%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU807^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:22 AM UTC 2026
% Result : Theorem 1.56s 1.93s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 939 ( 302 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 947 ( 133 ~; 109 |; 79 &; 569 @)
% ( 10 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 20 con; 0-2 aty)
% Number of variables : 219 ( 0 ^; 162 !; 57 ?; 219 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_11,type,
sP0: $i > $o ).
thf(func_def_12,type,
sK1: $i > $i > $i ).
thf(func_def_13,type,
sK2: $i > $i ).
thf(f1157,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1155,f69]) ).
thf(f69,plain,
( $true
= ( in @ sK6 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( setadjoinIL = $true )
& ( upairset2E = $true )
& ( foundationAx = $true )
& ( in__Cong = $true )
& ( $true
= ( in @ sK5 @ sK6 ) )
& ( $true
= ( in @ sK6 @ sK5 ) )
& ( setadjoinIR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f41,f42]) ).
thf(f42,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( ( in @ X1 @ X0 )
= $true ) )
=> ( ( $true
= ( in @ sK5 @ sK6 ) )
& ( $true
= ( in @ sK6 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( setadjoinIL = $true )
& ( upairset2E = $true )
& ( foundationAx = $true )
& ( in__Cong = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( setadjoinIR = $true ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( setadjoinIL = $true )
& ( upairset2E = $true )
& ( foundationAx = $true )
& ( in__Cong = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( setadjoinIR = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( upairset2E = $true )
& ( in__Cong = $true )
& ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ( foundationAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
~ ( ( foundationAx = $true )
=> ( ( setadjoinIL = $true )
=> ( ( setadjoinIR = $true )
=> ( ( in__Cong = $true )
=> ( ( upairset2E = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( $true
!= ( in @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( foundationAx = $true )
=> ( ( setadjoinIL = $true )
=> ( ( setadjoinIR = $true )
=> ( ( in__Cong = $true )
=> ( ( upairset2E = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( $true
!= ( in @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( foundationAx
=> ( setadjoinIL
=> ( setadjoinIR
=> ( in__Cong
=> ( upairset2E
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X0 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( foundationAx
=> ( setadjoinIL
=> ( setadjoinIR
=> ( in__Cong
=> ( upairset2E
=> ! [X2: $i,X0: $i] :
( ( in @ X0 @ X2 )
=> ~ ( in @ X2 @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( foundationAx
=> ( setadjoinIL
=> ( setadjoinIR
=> ( in__Cong
=> ( upairset2E
=> ! [X2: $i,X0: $i] :
( ( in @ X0 @ X2 )
=> ~ ( in @ X2 @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',notinself2) ).
thf(f1155,plain,
( $true
!= ( in @ sK6 @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1149]) ).
thf(f1149,plain,
( ( $true
!= ( in @ sK6 @ sK5 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1134,f70]) ).
thf(f70,plain,
( $true
= ( in @ sK5 @ sK6 ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f1134,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1129]) ).
thf(f1129,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f749,f106]) ).
thf(f106,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f76,f74]) ).
thf(f74,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f76,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK7 @ ( setadjoin @ sK7 @ sK8 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f45,f46]) ).
thf(f46,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) )
=> ( $true
!= ( in @ sK7 @ ( setadjoin @ sK7 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X3: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X3 ) )
= setadjoinIL ),
file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',setadjoinIL) ).
thf(f749,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ emptyset ) )
!= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X1 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f746]) ).
thf(f746,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setadjoin @ X2 @ emptyset ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f291,f107]) ).
thf(f107,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setadjoin @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
= ( in @ X4 @ ( setadjoin @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) ),
inference(definition_unfolding,[status(thm)],[f85,f68]) ).
thf(f68,plain,
setadjoinIR = $true,
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f85,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setadjoin @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( setadjoinIR != $true ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( setadjoinIR = $true )
| ( ( $true
!= ( in @ sK17 @ ( setadjoin @ sK16 @ sK18 ) ) )
& ( $true
= ( in @ sK17 @ sK18 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setadjoin @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ( setadjoinIR != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f58,f59]) ).
thf(f59,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
& ( ( in @ X1 @ X2 )
= $true ) )
=> ( ( $true
!= ( in @ sK17 @ ( setadjoin @ sK16 @ sK18 ) ) )
& ( $true
= ( in @ sK17 @ sK18 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f58,plain,
( ( ( setadjoinIR = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
& ( ( in @ X1 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setadjoin @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ( setadjoinIR != $true ) ) ),
inference(rectify,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( setadjoinIR = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
| ( setadjoinIR != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( setadjoinIR = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( setadjoinIR = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( setadjoinIR
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( setadjoinIR
= ( ! [X1: $i,X0: $i,X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',setadjoinIR) ).
thf(f291,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f131,f253]) ).
thf(f253,plain,
! [X0: $i,X1: $i] :
( ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X0 )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f249]) ).
thf(f249,plain,
! [X0: $i,X1: $i] :
( ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X0 )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f146,f106]) ).
thf(f146,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X0 ) ),
inference(superposition,[status(thm)],[f131,f124]) ).
thf(f124,plain,
! [X0: $i,X1: $i] :
( ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X1 )
| ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X0 ) ),
inference(subsumption_resolution,[status(thm)],[f123,f115]) ).
thf(f115,plain,
! [X0: $i,X1: $i] :
( $true
= ( sP0 @ ( setadjoin @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( sP0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f109,f106]) ).
thf(f109,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( sP0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true != $true )
| ( $true
= ( sP0 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f65,f72]) ).
thf(f72,plain,
foundationAx = $true,
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f65,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( sP0 @ X2 ) )
| ( foundationAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( foundationAx = $true )
| ( ( $true
= ( in @ sK4 @ sK3 ) )
& ( $true
!= ( sP0 @ sK3 ) ) ) )
& ( ! [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( sP0 @ X2 ) ) )
| ( foundationAx != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f37,f39,f38]) ).
thf(f38,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( sP0 @ X0 ) ) )
=> ( ? [X1: $i] :
( $true
= ( in @ X1 @ sK3 ) )
& ( $true
!= ( sP0 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ? [X1: $i] :
( $true
= ( in @ X1 @ sK3 ) )
=> ( $true
= ( in @ sK4 @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ( foundationAx = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( sP0 @ X0 ) ) ) )
& ( ! [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( sP0 @ X2 ) ) )
| ( foundationAx != $true ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( foundationAx = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( sP0 @ X0 ) ) ) )
& ( ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( sP0 @ X0 ) ) )
| ( foundationAx != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( foundationAx = $true )
<=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( sP0 @ X0 ) ) ) ),
inference(definition_folding,[status(thm)],[f26,f29]) ).
thf(f29,plain,
! [X0: $i] :
( ( $true
= ( sP0 @ X0 ) )
<=> ? [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
( ( foundationAx = $true )
<=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
| ? [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( foundationAx = $true )
<=> ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
=> ? [X2: $i] :
( ~ ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( foundationAx
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X0 )
& ( in @ X3 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( foundationAx
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ? [X1: $i] :
( ( in @ X1 @ X0 )
& ( in @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',foundationAx) ).
thf(f123,plain,
! [X0: $i,X1: $i] :
( ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X0 )
| ( $true
!= ( sP0 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
! [X0: $i,X1: $i] :
( ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X0 )
| ( $true
!= ( sP0 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( $true != $true )
| ( ( sK2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= X1 ) ),
inference(superposition,[status(thm)],[f108,f61]) ).
thf(f61,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK2 @ X0 ) @ X0 ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $i] :
( ( ( $true
= ( sP0 @ X0 ) )
| ! [X1: $i] :
( ( ( $true
= ( in @ ( sK1 @ X1 @ X0 ) @ X0 ) )
& ( $true
= ( in @ ( sK1 @ X1 @ X0 ) @ X1 ) ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ ( sK2 @ X0 ) )
!= $true ) )
& ( $true
= ( in @ ( sK2 @ X0 ) @ X0 ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f32,f34,f33]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ X1 ) ) )
=> ( ( $true
= ( in @ ( sK1 @ X1 @ X0 ) @ X0 ) )
& ( $true
= ( in @ ( sK1 @ X1 @ X0 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
! [X0: $i] :
( ? [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( $true
!= ( in @ X4 @ X3 ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
=> ( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ ( sK2 @ X0 ) )
!= $true ) )
& ( $true
= ( in @ ( sK2 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
! [X0: $i] :
( ( ( $true
= ( sP0 @ X0 ) )
| ! [X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ X1 ) ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ? [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( $true
!= ( in @ X4 @ X3 ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( $true
!= ( sP0 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $i] :
( ( ( $true
= ( sP0 @ X0 ) )
| ! [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ? [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( $true
!= ( sP0 @ X0 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f108,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X0 = X2 )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true != $true )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f84,f73]) ).
thf(f73,plain,
upairset2E = $true,
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f84,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( upairset2E != $true ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ( ( sK13 != sK15 )
& ( sK13 != sK14 )
& ( $true
= ( in @ sK13 @ ( setadjoin @ sK14 @ ( setadjoin @ sK15 @ emptyset ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f54,f55]) ).
thf(f55,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( X3 != X5 )
& ( X3 != X4 )
& ( $true
= ( in @ X3 @ ( setadjoin @ X4 @ ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ( ( sK13 != sK15 )
& ( sK13 != sK14 )
& ( $true
= ( in @ sK13 @ ( setadjoin @ sK14 @ ( setadjoin @ sK15 @ emptyset ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( X3 != X5 )
& ( X3 != X4 )
& ( $true
= ( in @ X3 @ ( setadjoin @ X4 @ ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( X0 = X1 )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( X0 != X1 )
& ( X0 != X2 )
& ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( X0 = X1 )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) )
<=> ( upairset2E = $true ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( X0 = X1 )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) )
<=> ( upairset2E = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) )
=> ( ( X0 = X1 )
| ( X0 = X2 ) ) )
<=> ( upairset2E = $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X0 = X1 )
| ( X0 = X2 ) ) )
= upairset2E ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X4: $i,X3: $i,X1: $i] :
( ( ( in @ X4 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X3 = X4 )
| ( X1 = X4 ) ) )
= upairset2E ),
file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',upairset2E) ).
thf(f131,plain,
! [X0: $i,X4: $i] :
( ( ( in @ X4 @ ( sK2 @ X0 ) )
!= $true )
| ( $true
!= ( in @ X4 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f62,f109]) ).
thf(f62,plain,
! [X0: $i,X4: $i] :
( ( ( in @ X4 @ ( sK2 @ X0 ) )
!= $true )
| ( $true
!= ( in @ X4 @ X0 ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU807^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:34:25 EST 2026
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.35 ---- Original DTF file ---
% 0.07/0.35 thf(spec,logic,$$dhol).
% 0.07/0.35 %------------------------------------------------------------------------------
% 0.07/0.35 % File : SEU807^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.35 % Domain : Set Theory
% 0.07/0.35 % Problem : The Foundation Axiom
% 0.07/0.35 % Version : Especial > Reduced > Especial.
% 0.07/0.35 % English : (! A:i.! B:i.in A B -> ~(in B A))
% 0.07/0.35
% 0.07/0.35 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.35 % Source : [Bro08]
% 0.07/0.35 % Names : ZFC309l [Bro08]
% 0.07/0.35
% 0.07/0.35 % Status : Theorem
% 0.07/0.35 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.07/0.35 % Syntax : Number of formulae : 14 ( 5 unt; 8 typ; 5 def)
% 0.07/0.35 % Number of atoms : 31 ( 9 equ; 0 cnn)
% 0.07/0.35 % Maximal formula atoms : 7 ( 5 avg)
% 0.07/0.35 % Number of connectives : 49 ( 2 ~; 1 |; 2 &; 32 @)
% 0.07/0.35 % ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% 0.07/0.35 % Maximal formula depth : 12 ( 3 avg)
% 0.07/0.35 % Number of types : 2 ( 0 usr)
% 0.07/0.35 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.07/0.35 % Number of symbols : 9 ( 8 usr; 6 con; 0-2 aty)
% 0.07/0.35 % Number of variables : 18 ( 0 ^; 15 !; 3 ?; 18 :)
% 0.07/0.35 % SPC : TH0_THM_EQU_NAR
% 0.07/0.35
% 0.07/0.35 % Comments : http://mathgate.info/detsetitem.php?id=436
% 0.07/0.35 %------------------------------------------------------------------------------
% 0.07/0.35 thf(in_type,type,
% 0.07/0.35 in: $i > $i > $o ).
% 0.07/0.35
% 0.07/0.35 thf(emptyset_type,type,
% 0.07/0.35 emptyset: $i ).
% 0.07/0.35
% 0.07/0.35 thf(setadjoin_type,type,
% 0.07/0.35 setadjoin: $i > $i > $i ).
% 0.07/0.35
% 0.07/0.35 thf(foundationAx_type,type,
% 0.07/0.35 foundationAx: $o ).
% 0.07/0.35
% 0.07/0.35 thf(foundationAx,definition,
% 0.07/0.35 ( foundationAx
% 0.07/0.35 = ( ! [A: $i] :
% 0.07/0.35 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.07/0.35 => ? [B: $i] :
% 0.07/0.35 ( ( in @ B @ A )
% 0.07/0.35 & ~ ? [Xx: $i] :
% 0.07/0.35 ( ( in @ Xx @ B )
% 0.07/0.35 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.07/0.35
% 0.07/0.35 thf(setadjoinIL_type,type,
% 0.07/0.35 setadjoinIL: $o ).
% 0.07/0.35
% 0.07/0.35 thf(setadjoinIL,definition,
% 0.07/0.35 ( setadjoinIL
% 0.07/0.35 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.07/0.35
% 0.07/0.35 thf(setadjoinIR_type,type,
% 0.07/0.35 setadjoinIR: $o ).
% 0.07/0.35
% 0.07/0.35 thf(setadjoinIR,definition,
% 0.07/0.35 ( setadjoinIR
% 0.07/0.35 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.35 ( ( in @ Xy @ A )
% 0.07/0.35 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.07/0.35
% 0.07/0.35 thf(in__Cong_type,type,
% 0.07/0.35 in__Cong: $o ).
% 0.07/0.35
% 0.07/0.35 thf(in__Cong,definition,
% 0.07/0.35 ( in__Cong
% 0.07/0.35 = ( ! [A: $i,B: $i] :
% 0.07/0.35 ( ( A = B )
% 0.07/0.35 => ! [Xx: $i,Xy: $i] :
% 0.07/0.35 ( ( Xx = Xy )
% 0.07/0.35 => ( ( in @ Xx @ A )
% 0.07/0.35 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.07/0.35
% 0.07/0.35 thf(upairset2E_type,type,
% 0.07/0.35 upairset2E: $o ).
% 0.07/0.35
% 0.07/0.35 thf(upairset2E,definition,
% 0.07/0.35 ( upairset2E
% 0.07/0.35 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.07/0.35 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.07/0.35 => ( ( Xz = Xx )
% 0.07/0.35 | ( Xz = Xy ) ) ) ) ) ).
% 0.07/0.35
% 0.07/0.35 thf(notinself2,conjecture,
% 0.07/0.35 ( foundationAx
% 0.07/0.35 => ( setadjoinIL
% 0.07/0.35 => ( setadjoinIR
% 0.07/0.35 => ( in__Cong
% 0.07/0.35 => ( upairset2E
% 0.07/0.35 => ! [A: $i,B: $i] :
% 0.07/0.35 ( ( in @ A @ B )
% 0.07/0.35 => ~ ( in @ B @ A ) ) ) ) ) ) ) ).
% 0.07/0.35
% 0.07/0.35 %------------------------------------------------------------------------------
% 0.07/0.35 ------------------------
% 1.43/1.26 ---- Embedded in THF ---
% 1.43/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.26 %%% Generated on Tue Feb 24 07:34:26 EST 2026
% 1.43/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.26 %%% Logic specification used:
% 1.43/1.26 %%% thf(spec, logic, $$dhol).
% 1.43/1.26
% 1.43/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2DTF12860.p
% See solution above
% 1.43/1.26 ------------------------
% 1.43/1.27 ---- Cleaned THF ---
% 1.43/1.27 thf(in_type,type,
% 1.43/1.27 in: $i > $i > $o ).
% 1.43/1.27
% 1.43/1.27 thf(emptyset_type,type,
% 1.43/1.27 emptyset: $i ).
% 1.43/1.27
% 1.43/1.27 thf(setadjoin_type,type,
% 1.43/1.27 setadjoin: $i > $i > $i ).
% 1.43/1.27
% 1.43/1.27 thf(foundationAx_type,type,
% 1.43/1.27 foundationAx: $o ).
% 1.43/1.27
% 1.43/1.27 thf(foundationAx,definition,
% 1.43/1.27 ( foundationAx
% 1.43/1.27 = ( ! [A: $i] :
% 1.43/1.27 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.43/1.27 => ? [B: $i] :
% 1.43/1.27 ( ( in @ B @ A )
% 1.43/1.27 & ~ ? [Xx: $i] :
% 1.43/1.27 ( ( in @ Xx @ B )
% 1.43/1.27 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.43/1.27
% 1.43/1.27 thf(setadjoinIL_type,type,
% 1.43/1.27 setadjoinIL: $o ).
% 1.43/1.27
% 1.43/1.27 thf(setadjoinIL,definition,
% 1.43/1.27 ( setadjoinIL
% 1.43/1.27 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.43/1.27
% 1.43/1.27 thf(setadjoinIR_type,type,
% 1.43/1.27 setadjoinIR: $o ).
% 1.43/1.27
% 1.43/1.27 thf(setadjoinIR,definition,
% 1.43/1.27 ( setadjoinIR
% 1.43/1.27 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.43/1.27 ( ( in @ Xy @ A )
% 1.43/1.27 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.43/1.27
% 1.43/1.27 thf(in__Cong_type,type,
% 1.43/1.27 in__Cong: $o ).
% 1.43/1.27
% 1.43/1.27 thf(in__Cong,definition,
% 1.43/1.27 ( in__Cong
% 1.43/1.27 = ( ! [A: $i,B: $i] :
% 1.43/1.27 ( ( A = B )
% 1.43/1.27 => ! [Xx: $i,Xy: $i] :
% 1.43/1.27 ( ( Xx = Xy )
% 1.43/1.27 => ( ( in @ Xx @ A )
% 1.43/1.27 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 1.43/1.27
% 1.43/1.27 thf(upairset2E_type,type,
% 1.43/1.27 upairset2E: $o ).
% 1.43/1.27
% 1.43/1.27 thf(upairset2E,definition,
% 1.43/1.27 ( upairset2E
% 1.43/1.27 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.43/1.27 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.43/1.27 => ( ( Xz = Xx )
% 1.43/1.27 | ( Xz = Xy ) ) ) ) ) ).
% 1.43/1.27
% 1.43/1.27 thf(notinself2,conjecture,
% 1.43/1.27 ( foundationAx
% 1.43/1.27 => ( setadjoinIL
% 1.43/1.27 => ( setadjoinIR
% 1.43/1.27 => ( in__Cong
% 1.43/1.27 => ( upairset2E
% 1.43/1.27 => ! [A: $i,B: $i] :
% 1.43/1.27 ( ( in @ A @ B )
% 1.43/1.27 => ~ ( in @ B @ A ) ) ) ) ) ) ) ).
% 1.43/1.27 ------------------------
% 1.43/1.29 % (12958)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_12860 for (2999ds/4Mi)
% 1.43/1.29 % (12962)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_12860 for (2999ds/275Mi)
% 1.43/1.29 % (12963)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/18Mi)
% 1.43/1.29 % (12961)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_12860 for (2999ds/2Mi)
% 1.43/1.29 % (12960)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/2Mi)
% 1.43/1.29 % (12959)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_12860 for (2999ds/27Mi)
% 1.43/1.29 % (12957)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/183Mi)
% 1.43/1.29 % (12960)Instruction limit reached!
% 1.43/1.29 % (12960)------------------------------
% 1.43/1.29 % (12960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.29 % (12960)Termination reason: Unknown
% 1.43/1.29 % (12960)Termination phase: Unused predicate definition removal
% 1.43/1.29 % (12961)Instruction limit reached!
% 1.43/1.29 % (12961)------------------------------
% 1.43/1.29 % (12961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.29 % (12961)Termination reason: Unknown
% 1.43/1.29 % (12961)Termination phase: Property scanning
% 1.43/1.29
% 1.43/1.29 % (12961)Memory used [KB]: 1023
% 1.43/1.29 % (12961)Time elapsed: 0.003 s
% 1.43/1.29 % (12961)Instructions burned: 3 (million)
% 1.43/1.29 % (12961)------------------------------
% 1.43/1.29 % (12961)------------------------------
% 1.43/1.29
% 1.43/1.29 % (12960)Memory used [KB]: 1023
% 1.43/1.29 % (12960)Time elapsed: 0.003 s
% 1.43/1.29 % (12960)Instructions burned: 2 (million)
% 1.43/1.29 % (12960)------------------------------
% 1.43/1.29 % (12960)------------------------------
% 1.43/1.29 % (12958)Instruction limit reached!
% 1.43/1.29 % (12958)------------------------------
% 1.43/1.29 % (12958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.29 % (12958)Termination reason: Unknown
% 1.43/1.29 % (12958)Termination phase: Saturation
% 1.43/1.29
% 1.43/1.29 % (12958)Memory used [KB]: 5500
% 1.43/1.29 % (12958)Time elapsed: 0.004 s
% 1.43/1.29 % (12958)Instructions burned: 4 (million)
% 1.43/1.29 % (12958)------------------------------
% 1.43/1.29 % (12958)------------------------------
% 1.56/1.30 % (12963)Instruction limit reached!
% 1.56/1.30 % (12963)------------------------------
% 1.56/1.30 % (12963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (12963)Termination reason: Unknown
% 1.56/1.30 % (12963)Termination phase: Saturation
% 1.56/1.30
% 1.56/1.30 % (12963)Memory used [KB]: 5628
% 1.56/1.30 % (12963)Time elapsed: 0.012 s
% 1.56/1.30 % (12963)Instructions burned: 19 (million)
% 1.56/1.30 % (12963)------------------------------
% 1.56/1.30 % (12963)------------------------------
% 1.56/1.31 % (12959)Instruction limit reached!
% 1.56/1.31 % (12959)------------------------------
% 1.56/1.31 % (12959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (12959)Termination reason: Unknown
% 1.56/1.31 % (12959)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (12959)Memory used [KB]: 5628
% 1.56/1.31 % (12959)Time elapsed: 0.017 s
% 1.56/1.31 % (12959)Instructions burned: 28 (million)
% 1.56/1.31 % (12959)------------------------------
% 1.56/1.31 % (12959)------------------------------
% 1.56/1.31 % (12964)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/3Mi)
% 1.56/1.31 % (12965)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_12860 for (2999ds/37Mi)
% 1.56/1.31 % (12966)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_12860 for (2999ds/15Mi)
% 1.56/1.31 % (12964)Instruction limit reached!
% 1.56/1.31 % (12964)------------------------------
% 1.56/1.31 % (12964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (12964)Termination reason: Unknown
% 1.56/1.31 % (12964)Termination phase: Property scanning
% 1.56/1.31
% 1.56/1.31 % (12964)Memory used [KB]: 1023
% 1.56/1.31 % (12964)Time elapsed: 0.003 s
% 1.56/1.31 % (12964)Instructions burned: 3 (million)
% 1.56/1.31 % (12964)------------------------------
% 1.56/1.31 % (12964)------------------------------
% 1.56/1.32 % (12966)Instruction limit reached!
% 1.56/1.32 % (12966)------------------------------
% 1.56/1.32 % (12966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (12966)Termination reason: Unknown
% 1.56/1.32 % (12966)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (12966)Memory used [KB]: 5628
% 1.56/1.32 % (12966)Time elapsed: 0.010 s
% 1.56/1.32 % (12966)Instructions burned: 15 (million)
% 1.56/1.32 % (12966)------------------------------
% 1.56/1.32 % (12966)------------------------------
% 1.56/1.32 % (12967)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_12860 for (2999ds/3Mi)
% 1.56/1.32 % (12967)Instruction limit reached!
% 1.56/1.32 % (12967)------------------------------
% 1.56/1.32 % (12967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (12967)Termination reason: Unknown
% 1.56/1.32 % (12967)Termination phase: Property scanning
% 1.56/1.32
% 1.56/1.32 % (12967)Memory used [KB]: 1023
% 1.56/1.32 % (12967)Time elapsed: 0.003 s
% 1.56/1.32 % (12967)Instructions burned: 3 (million)
% 1.56/1.32 % (12967)------------------------------
% 1.56/1.32 % (12967)------------------------------
% 1.56/1.32 % (12968)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_12860 for (2999ds/1041Mi)
% 1.56/1.33 % (12969)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/7Mi)
% 1.56/1.33 % (12965)Instruction limit reached!
% 1.56/1.33 % (12965)------------------------------
% 1.56/1.33 % (12965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (12965)Termination reason: Unknown
% 1.56/1.33 % (12965)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (12965)Memory used [KB]: 5628
% 1.56/1.33 % (12965)Time elapsed: 0.020 s
% 1.56/1.33 % (12965)Instructions burned: 37 (million)
% 1.56/1.33 % (12965)------------------------------
% 1.56/1.33 % (12965)------------------------------
% 1.56/1.33 % (12969)Instruction limit reached!
% 1.56/1.33 % (12969)------------------------------
% 1.56/1.33 % (12969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (12969)Termination reason: Unknown
% 1.56/1.33 % (12969)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (12969)Memory used [KB]: 1023
% 1.56/1.33 % (12969)Time elapsed: 0.005 s
% 1.56/1.33 % (12969)Instructions burned: 7 (million)
% 1.56/1.33 % (12969)------------------------------
% 1.56/1.33 % (12969)------------------------------
% 1.56/1.33 % (12970)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/16Mi)
% 1.56/1.34 % (12971)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_12860 for (2999ds/3Mi)
% 1.56/1.34 % (12971)Instruction limit reached!
% 1.56/1.34 % (12971)------------------------------
% 1.56/1.34 % (12971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (12971)Termination reason: Unknown
% 1.56/1.34 % (12971)Termination phase: Twee Goal Transformation
% 1.56/1.34
% 1.56/1.34 % (12971)Memory used [KB]: 1023
% 1.56/1.34 % (12971)Time elapsed: 0.003 s
% 1.56/1.34 % (12971)Instructions burned: 4 (million)
% 1.56/1.34 % (12971)------------------------------
% 1.56/1.34 % (12971)------------------------------
% 1.56/1.34 % (12970)Instruction limit reached!
% 1.56/1.34 % (12970)------------------------------
% 1.56/1.34 % (12970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (12970)Termination reason: Unknown
% 1.56/1.34 % (12970)Termination phase: Saturation
% 1.56/1.34
% 1.56/1.34 % (12970)Memory used [KB]: 5756
% 1.56/1.34 % (12970)Time elapsed: 0.011 s
% 1.56/1.34 % (12970)Instructions burned: 17 (million)
% 1.56/1.34 % (12970)------------------------------
% 1.56/1.34 % (12970)------------------------------
% 1.56/1.34 % (12972)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_12860 for (2999ds/3Mi)
% 1.56/1.35 % (12972)Instruction limit reached!
% 1.56/1.35 % (12972)------------------------------
% 1.56/1.35 % (12972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (12972)Termination reason: Unknown
% 1.56/1.35 % (12972)Termination phase: Preprocessing 3
% 1.56/1.35
% 1.56/1.35 % (12972)Memory used [KB]: 1023
% 1.56/1.35 % (12972)Time elapsed: 0.003 s
% 1.56/1.35 % (12972)Instructions burned: 3 (million)
% 1.56/1.35 % (12972)------------------------------
% 1.56/1.35 % (12972)------------------------------
% 1.56/1.35 % (12973)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/7Mi)
% 1.56/1.35 % (12973)Refutation not found, incomplete strategy
% 1.56/1.35 % (12973)------------------------------
% 1.56/1.35 % (12973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (12973)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.35
% 1.56/1.35
% 1.56/1.35 % (12973)Memory used [KB]: 5500
% 1.56/1.35 % (12973)Time elapsed: 0.003 s
% 1.56/1.35 % (12973)Instructions burned: 4 (million)
% 1.56/1.35 % (12973)------------------------------
% 1.56/1.35 % (12973)------------------------------
% 1.56/1.35 % (12974)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/3Mi)
% 1.56/1.35 % (12974)Instruction limit reached!
% 1.56/1.35 % (12974)------------------------------
% 1.56/1.35 % (12974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (12974)Termination reason: Unknown
% 1.56/1.35 % (12974)Termination phase: Function definition elimination
% 1.56/1.35
% 1.56/1.35 % (12974)Memory used [KB]: 1023
% 1.56/1.35 % (12974)Time elapsed: 0.003 s
% 1.56/1.35 % (12974)Instructions burned: 3 (million)
% 1.56/1.35 % (12974)------------------------------
% 1.56/1.35 % (12974)------------------------------
% 1.56/1.36 % (12975)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/4Mi)
% 1.56/1.36 % (12976)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/18Mi)
% 1.56/1.36 % (12975)Instruction limit reached!
% 1.56/1.36 % (12975)------------------------------
% 1.56/1.36 % (12975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (12975)Termination reason: Unknown
% 1.56/1.36 % (12975)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (12975)Memory used [KB]: 5500
% 1.56/1.36 % (12975)Time elapsed: 0.004 s
% 1.56/1.36 % (12975)Instructions burned: 5 (million)
% 1.56/1.36 % (12975)------------------------------
% 1.56/1.36 % (12975)------------------------------
% 1.56/1.36 % (12977)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/710Mi)
% 1.56/1.37 % (12976)Instruction limit reached!
% 1.56/1.37 % (12976)------------------------------
% 1.56/1.37 % (12976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (12976)Termination reason: Unknown
% 1.56/1.37 % (12976)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (12976)Memory used [KB]: 5628
% 1.56/1.37 % (12976)Time elapsed: 0.012 s
% 1.56/1.37 % (12976)Instructions burned: 19 (million)
% 1.56/1.37 % (12976)------------------------------
% 1.56/1.37 % (12976)------------------------------
% 1.56/1.37 % (12978)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/6Mi)
% 1.56/1.37 % (12978)Instruction limit reached!
% 1.56/1.37 % (12978)------------------------------
% 1.56/1.37 % (12978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (12978)Termination reason: Unknown
% 1.56/1.37 % (12978)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (12978)Memory used [KB]: 5500
% 1.56/1.37 % (12978)Time elapsed: 0.005 s
% 1.56/1.37 % (12978)Instructions burned: 6 (million)
% 1.56/1.37 % (12978)------------------------------
% 1.56/1.37 % (12978)------------------------------
% 1.56/1.38 % (12979)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_12860 for (2999ds/902Mi)
% 1.56/1.38 % (12979)Refutation not found, incomplete strategy
% 1.56/1.38 % (12979)------------------------------
% 1.56/1.38 % (12979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (12979)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.38
% 1.56/1.38
% 1.56/1.38 % (12979)Memory used [KB]: 5500
% 1.56/1.38 % (12979)Time elapsed: 0.004 s
% 1.56/1.38 % (12979)Instructions burned: 4 (million)
% 1.56/1.38 % (12979)------------------------------
% 1.56/1.38 % (12979)------------------------------
% 1.56/1.38 % (12957)Instruction limit reached!
% 1.56/1.38 % (12957)------------------------------
% 1.56/1.38 % (12957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (12957)Termination reason: Unknown
% 1.56/1.38 % (12957)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (12957)Memory used [KB]: 6140
% 1.56/1.38 % (12957)Time elapsed: 0.093 s
% 1.56/1.38 % (12957)Instructions burned: 183 (million)
% 1.56/1.38 % (12957)------------------------------
% 1.56/1.38 % (12957)------------------------------
% 1.56/1.39 % (12980)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_12860 for (2999ds/21Mi)
% 1.56/1.39 % (12981)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/5Mi)
% 1.56/1.39 % (12981)Instruction limit reached!
% 1.56/1.39 % (12981)------------------------------
% 1.56/1.39 % (12981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (12981)Termination reason: Unknown
% 1.56/1.39 % (12981)Termination phase: Saturation
% 1.56/1.39
% 1.56/1.39 % (12981)Memory used [KB]: 5500
% 1.56/1.39 % (12981)Time elapsed: 0.005 s
% 1.56/1.39 % (12981)Instructions burned: 7 (million)
% 1.56/1.39 % (12981)------------------------------
% 1.56/1.39 % (12981)------------------------------
% 1.56/1.40 % (12980)Instruction limit reached!
% 1.56/1.40 % (12980)------------------------------
% 1.56/1.40 % (12980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.40 % (12982)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/6Mi)
% 1.56/1.40 % (12980)Termination reason: Unknown
% 1.56/1.40 % (12980)Termination phase: Saturation
% 1.56/1.40
% 1.56/1.40 % (12980)Memory used [KB]: 5628
% 1.56/1.40 % (12980)Time elapsed: 0.013 s
% 1.56/1.40 % (12980)Instructions burned: 22 (million)
% 1.56/1.40 % (12980)------------------------------
% 1.56/1.40 % (12980)------------------------------
% 1.56/1.40 % (12983)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12860 for (2999ds/377Mi)
% 1.56/1.40 % (12982)Instruction limit reached!
% 1.56/1.40 % (12982)------------------------------
% 1.56/1.40 % (12982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.40 % (12982)Termination reason: Unknown
% 1.56/1.40 % (12982)Termination phase: Saturation
% 1.56/1.40
% 1.56/1.40 % (12982)Memory used [KB]: 5500
% 1.56/1.40 % (12982)Time elapsed: 0.005 s
% 1.56/1.40 % (12982)Instructions burned: 7 (million)
% 1.56/1.40 % (12982)------------------------------
% 1.56/1.40 % (12982)------------------------------
% 1.56/1.41 % (12984)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_12860 for (2998ds/779Mi)
% 1.56/1.41 % (12962)Instruction limit reached!
% 1.56/1.41 % (12962)------------------------------
% 1.56/1.41 % (12962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.41 % (12962)Termination reason: Unknown
% 1.56/1.41 % (12962)Termination phase: Saturation
% 1.56/1.41
% 1.56/1.41 % (12962)Memory used [KB]: 6268
% 1.56/1.41 % (12962)Time elapsed: 0.121 s
% 1.56/1.41 % (12962)Instructions burned: 276 (million)
% 1.56/1.41 % (12962)------------------------------
% 1.56/1.41 % (12962)------------------------------
% 1.56/1.41 % (12985)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_12860 for (2998ds/19Mi)
% 1.56/1.42 % (12986)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12860 for (2998ds/879Mi)
% 1.56/1.42 % (12985)Refutation not found, incomplete strategy
% 1.56/1.42 % (12985)------------------------------
% 1.56/1.42 % (12985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.42 % (12985)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.42
% 1.56/1.42
% 1.56/1.42 % (12985)Memory used [KB]: 5500
% 1.56/1.42 % (12985)Time elapsed: 0.006 s
% 1.56/1.42 % (12985)Instructions burned: 9 (million)
% 1.56/1.42 % (12985)------------------------------
% 1.56/1.42 % (12985)------------------------------
% 1.56/1.43 % (12987)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12860 for (2998ds/17Mi)
% 1.56/1.44 % (12987)Instruction limit reached!
% 1.56/1.44 % (12987)------------------------------
% 1.56/1.44 % (12987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.44 % (12987)Termination reason: Unknown
% 1.56/1.44 % (12987)Termination phase: Saturation
% 1.56/1.44
% 1.56/1.44 % (12987)Memory used [KB]: 5628
% 1.56/1.44 % (12987)Time elapsed: 0.011 s
% 1.56/1.44 % (12988)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12860 for (2998ds/3Mi)
% 1.56/1.44 % (12987)Instructions burned: 17 (million)
% 1.56/1.44 % (12987)------------------------------
% 1.56/1.44 % (12987)------------------------------
% 1.56/1.44 % (12988)Instruction limit reached!
% 1.56/1.44 % (12988)------------------------------
% 1.56/1.44 % (12988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.44 % (12988)Termination reason: Unknown
% 1.56/1.44 % (12988)Termination phase: Saturation
% 1.56/1.44
% 1.56/1.44 % (12988)Memory used [KB]: 1023
% 1.56/1.44 % (12988)Time elapsed: 0.004 s
% 1.56/1.44 % (12988)Instructions burned: 4 (million)
% 1.56/1.44 % (12988)------------------------------
% 1.56/1.44 % (12988)------------------------------
% 1.56/1.45 % (12989)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12860 for (2998ds/30Mi)
% 1.56/1.45 % (12990)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_12860 for (2998ds/127Mi)
% 1.56/1.46 % (12989)Refutation not found, incomplete strategy
% 1.56/1.46 % (12989)------------------------------
% 1.56/1.46 % (12989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.46 % (12989)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.46
% 1.56/1.46
% 1.56/1.46 % (12989)Memory used [KB]: 5500
% 1.56/1.46 % (12989)Time elapsed: 0.007 s
% 1.56/1.46 % (12989)Instructions burned: 8 (million)
% 1.56/1.46 % (12989)------------------------------
% 1.56/1.46 % (12989)------------------------------
% 1.56/1.48 % (12991)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_12860 for (2998ds/100Mi)
% 1.56/1.51 % (12990)Instruction limit reached!
% 1.56/1.51 % (12990)------------------------------
% 1.56/1.51 % (12990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.51 % (12990)Termination reason: Unknown
% 1.56/1.51 % (12990)Termination phase: Saturation
% 1.56/1.51
% 1.56/1.51 % (12990)Memory used [KB]: 5628
% 1.56/1.51 % (12990)Time elapsed: 0.061 s
% 1.56/1.51 % (12990)Instructions burned: 127 (million)
% 1.56/1.51 % (12990)------------------------------
% 1.56/1.51 % (12990)------------------------------
% 1.56/1.53 % (12991)Instruction limit reached!
% 1.56/1.53 % (12991)------------------------------
% 1.56/1.53 % (12991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.53 % (12991)Termination reason: Unknown
% 1.56/1.53 % (12991)Termination phase: Saturation
% 1.56/1.53
% 1.56/1.53 % (12991)Memory used [KB]: 5756
% 1.56/1.53 % (12991)Time elapsed: 0.053 s
% 1.56/1.53 % (12991)Instructions burned: 100 (million)
% 1.56/1.53 % (12991)------------------------------
% 1.56/1.53 % (12991)------------------------------
% 1.56/1.53 % (12992)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_12860 for (2997ds/3Mi)
% 1.56/1.53 % (12992)Instruction limit reached!
% 1.56/1.53 % (12992)------------------------------
% 1.56/1.53 % (12992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.53 % (12992)Termination reason: Unknown
% 1.56/1.53 % (12992)Termination phase: Property scanning
% 1.56/1.53
% 1.56/1.53 % (12992)Memory used [KB]: 1023
% 1.56/1.53 % (12992)Time elapsed: 0.003 s
% 1.56/1.53 % (12992)Instructions burned: 4 (million)
% 1.56/1.53 % (12992)------------------------------
% 1.56/1.53 % (12992)------------------------------
% 1.56/1.54 % (12993)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_12860 for (2997ds/20Mi)
% 1.56/1.55 % (12994)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_12860 for (2997ds/86Mi)
% 1.56/1.55 % (12993)Instruction limit reached!
% 1.56/1.55 % (12993)------------------------------
% 1.56/1.55 % (12993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.55 % (12993)Termination reason: Unknown
% 1.56/1.55 % (12993)Termination phase: Saturation
% 1.56/1.55
% 1.56/1.55 % (12993)Memory used [KB]: 5628
% 1.56/1.55 % (12993)Time elapsed: 0.013 s
% 1.56/1.55 % (12993)Instructions burned: 20 (million)
% 1.56/1.55 % (12993)------------------------------
% 1.56/1.55 % (12993)------------------------------
% 1.56/1.57 % (12995)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_12860 for (2997ds/107Mi)
% 1.56/1.58 % (12983)Instruction limit reached!
% 1.56/1.58 % (12983)------------------------------
% 1.56/1.58 % (12983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.58 % (12983)Termination reason: Unknown
% 1.56/1.58 % (12983)Termination phase: Saturation
% 1.56/1.58
% 1.56/1.58 % (12983)Memory used [KB]: 6012
% 1.56/1.58 % (12983)Time elapsed: 0.183 s
% 1.56/1.58 % (12983)Instructions burned: 377 (million)
% 1.56/1.58 % (12983)------------------------------
% 1.56/1.58 % (12983)------------------------------
% 1.56/1.59 % (12994)Instruction limit reached!
% 1.56/1.59 % (12994)------------------------------
% 1.56/1.59 % (12994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.59 % (12994)Termination reason: Unknown
% 1.56/1.59 % (12994)Termination phase: Saturation
% 1.56/1.59
% 1.56/1.59 % (12994)Memory used [KB]: 6012
% 1.56/1.59 % (12994)Time elapsed: 0.046 s
% 1.56/1.59 % (12994)Instructions burned: 86 (million)
% 1.56/1.59 % (12994)------------------------------
% 1.56/1.59 % (12994)------------------------------
% 1.56/1.60 % (12996)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_12860 for (2996ds/39Mi)
% 1.56/1.61 % (12997)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_12860 for (2996ds/448Mi)
% 1.56/1.61 % (12997)Refutation not found, incomplete strategy
% 1.56/1.61 % (12997)------------------------------
% 1.56/1.61 % (12997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.61 % (12997)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.61
% 1.56/1.61
% 1.56/1.61 % (12997)Memory used [KB]: 5500
% 1.56/1.61 % (12997)Time elapsed: 0.005 s
% 1.56/1.61 % (12997)Instructions burned: 6 (million)
% 1.56/1.61 % (12997)------------------------------
% 1.56/1.61 % (12997)------------------------------
% 1.56/1.62 % (12996)Instruction limit reached!
% 1.56/1.62 % (12996)------------------------------
% 1.56/1.62 % (12996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.62 % (12996)Termination reason: Unknown
% 1.56/1.62 % (12996)Termination phase: Saturation
% 1.56/1.62
% 1.56/1.62 % (12996)Memory used [KB]: 5628
% 1.56/1.62 % (12996)Time elapsed: 0.021 s
% 1.56/1.62 % (12996)Instructions burned: 39 (million)
% 1.56/1.62 % (12996)------------------------------
% 1.56/1.62 % (12996)------------------------------
% 1.56/1.62 % (12995)Instruction limit reached!
% 1.56/1.62 % (12995)------------------------------
% 1.56/1.62 % (12995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.62 % (12995)Termination reason: Unknown
% 1.56/1.62 % (12995)Termination phase: Saturation
% 1.56/1.62
% 1.56/1.62 % (12995)Memory used [KB]: 5756
% 1.56/1.62 % (12995)Time elapsed: 0.056 s
% 1.56/1.62 % (12995)Instructions burned: 107 (million)
% 1.56/1.62 % (12995)------------------------------
% 1.56/1.62 % (12995)------------------------------
% 1.56/1.63 % (12998)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_12860 for (2996ds/46Mi)
% 1.56/1.63 % (12999)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_12860 for (2996ds/98Mi)
% 1.56/1.64 % (13000)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_12860 for (2996ds/507Mi)
% 1.56/1.66 % (12998)Instruction limit reached!
% 1.56/1.66 % (12998)------------------------------
% 1.56/1.66 % (12998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.66 % (12998)Termination reason: Unknown
% 1.56/1.66 % (12998)Termination phase: Saturation
% 1.56/1.66
% 1.56/1.66 % (12998)Memory used [KB]: 5756
% 1.56/1.66 % (12998)Time elapsed: 0.026 s
% 1.56/1.66 % (12998)Instructions burned: 47 (million)
% 1.56/1.66 % (12998)------------------------------
% 1.56/1.66 % (12998)------------------------------
% 1.56/1.67 % (13001)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_12860 for (2996ds/149Mi)
% 1.56/1.68 % (12999)Instruction limit reached!
% 1.56/1.68 % (12999)------------------------------
% 1.56/1.68 % (12999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.68 % (12999)Termination reason: Unknown
% 1.56/1.68 % (12999)Termination phase: Saturation
% 1.56/1.68
% 1.56/1.68 % (12999)Memory used [KB]: 1279
% 1.56/1.68 % (12999)Time elapsed: 0.046 s
% 1.56/1.68 % (12999)Instructions burned: 99 (million)
% 1.56/1.68 % (12999)------------------------------
% 1.56/1.68 % (12999)------------------------------
% 1.56/1.69 % (13002)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_12860 for (2996ds/39Mi)
% 1.56/1.71 % (12977)Refutation not found, non-redundant clauses discarded% (12977)------------------------------
% 1.56/1.71 % (12977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.71 % (12977)Termination reason: Refutation not found, non-redundant clauses discarded
% 1.56/1.71
% 1.56/1.71 % (12977)Memory used [KB]: 6396
% 1.56/1.71 % (12977)Time elapsed: 0.346 s
% 1.56/1.71 % (12977)Instructions burned: 700 (million)
% 1.56/1.71 % (12977)------------------------------
% 1.56/1.71 % (12977)------------------------------
% 1.56/1.71 % (13002)Instruction limit reached!
% 1.56/1.71 % (13002)------------------------------
% 1.56/1.71 % (13002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.71 % (13002)Termination reason: Unknown
% 1.56/1.71 % (13002)Termination phase: Saturation
% 1.56/1.71
% 1.56/1.71 % (13002)Memory used [KB]: 5628
% 1.56/1.71 % (13002)Time elapsed: 0.023 s
% 1.56/1.71 % (13002)Instructions burned: 40 (million)
% 1.56/1.71 % (13002)------------------------------
% 1.56/1.71 % (13002)------------------------------
% 1.56/1.73 % (13003)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_12860 for (2995ds/6Mi)
% 1.56/1.73 % (13003)Instruction limit reached!
% 1.56/1.73 % (13003)------------------------------
% 1.56/1.73 % (13003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.73 % (13003)Termination reason: Unknown
% 1.56/1.73 % (13003)Termination phase: Saturation
% 1.56/1.73
% 1.56/1.73 % (13003)Memory used [KB]: 9978
% 1.56/1.73 % (13003)Time elapsed: 0.006 s
% 1.56/1.73 % (13003)Instructions burned: 7 (million)
% 1.56/1.73 % (13003)------------------------------
% 1.56/1.73 % (13003)------------------------------
% 1.56/1.73 % (13004)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_12860 for (2995ds/1087Mi)
% 1.56/1.75 % (13001)Instruction limit reached!
% 1.56/1.75 % (13001)------------------------------
% 1.56/1.75 % (13001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.75 % (13001)Termination reason: Unknown
% 1.56/1.75 % (13001)Termination phase: Saturation
% 1.56/1.75
% 1.56/1.75 % (13001)Memory used [KB]: 5884
% 1.56/1.75 % (13001)Time elapsed: 0.075 s
% 1.56/1.75 % (13001)Instructions burned: 149 (million)
% 1.56/1.75 % (13001)------------------------------
% 1.56/1.75 % (13001)------------------------------
% 1.56/1.75 % (13005)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_12860 for (2995ds/47Mi)
% 1.56/1.76 % (13006)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_12860 for (2995ds/44Mi)
% 1.56/1.77 % (13006)Refutation not found, incomplete strategy
% 1.56/1.77 % (13006)------------------------------
% 1.56/1.77 % (13006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.77 % (13006)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.77
% 1.56/1.77
% 1.56/1.77 % (13006)Memory used [KB]: 1023
% 1.56/1.77 % (13006)Time elapsed: 0.005 s
% 1.56/1.77 % (13006)Instructions burned: 6 (million)
% 1.56/1.77 % (13006)------------------------------
% 1.56/1.77 % (13006)------------------------------
% 1.56/1.77 % (13005)Instruction limit reached!
% 1.56/1.77 % (13005)------------------------------
% 1.56/1.77 % (13005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.77 % (13005)Termination reason: Unknown
% 1.56/1.77 % (13005)Termination phase: Saturation
% 1.56/1.77
% 1.56/1.77 % (13005)Memory used [KB]: 5756
% 1.56/1.77 % (13005)Time elapsed: 0.026 s
% 1.56/1.77 % (13005)Instructions burned: 47 (million)
% 1.56/1.77 % (13005)------------------------------
% 1.56/1.77 % (13005)------------------------------
% 1.56/1.78 % (13007)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_12860 for (2995ds/432Mi)
% 1.56/1.79 % (12984)Instruction limit reached!
% 1.56/1.79 % (12984)------------------------------
% 1.56/1.79 % (12984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.79 % (12984)Termination reason: Unknown
% 1.56/1.79 % (12984)Termination phase: Saturation
% 1.56/1.79
% 1.56/1.79 % (12984)Memory used [KB]: 6268
% 1.56/1.79 % (12984)Time elapsed: 0.378 s
% 1.56/1.79 % (12984)Instructions burned: 780 (million)
% 1.56/1.79 % (12984)------------------------------
% 1.56/1.79 % (12984)------------------------------
% 1.56/1.79 % (12968)Instruction limit reached!
% 1.56/1.79 % (12968)------------------------------
% 1.56/1.79 % (12968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.79 % (12968)Termination reason: Unknown
% 1.56/1.79 % (12968)Termination phase: Saturation
% 1.56/1.79
% 1.56/1.79 % (12968)Memory used [KB]: 7931
% 1.56/1.79 % (12968)Time elapsed: 0.466 s
% 1.56/1.79 % (12968)Instructions burned: 1043 (million)
% 1.56/1.79 % (12968)------------------------------
% 1.56/1.79 % (12968)------------------------------
% 1.56/1.79 % (13008)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_12860 for (2995ds/62Mi)
% 1.56/1.80 % (13009)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/31Mi)
% 1.56/1.80 % (13010)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/96Mi)
% 1.56/1.82 % (13009)Instruction limit reached!
% 1.56/1.82 % (13009)------------------------------
% 1.56/1.82 % (13009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.82 % (13009)Termination reason: Unknown
% 1.56/1.82 % (13009)Termination phase: Saturation
% 1.56/1.82
% 1.56/1.82 % (13009)Memory used [KB]: 5628
% 1.56/1.82 % (13009)Time elapsed: 0.018 s
% 1.56/1.82 % (13009)Instructions burned: 31 (million)
% 1.56/1.82 % (13009)------------------------------
% 1.56/1.82 % (13009)------------------------------
% 1.56/1.82 % (13008)Instruction limit reached!
% 1.56/1.82 % (13008)------------------------------
% 1.56/1.82 % (13008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.82 % (13008)Termination reason: Unknown
% 1.56/1.82 % (13008)Termination phase: Saturation
% 1.56/1.82
% 1.56/1.82 % (13008)Memory used [KB]: 5756
% 1.56/1.82 % (13008)Time elapsed: 0.034 s
% 1.56/1.82 % (13008)Instructions burned: 62 (million)
% 1.56/1.82 % (13008)------------------------------
% 1.56/1.82 % (13008)------------------------------
% 1.56/1.84 % (13011)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/453Mi)
% 1.56/1.84 % (13012)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/71Mi)
% 1.56/1.84 % (12986)Instruction limit reached!
% 1.56/1.84 % (12986)------------------------------
% 1.56/1.84 % (12986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.84 % (12986)Termination reason: Unknown
% 1.56/1.84 % (12986)Termination phase: Saturation
% 1.56/1.84
% 1.56/1.84 % (12986)Memory used [KB]: 6268
% 1.56/1.84 % (12986)Time elapsed: 0.427 s
% 1.56/1.84 % (12986)Instructions burned: 880 (million)
% 1.56/1.84 % (12986)------------------------------
% 1.56/1.84 % (12986)------------------------------
% 1.56/1.85 % (13010)Instruction limit reached!
% 1.56/1.85 % (13010)------------------------------
% 1.56/1.85 % (13010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.85 % (13010)Termination reason: Unknown
% 1.56/1.85 % (13010)Termination phase: Saturation
% 1.56/1.85
% 1.56/1.85 % (13010)Memory used [KB]: 5756
% 1.56/1.85 % (13010)Time elapsed: 0.050 s
% 1.56/1.85 % (13010)Instructions burned: 97 (million)
% 1.56/1.85 % (13010)------------------------------
% 1.56/1.85 % (13010)------------------------------
% 1.56/1.86 % (13013)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/83Mi)
% 1.56/1.86 % (13013)Refutation not found, incomplete strategy
% 1.56/1.86 % (13013)------------------------------
% 1.56/1.86 % (13013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.86 % (13013)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.86
% 1.56/1.86
% 1.56/1.86 % (13013)Memory used [KB]: 5500
% 1.56/1.86 % (13013)Time elapsed: 0.004 s
% 1.56/1.86 % (13013)Instructions burned: 4 (million)
% 1.56/1.86 % (13013)------------------------------
% 1.56/1.86 % (13013)------------------------------
% 1.56/1.87 % (13014)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/11Mi)
% 1.56/1.87 % (13012)Instruction limit reached!
% 1.56/1.87 % (13012)------------------------------
% 1.56/1.87 % (13012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.87 % (13012)Termination reason: Unknown
% 1.56/1.87 % (13012)Termination phase: Saturation
% 1.56/1.87
% 1.56/1.87 % (13012)Memory used [KB]: 5756
% 1.56/1.87 % (13012)Time elapsed: 0.037 s
% 1.56/1.87 % (13012)Instructions burned: 71 (million)
% 1.56/1.87 % (13012)------------------------------
% 1.56/1.87 % (13012)------------------------------
% 1.56/1.87 % (13014)Instruction limit reached!
% 1.56/1.87 % (13014)------------------------------
% 1.56/1.87 % (13014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.87 % (13014)Termination reason: Unknown
% 1.56/1.87 % (13014)Termination phase: Saturation
% 1.56/1.87
% 1.56/1.87 % (13014)Memory used [KB]: 5500
% 1.56/1.87 % (13014)Time elapsed: 0.008 s
% 1.56/1.87 % (13014)Instructions burned: 12 (million)
% 1.56/1.87 % (13014)------------------------------
% 1.56/1.87 % (13014)------------------------------
% 1.56/1.88 % (13015)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/41Mi)
% 1.56/1.89 % (13016)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/6Mi)
% 1.56/1.89 % (13017)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_12860 for (2994ds/150Mi)
% 1.56/1.89 % (13016)Instruction limit reached!
% 1.56/1.89 % (13016)------------------------------
% 1.56/1.89 % (13016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.89 % (13016)Termination reason: Unknown
% 1.56/1.89 % (13016)Termination phase: Saturation
% 1.56/1.89
% 1.56/1.89 % (13016)Memory used [KB]: 5500
% 1.56/1.89 % (13016)Time elapsed: 0.005 s
% 1.56/1.89 % (13016)Instructions burned: 6 (million)
% 1.56/1.89 % (13016)------------------------------
% 1.56/1.89 % (13016)------------------------------
% 1.56/1.89 % (13000)Instruction limit reached!
% 1.56/1.89 % (13000)------------------------------
% 1.56/1.89 % (13000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.89 % (13000)Termination reason: Unknown
% 1.56/1.89 % (13000)Termination phase: Saturation
% 1.56/1.89
% 1.56/1.89 % (13000)Memory used [KB]: 6652
% 1.56/1.89 % (13000)Time elapsed: 0.255 s
% 1.56/1.89 % (13000)Instructions burned: 509 (million)
% 1.56/1.89 % (13000)------------------------------
% 1.56/1.89 % (13000)------------------------------
% 1.56/1.90 % (13015)Instruction limit reached!
% 1.56/1.90 % (13015)------------------------------
% 1.56/1.90 % (13015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.90 % (13015)Termination reason: Unknown
% 1.56/1.90 % (13015)Termination phase: Saturation
% 1.56/1.90
% 1.56/1.90 % (13015)Memory used [KB]: 5628
% 1.56/1.90 % (13015)Time elapsed: 0.023 s
% 1.56/1.90 % (13015)Instructions burned: 42 (million)
% 1.56/1.90 % (13015)------------------------------
% 1.56/1.90 % (13015)------------------------------
% 1.56/1.91 % (13018)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_12860 for (2993ds/343Mi)
% 1.56/1.91 % (13018)Refutation not found, incomplete strategy
% 1.56/1.91 % (13018)------------------------------
% 1.56/1.91 % (13018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.91 % (13018)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.91
% 1.56/1.91
% 1.56/1.91 % (13018)Memory used [KB]: 5500
% 1.56/1.91 % (13018)Time elapsed: 0.004 s
% 1.56/1.91 % (13018)Instructions burned: 4 (million)
% 1.56/1.91 % (13018)------------------------------
% 1.56/1.91 % (13018)------------------------------
% 1.56/1.91 % (13019)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_12860 for (2993ds/109Mi)
% 1.56/1.92 % (13020)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_12860 for (2993ds/253Mi)
% 1.56/1.93 % (13021)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_12860 for (2993ds/140Mi)
% 1.56/1.93 % (13004)First to succeed.
% 1.56/1.93 % (13021)Refutation not found, incomplete strategy
% 1.56/1.93 % (13021)------------------------------
% 1.56/1.93 % (13021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.93 % (13021)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.93
% 1.56/1.93
% 1.56/1.93 % (13021)Memory used [KB]: 5500
% 1.56/1.93 % (13021)Time elapsed: 0.005 s
% 1.56/1.93 % (13021)Instructions burned: 6 (million)
% 1.56/1.93 % (13021)------------------------------
% 1.56/1.93 % (13021)------------------------------
% 1.56/1.93 % (13004)Refutation found. Thanks to Tanya!
% 1.56/1.93 % SZS status Theorem for DTF2THF_12860
% 1.56/1.93 % SZS output start Proof for DTF2THF_12860
% 1.56/1.93 thf(func_def_0, type, in: $i > $i > $o).
% 1.56/1.93 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.56/1.93 thf(func_def_11, type, sP0: $i > $o).
% 1.56/1.93 thf(func_def_12, type, sK1: $i > $i > $i).
% 1.56/1.93 thf(func_def_13, type, sK2: $i > $i).
% 1.56/1.93 thf(f1157,plain,(
% 1.56/1.93 $false),
% 1.56/1.93 inference(subsumption_resolution,[status(thm)],[f1155,f69])).
% 1.56/1.93 thf(f69,plain,(
% 1.56/1.93 ($true = (in @ sK6 @ sK5))),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f43])).
% 1.56/1.93 thf(f43,plain,(
% 1.56/1.93 (setadjoinIL = $true) & (upairset2E = $true) & (foundationAx = $true) & (in__Cong = $true) & (($true = (in @ sK5 @ sK6)) & ($true = (in @ sK6 @ sK5))) & (setadjoinIR = $true)),
% 1.56/1.93 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f41,f42])).
% 1.56/1.93 thf(f42,plain,(
% 1.56/1.93 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) & ((in @ X1 @ X0) = $true)) => (($true = (in @ sK5 @ sK6)) & ($true = (in @ sK6 @ sK5)))),
% 1.56/1.93 introduced(definition,[],[choice_axiom])).
% 1.56/1.93 thf(f41,plain,(
% 1.56/1.93 (setadjoinIL = $true) & (upairset2E = $true) & (foundationAx = $true) & (in__Cong = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) & ((in @ X1 @ X0) = $true)) & (setadjoinIR = $true)),
% 1.56/1.93 inference(rectify,[status(thm)],[f24])).
% 1.56/1.93 thf(f24,plain,(
% 1.56/1.93 (setadjoinIL = $true) & (upairset2E = $true) & (foundationAx = $true) & (in__Cong = $true) & ? [X1 : $i,X0 : $i] : (((in @ X1 @ X0) = $true) & ($true = (in @ X0 @ X1))) & (setadjoinIR = $true)),
% 1.56/1.93 inference(flattening,[status(thm)],[f23])).
% 1.56/1.93 thf(f23,plain,(
% 1.56/1.93 ((((? [X1 : $i,X0 : $i] : (((in @ X1 @ X0) = $true) & ($true = (in @ X0 @ X1))) & (upairset2E = $true)) & (in__Cong = $true)) & (setadjoinIR = $true)) & (setadjoinIL = $true)) & (foundationAx = $true)),
% 1.56/1.93 inference(ennf_transformation,[status(thm)],[f21])).
% 1.56/1.93 thf(f21,plain,(
% 1.56/1.93 ~((foundationAx = $true) => ((setadjoinIL = $true) => ((setadjoinIR = $true) => ((in__Cong = $true) => ((upairset2E = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) => ($true != (in @ X0 @ X1))))))))),
% 1.56/1.93 inference(flattening,[status(thm)],[f10])).
% 1.56/1.93 thf(f10,plain,(
% 1.56/1.93 ~((foundationAx = $true) => ((setadjoinIL = $true) => ((setadjoinIR = $true) => ((in__Cong = $true) => ((upairset2E = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) => ~($true = (in @ X0 @ X1))))))))),
% 1.56/1.93 inference(fool_elimination,[status(thm)],[f9])).
% 1.56/1.93 thf(f9,plain,(
% 1.56/1.93 ~(foundationAx => (setadjoinIL => (setadjoinIR => (in__Cong => (upairset2E => ! [X0 : $i,X1 : $i] : ((in @ X1 @ X0) => ~(in @ X0 @ X1)))))))),
% 1.56/1.93 inference(rectify,[status(thm)],[f7])).
% 1.56/1.93 thf(f7,negated_conjecture,(
% 1.56/1.93 ~(foundationAx => (setadjoinIL => (setadjoinIR => (in__Cong => (upairset2E => ! [X2 : $i,X0 : $i] : ((in @ X0 @ X2) => ~(in @ X2 @ X0)))))))),
% 1.56/1.93 inference(negated_conjecture,[status(cth)],[f6])).
% 1.56/1.93 thf(f6,conjecture,(
% 1.56/1.93 foundationAx => (setadjoinIL => (setadjoinIR => (in__Cong => (upairset2E => ! [X2 : $i,X0 : $i] : ((in @ X0 @ X2) => ~(in @ X2 @ X0))))))),
% 1.56/1.93 file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',notinself2)).
% 1.56/1.93 thf(f1155,plain,(
% 1.56/1.93 ($true != (in @ sK6 @ sK5))),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f1149])).
% 1.56/1.93 thf(f1149,plain,(
% 1.56/1.93 ($true != (in @ sK6 @ sK5)) | ($true != $true)),
% 1.56/1.93 inference(superposition,[status(thm)],[f1134,f70])).
% 1.56/1.93 thf(f70,plain,(
% 1.56/1.93 ($true = (in @ sK5 @ sK6))),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f43])).
% 1.56/1.93 thf(f1134,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ((in @ X1 @ X0) != $true)) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f1129])).
% 1.56/1.93 thf(f1129,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ X1 @ X0) != $true) | ($true != (in @ X0 @ X1))) )),
% 1.56/1.93 inference(superposition,[status(thm)],[f749,f106])).
% 1.56/1.93 thf(f106,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setadjoin @ X0 @ X1)))) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.56/1.93 thf(f91,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setadjoin @ X0 @ X1))) | ($true != $true)) )),
% 1.56/1.93 inference(definition_unfolding,[status(thm)],[f76,f74])).
% 1.56/1.93 thf(f74,plain,(
% 1.56/1.93 (setadjoinIL = $true)),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f43])).
% 1.56/1.93 thf(f76,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setadjoin @ X0 @ X1))) | (setadjoinIL != $true)) )),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f47])).
% 1.56/1.93 thf(f47,plain,(
% 1.56/1.93 (! [X0 : $i,X1 : $i] : ($true = (in @ X0 @ (setadjoin @ X0 @ X1))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ($true != (in @ sK7 @ (setadjoin @ sK7 @ sK8))))),
% 1.56/1.93 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f45,f46])).
% 1.56/1.93 thf(f46,plain,(
% 1.56/1.93 ? [X2 : $i,X3 : $i] : ($true != (in @ X2 @ (setadjoin @ X2 @ X3))) => ($true != (in @ sK7 @ (setadjoin @ sK7 @ sK8)))),
% 1.56/1.93 introduced(definition,[],[choice_axiom])).
% 1.56/1.93 thf(f45,plain,(
% 1.56/1.93 (! [X0 : $i,X1 : $i] : ($true = (in @ X0 @ (setadjoin @ X0 @ X1))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X2 : $i,X3 : $i] : ($true != (in @ X2 @ (setadjoin @ X2 @ X3))))),
% 1.56/1.93 inference(rectify,[status(thm)],[f44])).
% 1.56/1.93 thf(f44,plain,(
% 1.56/1.93 (! [X0 : $i,X1 : $i] : ($true = (in @ X0 @ (setadjoin @ X0 @ X1))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X0 @ (setadjoin @ X0 @ X1))))),
% 1.56/1.93 inference(nnf_transformation,[status(thm)],[f16])).
% 1.56/1.93 thf(f16,plain,(
% 1.56/1.93 ! [X0 : $i,X1 : $i] : ($true = (in @ X0 @ (setadjoin @ X0 @ X1))) <=> (setadjoinIL = $true)),
% 1.56/1.93 inference(fool_elimination,[status(thm)],[f15])).
% 1.56/1.93 thf(f15,plain,(
% 1.56/1.93 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
% 1.56/1.93 inference(rectify,[status(thm)],[f2])).
% 1.56/1.93 thf(f2,axiom,(
% 1.56/1.93 (! [X1 : $i,X3 : $i] : (in @ X1 @ (setadjoin @ X1 @ X3)) = setadjoinIL)),
% 1.56/1.93 file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',setadjoinIL)).
% 1.56/1.93 thf(f749,plain,(
% 1.56/1.93 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X2 @ emptyset)) != $true) | ($true != (in @ X0 @ X1)) | ((in @ X1 @ X2) != $true)) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f746])).
% 1.56/1.93 thf(f746,plain,(
% 1.56/1.93 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ((in @ X1 @ X2) != $true) | ((in @ X0 @ (setadjoin @ X2 @ emptyset)) != $true) | ($true != $true)) )),
% 1.56/1.93 inference(superposition,[status(thm)],[f291,f107])).
% 1.56/1.93 thf(f107,plain,(
% 1.56/1.93 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setadjoin @ X3 @ X5))) | ($true != (in @ X4 @ X5))) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.56/1.93 thf(f103,plain,(
% 1.56/1.93 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true = (in @ X4 @ (setadjoin @ X3 @ X5))) | ($true != (in @ X4 @ X5))) )),
% 1.56/1.93 inference(definition_unfolding,[status(thm)],[f85,f68])).
% 1.56/1.93 thf(f68,plain,(
% 1.56/1.93 (setadjoinIR = $true)),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f43])).
% 1.56/1.93 thf(f85,plain,(
% 1.56/1.93 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setadjoin @ X3 @ X5))) | ($true != (in @ X4 @ X5)) | (setadjoinIR != $true)) )),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f60])).
% 1.56/1.93 thf(f60,plain,(
% 1.56/1.93 ((setadjoinIR = $true) | (($true != (in @ sK17 @ (setadjoin @ sK16 @ sK18))) & ($true = (in @ sK17 @ sK18)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setadjoin @ X3 @ X5))) | ($true != (in @ X4 @ X5))) | (setadjoinIR != $true))),
% 1.56/1.93 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f58,f59])).
% 1.56/1.93 thf(f59,plain,(
% 1.56/1.93 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ X2))) & ((in @ X1 @ X2) = $true)) => (($true != (in @ sK17 @ (setadjoin @ sK16 @ sK18))) & ($true = (in @ sK17 @ sK18)))),
% 1.56/1.93 introduced(definition,[],[choice_axiom])).
% 1.56/1.93 thf(f58,plain,(
% 1.56/1.93 ((setadjoinIR = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ X2))) & ((in @ X1 @ X2) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setadjoin @ X3 @ X5))) | ($true != (in @ X4 @ X5))) | (setadjoinIR != $true))),
% 1.56/1.93 inference(rectify,[status(thm)],[f57])).
% 1.56/1.93 thf(f57,plain,(
% 1.56/1.93 ((setadjoinIR = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X2 @ (setadjoin @ X0 @ X1))) & ($true = (in @ X2 @ X1)))) & (! [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X0 @ X1))) | ($true != (in @ X2 @ X1))) | (setadjoinIR != $true))),
% 1.56/1.93 inference(nnf_transformation,[status(thm)],[f25])).
% 1.56/1.93 thf(f25,plain,(
% 1.56/1.93 (setadjoinIR = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X0 @ X1))) | ($true != (in @ X2 @ X1)))),
% 1.56/1.93 inference(ennf_transformation,[status(thm)],[f12])).
% 1.56/1.93 thf(f12,plain,(
% 1.56/1.93 (setadjoinIR = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X2 @ X1)) => ($true = (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 1.56/1.93 inference(fool_elimination,[status(thm)],[f11])).
% 1.56/1.93 thf(f11,plain,(
% 1.56/1.93 (setadjoinIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 1.56/1.93 inference(rectify,[status(thm)],[f3])).
% 1.56/1.93 thf(f3,axiom,(
% 1.56/1.93 (setadjoinIR = ! [X1 : $i,X0 : $i,X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ (setadjoin @ X1 @ X0))))),
% 1.56/1.93 file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',setadjoinIR)).
% 1.56/1.93 thf(f291,plain,(
% 1.56/1.93 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) | ($true != (in @ X0 @ X1)) | ((in @ X2 @ X0) != $true)) )),
% 1.56/1.93 inference(superposition,[status(thm)],[f131,f253])).
% 1.56/1.93 thf(f253,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X0) | ($true != (in @ X0 @ X1))) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f249])).
% 1.56/1.93 thf(f249,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X0) | ($true != (in @ X0 @ X1)) | ($true != $true)) )),
% 1.56/1.93 inference(superposition,[status(thm)],[f146,f106])).
% 1.56/1.93 thf(f146,plain,(
% 1.56/1.93 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) | ($true != (in @ X2 @ X1)) | ((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X0)) )),
% 1.56/1.93 inference(superposition,[status(thm)],[f131,f124])).
% 1.56/1.93 thf(f124,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X1) | ((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X0)) )),
% 1.56/1.93 inference(subsumption_resolution,[status(thm)],[f123,f115])).
% 1.56/1.93 thf(f115,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (($true = (sP0 @ (setadjoin @ X0 @ X1)))) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.56/1.93 thf(f114,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (sP0 @ (setadjoin @ X0 @ X1)))) )),
% 1.56/1.93 inference(superposition,[status(thm)],[f109,f106])).
% 1.56/1.93 thf(f109,plain,(
% 1.56/1.93 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ X2) != $true) | ($true = (sP0 @ X2))) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.56/1.93 thf(f90,plain,(
% 1.56/1.93 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ X2) != $true) | ($true != $true) | ($true = (sP0 @ X2))) )),
% 1.56/1.93 inference(definition_unfolding,[status(thm)],[f65,f72])).
% 1.56/1.93 thf(f72,plain,(
% 1.56/1.93 (foundationAx = $true)),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f43])).
% 1.56/1.93 thf(f65,plain,(
% 1.56/1.93 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ X2) != $true) | ($true = (sP0 @ X2)) | (foundationAx != $true)) )),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f40])).
% 1.56/1.93 thf(f40,plain,(
% 1.56/1.93 ((foundationAx = $true) | (($true = (in @ sK4 @ sK3)) & ($true != (sP0 @ sK3)))) & (! [X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) != $true) | ($true = (sP0 @ X2))) | (foundationAx != $true))),
% 1.56/1.93 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f37,f39,f38])).
% 1.56/1.93 thf(f38,plain,(
% 1.56/1.93 ? [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) & ($true != (sP0 @ X0))) => (? [X1 : $i] : ($true = (in @ X1 @ sK3)) & ($true != (sP0 @ sK3)))),
% 1.56/1.93 introduced(definition,[],[choice_axiom])).
% 1.56/1.93 thf(f39,plain,(
% 1.56/1.93 ? [X1 : $i] : ($true = (in @ X1 @ sK3)) => ($true = (in @ sK4 @ sK3))),
% 1.56/1.93 introduced(definition,[],[choice_axiom])).
% 1.56/1.93 thf(f37,plain,(
% 1.56/1.93 ((foundationAx = $true) | ? [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) & ($true != (sP0 @ X0)))) & (! [X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) != $true) | ($true = (sP0 @ X2))) | (foundationAx != $true))),
% 1.56/1.93 inference(rectify,[status(thm)],[f36])).
% 1.56/1.93 thf(f36,plain,(
% 1.56/1.93 ((foundationAx = $true) | ? [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) & ($true != (sP0 @ X0)))) & (! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) != $true) | ($true = (sP0 @ X0))) | (foundationAx != $true))),
% 1.56/1.93 inference(nnf_transformation,[status(thm)],[f30])).
% 1.56/1.93 thf(f30,plain,(
% 1.56/1.93 (foundationAx = $true) <=> ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) != $true) | ($true = (sP0 @ X0)))),
% 1.56/1.93 inference(definition_folding,[status(thm)],[f26,f29])).
% 1.56/1.93 thf(f29,plain,(
% 1.56/1.93 ! [X0 : $i] : (($true = (sP0 @ X0)) <=> ? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true)) & ((in @ X2 @ X0) = $true)))),
% 1.56/1.93 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.56/1.93 thf(f26,plain,(
% 1.56/1.93 (foundationAx = $true) <=> ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) != $true) | ? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true)) & ((in @ X2 @ X0) = $true)))),
% 1.56/1.93 inference(ennf_transformation,[status(thm)],[f20])).
% 1.56/1.93 thf(f20,plain,(
% 1.56/1.93 (foundationAx = $true) <=> ! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) => ? [X2 : $i] : (~? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ X0) = $true)))),
% 1.56/1.93 inference(fool_elimination,[status(thm)],[f19])).
% 1.56/1.93 thf(f19,plain,(
% 1.56/1.93 (foundationAx = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : ((in @ X2 @ X0) & ~? [X3 : $i] : ((in @ X3 @ X0) & (in @ X3 @ X2)))))),
% 1.56/1.93 inference(rectify,[status(thm)],[f1])).
% 1.56/1.93 thf(f1,axiom,(
% 1.56/1.93 (foundationAx = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : ((in @ X2 @ X0) & ~? [X1 : $i] : ((in @ X1 @ X0) & (in @ X1 @ X2)))))),
% 1.56/1.93 file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',foundationAx)).
% 1.56/1.93 thf(f123,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X0) | ($true != (sP0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) | ((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X1)) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.56/1.93 thf(f122,plain,(
% 1.56/1.93 ( ! [X0 : $i,X1 : $i] : (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X0) | ($true != (sP0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) | ($true != $true) | ((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = X1)) )),
% 1.56/1.93 inference(superposition,[status(thm)],[f108,f61])).
% 1.56/1.93 thf(f61,plain,(
% 1.56/1.93 ( ! [X0 : $i] : (($true = (in @ (sK2 @ X0) @ X0)) | ($true != (sP0 @ X0))) )),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f35])).
% 1.56/1.93 thf(f35,plain,(
% 1.56/1.93 ! [X0 : $i] : ((($true = (sP0 @ X0)) | ! [X1 : $i] : ((($true = (in @ (sK1 @ X1 @ X0) @ X0)) & ($true = (in @ (sK1 @ X1 @ X0) @ X1))) | ((in @ X1 @ X0) != $true))) & ((! [X4 : $i] : (($true != (in @ X4 @ X0)) | ((in @ X4 @ (sK2 @ X0)) != $true)) & ($true = (in @ (sK2 @ X0) @ X0))) | ($true != (sP0 @ X0))))),
% 1.56/1.93 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f32,f34,f33])).
% 1.56/1.93 thf(f33,plain,(
% 1.56/1.93 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ X1))) => (($true = (in @ (sK1 @ X1 @ X0) @ X0)) & ($true = (in @ (sK1 @ X1 @ X0) @ X1))))),
% 1.56/1.93 introduced(definition,[],[choice_axiom])).
% 1.56/1.93 thf(f34,plain,(
% 1.56/1.93 ! [X0 : $i] : (? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ($true != (in @ X4 @ X3))) & ((in @ X3 @ X0) = $true)) => (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ((in @ X4 @ (sK2 @ X0)) != $true)) & ($true = (in @ (sK2 @ X0) @ X0))))),
% 1.56/1.93 introduced(definition,[],[choice_axiom])).
% 1.56/1.93 thf(f32,plain,(
% 1.56/1.93 ! [X0 : $i] : ((($true = (sP0 @ X0)) | ! [X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ X1))) | ((in @ X1 @ X0) != $true))) & (? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ($true != (in @ X4 @ X3))) & ((in @ X3 @ X0) = $true)) | ($true != (sP0 @ X0))))),
% 1.56/1.93 inference(rectify,[status(thm)],[f31])).
% 1.56/1.93 thf(f31,plain,(
% 1.56/1.93 ! [X0 : $i] : ((($true = (sP0 @ X0)) | ! [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) = $true)) | ((in @ X2 @ X0) != $true))) & (? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true)) & ((in @ X2 @ X0) = $true)) | ($true != (sP0 @ X0))))),
% 1.56/1.93 inference(nnf_transformation,[status(thm)],[f29])).
% 1.56/1.93 thf(f108,plain,(
% 1.56/1.93 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) | (X0 = X2) | (X0 = X1)) )),
% 1.56/1.93 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.56/1.93 thf(f97,plain,(
% 1.56/1.93 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X1) | ($true != $true) | (X0 = X2) | ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))) )),
% 1.56/1.93 inference(definition_unfolding,[status(thm)],[f84,f73])).
% 1.56/1.93 thf(f73,plain,(
% 1.56/1.93 (upairset2E = $true)),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f43])).
% 1.56/1.93 thf(f84,plain,(
% 1.56/1.93 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | (X0 = X1) | ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) | (upairset2E != $true)) )),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f56])).
% 1.56/1.93 thf(f56,plain,(
% 1.56/1.93 (! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | (X0 = X1) | ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))) | (upairset2E != $true)) & ((upairset2E = $true) | ((sK13 != sK15) & (sK13 != sK14) & ($true = (in @ sK13 @ (setadjoin @ sK14 @ (setadjoin @ sK15 @ emptyset))))))),
% 1.56/1.93 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f54,f55])).
% 1.56/1.93 thf(f55,plain,(
% 1.56/1.93 ? [X3 : $i,X4 : $i,X5 : $i] : ((X3 != X5) & (X3 != X4) & ($true = (in @ X3 @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset))))) => ((sK13 != sK15) & (sK13 != sK14) & ($true = (in @ sK13 @ (setadjoin @ sK14 @ (setadjoin @ sK15 @ emptyset)))))),
% 1.56/1.93 introduced(definition,[],[choice_axiom])).
% 1.56/1.93 thf(f54,plain,(
% 1.56/1.93 (! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | (X0 = X1) | ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((X3 != X5) & (X3 != X4) & ($true = (in @ X3 @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset))))))),
% 1.56/1.93 inference(rectify,[status(thm)],[f53])).
% 1.56/1.93 thf(f53,plain,(
% 1.56/1.93 (! [X0 : $i,X2 : $i,X1 : $i] : ((X0 = X1) | (X0 = X2) | ($true != (in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset))))) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((X0 != X1) & (X0 != X2) & ($true = (in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset))))))),
% 1.56/1.93 inference(nnf_transformation,[status(thm)],[f28])).
% 1.56/1.93 thf(f28,plain,(
% 1.56/1.93 ! [X0 : $i,X2 : $i,X1 : $i] : ((X0 = X1) | (X0 = X2) | ($true != (in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset))))) <=> (upairset2E = $true)),
% 1.56/1.93 inference(flattening,[status(thm)],[f27])).
% 1.56/1.93 thf(f27,plain,(
% 1.56/1.93 ! [X1 : $i,X0 : $i,X2 : $i] : (((X0 = X1) | (X0 = X2)) | ($true != (in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset))))) <=> (upairset2E = $true)),
% 1.56/1.93 inference(ennf_transformation,[status(thm)],[f18])).
% 1.56/1.93 thf(f18,plain,(
% 1.56/1.93 ! [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) => ((X0 = X1) | (X0 = X2))) <=> (upairset2E = $true)),
% 1.56/1.93 inference(fool_elimination,[status(thm)],[f17])).
% 1.56/1.93 thf(f17,plain,(
% 1.56/1.93 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset))) => ((X0 = X1) | (X0 = X2))) = upairset2E)),
% 1.56/1.93 inference(rectify,[status(thm)],[f5])).
% 1.56/1.93 thf(f5,axiom,(
% 1.56/1.93 (! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X4 @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset))) => ((X3 = X4) | (X1 = X4))) = upairset2E)),
% 1.56/1.93 file('/export/starexec/sandbox2/tmp/tmp.oQeU15FsXg/DTF2THF_12860.p',upairset2E)).
% 1.56/1.93 thf(f131,plain,(
% 1.56/1.93 ( ! [X0 : $i,X4 : $i] : (((in @ X4 @ (sK2 @ X0)) != $true) | ($true != (in @ X4 @ X0))) )),
% 1.56/1.93 inference(subsumption_resolution,[status(thm)],[f62,f109])).
% 1.56/1.93 thf(f62,plain,(
% 1.56/1.93 ( ! [X0 : $i,X4 : $i] : (((in @ X4 @ (sK2 @ X0)) != $true) | ($true != (in @ X4 @ X0)) | ($true != (sP0 @ X0))) )),
% 1.56/1.93 inference(cnf_transformation,[status(thm)],[f35])).
% 1.56/1.93 % SZS output end Proof for DTF2THF_12860
% 1.56/1.93 % (13004)------------------------------
% 1.56/1.93 % (13004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.93 % (13004)Termination reason: Refutation
% 1.56/1.93
% 1.56/1.93 % (13004)Memory used [KB]: 6268
% 1.56/1.93 % (13004)Time elapsed: 0.203 s
% 1.56/1.93 % (13004)Instructions burned: 405 (million)
% 1.56/1.93 % (13004)------------------------------
% 1.56/1.93 % (13004)------------------------------
% 1.56/1.93 % (12956)Success in time 0.64 s
%------------------------------------------------------------------------------