%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU625^2 : 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 : n003.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 09:35:42 AM UTC 2026
% Result : Theorem 1.71s 1.42s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 101 ( 23 unt; 0 typ; 2 def)
% Number of atoms : 1107 ( 317 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 1155 ( 142 ~; 126 |; 80 &; 744 @)
% ( 12 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 26 con; 0-2 aty)
% Number of variables : 228 ( 0 ^; 170 !; 58 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_27,type,
sK14: $i > $i > $i ).
thf(f194,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f131,f169,f193]) ).
thf(f193,plain,
~ spl17_1,
inference(avatar_contradiction_clause,[status(thm)],[f192]) ).
thf(f192,plain,
( $false
| ~ spl17_1 ),
inference(subsumption_resolution,[status(thm)],[f190,f62]) ).
thf(f62,plain,
( $true
= ( in @ sK8 @ sK7 ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( binunionRsub = $true )
& ( subsetI2 = $true )
& ( binunionLsub = $true )
& ( $true
!= ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) ) )
& ( $true
= ( in @ sK8 @ sK7 ) )
& ( $true
= ( in @ sK6 @ sK5 ) )
& ( upairset2E = $true )
& ( subsetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f36,f38,f37]) ).
thf(f37,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
=> ( ? [X3: $i] :
( ( $true
!= ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) ) )
& ( $true
= ( in @ X3 @ sK7 ) ) )
& ( $true
= ( in @ sK6 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ? [X3: $i] :
( ( $true
!= ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) ) )
& ( $true
= ( in @ X3 @ sK7 ) ) )
=> ( ( $true
!= ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) ) )
& ( $true
= ( in @ sK8 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( binunionRsub = $true )
& ( subsetI2 = $true )
& ( binunionLsub = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( upairset2E = $true )
& ( subsetE = $true ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( binunionRsub = $true )
& ( subsetI2 = $true )
& ( binunionLsub = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( upairset2E = $true )
& ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( upairset2E = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( ( subsetI2 = $true )
=> ( ( subsetE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( upairset2E = $true )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( subsetI2
=> ( subsetE
=> ( binunionLsub
=> ( binunionRsub
=> ( upairset2E
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( subsetI2
=> ( subsetE
=> ( binunionLsub
=> ( binunionRsub
=> ( upairset2E
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( subsetI2
=> ( subsetE
=> ( binunionLsub
=> ( binunionRsub
=> ( upairset2E
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',upairsubunion) ).
thf(f190,plain,
( ( $true
!= ( in @ sK8 @ sK7 ) )
| ~ spl17_1 ),
inference(trivial_inequality_removal,[status(thm)],[f182]) ).
thf(f182,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK8 @ sK7 ) )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f177,f93]) ).
thf(f93,plain,
! [X2: $i,X3: $i] :
( $true
= ( subset @ X3 @ ( binunion @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( $true
= ( subset @ X3 @ ( binunion @ X2 @ X3 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f75,f66]) ).
thf(f66,plain,
binunionRsub = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f75,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ ( binunion @ X2 @ X3 ) ) )
| ( binunionRsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( binunionRsub = $true )
| ( $true
!= ( subset @ sK16 @ ( binunion @ sK15 @ sK16 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( subset @ X3 @ ( binunion @ X2 @ X3 ) ) )
| ( binunionRsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f50,f51]) ).
thf(f51,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X0 @ X1 ) )
!= $true )
=> ( $true
!= ( subset @ sK16 @ ( binunion @ sK15 @ sK16 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f50,plain,
( ( ( binunionRsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X0 @ X1 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( subset @ X3 @ ( binunion @ X2 @ X3 ) ) )
| ( binunionRsub != $true ) ) ),
inference(rectify,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( binunionRsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X0 @ X1 ) )
!= $true ) )
& ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( binunionRsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( binunionRsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( binunionRsub
= ( ! [X0: $i,X1: $i] : ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( binunionRsub
= ( ! [X0: $i,X1: $i] : ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',binunionRsub) ).
thf(f177,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ ( binunion @ sK5 @ sK7 ) )
!= $true )
| ( $true
!= ( in @ sK8 @ X0 ) ) )
| ~ spl17_1 ),
inference(subsumption_resolution,[status(thm)],[f171,f63]) ).
thf(f63,plain,
( $true
!= ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f171,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK8 @ X0 ) )
| ( $true
= ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) ) )
| ( ( subset @ X0 @ ( binunion @ sK5 @ sK7 ) )
!= $true ) )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f103,f126]) ).
thf(f126,plain,
( ( ( sK14 @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) )
= sK8 )
| ~ spl17_1 ),
inference(avatar_component_clause,[status(thm)],[f124]) ).
thf(f124,definition,
( spl17_1
<=> ( ( sK14 @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) )
= sK8 ) ),
introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition]) ).
thf(f103,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK14 @ X0 @ X1 ) @ X2 ) )
| ( ( subset @ X0 @ X1 )
= $true )
| ( $true
!= ( subset @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK14 @ X0 @ X1 ) @ X2 ) )
| ( $true != $true )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f95,f94]) ).
thf(f94,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( subset @ X2 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( $true != $true )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( subset @ X2 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f56,f59]) ).
thf(f59,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f56,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X0 ) )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X0 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( $true
!= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK1 @ sK2 )
= $true )
& ( $true
= ( subset @ sK2 @ sK0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f29,f30]) ).
thf(f30,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
& ( $true
= ( in @ X4 @ X5 ) )
& ( $true
= ( subset @ X5 @ X3 ) ) )
=> ( ( $true
!= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK1 @ sK2 )
= $true )
& ( $true
= ( subset @ sK2 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X0 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
& ( $true
= ( in @ X4 @ X5 ) )
& ( $true
= ( subset @ X5 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ X1 ) )
& ( $true
= ( subset @ X1 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true
= ( in @ X0 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',subsetE) ).
thf(f95,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ ( sK14 @ X4 @ X3 ) @ X3 ) )
| ( $true
= ( subset @ X4 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ( $true
!= ( in @ ( sK14 @ X4 @ X3 ) @ X3 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f71,f65]) ).
thf(f65,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f71,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ( $true
!= ( in @ ( sK14 @ X4 @ X3 ) @ X3 ) )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( subsetI2 = $true )
| ( ( $true
!= ( subset @ sK13 @ sK12 ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK13 ) )
| ( $true
= ( in @ X2 @ sK12 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ( ( $true
= ( in @ ( sK14 @ X4 @ X3 ) @ X4 ) )
& ( $true
!= ( in @ ( sK14 @ X4 @ X3 ) @ X3 ) ) ) )
| ( subsetI2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f45,f47,f46]) ).
thf(f46,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) )
=> ( ( $true
!= ( subset @ sK13 @ sK12 ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK13 ) )
| ( $true
= ( in @ X2 @ sK12 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( $true
!= ( in @ X5 @ X3 ) ) )
=> ( ( $true
= ( in @ ( sK14 @ X4 @ X3 ) @ X4 ) )
& ( $true
!= ( in @ ( sK14 @ X4 @ X3 ) @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( $true
!= ( in @ X5 @ X3 ) ) ) )
| ( subsetI2 != $true ) ) ),
inference(rectify,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( subsetI2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( subsetI2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( $true
= ( subset @ X1 @ X0 ) ) )
<=> ( subsetI2 = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= subsetI2 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI2 ),
file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',subsetI2) ).
thf(f169,plain,
~ spl17_2,
inference(avatar_contradiction_clause,[status(thm)],[f168]) ).
thf(f168,plain,
( $false
| ~ spl17_2 ),
inference(subsumption_resolution,[status(thm)],[f167,f61]) ).
thf(f61,plain,
( $true
= ( in @ sK6 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f167,plain,
( ( $true
!= ( in @ sK6 @ sK5 ) )
| ~ spl17_2 ),
inference(trivial_inequality_removal,[status(thm)],[f159]) ).
thf(f159,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK6 @ sK5 ) )
| ~ spl17_2 ),
inference(superposition,[status(thm)],[f141,f98]) ).
thf(f98,plain,
! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f58,f64]) ).
thf(f64,plain,
binunionLsub = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f58,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ( $true
!= ( subset @ sK4 @ ( binunion @ sK4 @ sK3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f33,f34]) ).
thf(f34,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( subset @ X3 @ ( binunion @ X3 @ X2 ) ) )
=> ( $true
!= ( subset @ sK4 @ ( binunion @ sK4 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ X3 @ ( binunion @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
<=> ( binunionLsub = $true ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X1 @ X0 ) )
= binunionLsub ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $i,X0: $i] :
( ( subset @ X0 @ ( binunion @ X0 @ X1 ) )
= binunionLsub ),
file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',binunionLsub) ).
thf(f141,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ ( binunion @ sK5 @ sK7 ) )
!= $true )
| ( $true
!= ( in @ sK6 @ X0 ) ) )
| ~ spl17_2 ),
inference(subsumption_resolution,[status(thm)],[f137,f63]) ).
thf(f137,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ ( binunion @ sK5 @ sK7 ) )
!= $true )
| ( $true
= ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) ) )
| ( $true
!= ( in @ sK6 @ X0 ) ) )
| ~ spl17_2 ),
inference(superposition,[status(thm)],[f103,f130]) ).
thf(f130,plain,
( ( ( sK14 @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) )
= sK6 )
| ~ spl17_2 ),
inference(avatar_component_clause,[status(thm)],[f128]) ).
thf(f128,definition,
( spl17_2
<=> ( ( sK14 @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) )
= sK6 ) ),
introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition]) ).
thf(f131,plain,
( spl17_1
| spl17_2 ),
inference(avatar_split_clause,[status(thm)],[f121,f128,f124]) ).
thf(f121,plain,
( ( ( sK14 @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) )
= sK8 )
| ( ( sK14 @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) )
= sK6 ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( ( sK14 @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) )
= sK8 )
| ( ( sK14 @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ ( binunion @ sK5 @ sK7 ) )
= sK6 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f63,f106]) ).
thf(f106,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 ) )
| ( ( sK14 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X1 )
| ( ( sK14 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK14 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X1 )
| ( ( sK14 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X0 )
| ( $true
= ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f96,f97]) ).
thf(f97,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( in @ ( sK14 @ X4 @ X3 ) @ X4 ) )
| ( $true
= ( subset @ X4 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( in @ ( sK14 @ X4 @ X3 ) @ X4 ) )
| ( $true
= ( subset @ X4 @ X3 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f72,f65]) ).
thf(f72,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ( $true
= ( in @ ( sK14 @ X4 @ X3 ) @ X4 ) )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f96,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X0 = X1 )
| ( X0 = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( X0 = X1 )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f70,f60]) ).
thf(f60,plain,
upairset2E = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f70,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X0 = X1 )
| ( X0 = X2 )
| ( upairset2E != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X0 = X1 )
| ( X0 = X2 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ( ( $true
= ( in @ sK9 @ ( setadjoin @ sK10 @ ( setadjoin @ sK11 @ emptyset ) ) ) )
& ( sK9 != sK10 )
& ( sK11 != sK9 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f41,f42]) ).
thf(f42,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setadjoin @ X4 @ ( setadjoin @ X5 @ emptyset ) ) )
= $true )
& ( X3 != X4 )
& ( X3 != X5 ) )
=> ( ( $true
= ( in @ sK9 @ ( setadjoin @ sK10 @ ( setadjoin @ sK11 @ emptyset ) ) ) )
& ( sK9 != sK10 )
& ( sK11 != sK9 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X0 = X1 )
| ( X0 = X2 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setadjoin @ X4 @ ( setadjoin @ X5 @ emptyset ) ) )
= $true )
& ( X3 != X4 )
& ( X3 != X5 ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X0 = X1 )
| ( X0 = X2 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
& ( X0 != X1 )
& ( X0 != X2 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X0 = X1 )
| ( X0 = X2 ) )
<=> ( upairset2E = $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( X0 = X1 )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) )
<=> ( upairset2E = $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
=> ( ( X0 = X1 )
| ( X0 = X2 ) ) )
<=> ( upairset2E = $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X0 = X2 )
| ( X0 = X1 ) ) )
= upairset2E ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X4: $i,X2: $i,X3: $i] :
( ( ( in @ X4 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X3 = X4 )
| ( X2 = X4 ) ) )
= upairset2E ),
file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',upairset2E) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU625^2 : 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
% 0.11/0.29 % Computer : n003.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:28:25 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.40 ---- Original DTF file ---
% 0.21/0.41 thf(spec,logic,$$dhol).
% 0.21/0.41 %------------------------------------------------------------------------------
% 0.21/0.41 % File : SEU625^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.41 % Domain : Set Theory
% 0.21/0.41 % Problem : Ordered Pairs - Cartesian Products
% 0.21/0.41 % Version : Especial > Reduced > Especial.
% 0.21/0.41 % English : (! A:i.! B:i.! x:i.in x A -> (! y:i.in y B -> subset (setadjoin x
% 0.21/0.41 % (setadjoin y emptyset)) (binunion A B)))
% 0.21/0.41
% 0.21/0.41 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.41 % Source : [Bro08]
% 0.21/0.41 % Names : ZFC127l [Bro08]
% 0.21/0.41
% 0.21/0.41 % Status : Theorem
% 0.21/0.41 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 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, 0.40 v6.2.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.21/0.41 % Syntax : Number of formulae : 16 ( 5 unt; 10 typ; 5 def)
% 0.21/0.41 % Number of atoms : 29 ( 7 equ; 0 cnn)
% 0.21/0.41 % Maximal formula atoms : 8 ( 4 avg)
% 0.21/0.41 % Number of connectives : 51 ( 0 ~; 1 |; 0 &; 38 @)
% 0.21/0.41 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.21/0.41 % Maximal formula depth : 17 ( 4 avg)
% 0.21/0.41 % Number of types : 2 ( 0 usr)
% 0.21/0.41 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.21/0.41 % Number of symbols : 11 ( 10 usr; 6 con; 0-2 aty)
% 0.21/0.41 % Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 0.21/0.41 % SPC : TH0_THM_EQU_NAR
% 0.21/0.41
% 0.21/0.41 % Comments : http://mathgate.info/detsetitem.php?id=182
% 0.21/0.41 %------------------------------------------------------------------------------
% 0.21/0.41 thf(in_type,type,
% 0.21/0.41 in: $i > $i > $o ).
% 0.21/0.41
% 0.21/0.41 thf(emptyset_type,type,
% 0.21/0.41 emptyset: $i ).
% 0.21/0.41
% 0.21/0.41 thf(setadjoin_type,type,
% 0.21/0.41 setadjoin: $i > $i > $i ).
% 0.21/0.41
% 0.21/0.41 thf(subset_type,type,
% 0.21/0.41 subset: $i > $i > $o ).
% 0.21/0.41
% 0.21/0.41 thf(subsetI2_type,type,
% 0.21/0.41 subsetI2: $o ).
% 0.21/0.41
% 0.21/0.41 thf(subsetI2,definition,
% 0.21/0.41 ( subsetI2
% 0.21/0.41 = ( ! [A: $i,B: $i] :
% 0.21/0.41 ( ! [Xx: $i] :
% 0.21/0.41 ( ( in @ Xx @ A )
% 0.21/0.41 => ( in @ Xx @ B ) )
% 0.21/0.41 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.41
% 0.21/0.41 thf(subsetE_type,type,
% 0.21/0.41 subsetE: $o ).
% 0.21/0.41
% 0.21/0.41 thf(subsetE,definition,
% 0.21/0.41 ( subsetE
% 0.21/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.41 ( ( subset @ A @ B )
% 0.21/0.41 => ( ( in @ Xx @ A )
% 0.21/0.41 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.21/0.41
% 0.21/0.41 thf(binunion_type,type,
% 0.21/0.41 binunion: $i > $i > $i ).
% 0.21/0.41
% 0.21/0.41 thf(binunionLsub_type,type,
% 0.21/0.41 binunionLsub: $o ).
% 0.21/0.41
% 0.21/0.41 thf(binunionLsub,definition,
% 0.21/0.41 ( binunionLsub
% 0.21/0.41 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.21/0.41
% 0.21/0.41 thf(binunionRsub_type,type,
% 0.21/0.41 binunionRsub: $o ).
% 0.21/0.41
% 0.21/0.41 thf(binunionRsub,definition,
% 0.21/0.41 ( binunionRsub
% 0.21/0.41 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.21/0.41
% 0.21/0.41 thf(upairset2E_type,type,
% 0.21/0.41 upairset2E: $o ).
% 0.21/0.41
% 0.21/0.41 thf(upairset2E,definition,
% 0.21/0.41 ( upairset2E
% 0.21/0.41 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.21/0.41 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.21/0.41 => ( ( Xz = Xx )
% 0.21/0.41 | ( Xz = Xy ) ) ) ) ) ).
% 0.21/0.41
% 0.21/0.41 thf(upairsubunion,conjecture,
% 0.21/0.41 ( subsetI2
% 0.21/0.41 => ( subsetE
% 0.21/0.41 => ( binunionLsub
% 0.21/0.41 => ( binunionRsub
% 0.21/0.41 => ( upairset2E
% 0.21/0.41 => ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.41 ( ( in @ Xx @ A )
% 0.21/0.41 => ! [Xy: $i] :
% 0.21/0.41 ( ( in @ Xy @ B )
% 0.21/0.41 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ).
% 0.21/0.41
% 0.21/0.41 %------------------------------------------------------------------------------
% 0.21/0.41 ------------------------
% 1.57/1.36 ---- Embedded in THF ---
% 1.57/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.36 %%% Generated on Tue Feb 24 12:28:26 EST 2026
% 1.57/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.36 %%% Logic specification used:
% 1.57/1.36 %%% thf(spec, logic, $$dhol).
% 1.57/1.36
% 1.57/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2DTF16353.p
% See solution above
% 1.57/1.36 ------------------------
% 1.57/1.37 ---- Cleaned THF ---
% 1.57/1.37 thf(in_type,type,
% 1.57/1.37 in: $i > $i > $o ).
% 1.57/1.37
% 1.57/1.37 thf(emptyset_type,type,
% 1.57/1.37 emptyset: $i ).
% 1.57/1.37
% 1.57/1.37 thf(setadjoin_type,type,
% 1.57/1.37 setadjoin: $i > $i > $i ).
% 1.57/1.37
% 1.57/1.37 thf(subset_type,type,
% 1.57/1.37 subset: $i > $i > $o ).
% 1.57/1.37
% 1.57/1.37 thf(subsetI2_type,type,
% 1.57/1.37 subsetI2: $o ).
% 1.57/1.37
% 1.57/1.37 thf(subsetI2,definition,
% 1.57/1.37 ( subsetI2
% 1.57/1.37 = ( ! [A: $i,B: $i] :
% 1.57/1.37 ( ! [Xx: $i] :
% 1.57/1.37 ( ( in @ Xx @ A )
% 1.57/1.37 => ( in @ Xx @ B ) )
% 1.57/1.37 => ( subset @ A @ B ) ) ) ) ).
% 1.57/1.37
% 1.57/1.37 thf(subsetE_type,type,
% 1.57/1.37 subsetE: $o ).
% 1.57/1.37
% 1.57/1.37 thf(subsetE,definition,
% 1.57/1.37 ( subsetE
% 1.57/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.57/1.37 ( ( subset @ A @ B )
% 1.57/1.37 => ( ( in @ Xx @ A )
% 1.57/1.37 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.57/1.37
% 1.57/1.37 thf(binunion_type,type,
% 1.57/1.37 binunion: $i > $i > $i ).
% 1.57/1.37
% 1.57/1.37 thf(binunionLsub_type,type,
% 1.57/1.37 binunionLsub: $o ).
% 1.57/1.37
% 1.57/1.37 thf(binunionLsub,definition,
% 1.57/1.37 ( binunionLsub
% 1.57/1.37 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 1.57/1.37
% 1.57/1.37 thf(binunionRsub_type,type,
% 1.57/1.37 binunionRsub: $o ).
% 1.57/1.37
% 1.57/1.37 thf(binunionRsub,definition,
% 1.57/1.37 ( binunionRsub
% 1.57/1.37 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 1.57/1.37
% 1.57/1.37 thf(upairset2E_type,type,
% 1.57/1.37 upairset2E: $o ).
% 1.57/1.37
% 1.57/1.37 thf(upairset2E,definition,
% 1.57/1.37 ( upairset2E
% 1.57/1.37 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.57/1.37 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.57/1.37 => ( ( Xz = Xx )
% 1.57/1.37 | ( Xz = Xy ) ) ) ) ) ).
% 1.57/1.37
% 1.57/1.37 thf(upairsubunion,conjecture,
% 1.57/1.37 ( subsetI2
% 1.57/1.37 => ( subsetE
% 1.57/1.37 => ( binunionLsub
% 1.57/1.37 => ( binunionRsub
% 1.57/1.37 => ( upairset2E
% 1.57/1.37 => ! [A: $i,B: $i,Xx: $i] :
% 1.57/1.37 ( ( in @ Xx @ A )
% 1.57/1.37 => ! [Xy: $i] :
% 1.57/1.37 ( ( in @ Xy @ B )
% 1.57/1.37 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ).
% 1.57/1.37 ------------------------
% 1.57/1.39 % (16453)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16353 for (2999ds/2Mi)
% 1.57/1.39 % (16456)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16353 for (2999ds/18Mi)
% 1.57/1.39 % (16454)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_16353 for (2999ds/2Mi)
% 1.57/1.39 % (16450)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16353 for (2999ds/183Mi)
% 1.57/1.39 % (16455)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_16353 for (2999ds/275Mi)
% 1.57/1.39 % (16451)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_16353 for (2999ds/4Mi)
% 1.57/1.39 % (16452)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_16353 for (2999ds/27Mi)
% 1.57/1.40 % (16453)Instruction limit reached!
% 1.57/1.40 % (16453)------------------------------
% 1.57/1.40 % (16453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.40 % (16453)Termination reason: Unknown
% 1.57/1.40 % (16453)Termination phase: Preprocessing 3
% 1.57/1.40 % (16454)Instruction limit reached!
% 1.57/1.40 % (16454)------------------------------
% 1.57/1.40 % (16454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.40 % (16454)Termination reason: Unknown
% 1.57/1.40 % (16454)Termination phase: Property scanning
% 1.57/1.40
% 1.57/1.40 % (16454)Memory used [KB]: 1023
% 1.57/1.40 % (16454)Time elapsed: 0.003 s
% 1.57/1.40 % (16454)Instructions burned: 3 (million)
% 1.57/1.40 % (16454)------------------------------
% 1.57/1.40 % (16454)------------------------------
% 1.57/1.40
% 1.57/1.40 % (16453)Memory used [KB]: 1023
% 1.57/1.40 % (16453)Time elapsed: 0.003 s
% 1.57/1.40 % (16453)Instructions burned: 2 (million)
% 1.57/1.40 % (16453)------------------------------
% 1.57/1.40 % (16453)------------------------------
% 1.71/1.40 % (16451)Instruction limit reached!
% 1.71/1.40 % (16451)------------------------------
% 1.71/1.40 % (16451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (16451)Termination reason: Unknown
% 1.71/1.40 % (16451)Termination phase: Saturation
% 1.71/1.40
% 1.71/1.40 % (16451)Memory used [KB]: 5500
% 1.71/1.40 % (16451)Time elapsed: 0.005 s
% 1.71/1.40 % (16451)Instructions burned: 5 (million)
% 1.71/1.40 % (16451)------------------------------
% 1.71/1.40 % (16451)------------------------------
% 1.71/1.40 % (16456)Instruction limit reached!
% 1.71/1.40 % (16456)------------------------------
% 1.71/1.40 % (16456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (16456)Termination reason: Unknown
% 1.71/1.40 % (16456)Termination phase: Saturation
% 1.71/1.40
% 1.71/1.40 % (16456)Memory used [KB]: 5628
% 1.71/1.40 % (16456)Time elapsed: 0.012 s
% 1.71/1.40 % (16456)Instructions burned: 18 (million)
% 1.71/1.40 % (16456)------------------------------
% 1.71/1.40 % (16456)------------------------------
% 1.71/1.41 % (16452)Instruction limit reached!
% 1.71/1.41 % (16452)------------------------------
% 1.71/1.41 % (16452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (16452)Termination reason: Unknown
% 1.71/1.41 % (16452)Termination phase: Saturation
% 1.71/1.41
% 1.71/1.41 % (16452)Memory used [KB]: 5628
% 1.71/1.41 % (16452)Time elapsed: 0.016 s
% 1.71/1.41 % (16452)Instructions burned: 28 (million)
% 1.71/1.41 % (16452)------------------------------
% 1.71/1.41 % (16452)------------------------------
% 1.71/1.41 % (16458)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_16353 for (2999ds/37Mi)
% 1.71/1.41 % (16457)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16353 for (2999ds/3Mi)
% 1.71/1.41 % (16455)First to succeed.
% 1.71/1.41 % (16457)Instruction limit reached!
% 1.71/1.41 % (16457)------------------------------
% 1.71/1.41 % (16457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (16457)Termination reason: Unknown
% 1.71/1.41 % (16457)Termination phase: Property scanning
% 1.71/1.41
% 1.71/1.41 % (16457)Memory used [KB]: 1023
% 1.71/1.41 % (16457)Time elapsed: 0.003 s
% 1.71/1.41 % (16457)Instructions burned: 3 (million)
% 1.71/1.41 % (16457)------------------------------
% 1.71/1.41 % (16457)------------------------------
% 1.71/1.41 % (16459)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_16353 for (2999ds/15Mi)
% 1.71/1.42 % (16450)Also succeeded, but the first one will report.
% 1.71/1.42 % (16455)Refutation found. Thanks to Tanya!
% 1.71/1.42 % SZS status Theorem for DTF2THF_16353
% 1.71/1.42 % SZS output start Proof for DTF2THF_16353
% 1.71/1.42 thf(func_def_0, type, in: $i > $i > $o).
% 1.71/1.42 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.71/1.42 thf(func_def_3, type, subset: $i > $i > $o).
% 1.71/1.42 thf(func_def_7, type, binunion: $i > $i > $i).
% 1.71/1.42 thf(func_def_27, type, sK14: $i > $i > $i).
% 1.71/1.42 thf(f194,plain,(
% 1.71/1.42 $false),
% 1.71/1.42 inference(avatar_sat_refutation,[status(thm)],[f131,f169,f193])).
% 1.71/1.42 thf(f193,plain,(
% 1.71/1.42 ~spl17_1),
% 1.71/1.42 inference(avatar_contradiction_clause,[status(thm)],[f192])).
% 1.71/1.42 thf(f192,plain,(
% 1.71/1.42 $false | ~spl17_1),
% 1.71/1.42 inference(subsumption_resolution,[status(thm)],[f190,f62])).
% 1.71/1.42 thf(f62,plain,(
% 1.71/1.42 ($true = (in @ sK8 @ sK7))),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.42 thf(f39,plain,(
% 1.71/1.42 (binunionRsub = $true) & (subsetI2 = $true) & (binunionLsub = $true) & ((($true != (subset @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7))) & ($true = (in @ sK8 @ sK7))) & ($true = (in @ sK6 @ sK5))) & (upairset2E = $true) & (subsetE = $true)),
% 1.71/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f36,f38,f37])).
% 1.71/1.42 thf(f37,plain,(
% 1.71/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X2)) != $true) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X1 @ X0))) => (? [X3 : $i] : (($true != (subset @ (setadjoin @ sK6 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ sK5 @ sK7))) & ($true = (in @ X3 @ sK7))) & ($true = (in @ sK6 @ sK5)))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f38,plain,(
% 1.71/1.42 ? [X3 : $i] : (($true != (subset @ (setadjoin @ sK6 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ sK5 @ sK7))) & ($true = (in @ X3 @ sK7))) => (($true != (subset @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7))) & ($true = (in @ sK8 @ sK7)))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f36,plain,(
% 1.71/1.42 (binunionRsub = $true) & (subsetI2 = $true) & (binunionLsub = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X2)) != $true) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X1 @ X0))) & (upairset2E = $true) & (subsetE = $true)),
% 1.71/1.42 inference(rectify,[status(thm)],[f24])).
% 1.71/1.42 thf(f24,plain,(
% 1.71/1.42 (binunionRsub = $true) & (subsetI2 = $true) & (binunionLsub = $true) & ? [X0 : $i,X2 : $i,X1 : $i] : (? [X3 : $i] : (((subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)) != $true) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ X0) = $true)) & (upairset2E = $true) & (subsetE = $true)),
% 1.71/1.42 inference(flattening,[status(thm)],[f23])).
% 1.71/1.42 thf(f23,plain,(
% 1.71/1.42 ((((? [X0 : $i,X2 : $i,X1 : $i] : (? [X3 : $i] : (((subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)) != $true) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ X0) = $true)) & (upairset2E = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (subsetE = $true)) & (subsetI2 = $true)),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f18])).
% 1.71/1.42 thf(f18,plain,(
% 1.71/1.42 ~((subsetI2 = $true) => ((subsetE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((upairset2E = $true) => ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ((subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)) = $true))))))))),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f17])).
% 1.71/1.42 thf(f17,plain,(
% 1.71/1.42 ~(subsetI2 => (subsetE => (binunionLsub => (binunionRsub => (upairset2E => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)))))))))),
% 1.71/1.42 inference(rectify,[status(thm)],[f7])).
% 1.71/1.42 thf(f7,negated_conjecture,(
% 1.71/1.42 ~(subsetI2 => (subsetE => (binunionLsub => (binunionRsub => (upairset2E => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)))))))))),
% 1.71/1.42 inference(negated_conjecture,[status(cth)],[f6])).
% 1.71/1.42 thf(f6,conjecture,(
% 1.71/1.42 subsetI2 => (subsetE => (binunionLsub => (binunionRsub => (upairset2E => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1))))))))),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',upairsubunion)).
% 1.71/1.42 thf(f190,plain,(
% 1.71/1.42 ($true != (in @ sK8 @ sK7)) | ~spl17_1),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f182])).
% 1.71/1.42 thf(f182,plain,(
% 1.71/1.42 ($true != $true) | ($true != (in @ sK8 @ sK7)) | ~spl17_1),
% 1.71/1.42 inference(superposition,[status(thm)],[f177,f93])).
% 1.71/1.42 thf(f93,plain,(
% 1.71/1.42 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ (binunion @ X2 @ X3)))) )),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.71/1.42 thf(f92,plain,(
% 1.71/1.42 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ($true = (subset @ X3 @ (binunion @ X2 @ X3)))) )),
% 1.71/1.42 inference(definition_unfolding,[status(thm)],[f75,f66])).
% 1.71/1.42 thf(f66,plain,(
% 1.71/1.42 (binunionRsub = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.42 thf(f75,plain,(
% 1.71/1.42 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ (binunion @ X2 @ X3))) | (binunionRsub != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f52])).
% 1.71/1.42 thf(f52,plain,(
% 1.71/1.42 ((binunionRsub = $true) | ($true != (subset @ sK16 @ (binunion @ sK15 @ sK16)))) & (! [X2 : $i,X3 : $i] : ($true = (subset @ X3 @ (binunion @ X2 @ X3))) | (binunionRsub != $true))),
% 1.71/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f50,f51])).
% 1.71/1.42 thf(f51,plain,(
% 1.71/1.42 ? [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X0 @ X1)) != $true) => ($true != (subset @ sK16 @ (binunion @ sK15 @ sK16)))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f50,plain,(
% 1.71/1.42 ((binunionRsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X0 @ X1)) != $true)) & (! [X2 : $i,X3 : $i] : ($true = (subset @ X3 @ (binunion @ X2 @ X3))) | (binunionRsub != $true))),
% 1.71/1.42 inference(rectify,[status(thm)],[f49])).
% 1.71/1.42 thf(f49,plain,(
% 1.71/1.42 ((binunionRsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X0 @ X1)) != $true)) & (! [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X0 @ X1)) = $true) | (binunionRsub != $true))),
% 1.71/1.42 inference(nnf_transformation,[status(thm)],[f14])).
% 1.71/1.42 thf(f14,plain,(
% 1.71/1.42 (binunionRsub = $true) <=> ! [X0 : $i,X1 : $i] : ((subset @ X1 @ (binunion @ X0 @ X1)) = $true)),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f13])).
% 1.71/1.42 thf(f13,plain,(
% 1.71/1.42 (binunionRsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 1.71/1.42 inference(rectify,[status(thm)],[f4])).
% 1.71/1.42 thf(f4,axiom,(
% 1.71/1.42 (binunionRsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',binunionRsub)).
% 1.71/1.42 thf(f177,plain,(
% 1.71/1.42 ( ! [X0 : $i] : (((subset @ X0 @ (binunion @ sK5 @ sK7)) != $true) | ($true != (in @ sK8 @ X0))) ) | ~spl17_1),
% 1.71/1.42 inference(subsumption_resolution,[status(thm)],[f171,f63])).
% 1.71/1.42 thf(f63,plain,(
% 1.71/1.42 ($true != (subset @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)))),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.42 thf(f171,plain,(
% 1.71/1.42 ( ! [X0 : $i] : (($true != (in @ sK8 @ X0)) | ($true = (subset @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7))) | ((subset @ X0 @ (binunion @ sK5 @ sK7)) != $true)) ) | ~spl17_1),
% 1.71/1.42 inference(superposition,[status(thm)],[f103,f126])).
% 1.71/1.42 thf(f126,plain,(
% 1.71/1.42 ((sK14 @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)) = sK8) | ~spl17_1),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f124])).
% 1.71/1.42 thf(f124,definition,(
% 1.71/1.42 spl17_1 <=> ((sK14 @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)) = sK8)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition])).
% 1.71/1.42 thf(f103,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK14 @ X0 @ X1) @ X2)) | ((subset @ X0 @ X1) = $true) | ($true != (subset @ X2 @ X1))) )),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.71/1.42 thf(f102,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK14 @ X0 @ X1) @ X2)) | ($true != $true) | ($true != (subset @ X2 @ X1)) | ((subset @ X0 @ X1) = $true)) )),
% 1.71/1.42 inference(superposition,[status(thm)],[f95,f94])).
% 1.71/1.42 thf(f94,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) | ($true != (subset @ X2 @ X0)) | ($true != (in @ X1 @ X2))) )),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.71/1.42 thf(f77,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ X2)) | ($true != $true) | ($true = (in @ X1 @ X0)) | ($true != (subset @ X2 @ X0))) )),
% 1.71/1.42 inference(definition_unfolding,[status(thm)],[f56,f59])).
% 1.71/1.42 thf(f59,plain,(
% 1.71/1.42 (subsetE = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.42 thf(f56,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true != (subset @ X2 @ X0)) | (subsetE != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f31])).
% 1.71/1.42 thf(f31,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true != (subset @ X2 @ X0))) | (subsetE != $true)) & ((subsetE = $true) | (($true != (in @ sK1 @ sK0)) & ((in @ sK1 @ sK2) = $true) & ($true = (subset @ sK2 @ sK0))))),
% 1.71/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f29,f30])).
% 1.71/1.42 thf(f30,plain,(
% 1.71/1.42 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) & ($true = (in @ X4 @ X5)) & ($true = (subset @ X5 @ X3))) => (($true != (in @ sK1 @ sK0)) & ((in @ sK1 @ sK2) = $true) & ($true = (subset @ sK2 @ sK0)))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f29,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true != (subset @ X2 @ X0))) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) & ($true = (in @ X4 @ X5)) & ($true = (subset @ X5 @ X3))))),
% 1.71/1.42 inference(rectify,[status(thm)],[f28])).
% 1.71/1.42 thf(f28,plain,(
% 1.71/1.42 (! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X2)) | ($true != (in @ X0 @ X1)) | ($true != (subset @ X1 @ X2))) | (subsetE != $true)) & ((subsetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X2)) & ($true = (in @ X0 @ X1)) & ($true = (subset @ X1 @ X2))))),
% 1.71/1.42 inference(nnf_transformation,[status(thm)],[f26])).
% 1.71/1.42 thf(f26,plain,(
% 1.71/1.42 ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X2)) | ($true != (in @ X0 @ X1)) | ($true != (subset @ X1 @ X2))) <=> (subsetE = $true)),
% 1.71/1.42 inference(flattening,[status(thm)],[f25])).
% 1.71/1.42 thf(f25,plain,(
% 1.71/1.42 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((($true = (in @ X0 @ X2)) | ($true != (in @ X0 @ X1))) | ($true != (subset @ X1 @ X2)))),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f12])).
% 1.71/1.42 thf(f12,plain,(
% 1.71/1.42 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) => (($true = (in @ X0 @ X1)) => ($true = (in @ X0 @ X2))))),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f11])).
% 1.71/1.42 thf(f11,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = subsetE)),
% 1.71/1.42 inference(rectify,[status(thm)],[f2])).
% 1.71/1.42 thf(f2,axiom,(
% 1.71/1.42 (! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',subsetE)).
% 1.71/1.42 thf(f95,plain,(
% 1.71/1.42 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK14 @ X4 @ X3) @ X3)) | ($true = (subset @ X4 @ X3))) )),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.71/1.42 thf(f90,plain,(
% 1.71/1.42 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | ($true != (in @ (sK14 @ X4 @ X3) @ X3)) | ($true != $true)) )),
% 1.71/1.42 inference(definition_unfolding,[status(thm)],[f71,f65])).
% 1.71/1.42 thf(f65,plain,(
% 1.71/1.42 (subsetI2 = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.42 thf(f71,plain,(
% 1.71/1.42 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | ($true != (in @ (sK14 @ X4 @ X3) @ X3)) | (subsetI2 != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f48])).
% 1.71/1.42 thf(f48,plain,(
% 1.71/1.42 ((subsetI2 = $true) | (($true != (subset @ sK13 @ sK12)) & ! [X2 : $i] : (($true != (in @ X2 @ sK13)) | ($true = (in @ X2 @ sK12))))) & (! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | (($true = (in @ (sK14 @ X4 @ X3) @ X4)) & ($true != (in @ (sK14 @ X4 @ X3) @ X3)))) | (subsetI2 != $true))),
% 1.71/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f45,f47,f46])).
% 1.71/1.42 thf(f46,plain,(
% 1.71/1.42 ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))) => (($true != (subset @ sK13 @ sK12)) & ! [X2 : $i] : (($true != (in @ X2 @ sK13)) | ($true = (in @ X2 @ sK12))))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f47,plain,(
% 1.71/1.42 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ($true != (in @ X5 @ X3))) => (($true = (in @ (sK14 @ X4 @ X3) @ X4)) & ($true != (in @ (sK14 @ X4 @ X3) @ X3))))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f45,plain,(
% 1.71/1.42 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)))) & (! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | ? [X5 : $i] : (((in @ X5 @ X4) = $true) & ($true != (in @ X5 @ X3)))) | (subsetI2 != $true))),
% 1.71/1.42 inference(rectify,[status(thm)],[f44])).
% 1.71/1.42 thf(f44,plain,(
% 1.71/1.42 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)))) & (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (subsetI2 != $true))),
% 1.71/1.42 inference(nnf_transformation,[status(thm)],[f27])).
% 1.71/1.42 thf(f27,plain,(
% 1.71/1.42 (subsetI2 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)))),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f10])).
% 1.71/1.42 thf(f10,plain,(
% 1.71/1.42 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ($true = (subset @ X1 @ X0))) <=> (subsetI2 = $true)),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f9])).
% 1.71/1.42 thf(f9,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
% 1.71/1.42 inference(rectify,[status(thm)],[f1])).
% 1.71/1.42 thf(f1,axiom,(
% 1.71/1.42 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',subsetI2)).
% 1.71/1.42 thf(f169,plain,(
% 1.71/1.42 ~spl17_2),
% 1.71/1.42 inference(avatar_contradiction_clause,[status(thm)],[f168])).
% 1.71/1.42 thf(f168,plain,(
% 1.71/1.42 $false | ~spl17_2),
% 1.71/1.42 inference(subsumption_resolution,[status(thm)],[f167,f61])).
% 1.71/1.42 thf(f61,plain,(
% 1.71/1.42 ($true = (in @ sK6 @ sK5))),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.42 thf(f167,plain,(
% 1.71/1.42 ($true != (in @ sK6 @ sK5)) | ~spl17_2),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f159])).
% 1.71/1.42 thf(f159,plain,(
% 1.71/1.42 ($true != $true) | ($true != (in @ sK6 @ sK5)) | ~spl17_2),
% 1.71/1.42 inference(superposition,[status(thm)],[f141,f98])).
% 1.71/1.42 thf(f98,plain,(
% 1.71/1.42 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0)))) )),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.71/1.42 thf(f81,plain,(
% 1.71/1.42 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (subset @ X1 @ (binunion @ X1 @ X0)))) )),
% 1.71/1.42 inference(definition_unfolding,[status(thm)],[f58,f64])).
% 1.71/1.42 thf(f64,plain,(
% 1.71/1.42 (binunionLsub = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.42 thf(f58,plain,(
% 1.71/1.42 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f35])).
% 1.71/1.42 thf(f35,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ($true != (subset @ sK4 @ (binunion @ sK4 @ sK3))))),
% 1.71/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f33,f34])).
% 1.71/1.42 thf(f34,plain,(
% 1.71/1.42 ? [X2 : $i,X3 : $i] : ($true != (subset @ X3 @ (binunion @ X3 @ X2))) => ($true != (subset @ sK4 @ (binunion @ sK4 @ sK3)))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f33,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ? [X2 : $i,X3 : $i] : ($true != (subset @ X3 @ (binunion @ X3 @ X2))))),
% 1.71/1.42 inference(rectify,[status(thm)],[f32])).
% 1.71/1.42 thf(f32,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ? [X0 : $i,X1 : $i] : ($true != (subset @ X1 @ (binunion @ X1 @ X0))))),
% 1.71/1.42 inference(nnf_transformation,[status(thm)],[f20])).
% 1.71/1.42 thf(f20,plain,(
% 1.71/1.42 ! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) <=> (binunionLsub = $true)),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f19])).
% 1.71/1.42 thf(f19,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X1 @ X0)) = binunionLsub)),
% 1.71/1.42 inference(rectify,[status(thm)],[f3])).
% 1.71/1.42 thf(f3,axiom,(
% 1.71/1.42 (! [X1 : $i,X0 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)) = binunionLsub)),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',binunionLsub)).
% 1.71/1.42 thf(f141,plain,(
% 1.71/1.42 ( ! [X0 : $i] : (((subset @ X0 @ (binunion @ sK5 @ sK7)) != $true) | ($true != (in @ sK6 @ X0))) ) | ~spl17_2),
% 1.71/1.42 inference(subsumption_resolution,[status(thm)],[f137,f63])).
% 1.71/1.42 thf(f137,plain,(
% 1.71/1.42 ( ! [X0 : $i] : (((subset @ X0 @ (binunion @ sK5 @ sK7)) != $true) | ($true = (subset @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7))) | ($true != (in @ sK6 @ X0))) ) | ~spl17_2),
% 1.71/1.42 inference(superposition,[status(thm)],[f103,f130])).
% 1.71/1.42 thf(f130,plain,(
% 1.71/1.42 ((sK14 @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)) = sK6) | ~spl17_2),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f128])).
% 1.71/1.42 thf(f128,definition,(
% 1.71/1.42 spl17_2 <=> ((sK14 @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)) = sK6)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition])).
% 1.71/1.42 thf(f131,plain,(
% 1.71/1.42 spl17_1 | spl17_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f121,f128,f124])).
% 1.71/1.42 thf(f121,plain,(
% 1.71/1.42 ((sK14 @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)) = sK8) | ((sK14 @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)) = sK6)),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.71/1.42 thf(f119,plain,(
% 1.71/1.42 ((sK14 @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)) = sK8) | ((sK14 @ (setadjoin @ sK6 @ (setadjoin @ sK8 @ emptyset)) @ (binunion @ sK5 @ sK7)) = sK6) | ($true != $true)),
% 1.71/1.42 inference(superposition,[status(thm)],[f63,f106])).
% 1.71/1.42 thf(f106,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2)) | ((sK14 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2) = X1) | ((sK14 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2) = X0)) )),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.71/1.42 thf(f105,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((sK14 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2) = X1) | ((sK14 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2) = X0) | ($true = (subset @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2)) | ($true != $true)) )),
% 1.71/1.42 inference(superposition,[status(thm)],[f96,f97])).
% 1.71/1.42 thf(f97,plain,(
% 1.71/1.42 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK14 @ X4 @ X3) @ X4)) | ($true = (subset @ X4 @ X3))) )),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.71/1.42 thf(f89,plain,(
% 1.71/1.42 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK14 @ X4 @ X3) @ X4)) | ($true = (subset @ X4 @ X3)) | ($true != $true)) )),
% 1.71/1.42 inference(definition_unfolding,[status(thm)],[f72,f65])).
% 1.71/1.42 thf(f72,plain,(
% 1.71/1.42 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | ($true = (in @ (sK14 @ X4 @ X3) @ X4)) | (subsetI2 != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f48])).
% 1.71/1.42 thf(f96,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) | (X0 = X1) | (X0 = X2)) )),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.71/1.42 thf(f83,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (X0 = X1) | (X0 = X2) | ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))) )),
% 1.71/1.42 inference(definition_unfolding,[status(thm)],[f70,f60])).
% 1.71/1.42 thf(f60,plain,(
% 1.71/1.42 (upairset2E = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.42 thf(f70,plain,(
% 1.71/1.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) | (X0 = X1) | (X0 = X2) | (upairset2E != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f43])).
% 1.71/1.42 thf(f43,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) | (X0 = X1) | (X0 = X2)) | (upairset2E != $true)) & ((upairset2E = $true) | (($true = (in @ sK9 @ (setadjoin @ sK10 @ (setadjoin @ sK11 @ emptyset)))) & (sK9 != sK10) & (sK11 != sK9)))),
% 1.71/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f41,f42])).
% 1.71/1.42 thf(f42,plain,(
% 1.71/1.42 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset))) = $true) & (X3 != X4) & (X3 != X5)) => (($true = (in @ sK9 @ (setadjoin @ sK10 @ (setadjoin @ sK11 @ emptyset)))) & (sK9 != sK10) & (sK11 != sK9))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f41,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) | (X0 = X1) | (X0 = X2)) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset))) = $true) & (X3 != X4) & (X3 != X5)))),
% 1.71/1.42 inference(rectify,[status(thm)],[f40])).
% 1.71/1.42 thf(f40,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) | (X0 = X1) | (X0 = X2)) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) & (X0 != X1) & (X0 != X2)))),
% 1.71/1.42 inference(nnf_transformation,[status(thm)],[f22])).
% 1.71/1.42 thf(f22,plain,(
% 1.71/1.42 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) | (X0 = X1) | (X0 = X2)) <=> (upairset2E = $true)),
% 1.71/1.42 inference(flattening,[status(thm)],[f21])).
% 1.71/1.42 thf(f21,plain,(
% 1.71/1.42 ! [X2 : $i,X1 : $i,X0 : $i] : (((X0 = X1) | (X0 = X2)) | ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))) <=> (upairset2E = $true)),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f16])).
% 1.71/1.42 thf(f16,plain,(
% 1.71/1.42 ! [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) => ((X0 = X1) | (X0 = X2))) <=> (upairset2E = $true)),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f15])).
% 1.71/1.42 thf(f15,plain,(
% 1.71/1.42 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X0 = X2) | (X0 = X1))) = upairset2E)),
% 1.71/1.42 inference(rectify,[status(thm)],[f5])).
% 1.71/1.42 thf(f5,axiom,(
% 1.71/1.42 (! [X4 : $i,X2 : $i,X3 : $i] : ((in @ X4 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) => ((X3 = X4) | (X2 = X4))) = upairset2E)),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.U0wqeeH1SB/DTF2THF_16353.p',upairset2E)).
% 1.71/1.42 % SZS output end Proof for DTF2THF_16353
% 1.71/1.42 % (16455)------------------------------
% 1.71/1.42 % (16455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (16455)Termination reason: Refutation
% 1.71/1.42
% 1.71/1.42 % (16455)Memory used [KB]: 5628
% 1.71/1.42 % (16455)Time elapsed: 0.023 s
% 1.71/1.42 % (16455)Instructions burned: 36 (million)
% 1.71/1.42 % (16455)------------------------------
% 1.71/1.42 % (16455)------------------------------
% 1.71/1.42 % (16449)Success in time 0.036 s
%------------------------------------------------------------------------------