%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU642^2 : 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 : n013.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 09:35:54 AM UTC 2026
% Result : Theorem 1.58s 1.34s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 608 ( 181 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 639 ( 75 ~; 66 |; 46 &; 414 @)
% ( 8 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 19 con; 0-2 aty)
% Number of variables : 116 ( 0 ^; 83 !; 33 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f108,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f90,f100,f107]) ).
thf(f107,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
| ~ spl12_1 ),
inference(subsumption_resolution,[status(thm)],[f105,f51]) ).
thf(f51,plain,
sK4 != sK5,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
= ( in @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK4 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( sK4 != sK5 )
& ( uniqinunit = $true )
& ( singletonsuniq = $true )
& ( upairset2E = $true )
& ( setadjoinIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f28,f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= $true )
& ( X1 != X2 ) )
=> ( ( $true
= ( in @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK4 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( sK4 != sK5 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= $true )
& ( X1 != X2 ) )
& ( uniqinunit = $true )
& ( singletonsuniq = $true )
& ( upairset2E = $true )
& ( setadjoinIL = $true ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
& ( X0 != X2 ) )
& ( uniqinunit = $true )
& ( singletonsuniq = $true )
& ( upairset2E = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
& ( X0 != X2 ) )
& ( singletonsuniq = $true )
& ( upairset2E = $true )
& ( uniqinunit = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( setadjoinIL = $true )
=> ( ( uniqinunit = $true )
=> ( ( upairset2E = $true )
=> ( ( singletonsuniq = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
=> ( X0 = X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( setadjoinIL
=> ( uniqinunit
=> ( upairset2E
=> ( singletonsuniq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( setadjoinIL
=> ( uniqinunit
=> ( upairset2E
=> ( singletonsuniq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( setadjoinIL
=> ( uniqinunit
=> ( upairset2E
=> ( singletonsuniq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2THF_27170.p',setukpairinjL1) ).
thf(f105,plain,
( ( sK4 = sK5 )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ( sK4 = sK5 )
| ( $true != $true )
| ~ spl12_1 ),
inference(superposition,[status(thm)],[f74,f103]) ).
thf(f103,plain,
( ( ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) )
= $true )
| ~ spl12_1 ),
inference(superposition,[status(thm)],[f73,f85]) ).
thf(f85,plain,
( ( ( setadjoin @ sK4 @ ( setadjoin @ sK3 @ emptyset ) )
= ( setadjoin @ sK5 @ emptyset ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl12_1
<=> ( ( setadjoin @ sK4 @ ( setadjoin @ sK3 @ emptyset ) )
= ( setadjoin @ sK5 @ emptyset ) ) ),
introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition]) ).
thf(f73,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f57,f47]) ).
thf(f47,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f57,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK8 @ ( setadjoin @ sK8 @ sK9 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f36,f37]) ).
thf(f37,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) )
=> ( $true
!= ( in @ sK8 @ ( setadjoin @ sK8 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2THF_27170.p',setadjoinIL) ).
thf(f74,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
!= $true )
| ( X2 = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f58,f50]) ).
thf(f50,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f58,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
!= $true )
| ( X2 = X3 )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( uniqinunit = $true )
| ( ( $true
= ( in @ sK10 @ ( setadjoin @ sK11 @ emptyset ) ) )
& ( sK11 != sK10 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
!= $true )
| ( X2 = X3 ) )
| ( uniqinunit != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f40,f41]) ).
thf(f41,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) )
=> ( ( $true
= ( in @ sK10 @ ( setadjoin @ sK11 @ emptyset ) ) )
& ( sK11 != sK10 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
!= $true )
| ( X2 = X3 ) )
| ( uniqinunit != $true ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( uniqinunit = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( uniqinunit = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
=> ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( uniqinunit
= ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2THF_27170.p',uniqinunit) ).
thf(f100,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[status(thm)],[f99]) ).
thf(f99,plain,
( $false
| ~ spl12_2 ),
inference(subsumption_resolution,[status(thm)],[f98,f51]) ).
thf(f98,plain,
( ( sK4 = sK5 )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( sK4 = sK5 )
| ( $true != $true )
| ~ spl12_2 ),
inference(superposition,[status(thm)],[f74,f96]) ).
thf(f96,plain,
( ( $true
= ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) ) )
| ~ spl12_2 ),
inference(superposition,[status(thm)],[f73,f89]) ).
thf(f89,plain,
( ( ( setadjoin @ sK4 @ emptyset )
= ( setadjoin @ sK5 @ emptyset ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl12_2
<=> ( ( setadjoin @ sK4 @ emptyset )
= ( setadjoin @ sK5 @ emptyset ) ) ),
introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition]) ).
thf(f90,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[status(thm)],[f81,f87,f83]) ).
thf(f81,plain,
( ( ( setadjoin @ sK4 @ ( setadjoin @ sK3 @ emptyset ) )
= ( setadjoin @ sK5 @ emptyset ) )
| ( ( setadjoin @ sK4 @ emptyset )
= ( setadjoin @ sK5 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( setadjoin @ sK4 @ ( setadjoin @ sK3 @ emptyset ) )
= ( setadjoin @ sK5 @ emptyset ) )
| ( $true != $true )
| ( ( setadjoin @ sK4 @ emptyset )
= ( setadjoin @ sK5 @ emptyset ) ) ),
inference(superposition,[status(thm)],[f76,f52]) ).
thf(f52,plain,
( $true
= ( in @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK4 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f76,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
| ( X4 = X5 )
| ( X3 = X4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ( ( in @ X4 @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
| ( X3 = X4 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f43,f48]) ).
thf(f48,plain,
upairset2E = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f43,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
| ( X4 = X5 )
| ( X3 = X4 )
| ( upairset2E != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( upairset2E = $true )
| ( ( ( in @ sK1 @ ( setadjoin @ sK2 @ ( setadjoin @ sK0 @ emptyset ) ) )
= $true )
& ( sK1 != sK2 )
& ( sK1 != sK0 ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
| ( X4 = X5 )
| ( X3 = X4 ) )
| ( upairset2E != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f25,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
& ( X1 != X2 )
& ( X0 != X1 ) )
=> ( ( ( in @ sK1 @ ( setadjoin @ sK2 @ ( setadjoin @ sK0 @ emptyset ) ) )
= $true )
& ( sK1 != sK2 )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( upairset2E = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
& ( X1 != X2 )
& ( X0 != X1 ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
| ( X4 = X5 )
| ( X3 = X4 ) )
| ( upairset2E != $true ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( upairset2E = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true )
& ( X0 != X1 )
& ( X1 != X2 ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
!= $true )
| ( X0 = X1 )
| ( X1 = X2 ) )
| ( upairset2E != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( upairset2E = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
!= $true )
| ( X0 = X1 )
| ( X1 = X2 ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( X1 = X2 )
| ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
!= $true ) )
<=> ( upairset2E = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true )
=> ( ( X1 = X2 )
| ( X0 = X1 ) ) )
<=> ( upairset2E = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X1 = X2 )
| ( X0 = X1 ) ) )
= upairset2E ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X1 = X2 )
| ( X0 = X2 ) ) )
= upairset2E ),
file('/export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2THF_27170.p',upairset2E) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU642^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n013.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:29:38 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.38 thf(spec,logic,$$dhol).
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 % File : SEU642^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.38 % Domain : Set Theory
% 0.16/0.38 % Problem : Ordered Pairs - Properties of Pairs
% 0.16/0.38 % Version : Especial > Reduced > Especial.
% 0.16/0.38 % English : (! x:i.! y:i.! z:i.in (setadjoin z emptyset) (setadjoin
% 0.16/0.38 % (setadjoin x emptyset) (setadjoin (setadjoin x
% 0.16/0.38 % (setadjoin y emptyset)) emptyset)) -> x = z)
% 0.16/0.38
% 0.16/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.38 % Source : [Bro08]
% 0.16/0.38 % Names : ZFC144l [Bro08]
% 0.16/0.38
% 0.16/0.38 % Status : Theorem
% 0.16/0.38 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.16/0.38 % Syntax : Number of formulae : 12 ( 4 unt; 7 typ; 4 def)
% 0.16/0.38 % Number of atoms : 22 ( 10 equ; 0 cnn)
% 0.16/0.38 % Maximal formula atoms : 6 ( 4 avg)
% 0.16/0.38 % Number of connectives : 41 ( 0 ~; 1 |; 0 &; 32 @)
% 0.16/0.38 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.16/0.38 % Maximal formula depth : 16 ( 4 avg)
% 0.16/0.38 % Number of types : 2 ( 0 usr)
% 0.16/0.38 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.38 % Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% 0.16/0.38 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.16/0.38 % SPC : TH0_THM_EQU_NAR
% 0.16/0.38
% 0.16/0.38 % Comments : http://mathgate.info/detsetitem.php?id=198
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 thf(in_type,type,
% 0.16/0.38 in: $i > $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyset_type,type,
% 0.16/0.38 emptyset: $i ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoin_type,type,
% 0.16/0.38 setadjoin: $i > $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIL_type,type,
% 0.16/0.38 setadjoinIL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIL,definition,
% 0.16/0.38 ( setadjoinIL
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(uniqinunit_type,type,
% 0.16/0.38 uniqinunit: $o ).
% 0.16/0.38
% 0.16/0.38 thf(uniqinunit,definition,
% 0.16/0.38 ( uniqinunit
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(upairset2E_type,type,
% 0.16/0.38 upairset2E: $o ).
% 0.16/0.38
% 0.16/0.38 thf(upairset2E,definition,
% 0.16/0.38 ( upairset2E
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.38 => ( ( Xz = Xx )
% 0.16/0.38 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(singletonsuniq_type,type,
% 0.16/0.38 singletonsuniq: $o ).
% 0.16/0.38
% 0.16/0.38 thf(singletonsuniq,definition,
% 0.16/0.38 ( singletonsuniq
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( ( setadjoin @ Xx @ emptyset )
% 0.16/0.38 = ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setukpairinjL1,conjecture,
% 0.16/0.38 ( setadjoinIL
% 0.16/0.38 => ( uniqinunit
% 0.16/0.38 => ( upairset2E
% 0.16/0.38 => ( singletonsuniq
% 0.16/0.38 => ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.38 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.38 => ( Xx = Xz ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 ------------------------
% 1.58/1.31 ---- Embedded in THF ---
% 1.58/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.31 %%% Generated on Tue Feb 24 12:29:39 EST 2026
% 1.58/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.31 %%% Logic specification used:
% 1.58/1.31 %%% thf(spec, logic, $$dhol).
% 1.58/1.31
% 1.58/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2DTF27170.p
% See solution above
% 1.58/1.31 ------------------------
% 1.58/1.32 ---- Cleaned THF ---
% 1.58/1.32 thf(in_type,type,
% 1.58/1.32 in: $i > $i > $o ).
% 1.58/1.32
% 1.58/1.32 thf(emptyset_type,type,
% 1.58/1.32 emptyset: $i ).
% 1.58/1.32
% 1.58/1.32 thf(setadjoin_type,type,
% 1.58/1.32 setadjoin: $i > $i > $i ).
% 1.58/1.32
% 1.58/1.32 thf(setadjoinIL_type,type,
% 1.58/1.32 setadjoinIL: $o ).
% 1.58/1.32
% 1.58/1.32 thf(setadjoinIL,definition,
% 1.58/1.32 ( setadjoinIL
% 1.58/1.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.58/1.32
% 1.58/1.32 thf(uniqinunit_type,type,
% 1.58/1.32 uniqinunit: $o ).
% 1.58/1.32
% 1.58/1.32 thf(uniqinunit,definition,
% 1.58/1.32 ( uniqinunit
% 1.58/1.32 = ( ! [Xx: $i,Xy: $i] :
% 1.58/1.32 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.58/1.32 => ( Xx = Xy ) ) ) ) ).
% 1.58/1.32
% 1.58/1.32 thf(upairset2E_type,type,
% 1.58/1.32 upairset2E: $o ).
% 1.58/1.32
% 1.58/1.32 thf(upairset2E,definition,
% 1.58/1.32 ( upairset2E
% 1.58/1.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.58/1.32 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.58/1.32 => ( ( Xz = Xx )
% 1.58/1.32 | ( Xz = Xy ) ) ) ) ) ).
% 1.58/1.32
% 1.58/1.32 thf(singletonsuniq_type,type,
% 1.58/1.32 singletonsuniq: $o ).
% 1.58/1.32
% 1.58/1.32 thf(singletonsuniq,definition,
% 1.58/1.32 ( singletonsuniq
% 1.58/1.32 = ( ! [Xx: $i,Xy: $i] :
% 1.58/1.32 ( ( ( setadjoin @ Xx @ emptyset )
% 1.58/1.32 = ( setadjoin @ Xy @ emptyset ) )
% 1.58/1.32 => ( Xx = Xy ) ) ) ) ).
% 1.58/1.32
% 1.58/1.32 thf(setukpairinjL1,conjecture,
% 1.58/1.32 ( setadjoinIL
% 1.58/1.32 => ( uniqinunit
% 1.58/1.32 => ( upairset2E
% 1.58/1.32 => ( singletonsuniq
% 1.58/1.32 => ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.58/1.32 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 1.58/1.32 => ( Xx = Xz ) ) ) ) ) ) ).
% 1.58/1.32 ------------------------
% 1.58/1.33 % (27272)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_27170 for (2999ds/2Mi)
% 1.58/1.33 % (27271)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27170 for (2999ds/2Mi)
% 1.58/1.33 % (27269)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_27170 for (2999ds/4Mi)
% 1.58/1.34 % (27271)Instruction limit reached!
% 1.58/1.34 % (27271)------------------------------
% 1.58/1.34 % (27271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27271)Termination reason: Unknown
% 1.58/1.34 % (27271)Termination phase: Preprocessing 3
% 1.58/1.34 % (27272)Instruction limit reached!
% 1.58/1.34 % (27272)------------------------------
% 1.58/1.34 % (27272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27272)Termination reason: Unknown
% 1.58/1.34 % (27272)Termination phase: Function definition elimination
% 1.58/1.34
% 1.58/1.34 % (27272)Memory used [KB]: 895
% 1.58/1.34 % (27272)Time elapsed: 0.003 s
% 1.58/1.34 % (27272)Instructions burned: 3 (million)
% 1.58/1.34 % (27272)------------------------------
% 1.58/1.34 % (27272)------------------------------
% 1.58/1.34
% 1.58/1.34 % (27271)Memory used [KB]: 895
% 1.58/1.34 % (27271)Time elapsed: 0.003 s
% 1.58/1.34 % (27271)Instructions burned: 2 (million)
% 1.58/1.34 % (27271)------------------------------
% 1.58/1.34 % (27271)------------------------------
% 1.58/1.34 % (27273)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_27170 for (2999ds/275Mi)
% 1.58/1.34 % (27268)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27170 for (2999ds/183Mi)
% 1.58/1.34 % (27270)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_27170 for (2999ds/27Mi)
% 1.58/1.34 % (27274)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27170 for (2999ds/18Mi)
% 1.58/1.34 % (27269)Instruction limit reached!
% 1.58/1.34 % (27269)------------------------------
% 1.58/1.34 % (27269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27269)Termination reason: Unknown
% 1.58/1.34 % (27269)Termination phase: Saturation
% 1.58/1.34
% 1.58/1.34 % (27269)Memory used [KB]: 5500
% 1.58/1.34 % (27269)Time elapsed: 0.004 s
% 1.58/1.34 % (27269)Instructions burned: 5 (million)
% 1.58/1.34 % (27269)------------------------------
% 1.58/1.34 % (27269)------------------------------
% 1.58/1.34 % (27273)First to succeed.
% 1.58/1.34 % (27274)Also succeeded, but the first one will report.
% 1.58/1.34 % (27270)Also succeeded, but the first one will report.
% 1.58/1.34 % (27273)Refutation found. Thanks to Tanya!
% 1.58/1.34 % SZS status Theorem for DTF2THF_27170
% 1.58/1.34 % SZS output start Proof for DTF2THF_27170
% 1.58/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.58/1.34 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.58/1.34 thf(f108,plain,(
% 1.58/1.34 $false),
% 1.58/1.34 inference(avatar_sat_refutation,[status(thm)],[f90,f100,f107])).
% 1.58/1.34 thf(f107,plain,(
% 1.58/1.34 ~spl12_1),
% 1.58/1.34 inference(avatar_contradiction_clause,[status(thm)],[f106])).
% 1.58/1.34 thf(f106,plain,(
% 1.58/1.34 $false | ~spl12_1),
% 1.58/1.34 inference(subsumption_resolution,[status(thm)],[f105,f51])).
% 1.58/1.34 thf(f51,plain,(
% 1.58/1.34 (sK4 != sK5)),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f30])).
% 1.58/1.34 thf(f30,plain,(
% 1.58/1.34 (($true = (in @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK4 @ emptyset) @ (setadjoin @ (setadjoin @ sK4 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) & (sK4 != sK5)) & (uniqinunit = $true) & (singletonsuniq = $true) & (upairset2E = $true) & (setadjoinIL = $true)),
% 1.58/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f28,f29])).
% 1.58/1.34 thf(f29,plain,(
% 1.58/1.34 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = $true) & (X1 != X2)) => (($true = (in @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK4 @ emptyset) @ (setadjoin @ (setadjoin @ sK4 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) & (sK4 != sK5))),
% 1.58/1.34 introduced(definition,[],[choice_axiom])).
% 1.58/1.34 thf(f28,plain,(
% 1.58/1.34 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = $true) & (X1 != X2)) & (uniqinunit = $true) & (singletonsuniq = $true) & (upairset2E = $true) & (setadjoinIL = $true)),
% 1.58/1.34 inference(rectify,[status(thm)],[f22])).
% 1.58/1.34 thf(f22,plain,(
% 1.58/1.34 ? [X1 : $i,X0 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = $true) & (X0 != X2)) & (uniqinunit = $true) & (singletonsuniq = $true) & (upairset2E = $true) & (setadjoinIL = $true)),
% 1.58/1.34 inference(flattening,[status(thm)],[f21])).
% 1.58/1.34 thf(f21,plain,(
% 1.58/1.34 (((? [X1 : $i,X0 : $i,X2 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = $true) & (X0 != X2)) & (singletonsuniq = $true)) & (upairset2E = $true)) & (uniqinunit = $true)) & (setadjoinIL = $true)),
% 1.58/1.34 inference(ennf_transformation,[status(thm)],[f15])).
% 1.58/1.34 thf(f15,plain,(
% 1.58/1.34 ~((setadjoinIL = $true) => ((uniqinunit = $true) => ((upairset2E = $true) => ((singletonsuniq = $true) => ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = $true) => (X0 = X2))))))),
% 1.58/1.34 inference(fool_elimination,[status(thm)],[f14])).
% 1.58/1.34 thf(f14,plain,(
% 1.58/1.34 ~(setadjoinIL => (uniqinunit => (upairset2E => (singletonsuniq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2))))))),
% 1.58/1.34 inference(rectify,[status(thm)],[f6])).
% 1.58/1.34 thf(f6,negated_conjecture,(
% 1.58/1.34 ~(setadjoinIL => (uniqinunit => (upairset2E => (singletonsuniq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2))))))),
% 1.58/1.34 inference(negated_conjecture,[status(cth)],[f5])).
% 1.58/1.34 thf(f5,conjecture,(
% 1.58/1.34 setadjoinIL => (uniqinunit => (upairset2E => (singletonsuniq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)))))),
% 1.58/1.34 file('/export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2THF_27170.p',setukpairinjL1)).
% 1.58/1.34 thf(f105,plain,(
% 1.58/1.34 (sK4 = sK5) | ~spl12_1),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.58/1.34 thf(f104,plain,(
% 1.58/1.34 (sK4 = sK5) | ($true != $true) | ~spl12_1),
% 1.58/1.34 inference(superposition,[status(thm)],[f74,f103])).
% 1.58/1.34 thf(f103,plain,(
% 1.58/1.34 ((in @ sK4 @ (setadjoin @ sK5 @ emptyset)) = $true) | ~spl12_1),
% 1.58/1.34 inference(superposition,[status(thm)],[f73,f85])).
% 1.58/1.34 thf(f85,plain,(
% 1.58/1.34 ((setadjoin @ sK4 @ (setadjoin @ sK3 @ emptyset)) = (setadjoin @ sK5 @ emptyset)) | ~spl12_1),
% 1.58/1.34 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.58/1.34 thf(f83,definition,(
% 1.58/1.34 spl12_1 <=> ((setadjoin @ sK4 @ (setadjoin @ sK3 @ emptyset)) = (setadjoin @ sK5 @ emptyset))),
% 1.58/1.34 introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition])).
% 1.58/1.34 thf(f73,plain,(
% 1.58/1.34 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1)) = $true)) )),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.58/1.34 thf(f68,plain,(
% 1.58/1.34 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | ($true != $true)) )),
% 1.58/1.34 inference(definition_unfolding,[status(thm)],[f57,f47])).
% 1.58/1.34 thf(f47,plain,(
% 1.58/1.34 (setadjoinIL = $true)),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f30])).
% 1.58/1.34 thf(f57,plain,(
% 1.58/1.34 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) )),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f38])).
% 1.58/1.34 thf(f38,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ($true != (in @ sK8 @ (setadjoin @ sK8 @ sK9))))),
% 1.58/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f36,f37])).
% 1.58/1.34 thf(f37,plain,(
% 1.58/1.34 ? [X2 : $i,X3 : $i] : ($true != (in @ X2 @ (setadjoin @ X2 @ X3))) => ($true != (in @ sK8 @ (setadjoin @ sK8 @ sK9)))),
% 1.58/1.34 introduced(definition,[],[choice_axiom])).
% 1.58/1.34 thf(f36,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X2 : $i,X3 : $i] : ($true != (in @ X2 @ (setadjoin @ X2 @ X3))))),
% 1.58/1.34 inference(rectify,[status(thm)],[f35])).
% 1.58/1.34 thf(f35,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) != $true))),
% 1.58/1.34 inference(nnf_transformation,[status(thm)],[f9])).
% 1.58/1.34 thf(f9,plain,(
% 1.58/1.34 ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) <=> (setadjoinIL = $true)),
% 1.58/1.34 inference(fool_elimination,[status(thm)],[f8])).
% 1.58/1.34 thf(f8,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
% 1.58/1.34 inference(rectify,[status(thm)],[f1])).
% 1.58/1.34 thf(f1,axiom,(
% 1.58/1.34 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
% 1.58/1.34 file('/export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2THF_27170.p',setadjoinIL)).
% 1.58/1.34 thf(f74,plain,(
% 1.58/1.34 ( ! [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) != $true) | (X2 = X3)) )),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.58/1.34 thf(f72,plain,(
% 1.58/1.34 ( ! [X2 : $i,X3 : $i] : ((X2 = X3) | ((in @ X2 @ (setadjoin @ X3 @ emptyset)) != $true) | ($true != $true)) )),
% 1.58/1.34 inference(definition_unfolding,[status(thm)],[f58,f50])).
% 1.58/1.34 thf(f50,plain,(
% 1.58/1.34 (uniqinunit = $true)),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f30])).
% 1.58/1.34 thf(f58,plain,(
% 1.58/1.34 ( ! [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) != $true) | (X2 = X3) | (uniqinunit != $true)) )),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 1.58/1.34 thf(f42,plain,(
% 1.58/1.34 ((uniqinunit = $true) | (($true = (in @ sK10 @ (setadjoin @ sK11 @ emptyset))) & (sK11 != sK10))) & (! [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) != $true) | (X2 = X3)) | (uniqinunit != $true))),
% 1.58/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f40,f41])).
% 1.58/1.34 thf(f41,plain,(
% 1.58/1.34 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & (X0 != X1)) => (($true = (in @ sK10 @ (setadjoin @ sK11 @ emptyset))) & (sK11 != sK10))),
% 1.58/1.34 introduced(definition,[],[choice_axiom])).
% 1.58/1.34 thf(f40,plain,(
% 1.58/1.34 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & (X0 != X1))) & (! [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) != $true) | (X2 = X3)) | (uniqinunit != $true))),
% 1.58/1.34 inference(rectify,[status(thm)],[f39])).
% 1.58/1.34 thf(f39,plain,(
% 1.58/1.34 ((uniqinunit = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & (X0 != X1))) & (! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true))),
% 1.58/1.34 inference(nnf_transformation,[status(thm)],[f23])).
% 1.58/1.34 thf(f23,plain,(
% 1.58/1.34 (uniqinunit = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) != $true) | (X0 = X1))),
% 1.58/1.34 inference(ennf_transformation,[status(thm)],[f13])).
% 1.58/1.34 thf(f13,plain,(
% 1.58/1.34 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 1.58/1.34 inference(fool_elimination,[status(thm)],[f12])).
% 1.58/1.34 thf(f12,plain,(
% 1.58/1.34 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)))),
% 1.58/1.34 inference(rectify,[status(thm)],[f2])).
% 1.58/1.34 thf(f2,axiom,(
% 1.58/1.34 (uniqinunit = ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.58/1.34 file('/export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2THF_27170.p',uniqinunit)).
% 1.58/1.34 thf(f100,plain,(
% 1.58/1.34 ~spl12_2),
% 1.58/1.34 inference(avatar_contradiction_clause,[status(thm)],[f99])).
% 1.58/1.34 thf(f99,plain,(
% 1.58/1.34 $false | ~spl12_2),
% 1.58/1.34 inference(subsumption_resolution,[status(thm)],[f98,f51])).
% 1.58/1.34 thf(f98,plain,(
% 1.58/1.34 (sK4 = sK5) | ~spl12_2),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.58/1.34 thf(f97,plain,(
% 1.58/1.34 (sK4 = sK5) | ($true != $true) | ~spl12_2),
% 1.58/1.34 inference(superposition,[status(thm)],[f74,f96])).
% 1.58/1.34 thf(f96,plain,(
% 1.58/1.34 ($true = (in @ sK5 @ (setadjoin @ sK4 @ emptyset))) | ~spl12_2),
% 1.58/1.34 inference(superposition,[status(thm)],[f73,f89])).
% 1.58/1.34 thf(f89,plain,(
% 1.58/1.34 ((setadjoin @ sK4 @ emptyset) = (setadjoin @ sK5 @ emptyset)) | ~spl12_2),
% 1.58/1.34 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.58/1.34 thf(f87,definition,(
% 1.58/1.34 spl12_2 <=> ((setadjoin @ sK4 @ emptyset) = (setadjoin @ sK5 @ emptyset))),
% 1.58/1.34 introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition])).
% 1.58/1.34 thf(f90,plain,(
% 1.58/1.34 spl12_1 | spl12_2),
% 1.58/1.34 inference(avatar_split_clause,[status(thm)],[f81,f87,f83])).
% 1.58/1.34 thf(f81,plain,(
% 1.58/1.34 ((setadjoin @ sK4 @ (setadjoin @ sK3 @ emptyset)) = (setadjoin @ sK5 @ emptyset)) | ((setadjoin @ sK4 @ emptyset) = (setadjoin @ sK5 @ emptyset))),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.58/1.34 thf(f80,plain,(
% 1.58/1.34 ((setadjoin @ sK4 @ (setadjoin @ sK3 @ emptyset)) = (setadjoin @ sK5 @ emptyset)) | ($true != $true) | ((setadjoin @ sK4 @ emptyset) = (setadjoin @ sK5 @ emptyset))),
% 1.58/1.34 inference(superposition,[status(thm)],[f76,f52])).
% 1.58/1.34 thf(f52,plain,(
% 1.58/1.34 ($true = (in @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK4 @ emptyset) @ (setadjoin @ (setadjoin @ sK4 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f30])).
% 1.58/1.34 thf(f76,plain,(
% 1.58/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setadjoin @ X5 @ (setadjoin @ X3 @ emptyset))) != $true) | (X4 = X5) | (X3 = X4)) )),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.58/1.34 thf(f64,plain,(
% 1.58/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((X4 = X5) | ((in @ X4 @ (setadjoin @ X5 @ (setadjoin @ X3 @ emptyset))) != $true) | (X3 = X4) | ($true != $true)) )),
% 1.58/1.34 inference(definition_unfolding,[status(thm)],[f43,f48])).
% 1.58/1.34 thf(f48,plain,(
% 1.58/1.34 (upairset2E = $true)),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f30])).
% 1.58/1.34 thf(f43,plain,(
% 1.58/1.34 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setadjoin @ X5 @ (setadjoin @ X3 @ emptyset))) != $true) | (X4 = X5) | (X3 = X4) | (upairset2E != $true)) )),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f27])).
% 1.58/1.34 thf(f27,plain,(
% 1.58/1.34 ((upairset2E = $true) | (((in @ sK1 @ (setadjoin @ sK2 @ (setadjoin @ sK0 @ emptyset))) = $true) & (sK1 != sK2) & (sK1 != sK0))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setadjoin @ X5 @ (setadjoin @ X3 @ emptyset))) != $true) | (X4 = X5) | (X3 = X4)) | (upairset2E != $true))),
% 1.58/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f25,f26])).
% 1.58/1.34 thf(f26,plain,(
% 1.58/1.34 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) = $true) & (X1 != X2) & (X0 != X1)) => (((in @ sK1 @ (setadjoin @ sK2 @ (setadjoin @ sK0 @ emptyset))) = $true) & (sK1 != sK2) & (sK1 != sK0))),
% 1.58/1.34 introduced(definition,[],[choice_axiom])).
% 1.58/1.34 thf(f25,plain,(
% 1.58/1.34 ((upairset2E = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) = $true) & (X1 != X2) & (X0 != X1))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setadjoin @ X5 @ (setadjoin @ X3 @ emptyset))) != $true) | (X4 = X5) | (X3 = X4)) | (upairset2E != $true))),
% 1.58/1.34 inference(rectify,[status(thm)],[f24])).
% 1.58/1.34 thf(f24,plain,(
% 1.58/1.34 ((upairset2E = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) = $true) & (X0 != X1) & (X1 != X2))) & (! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (X0 = X1) | (X1 = X2)) | (upairset2E != $true))),
% 1.58/1.34 inference(nnf_transformation,[status(thm)],[f19])).
% 1.58/1.34 thf(f19,plain,(
% 1.58/1.34 (upairset2E = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (X0 = X1) | (X1 = X2))),
% 1.58/1.34 inference(flattening,[status(thm)],[f18])).
% 1.58/1.34 thf(f18,plain,(
% 1.58/1.34 ! [X2 : $i,X1 : $i,X0 : $i] : (((X1 = X2) | (X0 = X1)) | ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) != $true)) <=> (upairset2E = $true)),
% 1.58/1.34 inference(ennf_transformation,[status(thm)],[f11])).
% 1.58/1.34 thf(f11,plain,(
% 1.58/1.34 ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) = $true) => ((X1 = X2) | (X0 = X1))) <=> (upairset2E = $true)),
% 1.58/1.34 inference(fool_elimination,[status(thm)],[f10])).
% 1.58/1.34 thf(f10,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) => ((X1 = X2) | (X0 = X1))) = upairset2E)),
% 1.58/1.34 inference(rectify,[status(thm)],[f3])).
% 1.58/1.34 thf(f3,axiom,(
% 1.58/1.34 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X1 = X2) | (X0 = X2))) = upairset2E)),
% 1.58/1.34 file('/export/starexec/sandbox/tmp/tmp.ls0CoCSNTt/DTF2THF_27170.p',upairset2E)).
% 1.58/1.34 % SZS output end Proof for DTF2THF_27170
% 1.58/1.34 % (27273)------------------------------
% 1.58/1.34 % (27273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27273)Termination reason: Refutation
% 1.58/1.34
% 1.58/1.34 % (27273)Memory used [KB]: 5500
% 1.58/1.34 % (27273)Time elapsed: 0.007 s
% 1.58/1.34 % (27273)Instructions burned: 7 (million)
% 1.58/1.34 % (27273)------------------------------
% 1.58/1.34 % (27273)------------------------------
% 1.58/1.34 % (27267)Success in time 0.022 s
%------------------------------------------------------------------------------