%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU811^2 : 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 : n027.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 09:37:24 AM UTC 2026
% Result : Theorem 1.49s 1.21s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 745 ( 251 equ; 0 cnn)
% Maximal formula atoms : 14 ( 11 avg)
% Number of connectives : 639 ( 95 ~; 80 |; 74 &; 330 @)
% ( 7 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 17 con; 0-2 aty)
% Number of variables : 135 ( 5 ^; 96 !; 34 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
omegaS: $i > $i ).
thf(f124,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f123,f59]) ).
thf(f59,plain,
sK5 != sK4,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( in @ sK5 @ omega )
= $true )
& ( sK5 != sK4 )
& ( ( omegaS @ sK5 )
= ( omegaS @ sK4 ) )
& ( ( in @ sK4 @ omega )
= $true )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true )
& ( notinself2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f26,f36,f35]) ).
thf(f35,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ omega )
= $true )
& ( X0 != X1 )
& ( ( omegaS @ X0 )
= ( omegaS @ X1 ) ) )
& ( ( in @ X0 @ omega )
= $true ) )
=> ( ? [X1: $i] :
( ( ( in @ X1 @ omega )
= $true )
& ( sK4 != X1 )
& ( ( omegaS @ X1 )
= ( omegaS @ sK4 ) ) )
& ( ( in @ sK4 @ omega )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X1: $i] :
( ( ( in @ X1 @ omega )
= $true )
& ( sK4 != X1 )
& ( ( omegaS @ X1 )
= ( omegaS @ sK4 ) ) )
=> ( ( ( in @ sK5 @ omega )
= $true )
& ( sK5 != sK4 )
& ( ( omegaS @ sK5 )
= ( omegaS @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ omega )
= $true )
& ( X0 != X1 )
& ( ( omegaS @ X0 )
= ( omegaS @ X1 ) ) )
& ( ( in @ X0 @ omega )
= $true ) )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true )
& ( notinself2 = $true ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( X0 != X1 )
& ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
& ( ( in @ X1 @ omega )
= $true ) )
& ( ( in @ X0 @ omega )
= $true ) )
& ( notinself2 = $true )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setadjoinE = $true )
=> ( ( in__Cong = $true )
=> ( ( notinself2 = $true )
=> ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ omega )
= $true )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',peanoSinj) ).
thf(f123,plain,
sK5 = sK4,
inference(subsumption_resolution,[status(thm)],[f122,f119]) ).
thf(f119,plain,
( ( in @ sK4 @ sK5 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $true != $true )
| ( ( in @ sK4 @ sK5 )
!= $true ) ),
inference(superposition,[status(thm)],[f99,f117]) ).
thf(f117,plain,
( ( in @ sK5 @ sK4 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f116,f59]) ).
thf(f116,plain,
( ( sK5 = sK4 )
| ( ( in @ sK5 @ sK4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $true != $true )
| ( ( in @ sK5 @ sK4 )
= $true )
| ( sK5 = sK4 ) ),
inference(superposition,[status(thm)],[f98,f103]) ).
thf(f103,plain,
( ( in @ sK5 @ ( setadjoin @ sK4 @ sK4 ) )
= $true ),
inference(superposition,[status(thm)],[f101,f102]) ).
thf(f102,plain,
( ( setadjoin @ sK4 @ sK4 )
= ( setadjoin @ sK5 @ sK5 ) ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 )
@ sK5 )
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 )
@ sK4 ) ),
inference(definition_unfolding,[status(thm)],[f58,f69,f69]) ).
thf(f69,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X0: $i] : ( setadjoin @ X0 @ X0 ) )
= omegaS ),
file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',omegaS) ).
thf(f58,plain,
( ( omegaS @ sK5 )
= ( omegaS @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f101,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f52,f54]) ).
thf(f54,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f52,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( ( in @ sK3 @ ( setadjoin @ sK3 @ sK2 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f32,f33]) ).
thf(f33,plain,
( ? [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
!= $true )
=> ( ( in @ sK3 @ ( setadjoin @ sK3 @ sK2 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
<=> ( setadjoinIL = $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.LJlhZfqz5O/DTF2THF_7537.p',setadjoinIL) ).
thf(f98,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( X0 = X2 )
| ( $true
= ( in @ X0 @ X1 ) ) ),
inference(condensation,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( X1 = X2 )
| ( $true = X3 )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f68,f55]) ).
thf(f55,plain,
setadjoinE = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f68,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true = X3 )
| ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( setadjoinE != $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ! [X3: $o] :
( ( $true = X3 )
| ( ( ( in @ X2 @ X0 )
= $true )
& ( $true != X3 ) )
| ( ( X1 = X2 )
& ( $true != X3 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ( ( $true
= ( in @ sK8 @ ( setadjoin @ sK7 @ sK6 ) ) )
& ( sK9 != $true )
& ( ( ( in @ sK8 @ sK6 )
!= $true )
| ( sK9 = $true ) )
& ( ( sK7 != sK8 )
| ( sK9 = $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f39,f41,f40]) ).
thf(f40,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X6 @ ( setadjoin @ X5 @ X4 ) )
= $true )
& ? [X7: $o] :
( ( $true != X7 )
& ( ( $true
!= ( in @ X6 @ X4 ) )
| ( $true = X7 ) )
& ( ( X5 != X6 )
| ( $true = X7 ) ) ) )
=> ( ( $true
= ( in @ sK8 @ ( setadjoin @ sK7 @ sK6 ) ) )
& ? [X7: $o] :
( ( $true != X7 )
& ( ( ( in @ sK8 @ sK6 )
!= $true )
| ( $true = X7 ) )
& ( ( sK7 != sK8 )
| ( $true = X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ? [X7: $o] :
( ( $true != X7 )
& ( ( ( in @ sK8 @ sK6 )
!= $true )
| ( $true = X7 ) )
& ( ( sK7 != sK8 )
| ( $true = X7 ) ) )
=> ( ( sK9 != $true )
& ( ( ( in @ sK8 @ sK6 )
!= $true )
| ( sK9 = $true ) )
& ( ( sK7 != sK8 )
| ( sK9 = $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ! [X3: $o] :
( ( $true = X3 )
| ( ( ( in @ X2 @ X0 )
= $true )
& ( $true != X3 ) )
| ( ( X1 = X2 )
& ( $true != X3 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X6 @ ( setadjoin @ X5 @ X4 ) )
= $true )
& ? [X7: $o] :
( ( $true != X7 )
& ( ( $true
!= ( in @ X6 @ X4 ) )
| ( $true = X7 ) )
& ( ( X5 != X6 )
| ( $true = X7 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ! [X3: $o] :
( ( $true = X3 )
| ( ( ( in @ X2 @ X0 )
= $true )
& ( $true != X3 ) )
| ( ( X1 = X2 )
& ( $true != X3 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( ( in @ X2 @ X0 )
!= $true )
| ( $true = X3 ) )
& ( ( X1 != X2 )
| ( $true = X3 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ! [X3: $o] :
( ( $true = X3 )
| ( ( ( in @ X2 @ X0 )
= $true )
& ( $true != X3 ) )
| ( ( X1 = X2 )
& ( $true != X3 ) ) ) )
<=> ( setadjoinE = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ( setadjoinE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( ( in @ X2 @ X0 )
= $true )
& ( $true != X3 ) )
| ( ( X1 = X2 )
& ( $true != X3 ) ) )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( setadjoinE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
=> ! [X3: $o] :
( ( ( X1 = X2 )
=> ( $true = X3 ) )
=> ( ( ( ( in @ X2 @ X0 )
= $true )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
=> ! [X3: $o] :
( ( ( X1 = X2 )
=> X3 )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> X3 ) ) )
= setadjoinE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> X3 )
=> ( ( ( in @ X1 @ X2 )
=> X3 )
=> X3 ) ) )
= setadjoinE ),
file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',setadjoinE) ).
thf(f99,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f50,f53]) ).
thf(f53,plain,
notinself2 = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f50,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( notinself2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( notinself2 != $true ) )
& ( ( notinself2 = $true )
| ( ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK0 @ sK1 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f28,f29]) ).
thf(f29,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( ( in @ X2 @ X3 )
= $true ) )
=> ( ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK0 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( notinself2 != $true ) )
& ( ( notinself2 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( ( in @ X2 @ X3 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( notinself2 != $true ) )
& ( ( notinself2 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ X0 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
<=> ( notinself2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( notinself2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true
!= ( in @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true
!= ( in @ X1 @ X0 ) ) )
<=> ( notinself2 = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) )
= notinself2 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i,X4: $i] :
( ( ( in @ X2 @ X4 )
=> ~ ( in @ X4 @ X2 ) )
= notinself2 ),
file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',notinself2) ).
thf(f122,plain,
( ( ( in @ sK4 @ sK5 )
= $true )
| ( sK5 = sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( ( in @ sK4 @ sK5 )
= $true )
| ( $true != $true )
| ( sK5 = sK4 ) ),
inference(superposition,[status(thm)],[f113,f101]) ).
thf(f113,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ sK4 @ sK4 ) ) )
| ( ( in @ X0 @ sK5 )
= $true )
| ( sK5 = X0 ) ),
inference(superposition,[status(thm)],[f98,f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU811^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:36:52 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SEU811^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.44 % Domain : Set Theory
% 0.18/0.44 % Problem : Omega and Peano
% 0.18/0.44 % Version : Especial > Reduced > Especial.
% 0.18/0.44 % English : (! x:i.in x omega -> (! y:i.in y omega -> omegaS x = omegaS y ->
% 0.18/0.44 % x = y))
% 0.18/0.44
% 0.18/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.44 % Source : [Bro08]
% 0.18/0.44 % Names : ZFC313l [Bro08]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.18/0.44 % Syntax : Number of formulae : 14 ( 5 unt; 8 typ; 5 def)
% 0.18/0.44 % Number of atoms : 27 ( 10 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 8 ( 4 avg)
% 0.18/0.44 % Number of connectives : 43 ( 1 ~; 0 |; 0 &; 26 @)
% 0.18/0.44 % ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 11 ( 3 avg)
% 0.18/0.44 % Number of types : 2 ( 0 usr)
% 0.18/0.44 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 9 ( 8 usr; 5 con; 0-2 aty)
% 0.18/0.44 % Number of variables : 15 ( 1 ^; 14 !; 0 ?; 15 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : http://mathgate.info/detsetitem.php?id=447
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(in_type,type,
% 0.18/0.44 in: $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(setadjoin_type,type,
% 0.18/0.44 setadjoin: $i > $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(omega_type,type,
% 0.18/0.44 omega: $i ).
% 0.18/0.44
% 0.18/0.44 thf(setadjoinIL_type,type,
% 0.18/0.44 setadjoinIL: $o ).
% 0.18/0.44
% 0.18/0.44 thf(setadjoinIL,definition,
% 0.18/0.44 ( setadjoinIL
% 0.18/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(setadjoinE_type,type,
% 0.18/0.44 setadjoinE: $o ).
% 0.18/0.44
% 0.18/0.44 thf(setadjoinE,definition,
% 0.18/0.44 ( setadjoinE
% 0.18/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.44 => ! [Xphi: $o] :
% 0.18/0.44 ( ( ( Xy = Xx )
% 0.18/0.44 => Xphi )
% 0.18/0.44 => ( ( ( in @ Xy @ A )
% 0.18/0.44 => Xphi )
% 0.18/0.44 => Xphi ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(in__Cong_type,type,
% 0.18/0.44 in__Cong: $o ).
% 0.18/0.44
% 0.18/0.44 thf(in__Cong,definition,
% 0.18/0.44 ( in__Cong
% 0.18/0.44 = ( ! [A: $i,B: $i] :
% 0.18/0.44 ( ( A = B )
% 0.18/0.44 => ! [Xx: $i,Xy: $i] :
% 0.18/0.44 ( ( Xx = Xy )
% 0.18/0.44 => ( ( in @ Xx @ A )
% 0.18/0.44 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(notinself2_type,type,
% 0.18/0.44 notinself2: $o ).
% 0.18/0.44
% 0.18/0.44 thf(notinself2,definition,
% 0.18/0.44 ( notinself2
% 0.18/0.44 = ( ! [A: $i,B: $i] :
% 0.18/0.44 ( ( in @ A @ B )
% 0.18/0.44 => ~ ( in @ B @ A ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(omegaS_type,type,
% 0.18/0.44 omegaS: $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(omegaS,definition,
% 0.18/0.44 ( omegaS
% 0.18/0.44 = ( ^ [Xx: $i] : ( setadjoin @ Xx @ Xx ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(peanoSinj,conjecture,
% 0.18/0.44 ( setadjoinIL
% 0.18/0.44 => ( setadjoinE
% 0.18/0.44 => ( in__Cong
% 0.18/0.44 => ( notinself2
% 0.18/0.44 => ! [Xx: $i] :
% 0.18/0.44 ( ( in @ Xx @ omega )
% 0.18/0.44 => ! [Xy: $i] :
% 0.18/0.44 ( ( in @ Xy @ omega )
% 0.18/0.44 => ( ( ( omegaS @ Xx )
% 0.18/0.44 = ( omegaS @ Xy ) )
% 0.18/0.44 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.37/1.17 ---- Embedded in THF ---
% 1.37/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.17 %%% Generated on Tue Feb 24 12:36:52 EST 2026
% 1.37/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.17 %%% Logic specification used:
% 1.37/1.17 %%% thf(spec, logic, $$dhol).
% 1.37/1.17
% 1.37/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2DTF7537.p
% See solution above
% 1.37/1.17 ------------------------
% 1.37/1.17 ---- Cleaned THF ---
% 1.37/1.17 thf(in_type,type,
% 1.37/1.17 in: $i > $i > $o ).
% 1.37/1.17
% 1.37/1.17 thf(setadjoin_type,type,
% 1.37/1.17 setadjoin: $i > $i > $i ).
% 1.37/1.17
% 1.37/1.17 thf(omega_type,type,
% 1.37/1.17 omega: $i ).
% 1.37/1.17
% 1.37/1.17 thf(setadjoinIL_type,type,
% 1.37/1.17 setadjoinIL: $o ).
% 1.37/1.17
% 1.37/1.17 thf(setadjoinIL,definition,
% 1.37/1.17 ( setadjoinIL
% 1.37/1.17 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.37/1.17
% 1.37/1.17 thf(setadjoinE_type,type,
% 1.37/1.17 setadjoinE: $o ).
% 1.37/1.17
% 1.37/1.17 thf(setadjoinE,definition,
% 1.37/1.17 ( setadjoinE
% 1.37/1.17 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.37/1.17 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.37/1.17 => ! [Xphi: $o] :
% 1.37/1.17 ( ( ( Xy = Xx )
% 1.37/1.17 => Xphi )
% 1.37/1.17 => ( ( ( in @ Xy @ A )
% 1.37/1.17 => Xphi )
% 1.37/1.17 => Xphi ) ) ) ) ) ).
% 1.37/1.17
% 1.37/1.17 thf(in__Cong_type,type,
% 1.37/1.17 in__Cong: $o ).
% 1.37/1.17
% 1.37/1.17 thf(in__Cong,definition,
% 1.37/1.17 ( in__Cong
% 1.37/1.17 = ( ! [A: $i,B: $i] :
% 1.37/1.17 ( ( A = B )
% 1.37/1.17 => ! [Xx: $i,Xy: $i] :
% 1.37/1.17 ( ( Xx = Xy )
% 1.37/1.17 => ( ( in @ Xx @ A )
% 1.37/1.17 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 1.37/1.17
% 1.37/1.17 thf(notinself2_type,type,
% 1.37/1.17 notinself2: $o ).
% 1.37/1.17
% 1.37/1.17 thf(notinself2,definition,
% 1.37/1.17 ( notinself2
% 1.37/1.17 = ( ! [A: $i,B: $i] :
% 1.37/1.17 ( ( in @ A @ B )
% 1.37/1.17 => ~ ( in @ B @ A ) ) ) ) ).
% 1.37/1.17
% 1.37/1.17 thf(omegaS_type,type,
% 1.37/1.17 omegaS: $i > $i ).
% 1.37/1.17
% 1.37/1.17 thf(omegaS,definition,
% 1.37/1.17 ( omegaS
% 1.37/1.17 = ( ^ [Xx: $i] : ( setadjoin @ Xx @ Xx ) ) ) ).
% 1.37/1.17
% 1.37/1.17 thf(peanoSinj,conjecture,
% 1.37/1.17 ( setadjoinIL
% 1.37/1.17 => ( setadjoinE
% 1.37/1.17 => ( in__Cong
% 1.37/1.17 => ( notinself2
% 1.37/1.17 => ! [Xx: $i] :
% 1.37/1.17 ( ( in @ Xx @ omega )
% 1.37/1.17 => ! [Xy: $i] :
% 1.37/1.17 ( ( in @ Xy @ omega )
% 1.37/1.17 => ( ( ( omegaS @ Xx )
% 1.37/1.17 = ( omegaS @ Xy ) )
% 1.37/1.17 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 1.37/1.17 ------------------------
% 1.37/1.19 % (7634)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7537 for (3000ds/183Mi)
% 1.37/1.19 % (7638)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_7537 for (3000ds/2Mi)
% 1.37/1.19 % (7637)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7537 for (3000ds/2Mi)
% 1.37/1.19 % (7639)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_7537 for (3000ds/275Mi)
% 1.37/1.19 % (7635)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_7537 for (3000ds/4Mi)
% 1.37/1.20 % (7636)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_7537 for (3000ds/27Mi)
% 1.37/1.20 % (7637)Instruction limit reached!
% 1.37/1.20 % (7637)------------------------------
% 1.37/1.20 % (7637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.20 % (7637)Termination reason: Unknown
% 1.37/1.20 % (7638)Instruction limit reached!
% 1.37/1.20 % (7638)------------------------------
% 1.37/1.20 % (7638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.20 % (7638)Termination reason: Unknown
% 1.37/1.20 % (7638)Termination phase: Function definition elimination
% 1.37/1.20
% 1.37/1.20 % (7638)Memory used [KB]: 1023
% 1.37/1.20 % (7638)Time elapsed: 0.003 s
% 1.37/1.20 % (7638)Instructions burned: 3 (million)
% 1.37/1.20 % (7638)------------------------------
% 1.37/1.20 % (7638)------------------------------
% 1.37/1.20 % (7637)Termination phase: Property scanning
% 1.37/1.20
% 1.37/1.20 % (7637)Memory used [KB]: 1023
% 1.37/1.20 % (7637)Time elapsed: 0.003 s
% 1.37/1.20 % (7637)Instructions burned: 3 (million)
% 1.37/1.20 % (7637)------------------------------
% 1.37/1.20 % (7637)------------------------------
% 1.49/1.20 % (7635)Instruction limit reached!
% 1.49/1.20 % (7635)------------------------------
% 1.49/1.20 % (7635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.20 % (7635)Termination reason: Unknown
% 1.49/1.20 % (7635)Termination phase: Saturation
% 1.49/1.20
% 1.49/1.20 % (7640)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7537 for (3000ds/18Mi)
% 1.49/1.20 % (7635)Memory used [KB]: 5500
% 1.49/1.20 % (7635)Time elapsed: 0.004 s
% 1.49/1.20 % (7635)Instructions burned: 5 (million)
% 1.49/1.20 % (7635)------------------------------
% 1.49/1.20 % (7635)------------------------------
% 1.49/1.20 % (7639)Refutation not found, incomplete strategy
% 1.49/1.20 % (7639)------------------------------
% 1.49/1.20 % (7639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.20 % (7639)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.20
% 1.49/1.20
% 1.49/1.20 % (7639)Memory used [KB]: 5500
% 1.49/1.20 % (7639)Time elapsed: 0.005 s
% 1.49/1.20 % (7639)Instructions burned: 5 (million)
% 1.49/1.20 % (7639)------------------------------
% 1.49/1.20 % (7639)------------------------------
% 1.49/1.20 % (7640)First to succeed.
% 1.49/1.21 % (7640)Refutation found. Thanks to Tanya!
% 1.49/1.21 % SZS status Theorem for DTF2THF_7537
% 1.49/1.21 % SZS output start Proof for DTF2THF_7537
% 1.49/1.21 thf(func_def_0, type, in: $i > $i > $o).
% 1.49/1.21 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 1.49/1.21 thf(func_def_8, type, omegaS: $i > $i).
% 1.49/1.21 thf(f124,plain,(
% 1.49/1.21 $false),
% 1.49/1.21 inference(subsumption_resolution,[status(thm)],[f123,f59])).
% 1.49/1.21 thf(f59,plain,(
% 1.49/1.21 (sK5 != sK4)),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f37])).
% 1.49/1.21 thf(f37,plain,(
% 1.49/1.21 ((((in @ sK5 @ omega) = $true) & (sK5 != sK4) & ((omegaS @ sK5) = (omegaS @ sK4))) & ((in @ sK4 @ omega) = $true)) & (in__Cong = $true) & (setadjoinE = $true) & (setadjoinIL = $true) & (notinself2 = $true)),
% 1.49/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f26,f36,f35])).
% 1.49/1.21 thf(f35,plain,(
% 1.49/1.21 ? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ omega) = $true) & (X0 != X1) & ((omegaS @ X0) = (omegaS @ X1))) & ((in @ X0 @ omega) = $true)) => (? [X1 : $i] : (((in @ X1 @ omega) = $true) & (sK4 != X1) & ((omegaS @ X1) = (omegaS @ sK4))) & ((in @ sK4 @ omega) = $true))),
% 1.49/1.21 introduced(definition,[],[choice_axiom])).
% 1.49/1.21 thf(f36,plain,(
% 1.49/1.21 ? [X1 : $i] : (((in @ X1 @ omega) = $true) & (sK4 != X1) & ((omegaS @ X1) = (omegaS @ sK4))) => (((in @ sK5 @ omega) = $true) & (sK5 != sK4) & ((omegaS @ sK5) = (omegaS @ sK4)))),
% 1.49/1.21 introduced(definition,[],[choice_axiom])).
% 1.49/1.21 thf(f26,plain,(
% 1.49/1.21 ? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ omega) = $true) & (X0 != X1) & ((omegaS @ X0) = (omegaS @ X1))) & ((in @ X0 @ omega) = $true)) & (in__Cong = $true) & (setadjoinE = $true) & (setadjoinIL = $true) & (notinself2 = $true)),
% 1.49/1.21 inference(flattening,[status(thm)],[f25])).
% 1.49/1.21 thf(f25,plain,(
% 1.49/1.21 (((? [X0 : $i] : (? [X1 : $i] : (((X0 != X1) & ((omegaS @ X0) = (omegaS @ X1))) & ((in @ X1 @ omega) = $true)) & ((in @ X0 @ omega) = $true)) & (notinself2 = $true)) & (in__Cong = $true)) & (setadjoinE = $true)) & (setadjoinIL = $true)),
% 1.49/1.21 inference(ennf_transformation,[status(thm)],[f12])).
% 1.49/1.21 thf(f12,plain,(
% 1.49/1.21 ~((setadjoinIL = $true) => ((setadjoinE = $true) => ((in__Cong = $true) => ((notinself2 = $true) => ! [X0 : $i] : (((in @ X0 @ omega) = $true) => ! [X1 : $i] : (((in @ X1 @ omega) = $true) => (((omegaS @ X0) = (omegaS @ X1)) => (X0 = X1))))))))),
% 1.49/1.21 inference(fool_elimination,[status(thm)],[f11])).
% 1.49/1.21 thf(f11,plain,(
% 1.49/1.21 ~(setadjoinIL => (setadjoinE => (in__Cong => (notinself2 => ! [X0 : $i] : ((in @ X0 @ omega) => ! [X1 : $i] : ((in @ X1 @ omega) => (((omegaS @ X0) = (omegaS @ X1)) => (X0 = X1))))))))),
% 1.49/1.21 inference(rectify,[status(thm)],[f7])).
% 1.49/1.21 thf(f7,negated_conjecture,(
% 1.49/1.21 ~(setadjoinIL => (setadjoinE => (in__Cong => (notinself2 => ! [X0 : $i] : ((in @ X0 @ omega) => ! [X1 : $i] : ((in @ X1 @ omega) => (((omegaS @ X0) = (omegaS @ X1)) => (X0 = X1))))))))),
% 1.49/1.21 inference(negated_conjecture,[status(cth)],[f6])).
% 1.49/1.21 thf(f6,conjecture,(
% 1.49/1.21 setadjoinIL => (setadjoinE => (in__Cong => (notinself2 => ! [X0 : $i] : ((in @ X0 @ omega) => ! [X1 : $i] : ((in @ X1 @ omega) => (((omegaS @ X0) = (omegaS @ X1)) => (X0 = X1)))))))),
% 1.49/1.21 file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',peanoSinj)).
% 1.49/1.21 thf(f123,plain,(
% 1.49/1.21 (sK5 = sK4)),
% 1.49/1.21 inference(subsumption_resolution,[status(thm)],[f122,f119])).
% 1.49/1.21 thf(f119,plain,(
% 1.49/1.21 ((in @ sK4 @ sK5) != $true)),
% 1.49/1.21 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.49/1.21 thf(f118,plain,(
% 1.49/1.21 ($true != $true) | ((in @ sK4 @ sK5) != $true)),
% 1.49/1.21 inference(superposition,[status(thm)],[f99,f117])).
% 1.49/1.21 thf(f117,plain,(
% 1.49/1.21 ((in @ sK5 @ sK4) = $true)),
% 1.49/1.21 inference(subsumption_resolution,[status(thm)],[f116,f59])).
% 1.49/1.21 thf(f116,plain,(
% 1.49/1.21 (sK5 = sK4) | ((in @ sK5 @ sK4) = $true)),
% 1.49/1.21 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.49/1.21 thf(f115,plain,(
% 1.49/1.21 ($true != $true) | ((in @ sK5 @ sK4) = $true) | (sK5 = sK4)),
% 1.49/1.21 inference(superposition,[status(thm)],[f98,f103])).
% 1.49/1.21 thf(f103,plain,(
% 1.49/1.21 ((in @ sK5 @ (setadjoin @ sK4 @ sK4)) = $true)),
% 1.49/1.21 inference(superposition,[status(thm)],[f101,f102])).
% 1.49/1.21 thf(f102,plain,(
% 1.49/1.21 ((setadjoin @ sK4 @ sK4) = (setadjoin @ sK5 @ sK5))),
% 1.49/1.21 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.49/1.21 thf(f79,plain,(
% 1.49/1.21 (((^[Y0 : $i]: (setadjoin @ Y0 @ Y0)) @ sK5) = ((^[Y0 : $i]: (setadjoin @ Y0 @ Y0)) @ sK4))),
% 1.49/1.21 inference(definition_unfolding,[status(thm)],[f58,f69,f69])).
% 1.49/1.21 thf(f69,plain,(
% 1.49/1.21 (omegaS = (^[Y0 : $i]: (setadjoin @ Y0 @ Y0)))),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f19])).
% 1.49/1.21 thf(f19,plain,(
% 1.49/1.21 (omegaS = (^[Y0 : $i]: (setadjoin @ Y0 @ Y0)))),
% 1.49/1.21 inference(fool_elimination,[status(thm)],[f5])).
% 1.49/1.21 thf(f5,axiom,(
% 1.49/1.21 ((^[X0 : $i] : (setadjoin @ X0 @ X0)) = omegaS)),
% 1.49/1.21 file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',omegaS)).
% 1.49/1.21 thf(f58,plain,(
% 1.49/1.21 ((omegaS @ sK5) = (omegaS @ sK4))),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f37])).
% 1.49/1.21 thf(f101,plain,(
% 1.49/1.21 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X0)))) )),
% 1.49/1.21 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.49/1.21 thf(f77,plain,(
% 1.49/1.21 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | ($true != $true)) )),
% 1.49/1.21 inference(definition_unfolding,[status(thm)],[f52,f54])).
% 1.49/1.21 thf(f54,plain,(
% 1.49/1.21 (setadjoinIL = $true)),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f37])).
% 1.49/1.21 thf(f52,plain,(
% 1.49/1.21 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) )),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f34])).
% 1.49/1.21 thf(f34,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ((in @ sK3 @ (setadjoin @ sK3 @ sK2)) != $true))),
% 1.49/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f32,f33])).
% 1.49/1.21 thf(f33,plain,(
% 1.49/1.21 ? [X2 : $i,X3 : $i] : ((in @ X3 @ (setadjoin @ X3 @ X2)) != $true) => ((in @ sK3 @ (setadjoin @ sK3 @ sK2)) != $true)),
% 1.49/1.21 introduced(definition,[],[choice_axiom])).
% 1.49/1.21 thf(f32,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X2 : $i,X3 : $i] : ((in @ X3 @ (setadjoin @ X3 @ X2)) != $true))),
% 1.49/1.21 inference(rectify,[status(thm)],[f31])).
% 1.49/1.21 thf(f31,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))))),
% 1.49/1.21 inference(nnf_transformation,[status(thm)],[f16])).
% 1.49/1.21 thf(f16,plain,(
% 1.49/1.21 ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) <=> (setadjoinIL = $true)),
% 1.49/1.21 inference(fool_elimination,[status(thm)],[f15])).
% 1.49/1.21 thf(f15,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)) = setadjoinIL)),
% 1.49/1.21 inference(rectify,[status(thm)],[f1])).
% 1.49/1.21 thf(f1,axiom,(
% 1.49/1.21 (! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
% 1.49/1.21 file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',setadjoinIL)).
% 1.49/1.21 thf(f98,plain,(
% 1.49/1.21 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X2 @ X1))) | (X0 = X2) | ($true = (in @ X0 @ X1))) )),
% 1.49/1.21 inference(condensation,[status(thm)],[f97])).
% 1.49/1.21 thf(f97,plain,(
% 1.49/1.21 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | (X1 = X2) | ($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | ($true = X3)) )),
% 1.49/1.21 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.49/1.21 thf(f80,plain,(
% 1.49/1.21 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : ((X1 = X2) | ($true = X3) | ($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | ((in @ X2 @ X0) = $true) | ($true != $true)) )),
% 1.49/1.21 inference(definition_unfolding,[status(thm)],[f68,f55])).
% 1.49/1.21 thf(f55,plain,(
% 1.49/1.21 (setadjoinE = $true)),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f37])).
% 1.49/1.21 thf(f68,plain,(
% 1.49/1.21 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | ($true = X3) | ((in @ X2 @ X0) = $true) | (X1 = X2) | (setadjoinE != $true)) )),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f42])).
% 1.49/1.21 thf(f42,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | ! [X3 : $o] : (($true = X3) | (((in @ X2 @ X0) = $true) & ($true != X3)) | ((X1 = X2) & ($true != X3)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | (($true = (in @ sK8 @ (setadjoin @ sK7 @ sK6))) & ((sK9 != $true) & (((in @ sK8 @ sK6) != $true) | (sK9 = $true)) & ((sK7 != sK8) | (sK9 = $true)))))),
% 1.49/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f39,f41,f40])).
% 1.49/1.21 thf(f40,plain,(
% 1.49/1.21 ? [X4 : $i,X5 : $i,X6 : $i] : (((in @ X6 @ (setadjoin @ X5 @ X4)) = $true) & ? [X7 : $o] : (($true != X7) & (($true != (in @ X6 @ X4)) | ($true = X7)) & ((X5 != X6) | ($true = X7)))) => (($true = (in @ sK8 @ (setadjoin @ sK7 @ sK6))) & ? [X7 : $o] : (($true != X7) & (((in @ sK8 @ sK6) != $true) | ($true = X7)) & ((sK7 != sK8) | ($true = X7))))),
% 1.49/1.21 introduced(definition,[],[choice_axiom])).
% 1.49/1.21 thf(f41,plain,(
% 1.49/1.21 ? [X7 : $o] : (($true != X7) & (((in @ sK8 @ sK6) != $true) | ($true = X7)) & ((sK7 != sK8) | ($true = X7))) => ((sK9 != $true) & (((in @ sK8 @ sK6) != $true) | (sK9 = $true)) & ((sK7 != sK8) | (sK9 = $true)))),
% 1.49/1.21 introduced(definition,[],[choice_axiom])).
% 1.49/1.21 thf(f39,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | ! [X3 : $o] : (($true = X3) | (((in @ X2 @ X0) = $true) & ($true != X3)) | ((X1 = X2) & ($true != X3)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (((in @ X6 @ (setadjoin @ X5 @ X4)) = $true) & ? [X7 : $o] : (($true != X7) & (($true != (in @ X6 @ X4)) | ($true = X7)) & ((X5 != X6) | ($true = X7)))))),
% 1.49/1.21 inference(rectify,[status(thm)],[f38])).
% 1.49/1.21 thf(f38,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | ! [X3 : $o] : (($true = X3) | (((in @ X2 @ X0) = $true) & ($true != X3)) | ((X1 = X2) & ($true != X3)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setadjoin @ X1 @ X0))) & ? [X3 : $o] : (($true != X3) & (((in @ X2 @ X0) != $true) | ($true = X3)) & ((X1 != X2) | ($true = X3)))))),
% 1.49/1.21 inference(nnf_transformation,[status(thm)],[f24])).
% 1.49/1.21 thf(f24,plain,(
% 1.49/1.21 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | ! [X3 : $o] : (($true = X3) | (((in @ X2 @ X0) = $true) & ($true != X3)) | ((X1 = X2) & ($true != X3)))) <=> (setadjoinE = $true)),
% 1.49/1.21 inference(flattening,[status(thm)],[f23])).
% 1.49/1.21 thf(f23,plain,(
% 1.49/1.21 (setadjoinE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((($true = X3) | (((in @ X2 @ X0) = $true) & ($true != X3))) | ((X1 = X2) & ($true != X3))) | ($true != (in @ X2 @ (setadjoin @ X1 @ X0))))),
% 1.49/1.21 inference(ennf_transformation,[status(thm)],[f14])).
% 1.49/1.21 thf(f14,plain,(
% 1.49/1.21 (setadjoinE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setadjoin @ X1 @ X0))) => ! [X3 : $o] : (((X1 = X2) => ($true = X3)) => ((((in @ X2 @ X0) = $true) => ($true = X3)) => ($true = X3))))),
% 1.49/1.21 inference(fool_elimination,[status(thm)],[f13])).
% 1.49/1.21 thf(f13,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X0)) => ! [X3 : $o] : (((X1 = X2) => X3) => (((in @ X2 @ X0) => X3) => X3))) = setadjoinE)),
% 1.49/1.21 inference(rectify,[status(thm)],[f2])).
% 1.49/1.21 thf(f2,axiom,(
% 1.49/1.21 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ X2)) => ! [X3 : $o] : (((X0 = X1) => X3) => (((in @ X1 @ X2) => X3) => X3))) = setadjoinE)),
% 1.49/1.21 file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',setadjoinE)).
% 1.49/1.21 thf(f99,plain,(
% 1.49/1.21 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X0 @ X1))) )),
% 1.49/1.21 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.49/1.21 thf(f74,plain,(
% 1.49/1.21 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X0 @ X1)) | ($true != $true)) )),
% 1.49/1.21 inference(definition_unfolding,[status(thm)],[f50,f53])).
% 1.49/1.21 thf(f53,plain,(
% 1.49/1.21 (notinself2 = $true)),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f37])).
% 1.49/1.21 thf(f50,plain,(
% 1.49/1.21 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X0 @ X1)) | (notinself2 != $true)) )),
% 1.49/1.21 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.21 thf(f30,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X0 @ X1))) | (notinself2 != $true)) & ((notinself2 = $true) | (($true = (in @ sK1 @ sK0)) & ((in @ sK0 @ sK1) = $true)))),
% 1.49/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f28,f29])).
% 1.49/1.21 thf(f29,plain,(
% 1.49/1.21 ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ X2)) & ((in @ X2 @ X3) = $true)) => (($true = (in @ sK1 @ sK0)) & ((in @ sK0 @ sK1) = $true))),
% 1.49/1.21 introduced(definition,[],[choice_axiom])).
% 1.49/1.21 thf(f28,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X0 @ X1))) | (notinself2 != $true)) & ((notinself2 = $true) | ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ X2)) & ((in @ X2 @ X3) = $true)))),
% 1.49/1.21 inference(rectify,[status(thm)],[f27])).
% 1.49/1.21 thf(f27,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X0 @ X1))) | (notinself2 != $true)) & ((notinself2 = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) & ($true = (in @ X0 @ X1))))),
% 1.49/1.21 inference(nnf_transformation,[status(thm)],[f21])).
% 1.49/1.21 thf(f21,plain,(
% 1.49/1.21 ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X0 @ X1))) <=> (notinself2 = $true)),
% 1.49/1.21 inference(ennf_transformation,[status(thm)],[f20])).
% 1.49/1.21 thf(f20,plain,(
% 1.49/1.21 (notinself2 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) => ($true != (in @ X1 @ X0)))),
% 1.49/1.21 inference(flattening,[status(thm)],[f10])).
% 1.49/1.21 thf(f10,plain,(
% 1.49/1.21 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) => ~($true = (in @ X1 @ X0))) <=> (notinself2 = $true)),
% 1.49/1.21 inference(fool_elimination,[status(thm)],[f9])).
% 1.49/1.21 thf(f9,plain,(
% 1.49/1.21 (! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => ~(in @ X1 @ X0)) = notinself2)),
% 1.49/1.21 inference(rectify,[status(thm)],[f4])).
% 1.49/1.21 thf(f4,axiom,(
% 1.49/1.21 (! [X2 : $i,X4 : $i] : ((in @ X2 @ X4) => ~(in @ X4 @ X2)) = notinself2)),
% 1.49/1.21 file('/export/starexec/sandbox/tmp/tmp.LJlhZfqz5O/DTF2THF_7537.p',notinself2)).
% 1.49/1.21 thf(f122,plain,(
% 1.49/1.21 ((in @ sK4 @ sK5) = $true) | (sK5 = sK4)),
% 1.49/1.21 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.49/1.21 thf(f120,plain,(
% 1.49/1.21 ((in @ sK4 @ sK5) = $true) | ($true != $true) | (sK5 = sK4)),
% 1.49/1.21 inference(superposition,[status(thm)],[f113,f101])).
% 1.49/1.21 thf(f113,plain,(
% 1.49/1.21 ( ! [X0 : $i] : (($true != (in @ X0 @ (setadjoin @ sK4 @ sK4))) | ((in @ X0 @ sK5) = $true) | (sK5 = X0)) )),
% 1.49/1.21 inference(superposition,[status(thm)],[f98,f102])).
% 1.49/1.21 % SZS output end Proof for DTF2THF_7537
% 1.49/1.21 % (7640)------------------------------
% 1.49/1.21 % (7640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.21 % (7640)Termination reason: Refutation
% 1.49/1.21
% 1.49/1.21 % (7640)Memory used [KB]: 5628
% 1.49/1.21 % (7640)Time elapsed: 0.009 s
% 1.49/1.21 % (7640)Instructions burned: 8 (million)
% 1.49/1.21 % (7640)------------------------------
% 1.49/1.21 % (7640)------------------------------
% 1.49/1.21 % (7633)Success in time 0.026 s
%------------------------------------------------------------------------------