),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f666])).
% 1.69/1.40 thf(f666,plain,(
% 1.69/1.40 ($true != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK6) | (~spl8_11 | ~spl8_28)),
% 1.69/1.40 inference(duplicate_literal_removal,[status(thm)],[f664])).
% 1.69/1.40 thf(f664,plain,(
% 1.69/1.40 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK6) | (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) = $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ sK6)) = $true) | (~spl8_11 | ~spl8_28)),
% 1.69/1.40 inference(superposition,[status(thm)],[f637,f246])).
% 1.69/1.40 thf(f246,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true = (sK5 @ (sK2 @ X0 @ sK6))) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK6)))) ) | ~spl8_28),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f245])).
% 1.69/1.40 thf(f637,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real' > $o] : (((sK5 @ (sK2 @ ('const/sets/inf' @ sK5) @ X0)) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) ) | ~spl8_11),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f632])).
% 1.69/1.40 thf(f632,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real' > $o] : (((sK5 @ (sK2 @ ('const/sets/inf' @ sK5) @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ ('const/sets/inf' @ X0)) = $true) | ($true != $true)) ) | ~spl8_11),
% 1.69/1.40 inference(superposition,[status(thm)],[f56,f131])).
% 1.69/1.40 thf(f131,plain,(
% 1.69/1.40 ( ! [X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ X1)) | ($true != (sK5 @ X1))) ) | ~spl8_11),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f130])).
% 1.69/1.40 thf(f56,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK2 @ X1 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f36])).
% 1.69/1.40 thf(f36,plain,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ X0) @ X0) = $true) & (('const/realax/real_le' @ X1 @ (sK2 @ X1 @ X0)) != $true)))),
% 1.69/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f31,f35])).
% 1.69/1.40 thf(f35,plain,(
% 1.69/1.40 ! [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' @ X1 @ X2) != $true)) => ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ X0) @ X0) = $true) & (('const/realax/real_le' @ X1 @ (sK2 @ X1 @ X0)) != $true)))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f31,plain,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true)))),
% 1.69/1.40 inference(flattening,[status(thm)],[f30])).
% 1.69/1.40 thf(f30,plain,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true))))),
% 1.69/1.40 inference(ennf_transformation,[status(thm)],[f22])).
% 1.69/1.40 thf(f22,plain,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X1 @ X2) = $true))) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true))),
% 1.69/1.40 inference(fool_elimination,[status(thm)],[f21])).
% 1.69/1.40 thf(f21,plain,(
% 1.69/1.40 ! [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' @ X1 @ X2)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 1.69/1.40 inference(rectify,[status(thm)],[f1])).
% 1.69/1.40 thf(f1,axiom,(
% 1.69/1.40 ! [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' @ X1 @ X2)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 1.69/1.40 file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/REAL_LE_INF_')).
% 1.69/1.40 thf(f599,plain,(
% 1.69/1.40 ~spl8_6 | ~spl8_14),
% 1.69/1.40 inference(avatar_contradiction_clause,[status(thm)],[f598])).
% 1.69/1.40 thf(f598,plain,(
% 1.69/1.40 $false | (~spl8_6 | ~spl8_14)),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f597])).
% 1.69/1.40 thf(f597,plain,(
% 1.69/1.40 ($true != $true) | (~spl8_6 | ~spl8_14)),
% 1.69/1.40 inference(superposition,[status(thm)],[f402,f162])).
% 1.69/1.40 thf(f162,plain,(
% 1.69/1.40 ((sK5 @ sK11) = $true) | ~spl8_14),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f160])).
% 1.69/1.40 thf(f160,definition,(
% 1.69/1.40 spl8_14 <=> ((sK5 @ sK11) = $true)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_14])],[avatar_definition])).
% 1.69/1.40 thf(f402,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true != (sK5 @ X0))) ) | ~spl8_6),
% 1.69/1.40 inference(superposition,[status(thm)],[f371,f60])).
% 1.69/1.40 thf(f60,plain,(
% 1.69/1.40 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (((X1 @ X2) = ('const/sets/IN' @ X0 @ X2 @ X1))) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.40 thf(f23,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((X1 @ X2) = ('const/sets/IN' @ X0 @ X2 @ X1))),
% 1.69/1.40 inference(rectify,[status(thm)],[f3])).
% 1.69/1.40 thf(f3,axiom,(
% 1.69/1.40 ! [X0 : $tType,X3 : X0 > $o,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ X3) = (X3 @ X1))),
% 1.69/1.40 file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/IN_')).
% 1.69/1.40 thf(f371,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK5))) ) | ~spl8_6),
% 1.69/1.40 inference(superposition,[status(thm)],[f55,f112])).
% 1.69/1.40 thf(f112,plain,(
% 1.69/1.40 ('const/sets/EMPTY' @ 'type/realax/real' = sK5) | ~spl8_6),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f110])).
% 1.69/1.40 thf(f110,definition,(
% 1.69/1.40 spl8_6 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK5)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 1.69/1.40 thf(f55,plain,(
% 1.69/1.40 ( ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f24])).
% 1.69/1.40 thf(f24,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)),
% 1.69/1.40 inference(flattening,[status(thm)],[f16])).
% 1.69/1.40 thf(f16,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0] : ~(('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)),
% 1.69/1.40 inference(fool_elimination,[status(thm)],[f15])).
% 1.69/1.40 thf(f15,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 1.69/1.40 inference(rectify,[status(thm)],[f4])).
% 1.69/1.40 thf(f4,axiom,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 1.69/1.40 file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/NOT_IN_EMPTY_')).
% 1.69/1.40 thf(f591,plain,(
% 1.69/1.40 ~spl8_13 | ~spl8_16),
% 1.69/1.40 inference(avatar_contradiction_clause,[status(thm)],[f590])).
% 1.69/1.40 thf(f590,plain,(
% 1.69/1.40 $false | (~spl8_13 | ~spl8_16)),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f586])).
% 1.69/1.40 thf(f586,plain,(
% 1.69/1.40 ($true = $false) | (~spl8_13 | ~spl8_16)),
% 1.69/1.40 inference(superposition,[status(thm)],[f171,f158])).
% 1.69/1.40 thf(f158,plain,(
% 1.69/1.40 ((sK6 @ sK11) = $true) | ~spl8_13),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f156])).
% 1.69/1.40 thf(f156,definition,(
% 1.69/1.40 spl8_13 <=> ((sK6 @ sK11) = $true)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_13])],[avatar_definition])).
% 1.69/1.40 thf(f171,plain,(
% 1.69/1.40 ((sK6 @ sK11) = $false) | ~spl8_16),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f169])).
% 1.69/1.40 thf(f169,definition,(
% 1.69/1.40 spl8_16 <=> ((sK6 @ sK11) = $false)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_16])],[avatar_definition])).
% 1.69/1.40 thf(f560,plain,(
% 1.69/1.40 ~spl8_13 | ~spl8_15),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f556,f165,f156])).
% 1.69/1.40 thf(f165,definition,(
% 1.69/1.40 spl8_15 <=> ((sK5 @ sK11) = $false)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_15])],[avatar_definition])).
% 1.69/1.40 thf(f556,plain,(
% 1.69/1.40 ((sK6 @ sK11) != $true) | ~spl8_15),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f553])).
% 1.69/1.40 thf(f553,plain,(
% 1.69/1.40 ((sK6 @ sK11) != $true) | ($true = $false) | ~spl8_15),
% 1.69/1.40 inference(superposition,[status(thm)],[f167,f205])).
% 1.69/1.40 thf(f205,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true = (sK5 @ X0)) | ($true != (sK6 @ X0))) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f92,f60])).
% 1.69/1.40 thf(f92,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK6)) | ($true = (sK5 @ X0))) )),
% 1.69/1.40 inference(forward_demodulation,[status(thm)],[f91,f60])).
% 1.69/1.40 thf(f91,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK6)) | ($true = ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK5))) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.69/1.40 thf(f90,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK6)) | ($true = ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK5)) | ($true != $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f63,f67])).
% 1.69/1.40 thf(f67,plain,(
% 1.69/1.40 ($true = ('const/sets/SUBSET' @ 'type/realax/real' @ sK6 @ sK5))),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f47])).
% 1.69/1.40 thf(f63,plain,(
% 1.69/1.40 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true) | ($true != ('const/sets/IN' @ X0 @ X3 @ X1))) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f44])).
% 1.69/1.40 thf(f44,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1) = $true) & ($true != ('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X2)))))),
% 1.69/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f42,f43])).
% 1.69/1.40 thf(f43,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) = $true) & (('const/sets/IN' @ X0 @ X4 @ X2) != $true)) => ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1) = $true) & ($true != ('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X2))))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f42,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) = $true) & (('const/sets/IN' @ X0 @ X4 @ X2) != $true))))),
% 1.69/1.40 inference(rectify,[status(thm)],[f41])).
% 1.69/1.40 thf(f41,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ? [X3 : X0] : (($true = ('const/sets/IN' @ X0 @ X3 @ X1)) & (('const/sets/IN' @ X0 @ X3 @ X2) != $true))))),
% 1.69/1.40 inference(nnf_transformation,[status(thm)],[f29])).
% 1.69/1.40 thf(f29,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) <=> (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true))),
% 1.69/1.40 inference(ennf_transformation,[status(thm)],[f12])).
% 1.69/1.40 thf(f12,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) <=> ! [X3 : X0] : (($true = ('const/sets/IN' @ X0 @ X3 @ X1)) => (('const/sets/IN' @ X0 @ X3 @ X2) = $true)))),
% 1.69/1.40 inference(fool_elimination,[status(thm)],[f11])).
% 1.69/1.40 thf(f11,plain,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)) = ('const/sets/SUBSET' @ X0 @ X1 @ X2))),
% 1.69/1.40 inference(rectify,[status(thm)],[f6])).
% 1.69/1.40 thf(f6,axiom,(
% 1.69/1.40 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/sets/IN' @ X0 @ X4 @ X2)) = ('const/sets/SUBSET' @ X0 @ X1 @ X2))),
% 1.69/1.40 file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/SUBSET_')).
% 1.69/1.40 thf(f167,plain,(
% 1.69/1.40 ((sK5 @ sK11) = $false) | ~spl8_15),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f165])).
% 1.69/1.40 thf(f362,plain,(
% 1.69/1.40 spl8_6 | spl8_11 | ~spl8_8),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f334,f118,f130,f110])).
% 1.69/1.40 thf(f118,definition,(
% 1.69/1.40 spl8_8 <=> ! [X0 : 'type/realax/real'] : ($true = ('const/realax/real_le' @ sK7 @ (sK0 @ X0 @ sK5)))),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition])).
% 1.69/1.40 thf(f334,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true != (sK5 @ X0)) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK5)) ) | ~spl8_8),
% 1.69/1.40 inference(forward_demodulation,[status(thm)],[f333,f60])).
% 1.69/1.40 thf(f333,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ X0)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK5)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK5)) ) | ~spl8_8),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f332])).
% 1.69/1.40 thf(f332,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK5) | ($true != $true) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ X0)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK5))) ) | ~spl8_8),
% 1.69/1.40 inference(superposition,[status(thm)],[f49,f119])).
% 1.69/1.40 thf(f119,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK7 @ (sK0 @ X0 @ sK5)))) ) | ~spl8_8),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f118])).
% 1.69/1.40 thf(f49,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0))) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f34])).
% 1.69/1.40 thf(f34,plain,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o] : (! [X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) | (! [X3 : 'type/realax/real'] : ((($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X3 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ X3 @ (sK1 @ X3 @ X0)))) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) & ! [X5 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.69/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f28,f33,f32])).
% 1.69/1.40 thf(f32,plain,(
% 1.69/1.40 ! [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' @ X1 @ X2) != $true)) => (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f33,plain,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o,X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) & ($true != ('const/realax/real_le' @ X3 @ X4))) => (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X3 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ X3 @ (sK1 @ X3 @ X0)))))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f28,plain,(
% 1.69/1.40 ! [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' @ X1 @ X2) != $true)) | (! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) & ($true != ('const/realax/real_le' @ X3 @ X4))) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) & ! [X5 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.69/1.40 inference(flattening,[status(thm)],[f27])).
% 1.69/1.40 thf(f27,plain,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o] : ((! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) & ($true != ('const/realax/real_le' @ X3 @ X4))) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) & ! [X5 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 1.69/1.40 inference(ennf_transformation,[status(thm)],[f20])).
% 1.69/1.40 thf(f20,plain,(
% 1.69/1.40 ! [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' @ X1 @ X2) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X5 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) => ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))) & ! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) => ($true = ('const/realax/real_le' @ X3 @ X4))) => ($true = ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))))))),
% 1.69/1.40 inference(fool_elimination,[status(thm)],[f19])).
% 1.69/1.40 thf(f19,plain,(
% 1.69/1.40 ! [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' @ X1 @ X2))) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X3 @ X4)) => ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))),
% 1.69/1.40 inference(rectify,[status(thm)],[f7])).
% 1.69/1.40 thf(f7,axiom,(
% 1.69/1.40 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => (! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 1.69/1.40 file('/export/starexec/sandbox2/tmp/tmp.lC3BaVWaBu/DTF2THF_9440.p','thm/sets/INF_')).
% 1.69/1.40 thf(f256,plain,(
% 1.69/1.40 spl8_28 | spl8_29),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f206,f249,f245])).
% 1.69/1.40 thf(f206,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true = (sK5 @ (sK2 @ X0 @ sK6))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK6) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK6)))) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f199])).
% 1.69/1.40 thf(f199,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real'] : (($true = (sK5 @ (sK2 @ X0 @ sK6))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK6) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK6))) | ($true != $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f92,f57])).
% 1.69/1.40 thf(f57,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ X0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f36])).
% 1.69/1.40 thf(f172,plain,(
% 1.69/1.40 spl8_15 | spl8_16 | ~spl8_6),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f154,f110,f169,f165])).
% 1.69/1.40 thf(f154,plain,(
% 1.69/1.40 ((sK5 @ sK11) = $false) | ((sK6 @ sK11) = $false) | ~spl8_6),
% 1.69/1.40 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.69/1.40 thf(f152,plain,(
% 1.69/1.40 ((sK6 @ sK11) != (sK5 @ sK11)) | ~spl8_6),
% 1.69/1.40 inference(negative_extensionality,[status(thm)],[f138])).
% 1.69/1.40 thf(f138,plain,(
% 1.69/1.40 (sK6 != sK5) | ~spl8_6),
% 1.69/1.40 inference(superposition,[status(thm)],[f66,f112])).
% 1.69/1.40 thf(f163,plain,(
% 1.69/1.40 spl8_13 | spl8_14 | ~spl8_6),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f153,f110,f160,f156])).
% 1.69/1.40 thf(f153,plain,(
% 1.69/1.40 ((sK6 @ sK11) = $true) | ((sK5 @ sK11) = $true) | ~spl8_6),
% 1.69/1.40 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.69/1.40 thf(f132,plain,(
% 1.69/1.40 spl8_11 | spl8_8 | spl8_6),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f128,f110,f118,f130])).
% 1.69/1.40 thf(f128,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ X1)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK5) | ($true = ('const/realax/real_le' @ sK7 @ (sK0 @ X0 @ sK5))) | ($true != (sK5 @ X1))) )),
% 1.69/1.40 inference(forward_demodulation,[status(thm)],[f102,f60])).
% 1.69/1.40 thf(f102,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ X1)) | ($true = ('const/realax/real_le' @ sK7 @ (sK0 @ X0 @ sK5))) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK5) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK5)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.69/1.40 thf(f96,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK5) != $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK5) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK5) @ X1)) | ($true = ('const/realax/real_le' @ sK7 @ (sK0 @ X0 @ sK5)))) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f65,f52])).
% 1.69/1.40 thf(f52,plain,(
% 1.69/1.40 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f34])).
% 1.69/1.40 thf(f65,plain,(
% 1.69/1.40 ( ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK5)) | ($true = ('const/realax/real_le' @ sK7 @ X3))) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f47])).
% 1.69/1.40 % SZS output end Proof for DTF2THF_9440
% 1.69/1.40 % (9789)------------------------------
% 1.69/1.40 % (9789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (9789)Termination reason: Refutation
% 1.69/1.40
% 1.69/1.40 % (9789)Memory used [KB]: 6012
% 1.69/1.40 % (9789)Time elapsed: 0.022 s
% 1.69/1.40 % (9789)Instructions burned: 52 (million)
% 1.69/1.40 % (9789)------------------------------
% 1.69/1.40 % (9789)------------------------------
% 1.69/1.40 % (9766)Success in time 0.101 s
%------------------------------------------------------------------------------