%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU709^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:36:34 AM UTC 2026
% Result : Theorem 1.70s 1.34s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 74 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 953 ( 282 equ; 0 cnn)
% Maximal formula atoms : 10 ( 12 avg)
% Number of connectives : 1035 ( 122 ~; 91 |; 84 &; 672 @)
% ( 9 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 24 con; 0-4 aty)
% Number of variables : 204 ( 0 ^; 146 !; 58 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_34,type,
ph21:
!>[X0: $tType] : X0 ).
thf(f118,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f117,f106]) ).
thf(f106,plain,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f73,f67]) ).
thf(f67,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( in @ ( if @ sK10 @ sK8 @ sK9 @ sK11 ) @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true )
& ( ( in @ sK11 @ sK10 )
= $true )
& ( ( in @ sK9 @ sK10 )
= $true )
& ( iftrue = $true )
& ( secondinupair = $true )
& ( setadjoinIL = $true )
& ( iffalse = $true )
& ( in__Cong = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f39,f41,f40]) ).
thf(f40,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( if @ X2 @ X0 @ X1 @ X3 ) @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X1 @ X2 )
= $true ) )
=> ( ? [X3: $i] :
( ( ( in @ ( if @ sK10 @ sK8 @ sK9 @ X3 ) @ ( setadjoin @ sK9 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ sK10 )
= $true ) )
& ( ( in @ sK9 @ sK10 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ? [X3: $i] :
( ( ( in @ ( if @ sK10 @ sK8 @ sK9 @ X3 ) @ ( setadjoin @ sK9 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ sK10 )
= $true ) )
=> ( ( ( in @ ( if @ sK10 @ sK8 @ sK9 @ sK11 ) @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true )
& ( ( in @ sK11 @ sK10 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( if @ X2 @ X0 @ X1 @ X3 ) @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X1 @ X2 )
= $true ) )
& ( iftrue = $true )
& ( secondinupair = $true )
& ( setadjoinIL = $true )
& ( iffalse = $true )
& ( in__Cong = $true ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ? [X1: $o,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( iftrue = $true )
& ( secondinupair = $true )
& ( setadjoinIL = $true )
& ( iffalse = $true )
& ( in__Cong = $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ? [X1: $o,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( iffalse = $true )
& ( iftrue = $true )
& ( secondinupair = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( ( setadjoinIL = $true )
=> ( ( in__Cong = $true )
=> ( ( secondinupair = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ! [X2: $i,X0: $i,X1: $o] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X2: $i,X4: $o,X0: $i] :
( ( in @ X0 @ X2 )
=> ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( in @ ( if @ X2 @ X4 @ X0 @ X1 ) @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X2: $i,X4: $o,X0: $i] :
( ( in @ X0 @ X2 )
=> ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( in @ ( if @ X2 @ X4 @ X0 @ X1 ) @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',iftrueorfalse) ).
thf(f73,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( setadjoinIL = $true )
| ( ( in @ sK12 @ ( setadjoin @ sK12 @ sK13 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f44,f45]) ).
thf(f45,plain,
( ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
=> ( ( in @ sK12 @ ( setadjoin @ sK12 @ sK13 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( setadjoinIL = $true )
| ? [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) )
& ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( setadjoinIL = $true )
<=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',setadjoinIL) ).
thf(f117,plain,
( ( in @ sK9 @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f116,f71]) ).
thf(f71,plain,
( ( in @ sK11 @ sK10 )
= $true ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f116,plain,
( ( ( in @ sK11 @ sK10 )
!= $true )
| ( ( in @ sK9 @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f114,f70]) ).
thf(f70,plain,
( ( in @ sK9 @ sK10 )
= $true ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f114,plain,
( ( ( in @ sK9 @ sK10 )
!= $true )
| ( ( in @ sK9 @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true )
| ( ( in @ sK11 @ sK10 )
!= $true ) ),
inference(superposition,[status(thm)],[f113,f103]) ).
thf(f103,plain,
! [X3: $i,X0: $i,X1: $i] :
( ( ( if @ X0 @ $true @ X1 @ X3 )
= X1 )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
! [X3: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( if @ X0 @ $true @ X1 @ X3 )
= X1 ) ),
inference(equality_resolution,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $o,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true != X2 )
| ( ( if @ X0 @ X2 @ X1 @ X3 )
= X1 )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f81,f69]) ).
thf(f69,plain,
iftrue = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f81,plain,
! [X2: $o,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true != X2 )
| ( ( if @ X0 @ X2 @ X1 @ X3 )
= X1 )
| ( ( in @ X1 @ X0 )
!= $true )
| ( iftrue != $true ) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ! [X0: $i,X1: $i,X2: $o] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true != X2 )
| ( ( if @ X0 @ X2 @ X1 @ X3 )
= X1 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( iftrue != $true ) )
& ( ( iftrue = $true )
| ( ( ( in @ sK19 @ sK16 )
= $true )
& ( sK18 = $true )
& ( ( if @ sK16 @ sK18 @ sK17 @ sK19 )
!= sK17 )
& ( ( in @ sK17 @ sK16 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f52,f54,f53]) ).
thf(f53,plain,
( ? [X4: $i,X5: $i,X6: $o] :
( ? [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
& ( $true = X6 )
& ( ( if @ X4 @ X6 @ X5 @ X7 )
!= X5 ) )
& ( $true
= ( in @ X5 @ X4 ) ) )
=> ( ? [X7: $i] :
( ( ( in @ X7 @ sK16 )
= $true )
& ( sK18 = $true )
& ( ( if @ sK16 @ sK18 @ sK17 @ X7 )
!= sK17 ) )
& ( ( in @ sK17 @ sK16 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ? [X7: $i] :
( ( ( in @ X7 @ sK16 )
= $true )
& ( sK18 = $true )
& ( ( if @ sK16 @ sK18 @ sK17 @ X7 )
!= sK17 ) )
=> ( ( ( in @ sK19 @ sK16 )
= $true )
& ( sK18 = $true )
& ( ( if @ sK16 @ sK18 @ sK17 @ sK19 )
!= sK17 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f52,plain,
( ( ! [X0: $i,X1: $i,X2: $o] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true != X2 )
| ( ( if @ X0 @ X2 @ X1 @ X3 )
= X1 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( iftrue != $true ) )
& ( ( iftrue = $true )
| ? [X4: $i,X5: $i,X6: $o] :
( ? [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
& ( $true = X6 )
& ( ( if @ X4 @ X6 @ X5 @ X7 )
!= X5 ) )
& ( $true
= ( in @ X5 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ! [X2: $i,X1: $i,X0: $o] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true != X0 )
| ( ( if @ X2 @ X0 @ X1 @ X3 )
= X1 ) )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( iftrue != $true ) )
& ( ( iftrue = $true )
| ? [X2: $i,X1: $i,X0: $o] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true = X0 )
& ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X1 ) )
& ( ( in @ X1 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ! [X2: $i,X1: $i,X0: $o] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true != X0 )
| ( ( if @ X2 @ X0 @ X1 @ X3 )
= X1 ) )
| ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( iftrue = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X2: $i,X1: $i,X0: $o] :
( ! [X3: $i] :
( ( ( if @ X2 @ X0 @ X1 @ X3 )
= X1 )
| ( $true != X0 )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( iftrue = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: $i,X1: $i,X0: $o] :
( ( ( in @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true = X0 )
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X1 ) ) ) )
<=> ( iftrue = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( X0
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X1 ) ) ) )
= iftrue ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X4: $o,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( X4
=> ( ( if @ X2 @ X4 @ X0 @ X1 )
= X0 ) ) ) )
= iftrue ),
file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',iftrue) ).
thf(f113,plain,
( ( in @ ( if @ sK10 @ $true @ sK9 @ sK11 ) @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true ),
inference(superposition,[status(thm)],[f72,f112]) ).
thf(f112,plain,
$true = sK8,
inference(subsumption_resolution,[status(thm)],[f111,f105]) ).
thf(f105,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f76,f68]) ).
thf(f68,plain,
secondinupair = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f76,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ( ( in @ sK14 @ ( setadjoin @ sK15 @ ( setadjoin @ sK14 @ emptyset ) ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f48,f49]) ).
thf(f49,plain,
( ? [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
!= $true )
=> ( ( in @ sK14 @ ( setadjoin @ sK15 @ ( setadjoin @ sK14 @ emptyset ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ? [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ? [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
<=> ( secondinupair = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',secondinupair) ).
thf(f111,plain,
( ( ( in @ sK11 @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true )
| ( $true = sK8 ) ),
inference(subsumption_resolution,[status(thm)],[f110,f70]) ).
thf(f110,plain,
( ( $true = sK8 )
| ( ( in @ sK9 @ sK10 )
!= $true )
| ( ( in @ sK11 @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f109,f71]) ).
thf(f109,plain,
( ( ( in @ sK11 @ sK10 )
!= $true )
| ( ( in @ sK9 @ sK10 )
!= $true )
| ( $true = sK8 )
| ( ( in @ sK11 @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f72,f104]) ).
thf(f104,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( ( if @ X5 @ X4 @ X6 @ X7 )
= X7 )
| ( $true = X4 )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X6 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( ( if @ X5 @ X4 @ X6 @ X7 )
= X7 )
| ( $true != $true )
| ( $true = X4 )
| ( ( in @ X6 @ X5 )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f56,f66]) ).
thf(f66,plain,
iffalse = $true,
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f56,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( ( if @ X5 @ X4 @ X6 @ X7 )
= X7 )
| ( ( in @ X7 @ X5 )
!= $true )
| ( $true = X4 )
| ( ( in @ X6 @ X5 )
!= $true )
| ( iffalse != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( iffalse = $true )
| ( ( sK3
!= ( if @ sK1 @ sK0 @ sK2 @ sK3 ) )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( sK0 != $true )
& ( ( in @ sK2 @ sK1 )
= $true ) ) )
& ( ! [X4: $o,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( if @ X5 @ X4 @ X6 @ X7 )
= X7 )
| ( ( in @ X7 @ X5 )
!= $true )
| ( $true = X4 ) )
| ( ( in @ X6 @ X5 )
!= $true ) )
| ( iffalse != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f30,f32,f31]) ).
thf(f31,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( if @ X1 @ X0 @ X2 @ X3 )
!= X3 )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true != X0 ) )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ? [X3: $i] :
( ( ( if @ sK1 @ sK0 @ sK2 @ X3 )
!= X3 )
& ( ( in @ X3 @ sK1 )
= $true )
& ( sK0 != $true ) )
& ( ( in @ sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X3: $i] :
( ( ( if @ sK1 @ sK0 @ sK2 @ X3 )
!= X3 )
& ( ( in @ X3 @ sK1 )
= $true )
& ( sK0 != $true ) )
=> ( ( sK3
!= ( if @ sK1 @ sK0 @ sK2 @ sK3 ) )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( sK0 != $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ( ( iffalse = $true )
| ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( if @ X1 @ X0 @ X2 @ X3 )
!= X3 )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true != X0 ) )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X4: $o,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( if @ X5 @ X4 @ X6 @ X7 )
= X7 )
| ( ( in @ X7 @ X5 )
!= $true )
| ( $true = X4 ) )
| ( ( in @ X6 @ X5 )
!= $true ) )
| ( iffalse != $true ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( iffalse = $true )
| ? [X2: $o,X0: $i,X1: $i] :
( ? [X3: $i] :
( ( ( if @ X0 @ X2 @ X1 @ X3 )
!= X3 )
& ( ( in @ X3 @ X0 )
= $true )
& ( $true != X2 ) )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $o,X0: $i,X1: $i] :
( ! [X3: $i] :
( ( ( if @ X0 @ X2 @ X1 @ X3 )
= X3 )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true = X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( iffalse != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( iffalse = $true )
<=> ! [X2: $o,X0: $i,X1: $i] :
( ! [X3: $i] :
( ( ( if @ X0 @ X2 @ X1 @ X3 )
= X3 )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true = X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X1: $i,X2: $o,X0: $i] :
( ! [X3: $i] :
( ( ( if @ X0 @ X2 @ X1 @ X3 )
= X3 )
| ( $true = X2 )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( iffalse = $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X1: $i,X2: $o,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( $true != X2 )
=> ( ( if @ X0 @ X2 @ X1 @ X3 )
= X3 ) ) ) )
<=> ( iffalse = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ( iffalse = $true )
<=> ! [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( $true != X2 )
=> ( ( if @ X0 @ X2 @ X1 @ X3 )
= X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( iffalse
= ( ! [X0: $i,X1: $i,X2: $o] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X2
=> ( ( if @ X0 @ X2 @ X1 @ X3 )
= X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( iffalse
= ( ! [X2: $i,X0: $i,X4: $o] :
( ( in @ X0 @ X2 )
=> ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( ~ X4
=> ( ( if @ X2 @ X4 @ X0 @ X1 )
= X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',iffalse) ).
thf(f72,plain,
( ( in @ ( if @ sK10 @ sK8 @ sK9 @ sK11 ) @ ( setadjoin @ sK9 @ ( setadjoin @ sK11 @ emptyset ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU709^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:31:39 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU709^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Conditionals
% 0.31/0.47 % Version : Especial > Reduced > Especial.
% 0.31/0.47 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A ->
% 0.31/0.47 % in (if A phi x y) (setadjoin x (setadjoin y emptyset))))
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC211l [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 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
% 0.31/0.47 % Syntax : Number of formulae : 15 ( 5 unt; 9 typ; 5 def)
% 0.31/0.47 % Number of atoms : 30 ( 9 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 8 ( 5 avg)
% 0.31/0.47 % Number of connectives : 61 ( 1 ~; 0 |; 0 &; 44 @)
% 0.31/0.47 % ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 18 ( 4 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 10 ( 9 usr; 6 con; 0-4 aty)
% 0.31/0.47 % Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=265
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset_type,type,
% 0.31/0.47 emptyset: $i ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin_type,type,
% 0.31/0.47 setadjoin: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL_type,type,
% 0.31/0.47 setadjoinIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL,definition,
% 0.31/0.47 ( setadjoinIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong_type,type,
% 0.31/0.47 in__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong,definition,
% 0.31/0.47 ( in__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(secondinupair_type,type,
% 0.31/0.47 secondinupair: $o ).
% 0.31/0.47
% 0.31/0.47 thf(secondinupair,definition,
% 0.31/0.47 ( secondinupair
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(if_type,type,
% 0.31/0.47 if: $i > $o > $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(iftrue_type,type,
% 0.31/0.47 iftrue: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iftrue,definition,
% 0.31/0.47 ( iftrue
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.31/0.47 = Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iffalse_type,type,
% 0.31/0.47 iffalse: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iffalse,definition,
% 0.31/0.47 ( iffalse
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( ~ Xphi
% 0.31/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.31/0.47 = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iftrueorfalse,conjecture,
% 0.31/0.47 ( setadjoinIL
% 0.31/0.47 => ( in__Cong
% 0.31/0.47 => ( secondinupair
% 0.31/0.47 => ( iftrue
% 0.31/0.47 => ( iffalse
% 0.31/0.47 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.51/1.29 ---- Embedded in THF ---
% 1.51/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.29 %%% Generated on Tue Feb 24 12:31:40 EST 2026
% 1.51/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.29 %%% Logic specification used:
% 1.51/1.29 %%% thf(spec, logic, $$dhol).
% 1.51/1.29
% 1.51/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2DTF20681.p
% See solution above
% 1.51/1.29 ------------------------
% 1.70/1.30 ---- Cleaned THF ---
% 1.70/1.30 thf(in_type,type,
% 1.70/1.30 in: $i > $i > $o ).
% 1.70/1.30
% 1.70/1.30 thf(emptyset_type,type,
% 1.70/1.30 emptyset: $i ).
% 1.70/1.30
% 1.70/1.30 thf(setadjoin_type,type,
% 1.70/1.30 setadjoin: $i > $i > $i ).
% 1.70/1.30
% 1.70/1.30 thf(setadjoinIL_type,type,
% 1.70/1.30 setadjoinIL: $o ).
% 1.70/1.30
% 1.70/1.30 thf(setadjoinIL,definition,
% 1.70/1.30 ( setadjoinIL
% 1.70/1.30 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(in__Cong_type,type,
% 1.70/1.30 in__Cong: $o ).
% 1.70/1.30
% 1.70/1.30 thf(in__Cong,definition,
% 1.70/1.30 ( in__Cong
% 1.70/1.30 = ( ! [A: $i,B: $i] :
% 1.70/1.30 ( ( A = B )
% 1.70/1.30 => ! [Xx: $i,Xy: $i] :
% 1.70/1.30 ( ( Xx = Xy )
% 1.70/1.30 => ( ( in @ Xx @ A )
% 1.70/1.30 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(secondinupair_type,type,
% 1.70/1.30 secondinupair: $o ).
% 1.70/1.30
% 1.70/1.30 thf(secondinupair,definition,
% 1.70/1.30 ( secondinupair
% 1.70/1.30 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(if_type,type,
% 1.70/1.30 if: $i > $o > $i > $i > $i ).
% 1.70/1.30
% 1.70/1.30 thf(iftrue_type,type,
% 1.70/1.30 iftrue: $o ).
% 1.70/1.30
% 1.70/1.30 thf(iftrue,definition,
% 1.70/1.30 ( iftrue
% 1.70/1.30 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.70/1.30 ( ( in @ Xx @ A )
% 1.70/1.30 => ! [Xy: $i] :
% 1.70/1.30 ( ( in @ Xy @ A )
% 1.70/1.30 => ( Xphi
% 1.70/1.30 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 1.70/1.30 = Xx ) ) ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(iffalse_type,type,
% 1.70/1.30 iffalse: $o ).
% 1.70/1.30
% 1.70/1.30 thf(iffalse,definition,
% 1.70/1.30 ( iffalse
% 1.70/1.30 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.70/1.30 ( ( in @ Xx @ A )
% 1.70/1.30 => ! [Xy: $i] :
% 1.70/1.30 ( ( in @ Xy @ A )
% 1.70/1.30 => ( ~ Xphi
% 1.70/1.30 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 1.70/1.30 = Xy ) ) ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(iftrueorfalse,conjecture,
% 1.70/1.30 ( setadjoinIL
% 1.70/1.30 => ( in__Cong
% 1.70/1.30 => ( secondinupair
% 1.70/1.30 => ( iftrue
% 1.70/1.30 => ( iffalse
% 1.70/1.30 => ! [A: $i,Xphi: $o,Xx: $i] :
% 1.70/1.30 ( ( in @ Xx @ A )
% 1.70/1.30 => ! [Xy: $i] :
% 1.70/1.30 ( ( in @ Xy @ A )
% 1.70/1.30 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) ) ).
% 1.70/1.30 ------------------------
% 1.70/1.32 % (21012)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20681 for (2999ds/2Mi)
% 1.70/1.32 % (21012)Instruction limit reached!
% 1.70/1.32 % (21012)------------------------------
% 1.70/1.32 % (21012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.32 % (21012)Termination reason: Unknown
% 1.70/1.32 % (21012)Termination phase: shuffling
% 1.70/1.32
% 1.70/1.32 % (21012)Memory used [KB]: 895
% 1.70/1.32 % (21012)Time elapsed: 0.002 s
% 1.70/1.32 % (21012)Instructions burned: 2 (million)
% 1.70/1.32 % (21012)------------------------------
% 1.70/1.32 % (21012)------------------------------
% 1.70/1.33 % (21010)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_20681 for (2999ds/4Mi)
% 1.70/1.33 % (21009)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20681 for (2999ds/183Mi)
% 1.70/1.33 % (21011)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_20681 for (2999ds/27Mi)
% 1.70/1.33 % (21013)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_20681 for (2999ds/2Mi)
% 1.70/1.33 % (21014)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_20681 for (2999ds/275Mi)
% 1.70/1.33 % (21015)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20681 for (2999ds/18Mi)
% 1.70/1.33 % (21013)Instruction limit reached!
% 1.70/1.33 % (21013)------------------------------
% 1.70/1.33 % (21013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (21013)Termination reason: Unknown
% 1.70/1.33 % (21013)Termination phase: shuffling
% 1.70/1.33
% 1.70/1.33 % (21013)Memory used [KB]: 1023
% 1.70/1.33 % (21013)Time elapsed: 0.003 s
% 1.70/1.33 % (21013)Instructions burned: 2 (million)
% 1.70/1.33 % (21013)------------------------------
% 1.70/1.33 % (21013)------------------------------
% 1.70/1.33 % (21016)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20681 for (2999ds/3Mi)
% 1.70/1.33 % (21010)Instruction limit reached!
% 1.70/1.33 % (21010)------------------------------
% 1.70/1.33 % (21010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (21010)Termination reason: Unknown
% 1.70/1.33 % (21010)Termination phase: Saturation
% 1.70/1.33
% 1.70/1.33 % (21010)Memory used [KB]: 5500
% 1.70/1.33 % (21010)Time elapsed: 0.005 s
% 1.70/1.33 % (21010)Instructions burned: 5 (million)
% 1.70/1.33 % (21010)------------------------------
% 1.70/1.33 % (21010)------------------------------
% 1.70/1.33 % (21016)Instruction limit reached!
% 1.70/1.33 % (21016)------------------------------
% 1.70/1.33 % (21016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (21016)Termination reason: Unknown
% 1.70/1.33 % (21016)Termination phase: Property scanning
% 1.70/1.33
% 1.70/1.33 % (21016)Memory used [KB]: 1023
% 1.70/1.33 % (21016)Time elapsed: 0.002 s
% 1.70/1.33 % (21016)Instructions burned: 4 (million)
% 1.70/1.33 % (21016)------------------------------
% 1.70/1.33 % (21016)------------------------------
% 1.70/1.33 % (21014)First to succeed.
% 1.70/1.34 % (21014)Refutation found. Thanks to Tanya!
% 1.70/1.34 % SZS status Theorem for DTF2THF_20681
% 1.70/1.34 % SZS output start Proof for DTF2THF_20681
% 1.70/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.70/1.34 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.70/1.34 thf(func_def_7, type, if: $i > $o > $i > $i > $i).
% 1.70/1.34 thf(func_def_34, type, ph21: !>[X0: $tType]:(X0)).
% 1.70/1.34 thf(f118,plain,(
% 1.70/1.34 $false),
% 1.70/1.34 inference(subsumption_resolution,[status(thm)],[f117,f106])).
% 1.70/1.34 thf(f106,plain,(
% 1.70/1.34 ( ! [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X2 @ X3)) = $true)) )),
% 1.70/1.34 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.70/1.34 thf(f92,plain,(
% 1.70/1.34 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ((in @ X2 @ (setadjoin @ X2 @ X3)) = $true)) )),
% 1.70/1.34 inference(definition_unfolding,[status(thm)],[f73,f67])).
% 1.70/1.34 thf(f67,plain,(
% 1.70/1.34 (setadjoinIL = $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 1.70/1.34 thf(f42,plain,(
% 1.70/1.34 ((((in @ (if @ sK10 @ sK8 @ sK9 @ sK11) @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true) & ((in @ sK11 @ sK10) = $true)) & ((in @ sK9 @ sK10) = $true)) & (iftrue = $true) & (secondinupair = $true) & (setadjoinIL = $true) & (iffalse = $true) & (in__Cong = $true)),
% 1.70/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f39,f41,f40])).
% 1.70/1.34 thf(f40,plain,(
% 1.70/1.34 ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ (if @ X2 @ X0 @ X1 @ X3) @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset))) != $true) & ((in @ X3 @ X2) = $true)) & ((in @ X1 @ X2) = $true)) => (? [X3 : $i] : (((in @ (if @ sK10 @ sK8 @ sK9 @ X3) @ (setadjoin @ sK9 @ (setadjoin @ X3 @ emptyset))) != $true) & ((in @ X3 @ sK10) = $true)) & ((in @ sK9 @ sK10) = $true))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f41,plain,(
% 1.70/1.34 ? [X3 : $i] : (((in @ (if @ sK10 @ sK8 @ sK9 @ X3) @ (setadjoin @ sK9 @ (setadjoin @ X3 @ emptyset))) != $true) & ((in @ X3 @ sK10) = $true)) => (((in @ (if @ sK10 @ sK8 @ sK9 @ sK11) @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true) & ((in @ sK11 @ sK10) = $true))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f39,plain,(
% 1.70/1.34 ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ (if @ X2 @ X0 @ X1 @ X3) @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset))) != $true) & ((in @ X3 @ X2) = $true)) & ((in @ X1 @ X2) = $true)) & (iftrue = $true) & (secondinupair = $true) & (setadjoinIL = $true) & (iffalse = $true) & (in__Cong = $true)),
% 1.70/1.34 inference(rectify,[status(thm)],[f27])).
% 1.70/1.34 thf(f27,plain,(
% 1.70/1.34 ? [X1 : $o,X2 : $i,X0 : $i] : (? [X3 : $i] : (((in @ (if @ X0 @ X1 @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ X0) = $true)) & (iftrue = $true) & (secondinupair = $true) & (setadjoinIL = $true) & (iffalse = $true) & (in__Cong = $true)),
% 1.70/1.34 inference(flattening,[status(thm)],[f26])).
% 1.70/1.34 thf(f26,plain,(
% 1.70/1.34 ((((? [X1 : $o,X2 : $i,X0 : $i] : (? [X3 : $i] : (((in @ (if @ X0 @ X1 @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ X0) = $true)) & (iffalse = $true)) & (iftrue = $true)) & (secondinupair = $true)) & (in__Cong = $true)) & (setadjoinIL = $true)),
% 1.70/1.34 inference(ennf_transformation,[status(thm)],[f20])).
% 1.70/1.34 thf(f20,plain,(
% 1.70/1.34 ~((setadjoinIL = $true) => ((in__Cong = $true) => ((secondinupair = $true) => ((iftrue = $true) => ((iffalse = $true) => ! [X2 : $i,X0 : $i,X1 : $o] : (((in @ X2 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((in @ (if @ X0 @ X1 @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) = $true))))))))),
% 1.70/1.34 inference(fool_elimination,[status(thm)],[f19])).
% 1.70/1.34 thf(f19,plain,(
% 1.70/1.34 ~(setadjoinIL => (in__Cong => (secondinupair => (iftrue => (iffalse => ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (if @ X0 @ X1 @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))))))))),
% 1.70/1.34 inference(rectify,[status(thm)],[f7])).
% 1.70/1.34 thf(f7,negated_conjecture,(
% 1.70/1.34 ~(setadjoinIL => (in__Cong => (secondinupair => (iftrue => (iffalse => ! [X2 : $i,X4 : $o,X0 : $i] : ((in @ X0 @ X2) => ! [X1 : $i] : ((in @ X1 @ X2) => (in @ (if @ X2 @ X4 @ X0 @ X1) @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))))))))),
% 1.70/1.34 inference(negated_conjecture,[status(cth)],[f6])).
% 1.70/1.34 thf(f6,conjecture,(
% 1.70/1.34 setadjoinIL => (in__Cong => (secondinupair => (iftrue => (iffalse => ! [X2 : $i,X4 : $o,X0 : $i] : ((in @ X0 @ X2) => ! [X1 : $i] : ((in @ X1 @ X2) => (in @ (if @ X2 @ X4 @ X0 @ X1) @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))))))),
% 1.70/1.34 file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',iftrueorfalse)).
% 1.70/1.34 thf(f73,plain,(
% 1.70/1.34 ( ! [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X2 @ X3)) = $true) | (setadjoinIL != $true)) )),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f46])).
% 1.70/1.34 thf(f46,plain,(
% 1.70/1.34 ((setadjoinIL = $true) | ((in @ sK12 @ (setadjoin @ sK12 @ sK13)) != $true)) & (! [X2 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X2 @ X3)) = $true) | (setadjoinIL != $true))),
% 1.70/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f44,f45])).
% 1.70/1.34 thf(f45,plain,(
% 1.70/1.34 ? [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) != $true) => ((in @ sK12 @ (setadjoin @ sK12 @ sK13)) != $true)),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f44,plain,(
% 1.70/1.34 ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) != $true)) & (! [X2 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X2 @ X3)) = $true) | (setadjoinIL != $true))),
% 1.70/1.34 inference(rectify,[status(thm)],[f43])).
% 1.70/1.34 thf(f43,plain,(
% 1.70/1.34 ((setadjoinIL = $true) | ? [X1 : $i,X0 : $i] : ((in @ X1 @ (setadjoin @ X1 @ X0)) != $true)) & (! [X1 : $i,X0 : $i] : ((in @ X1 @ (setadjoin @ X1 @ X0)) = $true) | (setadjoinIL != $true))),
% 1.70/1.34 inference(nnf_transformation,[status(thm)],[f16])).
% 1.70/1.34 thf(f16,plain,(
% 1.70/1.34 (setadjoinIL = $true) <=> ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setadjoin @ X1 @ X0)) = $true)),
% 1.70/1.34 inference(fool_elimination,[status(thm)],[f15])).
% 1.70/1.34 thf(f15,plain,(
% 1.70/1.34 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)) = setadjoinIL)),
% 1.70/1.34 inference(rectify,[status(thm)],[f1])).
% 1.70/1.34 thf(f1,axiom,(
% 1.70/1.34 (! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
% 1.70/1.34 file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',setadjoinIL)).
% 1.70/1.34 thf(f117,plain,(
% 1.70/1.34 ((in @ sK9 @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true)),
% 1.70/1.34 inference(subsumption_resolution,[status(thm)],[f116,f71])).
% 1.70/1.34 thf(f71,plain,(
% 1.70/1.34 ((in @ sK11 @ sK10) = $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 1.70/1.34 thf(f116,plain,(
% 1.70/1.34 ((in @ sK11 @ sK10) != $true) | ((in @ sK9 @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true)),
% 1.70/1.34 inference(subsumption_resolution,[status(thm)],[f114,f70])).
% 1.70/1.34 thf(f70,plain,(
% 1.70/1.34 ((in @ sK9 @ sK10) = $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 1.70/1.34 thf(f114,plain,(
% 1.70/1.34 ((in @ sK9 @ sK10) != $true) | ((in @ sK9 @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true) | ((in @ sK11 @ sK10) != $true)),
% 1.70/1.34 inference(superposition,[status(thm)],[f113,f103])).
% 1.70/1.34 thf(f103,plain,(
% 1.70/1.34 ( ! [X3 : $i,X0 : $i,X1 : $i] : (((if @ X0 @ $true @ X1 @ X3) = X1) | ((in @ X1 @ X0) != $true) | ((in @ X3 @ X0) != $true)) )),
% 1.70/1.34 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.70/1.34 thf(f102,plain,(
% 1.70/1.34 ( ! [X3 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ($true != $true) | ((in @ X3 @ X0) != $true) | ((if @ X0 @ $true @ X1 @ X3) = X1)) )),
% 1.70/1.34 inference(equality_resolution,[status(thm)],[f95])).
% 1.70/1.34 thf(f95,plain,(
% 1.70/1.34 ( ! [X2 : $o,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ X0) != $true) | ($true != X2) | ((if @ X0 @ X2 @ X1 @ X3) = X1) | ((in @ X1 @ X0) != $true) | ($true != $true)) )),
% 1.70/1.34 inference(definition_unfolding,[status(thm)],[f81,f69])).
% 1.70/1.34 thf(f69,plain,(
% 1.70/1.34 (iftrue = $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 1.70/1.34 thf(f81,plain,(
% 1.70/1.34 ( ! [X2 : $o,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ X0) != $true) | ($true != X2) | ((if @ X0 @ X2 @ X1 @ X3) = X1) | ((in @ X1 @ X0) != $true) | (iftrue != $true)) )),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f55])).
% 1.70/1.34 thf(f55,plain,(
% 1.70/1.34 (! [X0 : $i,X1 : $i,X2 : $o] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ($true != X2) | ((if @ X0 @ X2 @ X1 @ X3) = X1)) | ((in @ X1 @ X0) != $true)) | (iftrue != $true)) & ((iftrue = $true) | ((((in @ sK19 @ sK16) = $true) & (sK18 = $true) & ((if @ sK16 @ sK18 @ sK17 @ sK19) != sK17)) & ((in @ sK17 @ sK16) = $true)))),
% 1.70/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f52,f54,f53])).
% 1.70/1.34 thf(f53,plain,(
% 1.70/1.34 ? [X4 : $i,X5 : $i,X6 : $o] : (? [X7 : $i] : (((in @ X7 @ X4) = $true) & ($true = X6) & ((if @ X4 @ X6 @ X5 @ X7) != X5)) & ($true = (in @ X5 @ X4))) => (? [X7 : $i] : (((in @ X7 @ sK16) = $true) & (sK18 = $true) & ((if @ sK16 @ sK18 @ sK17 @ X7) != sK17)) & ((in @ sK17 @ sK16) = $true))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f54,plain,(
% 1.70/1.34 ? [X7 : $i] : (((in @ X7 @ sK16) = $true) & (sK18 = $true) & ((if @ sK16 @ sK18 @ sK17 @ X7) != sK17)) => (((in @ sK19 @ sK16) = $true) & (sK18 = $true) & ((if @ sK16 @ sK18 @ sK17 @ sK19) != sK17))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f52,plain,(
% 1.70/1.34 (! [X0 : $i,X1 : $i,X2 : $o] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ($true != X2) | ((if @ X0 @ X2 @ X1 @ X3) = X1)) | ((in @ X1 @ X0) != $true)) | (iftrue != $true)) & ((iftrue = $true) | ? [X4 : $i,X5 : $i,X6 : $o] : (? [X7 : $i] : (((in @ X7 @ X4) = $true) & ($true = X6) & ((if @ X4 @ X6 @ X5 @ X7) != X5)) & ($true = (in @ X5 @ X4))))),
% 1.70/1.34 inference(rectify,[status(thm)],[f51])).
% 1.70/1.34 thf(f51,plain,(
% 1.70/1.34 (! [X2 : $i,X1 : $i,X0 : $o] : (! [X3 : $i] : (((in @ X3 @ X2) != $true) | ($true != X0) | ((if @ X2 @ X0 @ X1 @ X3) = X1)) | ((in @ X1 @ X2) != $true)) | (iftrue != $true)) & ((iftrue = $true) | ? [X2 : $i,X1 : $i,X0 : $o] : (? [X3 : $i] : (((in @ X3 @ X2) = $true) & ($true = X0) & ((if @ X2 @ X0 @ X1 @ X3) != X1)) & ((in @ X1 @ X2) = $true)))),
% 1.70/1.34 inference(nnf_transformation,[status(thm)],[f25])).
% 1.70/1.34 thf(f25,plain,(
% 1.70/1.34 ! [X2 : $i,X1 : $i,X0 : $o] : (! [X3 : $i] : (((in @ X3 @ X2) != $true) | ($true != X0) | ((if @ X2 @ X0 @ X1 @ X3) = X1)) | ((in @ X1 @ X2) != $true)) <=> (iftrue = $true)),
% 1.70/1.34 inference(flattening,[status(thm)],[f24])).
% 1.70/1.34 thf(f24,plain,(
% 1.70/1.34 ! [X2 : $i,X1 : $i,X0 : $o] : (! [X3 : $i] : ((((if @ X2 @ X0 @ X1 @ X3) = X1) | ($true != X0)) | ((in @ X3 @ X2) != $true)) | ((in @ X1 @ X2) != $true)) <=> (iftrue = $true)),
% 1.70/1.34 inference(ennf_transformation,[status(thm)],[f12])).
% 1.70/1.34 thf(f12,plain,(
% 1.70/1.34 ! [X2 : $i,X1 : $i,X0 : $o] : (((in @ X1 @ X2) = $true) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => (($true = X0) => ((if @ X2 @ X0 @ X1 @ X3) = X1)))) <=> (iftrue = $true)),
% 1.70/1.34 inference(fool_elimination,[status(thm)],[f11])).
% 1.70/1.34 thf(f11,plain,(
% 1.70/1.34 (! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X0 => ((if @ X2 @ X0 @ X1 @ X3) = X1)))) = iftrue)),
% 1.70/1.34 inference(rectify,[status(thm)],[f4])).
% 1.70/1.34 thf(f4,axiom,(
% 1.70/1.34 (! [X4 : $o,X0 : $i,X2 : $i] : ((in @ X0 @ X2) => ! [X1 : $i] : ((in @ X1 @ X2) => (X4 => ((if @ X2 @ X4 @ X0 @ X1) = X0)))) = iftrue)),
% 1.70/1.34 file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',iftrue)).
% 1.70/1.34 thf(f113,plain,(
% 1.70/1.34 ((in @ (if @ sK10 @ $true @ sK9 @ sK11) @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true)),
% 1.70/1.34 inference(superposition,[status(thm)],[f72,f112])).
% 1.70/1.34 thf(f112,plain,(
% 1.70/1.34 ($true = sK8)),
% 1.70/1.34 inference(subsumption_resolution,[status(thm)],[f111,f105])).
% 1.70/1.34 thf(f105,plain,(
% 1.70/1.34 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true)) )),
% 1.70/1.34 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.70/1.34 thf(f93,plain,(
% 1.70/1.34 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | ($true != $true)) )),
% 1.70/1.34 inference(definition_unfolding,[status(thm)],[f76,f68])).
% 1.70/1.34 thf(f68,plain,(
% 1.70/1.34 (secondinupair = $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 1.70/1.34 thf(f76,plain,(
% 1.70/1.34 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (secondinupair != $true)) )),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f50])).
% 1.70/1.34 thf(f50,plain,(
% 1.70/1.34 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (secondinupair != $true)) & ((secondinupair = $true) | ((in @ sK14 @ (setadjoin @ sK15 @ (setadjoin @ sK14 @ emptyset))) != $true))),
% 1.70/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f48,f49])).
% 1.70/1.34 thf(f49,plain,(
% 1.70/1.34 ? [X2 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))) != $true) => ((in @ sK14 @ (setadjoin @ sK15 @ (setadjoin @ sK14 @ emptyset))) != $true)),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f48,plain,(
% 1.70/1.34 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (secondinupair != $true)) & ((secondinupair = $true) | ? [X2 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))) != $true))),
% 1.70/1.34 inference(rectify,[status(thm)],[f47])).
% 1.70/1.34 thf(f47,plain,(
% 1.70/1.34 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) | (secondinupair != $true)) & ((secondinupair = $true) | ? [X1 : $i,X0 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true))),
% 1.70/1.34 inference(nnf_transformation,[status(thm)],[f14])).
% 1.70/1.34 thf(f14,plain,(
% 1.70/1.34 ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) <=> (secondinupair = $true)),
% 1.70/1.34 inference(fool_elimination,[status(thm)],[f13])).
% 1.70/1.34 thf(f13,plain,(
% 1.70/1.34 (secondinupair = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 1.70/1.34 inference(rectify,[status(thm)],[f3])).
% 1.70/1.34 thf(f3,axiom,(
% 1.70/1.34 (secondinupair = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 1.70/1.34 file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',secondinupair)).
% 1.70/1.34 thf(f111,plain,(
% 1.70/1.34 ((in @ sK11 @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true) | ($true = sK8)),
% 1.70/1.34 inference(subsumption_resolution,[status(thm)],[f110,f70])).
% 1.70/1.34 thf(f110,plain,(
% 1.70/1.34 ($true = sK8) | ((in @ sK9 @ sK10) != $true) | ((in @ sK11 @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true)),
% 1.70/1.34 inference(subsumption_resolution,[status(thm)],[f109,f71])).
% 1.70/1.34 thf(f109,plain,(
% 1.70/1.34 ((in @ sK11 @ sK10) != $true) | ((in @ sK9 @ sK10) != $true) | ($true = sK8) | ((in @ sK11 @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true)),
% 1.70/1.34 inference(superposition,[status(thm)],[f72,f104])).
% 1.70/1.34 thf(f104,plain,(
% 1.70/1.34 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (((if @ X5 @ X4 @ X6 @ X7) = X7) | ($true = X4) | ((in @ X7 @ X5) != $true) | ((in @ X6 @ X5) != $true)) )),
% 1.70/1.34 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.70/1.34 thf(f86,plain,(
% 1.70/1.34 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (((if @ X5 @ X4 @ X6 @ X7) = X7) | ($true != $true) | ($true = X4) | ((in @ X6 @ X5) != $true) | ((in @ X7 @ X5) != $true)) )),
% 1.70/1.34 inference(definition_unfolding,[status(thm)],[f56,f66])).
% 1.70/1.34 thf(f66,plain,(
% 1.70/1.34 (iffalse = $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 1.70/1.34 thf(f56,plain,(
% 1.70/1.34 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (((if @ X5 @ X4 @ X6 @ X7) = X7) | ((in @ X7 @ X5) != $true) | ($true = X4) | ((in @ X6 @ X5) != $true) | (iffalse != $true)) )),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f33])).
% 1.70/1.34 thf(f33,plain,(
% 1.70/1.34 ((iffalse = $true) | (((sK3 != (if @ sK1 @ sK0 @ sK2 @ sK3)) & ((in @ sK3 @ sK1) = $true) & (sK0 != $true)) & ((in @ sK2 @ sK1) = $true))) & (! [X4 : $o,X5 : $i,X6 : $i] : (! [X7 : $i] : (((if @ X5 @ X4 @ X6 @ X7) = X7) | ((in @ X7 @ X5) != $true) | ($true = X4)) | ((in @ X6 @ X5) != $true)) | (iffalse != $true))),
% 1.70/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f30,f32,f31])).
% 1.70/1.34 thf(f31,plain,(
% 1.70/1.34 ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((if @ X1 @ X0 @ X2 @ X3) != X3) & ((in @ X3 @ X1) = $true) & ($true != X0)) & ((in @ X2 @ X1) = $true)) => (? [X3 : $i] : (((if @ sK1 @ sK0 @ sK2 @ X3) != X3) & ((in @ X3 @ sK1) = $true) & (sK0 != $true)) & ((in @ sK2 @ sK1) = $true))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f32,plain,(
% 1.70/1.34 ? [X3 : $i] : (((if @ sK1 @ sK0 @ sK2 @ X3) != X3) & ((in @ X3 @ sK1) = $true) & (sK0 != $true)) => ((sK3 != (if @ sK1 @ sK0 @ sK2 @ sK3)) & ((in @ sK3 @ sK1) = $true) & (sK0 != $true))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f30,plain,(
% 1.70/1.34 ((iffalse = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((if @ X1 @ X0 @ X2 @ X3) != X3) & ((in @ X3 @ X1) = $true) & ($true != X0)) & ((in @ X2 @ X1) = $true))) & (! [X4 : $o,X5 : $i,X6 : $i] : (! [X7 : $i] : (((if @ X5 @ X4 @ X6 @ X7) = X7) | ((in @ X7 @ X5) != $true) | ($true = X4)) | ((in @ X6 @ X5) != $true)) | (iffalse != $true))),
% 1.70/1.34 inference(rectify,[status(thm)],[f29])).
% 1.70/1.34 thf(f29,plain,(
% 1.70/1.34 ((iffalse = $true) | ? [X2 : $o,X0 : $i,X1 : $i] : (? [X3 : $i] : (((if @ X0 @ X2 @ X1 @ X3) != X3) & ((in @ X3 @ X0) = $true) & ($true != X2)) & ((in @ X1 @ X0) = $true))) & (! [X2 : $o,X0 : $i,X1 : $i] : (! [X3 : $i] : (((if @ X0 @ X2 @ X1 @ X3) = X3) | ((in @ X3 @ X0) != $true) | ($true = X2)) | ((in @ X1 @ X0) != $true)) | (iffalse != $true))),
% 1.70/1.34 inference(nnf_transformation,[status(thm)],[f23])).
% 1.70/1.34 thf(f23,plain,(
% 1.70/1.34 (iffalse = $true) <=> ! [X2 : $o,X0 : $i,X1 : $i] : (! [X3 : $i] : (((if @ X0 @ X2 @ X1 @ X3) = X3) | ((in @ X3 @ X0) != $true) | ($true = X2)) | ((in @ X1 @ X0) != $true))),
% 1.70/1.34 inference(flattening,[status(thm)],[f22])).
% 1.70/1.34 thf(f22,plain,(
% 1.70/1.34 ! [X1 : $i,X2 : $o,X0 : $i] : (! [X3 : $i] : ((((if @ X0 @ X2 @ X1 @ X3) = X3) | ($true = X2)) | ((in @ X3 @ X0) != $true)) | ((in @ X1 @ X0) != $true)) <=> (iffalse = $true)),
% 1.70/1.34 inference(ennf_transformation,[status(thm)],[f21])).
% 1.70/1.34 thf(f21,plain,(
% 1.70/1.34 ! [X1 : $i,X2 : $o,X0 : $i] : (((in @ X1 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (($true != X2) => ((if @ X0 @ X2 @ X1 @ X3) = X3)))) <=> (iffalse = $true)),
% 1.70/1.34 inference(flattening,[status(thm)],[f18])).
% 1.70/1.34 thf(f18,plain,(
% 1.70/1.34 (iffalse = $true) <=> ! [X0 : $i,X1 : $i,X2 : $o] : (((in @ X1 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (~($true = X2) => ((if @ X0 @ X2 @ X1 @ X3) = X3))))),
% 1.70/1.34 inference(fool_elimination,[status(thm)],[f17])).
% 1.70/1.34 thf(f17,plain,(
% 1.70/1.34 (iffalse = ! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X2 => ((if @ X0 @ X2 @ X1 @ X3) = X3)))))),
% 1.70/1.34 inference(rectify,[status(thm)],[f5])).
% 1.70/1.34 thf(f5,axiom,(
% 1.70/1.34 (iffalse = ! [X2 : $i,X0 : $i,X4 : $o] : ((in @ X0 @ X2) => ! [X1 : $i] : ((in @ X1 @ X2) => (~X4 => ((if @ X2 @ X4 @ X0 @ X1) = X1)))))),
% 1.70/1.34 file('/export/starexec/sandbox/tmp/tmp.i3gWjqKvLM/DTF2THF_20681.p',iffalse)).
% 1.70/1.34 thf(f72,plain,(
% 1.70/1.34 ((in @ (if @ sK10 @ sK8 @ sK9 @ sK11) @ (setadjoin @ sK9 @ (setadjoin @ sK11 @ emptyset))) != $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 1.70/1.34 % SZS output end Proof for DTF2THF_20681
% 1.70/1.34 % (21014)------------------------------
% 1.70/1.34 % (21014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (21014)Termination reason: Refutation
% 1.70/1.34
% 1.70/1.34 % (21014)Memory used [KB]: 5628
% 1.70/1.34 % (21014)Time elapsed: 0.010 s
% 1.70/1.34 % (21014)Instructions burned: 7 (million)
% 1.70/1.34 % (21014)------------------------------
% 1.70/1.34 % (21014)------------------------------
% 1.70/1.34 % (21008)Success in time 0.026 s
%------------------------------------------------------------------------------