%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU585^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 09:35:25 AM UTC 2026
% Result : Theorem 1.71s 1.33s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 88 ( 19 unt; 0 typ; 3 def)
% Number of atoms : 1111 ( 355 equ; 0 cnn)
% Maximal formula atoms : 14 ( 12 avg)
% Number of connectives : 1064 ( 138 ~; 157 |; 93 &; 596 @)
% ( 11 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 22 con; 0-3 aty)
% Number of variables : 209 ( 10 ^; 151 !; 48 ?; 209 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_8,type,
binunion: $i > $i > $i ).
thf(func_def_20,type,
sK6: $o > $i > $i > $i ).
thf(f151,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f104,f105,f110,f141]) ).
thf(f141,plain,
( spl14_2
| spl14_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f140]) ).
thf(f140,plain,
( $false
| spl14_2
| spl14_3 ),
inference(subsumption_resolution,[status(thm)],[f136,f109]) ).
thf(f109,plain,
( ( $true
!= ( in @ sK11 @ sK10 ) )
| spl14_3 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl14_3
<=> ( $true
= ( in @ sK11 @ sK10 ) ) ),
introduced(definition,[new_symbols(naming,[spl14_3])],[avatar_definition]) ).
thf(f136,plain,
( ( $true
= ( in @ sK11 @ sK10 ) )
| spl14_2 ),
inference(condensation,[status(thm)],[f135]) ).
thf(f135,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true
= ( in @ sK11 @ sK10 ) ) )
| spl14_2 ),
inference(duplicate_literal_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = X0 )
| ( $true
= ( in @ sK11 @ sK10 ) ) )
| spl14_2 ),
inference(superposition,[status(thm)],[f114,f127]) ).
thf(f127,plain,
( ! [X0: $o] :
( ( sK10
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) )
| ( $true = X0 ) )
| spl14_2 ),
inference(subsumption_resolution,[status(thm)],[f126,f103]) ).
thf(f103,plain,
( ( $true
!= ( in @ sK11 @ sK13 ) )
| spl14_2 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl14_2
<=> ( $true
= ( in @ sK11 @ sK13 ) ) ),
introduced(definition,[new_symbols(naming,[spl14_2])],[avatar_definition]) ).
thf(f126,plain,
! [X0: $o] :
( ( $true = X0 )
| ( sK10
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) )
| ( $true
= ( in @ sK11 @ sK13 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f123]) ).
thf(f123,plain,
! [X0: $o] :
( ( sK10
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) )
| ( $true = X0 )
| ( $true = X0 )
| ( $true
= ( in @ sK11 @ sK13 ) ) ),
inference(superposition,[status(thm)],[f114,f120]) ).
thf(f120,plain,
! [X0: $o] :
( ( sK13
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) )
| ( $true = X0 )
| ( sK10
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
! [X0: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( sK13
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) )
| ( sK10
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) ) ),
inference(superposition,[status(thm)],[f90,f116]) ).
thf(f116,plain,
! [X0: $o] :
( ( ( in @ ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) @ ( setadjoin @ sK10 @ emptyset ) )
= $true )
| ( $true = X0 )
| ( sK13
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( in @ ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) @ ( setadjoin @ sK10 @ emptyset ) )
= $true )
| ( $true != $true )
| ( sK13
= ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) ) ),
inference(superposition,[status(thm)],[f94,f112]) ).
thf(f112,plain,
! [X0: $o] :
( ( $true
= ( in @ ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) ) )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $true
= ( in @ ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f89,f91]) ).
thf(f91,plain,
( $true
= ( in @ sK11 @ ( setunion @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
( $true
= ( in @ sK11
@ ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
@ sK13
@ sK10 ) ) ),
inference(definition_unfolding,[status(thm)],[f60,f59]) ).
thf(f59,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [X0: $i,X1: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
= binunion ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X2: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) ) )
= binunion ),
file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',binunion) ).
thf(f60,plain,
( $true
= ( in @ sK11 @ ( binunion @ sK13 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( setadjoinE = $true )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( ( $true
!= ( in @ sK11 @ sK10 ) )
| ( $true = sK12 ) )
& ( ( $true
!= ( in @ sK11 @ sK13 ) )
| ( $true = sK12 ) )
& ( $true != sK12 )
& ( $true
= ( in @ sK11 @ ( binunion @ sK13 @ sK10 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f21,f40]) ).
thf(f40,plain,
( ? [X0: $i,X1: $i,X2: $o,X3: $i] :
( ( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true = X2 ) )
& ( ( $true
!= ( in @ X1 @ X3 ) )
| ( $true = X2 ) )
& ( $true != X2 )
& ( $true
= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) ) )
=> ( ( ( $true
!= ( in @ sK11 @ sK10 ) )
| ( $true = sK12 ) )
& ( ( $true
!= ( in @ sK11 @ sK13 ) )
| ( $true = sK12 ) )
& ( $true != sK12 )
& ( $true
= ( in @ sK11 @ ( binunion @ sK13 @ sK10 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( setadjoinE = $true )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ? [X0: $i,X1: $i,X2: $o,X3: $i] :
( ( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true = X2 ) )
& ( ( $true
!= ( in @ X1 @ X3 ) )
| ( $true = X2 ) )
& ( $true != X2 )
& ( $true
= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i,X2: $o,X3: $i] :
( ( $true != X2 )
& ( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true = X2 ) )
& ( ( $true
!= ( in @ X1 @ X3 ) )
| ( $true = X2 ) )
& ( $true
= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) ) )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( setadjoinE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( setadjoinE = $true )
=> ( ( setunionE = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i,X1: $i,X2: $o,X3: $i] :
( ( $true
= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) )
=> ( ( ( $true
= ( in @ X1 @ X3 ) )
=> ( $true = X2 ) )
=> ( ( ( $true
= ( in @ X1 @ X0 ) )
=> ( $true = X2 ) )
=> ( $true = X2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [X0: $i,X1: $i,X2: $o,X3: $i] :
( ( in @ X1 @ ( binunion @ X3 @ X0 ) )
=> ( ( ( in @ X1 @ X3 )
=> X2 )
=> ( ( ( in @ X1 @ X0 )
=> X2 )
=> X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [X4: $i,X0: $i,X3: $o,X1: $i] :
( ( in @ X0 @ ( binunion @ X1 @ X4 ) )
=> ( ( ( in @ X0 @ X1 )
=> X3 )
=> ( ( ( in @ X0 @ X4 )
=> X3 )
=> X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [X4: $i,X0: $i,X3: $o,X1: $i] :
( ( in @ X0 @ ( binunion @ X1 @ X4 ) )
=> ( ( ( in @ X0 @ X1 )
=> X3 )
=> ( ( ( in @ X0 @ X4 )
=> X3 )
=> X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',binunionEcases) ).
thf(f89,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( $true
= ( in @ ( sK6 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( $true = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK6 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( $true != $true )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( $true = X2 ) ),
inference(definition_unfolding,[status(thm)],[f57,f64]) ).
thf(f64,plain,
setunionE = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f57,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( $true = X2 )
| ( $true
= ( in @ ( sK6 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( setunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $o] :
( ( $true = X2 )
| ( ( $true != X2 )
& ( $true
= ( in @ ( sK6 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ X0 @ ( sK6 @ X2 @ X1 @ X0 ) )
= $true ) ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) )
| ( setunionE != $true ) )
& ( ( setunionE = $true )
| ( ( $true != sK9 )
& ! [X7: $i] :
( ( $true = sK9 )
| ( $true
!= ( in @ X7 @ sK8 ) )
| ( $true
!= ( in @ sK7 @ X7 ) ) )
& ( $true
= ( in @ sK7 @ ( setunion @ sK8 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f35,f38,f37,f36]) ).
thf(f36,plain,
! [X0: $i,X1: $i,X2: $o] :
( ? [X3: $i] :
( ( $true != X2 )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X0 @ X3 ) ) )
=> ( ( $true != X2 )
& ( $true
= ( in @ ( sK6 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ X0 @ ( sK6 @ X2 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $o] :
( ( $true != X6 )
& ! [X7: $i] :
( ( $true = X6 )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ X7 ) ) ) )
& ( $true
= ( in @ X4 @ ( setunion @ X5 ) ) ) )
=> ( ? [X6: $o] :
( ( $true != X6 )
& ! [X7: $i] :
( ( $true = X6 )
| ( $true
!= ( in @ X7 @ sK8 ) )
| ( $true
!= ( in @ sK7 @ X7 ) ) ) )
& ( $true
= ( in @ sK7 @ ( setunion @ sK8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ? [X6: $o] :
( ( $true != X6 )
& ! [X7: $i] :
( ( $true = X6 )
| ( $true
!= ( in @ X7 @ sK8 ) )
| ( $true
!= ( in @ sK7 @ X7 ) ) ) )
=> ( ( $true != sK9 )
& ! [X7: $i] :
( ( $true = sK9 )
| ( $true
!= ( in @ X7 @ sK8 ) )
| ( $true
!= ( in @ sK7 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $o] :
( ( $true = X2 )
| ? [X3: $i] :
( ( $true != X2 )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X0 @ X3 ) ) ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) )
| ( setunionE != $true ) )
& ( ( setunionE = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $o] :
( ( $true != X6 )
& ! [X7: $i] :
( ( $true = X6 )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ X7 ) ) ) )
& ( $true
= ( in @ X4 @ ( setunion @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $o] :
( ( $true = X2 )
| ? [X3: $i] :
( ( $true != X2 )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X0 @ X3 ) ) ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) )
| ( setunionE != $true ) )
& ( ( setunionE = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $o] :
( ( $true != X2 )
& ! [X3: $i] :
( ( $true = X2 )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X0 @ X3 ) ) ) )
& ( ( in @ X0 @ ( setunion @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $o] :
( ( $true = X2 )
| ? [X3: $i] :
( ( $true != X2 )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X0 @ X3 ) ) ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) )
<=> ( setunionE = $true ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $o] :
( ( $true = X2 )
| ? [X3: $i] :
( ( $true != X2 )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X0 @ X3 ) ) ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) )
<=> ( setunionE = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( $true
= ( in @ X0 @ X3 ) )
=> ( ( $true
= ( in @ X3 @ X1 ) )
=> ( $true = X2 ) ) )
=> ( $true = X2 ) ) )
<=> ( setunionE = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X0 @ X3 )
=> ( ( in @ X3 @ X1 )
=> X2 ) )
=> X2 ) )
= setunionE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
=> ! [X3: $o] :
( ! [X4: $i] :
( ( in @ X0 @ X4 )
=> ( ( in @ X4 @ X1 )
=> X3 ) )
=> X3 ) )
= setunionE ),
file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',setunionE) ).
thf(f94,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( X0 = X2 )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(condensation,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( $true = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true = X3 )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( X0 = X1 ) ),
inference(definition_unfolding,[status(thm)],[f47,f66]) ).
thf(f66,plain,
setadjoinE = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f47,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true = X3 )
| ( X0 = X1 )
| ( setadjoinE != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ! [X3: $o] :
( ( ( $true != X3 )
& ( $true
= ( in @ X1 @ X2 ) ) )
| ( $true = X3 )
| ( ( X0 = X1 )
& ( $true != X3 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ( ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) ) )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) )
& ( $true != sK3 )
& ( ( sK1 != sK0 )
| ( $true = sK3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f26,f28,f27]) ).
thf(f27,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ( $true
= ( in @ X5 @ ( setadjoin @ X4 @ X6 ) ) )
& ? [X7: $o] :
( ( ( $true = X7 )
| ( $true
!= ( in @ X5 @ X6 ) ) )
& ( $true != X7 )
& ( ( X4 != X5 )
| ( $true = X7 ) ) ) )
=> ( ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ sK2 ) ) )
& ? [X7: $o] :
( ( ( $true = X7 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) )
& ( $true != X7 )
& ( ( sK1 != sK0 )
| ( $true = X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X7: $o] :
( ( ( $true = X7 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) )
& ( $true != X7 )
& ( ( sK1 != sK0 )
| ( $true = X7 ) ) )
=> ( ( ( $true = sK3 )
| ( $true
!= ( in @ sK1 @ sK2 ) ) )
& ( $true != sK3 )
& ( ( sK1 != sK0 )
| ( $true = sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ! [X3: $o] :
( ( ( $true != X3 )
& ( $true
= ( in @ X1 @ X2 ) ) )
| ( $true = X3 )
| ( ( X0 = X1 )
& ( $true != X3 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( $true
= ( in @ X5 @ ( setadjoin @ X4 @ X6 ) ) )
& ? [X7: $o] :
( ( ( $true = X7 )
| ( $true
!= ( in @ X5 @ X6 ) ) )
& ( $true != X7 )
& ( ( X4 != X5 )
| ( $true = X7 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ! [X3: $o] :
( ( ( $true != X3 )
& ( $true
= ( in @ X1 @ X2 ) ) )
| ( $true = X3 )
| ( ( X0 = X1 )
& ( $true != X3 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
& ? [X3: $o] :
( ( ( $true = X3 )
| ( $true
!= ( in @ X1 @ X2 ) ) )
& ( $true != X3 )
& ( ( X0 != X1 )
| ( $true = X3 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ! [X3: $o] :
( ( ( $true != X3 )
& ( $true
= ( in @ X1 @ X2 ) ) )
| ( $true = X3 )
| ( ( X0 = X1 )
& ( $true != X3 ) ) ) )
<=> ( setadjoinE = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( $true
= ( in @ X1 @ X2 ) ) )
| ( ( X0 = X1 )
& ( $true != X3 ) ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) )
<=> ( setadjoinE = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> ( $true = X3 ) )
=> ( ( ( $true
= ( in @ X1 @ X2 ) )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) )
<=> ( setadjoinE = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> X3 )
=> ( ( ( in @ X1 @ X2 )
=> X3 )
=> X3 ) ) )
= setadjoinE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= setadjoinE ),
file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',setadjoinE) ).
thf(f90,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
| ( X2 = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true != $true )
| ( $true
!= ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(definition_unfolding,[status(thm)],[f50,f65]) ).
thf(f65,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f50,plain,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true
!= ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( uniqinunit = $true )
| ( ( sK5 != sK4 )
& ( $true
= ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true
!= ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( uniqinunit != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f31,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
=> ( ( sK5 != sK4 )
& ( $true
= ( in @ sK5 @ ( setadjoin @ sK4 @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true
!= ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( uniqinunit != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( uniqinunit != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( uniqinunit = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( uniqinunit = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( uniqinunit
= ( ! [X2: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',uniqinunit) ).
thf(f114,plain,
! [X0: $o] :
( ( $true
= ( in @ sK11 @ ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) ) )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
! [X0: $o] :
( ( $true
= ( in @ sK11 @ ( sK6 @ X0 @ ( setadjoin @ sK13 @ ( setadjoin @ sK10 @ emptyset ) ) @ sK11 ) ) )
| ( $true != $true )
| ( $true = X0 ) ),
inference(superposition,[status(thm)],[f95,f91]) ).
thf(f95,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( $true = X2 )
| ( ( in @ X0 @ ( sK6 @ X2 @ X1 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true = X2 )
| ( ( in @ X0 @ ( sK6 @ X2 @ X1 @ X0 ) )
= $true )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f56,f64]) ).
thf(f56,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( $true = X2 )
| ( ( in @ X0 @ ( sK6 @ X2 @ X1 @ X0 ) )
= $true )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( setunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f110,plain,
( ~ spl14_3
| spl14_1 ),
inference(avatar_split_clause,[status(thm)],[f63,f97,f107]) ).
thf(f97,definition,
( spl14_1
<=> ( $true = sK12 ) ),
introduced(definition,[new_symbols(naming,[spl14_1])],[avatar_definition]) ).
thf(f63,plain,
( ( $true
!= ( in @ sK11 @ sK10 ) )
| ( $true = sK12 ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f105,plain,
~ spl14_1,
inference(avatar_split_clause,[status(thm)],[f61,f97]) ).
thf(f61,plain,
$true != sK12,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f104,plain,
( spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[status(thm)],[f62,f101,f97]) ).
thf(f62,plain,
( ( $true = sK12 )
| ( $true
!= ( in @ sK11 @ sK13 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU585^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n020.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:27:57 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SEU585^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.47 % Domain : Set Theory
% 0.21/0.47 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.21/0.47 % Version : Especial > Reduced > Especial.
% 0.21/0.47 % English : (! A:i.! B:i.! x:i.! phi:o.in x (binunion A B) ->
% 0.21/0.47 % (in x A -> phi) -> (in x B -> phi) -> phi)
% 0.21/0.47
% 0.21/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.47 % Source : [Bro08]
% 0.21/0.47 % Names : ZFC087l [Bro08]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.67 v3.7.0
% 0.21/0.47 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.21/0.47 % Number of atoms : 21 ( 6 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 6 ( 4 avg)
% 0.21/0.47 % Number of connectives : 48 ( 0 ~; 0 |; 0 &; 30 @)
% 0.21/0.47 % ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 14 ( 4 avg)
% 0.21/0.47 % Number of types : 2 ( 0 usr)
% 0.21/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.21/0.47 % Number of variables : 16 ( 2 ^; 14 !; 0 ?; 16 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : http://mathgate.info/detsetitem.php?id=161
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(in_type,type,
% 0.21/0.47 in: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(emptyset_type,type,
% 0.21/0.47 emptyset: $i ).
% 0.21/0.47
% 0.21/0.47 thf(setadjoin_type,type,
% 0.21/0.47 setadjoin: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(setunion_type,type,
% 0.21/0.47 setunion: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(setadjoinE_type,type,
% 0.21/0.47 setadjoinE: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setadjoinE,definition,
% 0.21/0.47 ( setadjoinE
% 0.21/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.47 => ! [Xphi: $o] :
% 0.21/0.47 ( ( ( Xy = Xx )
% 0.21/0.47 => Xphi )
% 0.21/0.47 => ( ( ( in @ Xy @ A )
% 0.21/0.47 => Xphi )
% 0.21/0.47 => Xphi ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setunionE_type,type,
% 0.21/0.47 setunionE: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setunionE,definition,
% 0.21/0.47 ( setunionE
% 0.21/0.47 = ( ! [A: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.47 => ! [Xphi: $o] :
% 0.21/0.47 ( ! [B: $i] :
% 0.21/0.47 ( ( in @ Xx @ B )
% 0.21/0.47 => ( ( in @ B @ A )
% 0.21/0.47 => Xphi ) )
% 0.21/0.47 => Xphi ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(uniqinunit_type,type,
% 0.21/0.47 uniqinunit: $o ).
% 0.21/0.47
% 0.21/0.47 thf(uniqinunit,definition,
% 0.21/0.47 ( uniqinunit
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunion_type,type,
% 0.21/0.47 binunion: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(binunion,definition,
% 0.21/0.47 ( binunion
% 0.21/0.47 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunionEcases,conjecture,
% 0.21/0.47 ( setadjoinE
% 0.21/0.47 => ( setunionE
% 0.21/0.47 => ( uniqinunit
% 0.21/0.47 => ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.21/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.21/0.47 => ( ( ( in @ Xx @ A )
% 0.21/0.47 => Xphi )
% 0.21/0.47 => ( ( ( in @ Xx @ B )
% 0.21/0.47 => Xphi )
% 0.21/0.47 => Xphi ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.52/1.29 ---- Embedded in THF ---
% 1.52/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.30 %%% Generated on Tue Feb 24 12:27:58 EST 2026
% 1.52/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.30 %%% Logic specification used:
% 1.52/1.30 %%% thf(spec, logic, $$dhol).
% 1.52/1.30
% 1.52/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2DTF22508.p
% See solution above
% 1.52/1.30 ------------------------
% 1.71/1.31 ---- Cleaned THF ---
% 1.71/1.31 thf(in_type,type,
% 1.71/1.31 in: $i > $i > $o ).
% 1.71/1.31
% 1.71/1.31 thf(emptyset_type,type,
% 1.71/1.31 emptyset: $i ).
% 1.71/1.31
% 1.71/1.31 thf(setadjoin_type,type,
% 1.71/1.31 setadjoin: $i > $i > $i ).
% 1.71/1.31
% 1.71/1.31 thf(setunion_type,type,
% 1.71/1.31 setunion: $i > $i ).
% 1.71/1.31
% 1.71/1.31 thf(setadjoinE_type,type,
% 1.71/1.31 setadjoinE: $o ).
% 1.71/1.31
% 1.71/1.31 thf(setadjoinE,definition,
% 1.71/1.31 ( setadjoinE
% 1.71/1.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.71/1.31 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.71/1.31 => ! [Xphi: $o] :
% 1.71/1.31 ( ( ( Xy = Xx )
% 1.71/1.31 => Xphi )
% 1.71/1.31 => ( ( ( in @ Xy @ A )
% 1.71/1.31 => Xphi )
% 1.71/1.31 => Xphi ) ) ) ) ) ).
% 1.71/1.31
% 1.71/1.31 thf(setunionE_type,type,
% 1.71/1.31 setunionE: $o ).
% 1.71/1.31
% 1.71/1.31 thf(setunionE,definition,
% 1.71/1.31 ( setunionE
% 1.71/1.31 = ( ! [A: $i,Xx: $i] :
% 1.71/1.31 ( ( in @ Xx @ ( setunion @ A ) )
% 1.71/1.31 => ! [Xphi: $o] :
% 1.71/1.31 ( ! [B: $i] :
% 1.71/1.31 ( ( in @ Xx @ B )
% 1.71/1.31 => ( ( in @ B @ A )
% 1.71/1.31 => Xphi ) )
% 1.71/1.31 => Xphi ) ) ) ) ).
% 1.71/1.31
% 1.71/1.31 thf(uniqinunit_type,type,
% 1.71/1.31 uniqinunit: $o ).
% 1.71/1.31
% 1.71/1.31 thf(uniqinunit,definition,
% 1.71/1.31 ( uniqinunit
% 1.71/1.31 = ( ! [Xx: $i,Xy: $i] :
% 1.71/1.31 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.71/1.31 => ( Xx = Xy ) ) ) ) ).
% 1.71/1.31
% 1.71/1.31 thf(binunion_type,type,
% 1.71/1.31 binunion: $i > $i > $i ).
% 1.71/1.31
% 1.71/1.31 thf(binunion,definition,
% 1.71/1.31 ( binunion
% 1.71/1.31 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.71/1.31
% 1.71/1.31 thf(binunionEcases,conjecture,
% 1.71/1.31 ( setadjoinE
% 1.71/1.31 => ( setunionE
% 1.71/1.31 => ( uniqinunit
% 1.71/1.31 => ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 1.71/1.31 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 1.71/1.31 => ( ( ( in @ Xx @ A )
% 1.71/1.31 => Xphi )
% 1.71/1.31 => ( ( ( in @ Xx @ B )
% 1.71/1.31 => Xphi )
% 1.71/1.31 => Xphi ) ) ) ) ) ) ).
% 1.71/1.31 ------------------------
% 1.71/1.32 % (22628)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22508 for (3000ds/18Mi)
% 1.71/1.32 % (22627)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_22508 for (3000ds/275Mi)
% 1.71/1.32 % (22628)First to succeed.
% 1.71/1.33 % (22628)Refutation found. Thanks to Tanya!
% 1.71/1.33 % SZS status Theorem for DTF2THF_22508
% 1.71/1.33 % SZS output start Proof for DTF2THF_22508
% 1.71/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.71/1.33 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.71/1.33 thf(func_def_3, type, setunion: $i > $i).
% 1.71/1.33 thf(func_def_8, type, binunion: $i > $i > $i).
% 1.71/1.33 thf(func_def_20, type, sK6: $o > $i > $i > $i).
% 1.71/1.33 thf(f151,plain,(
% 1.71/1.33 $false),
% 1.71/1.33 inference(avatar_sat_refutation,[status(thm)],[f104,f105,f110,f141])).
% 1.71/1.33 thf(f141,plain,(
% 1.71/1.33 spl14_2 | spl14_3),
% 1.71/1.33 inference(avatar_contradiction_clause,[status(thm)],[f140])).
% 1.71/1.33 thf(f140,plain,(
% 1.71/1.33 $false | (spl14_2 | spl14_3)),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f136,f109])).
% 1.71/1.33 thf(f109,plain,(
% 1.71/1.33 ($true != (in @ sK11 @ sK10)) | spl14_3),
% 1.71/1.33 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.71/1.33 thf(f107,definition,(
% 1.71/1.33 spl14_3 <=> ($true = (in @ sK11 @ sK10))),
% 1.71/1.33 introduced(definition,[new_symbols(naming,[spl14_3])],[avatar_definition])).
% 1.71/1.33 thf(f136,plain,(
% 1.71/1.33 ($true = (in @ sK11 @ sK10)) | spl14_2),
% 1.71/1.33 inference(condensation,[status(thm)],[f135])).
% 1.71/1.33 thf(f135,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true = X0) | ($true = (in @ sK11 @ sK10))) ) | spl14_2),
% 1.71/1.33 inference(duplicate_literal_removal,[status(thm)],[f132])).
% 1.71/1.33 thf(f132,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true = X0) | ($true = X0) | ($true = (in @ sK11 @ sK10))) ) | spl14_2),
% 1.71/1.33 inference(superposition,[status(thm)],[f114,f127])).
% 1.71/1.33 thf(f127,plain,(
% 1.71/1.33 ( ! [X0 : $o] : ((sK10 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11)) | ($true = X0)) ) | spl14_2),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f126,f103])).
% 1.71/1.33 thf(f103,plain,(
% 1.71/1.33 ($true != (in @ sK11 @ sK13)) | spl14_2),
% 1.71/1.33 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.71/1.33 thf(f101,definition,(
% 1.71/1.33 spl14_2 <=> ($true = (in @ sK11 @ sK13))),
% 1.71/1.33 introduced(definition,[new_symbols(naming,[spl14_2])],[avatar_definition])).
% 1.71/1.33 thf(f126,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true = X0) | (sK10 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11)) | ($true = (in @ sK11 @ sK13))) )),
% 1.71/1.33 inference(duplicate_literal_removal,[status(thm)],[f123])).
% 1.71/1.33 thf(f123,plain,(
% 1.71/1.33 ( ! [X0 : $o] : ((sK10 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11)) | ($true = X0) | ($true = X0) | ($true = (in @ sK11 @ sK13))) )),
% 1.71/1.33 inference(superposition,[status(thm)],[f114,f120])).
% 1.71/1.33 thf(f120,plain,(
% 1.71/1.33 ( ! [X0 : $o] : ((sK13 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11)) | ($true = X0) | (sK10 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11))) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.71/1.33 thf(f117,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true != $true) | ($true = X0) | (sK13 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11)) | (sK10 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11))) )),
% 1.71/1.33 inference(superposition,[status(thm)],[f90,f116])).
% 1.71/1.33 thf(f116,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (((in @ (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11) @ (setadjoin @ sK10 @ emptyset)) = $true) | ($true = X0) | (sK13 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11))) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.71/1.33 thf(f115,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true = X0) | ((in @ (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11) @ (setadjoin @ sK10 @ emptyset)) = $true) | ($true != $true) | (sK13 = (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11))) )),
% 1.71/1.33 inference(superposition,[status(thm)],[f94,f112])).
% 1.71/1.33 thf(f112,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true = (in @ (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11) @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) | ($true = X0)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.71/1.33 thf(f111,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true = X0) | ($true = (in @ (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11) @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) | ($true != $true)) )),
% 1.71/1.33 inference(superposition,[status(thm)],[f89,f91])).
% 1.71/1.33 thf(f91,plain,(
% 1.71/1.33 ($true = (in @ sK11 @ (setunion @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))))),
% 1.71/1.33 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.71/1.33 thf(f84,plain,(
% 1.71/1.33 ($true = (in @ sK11 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ sK13 @ sK10)))),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f60,f59])).
% 1.71/1.33 thf(f59,plain,(
% 1.71/1.33 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.33 thf(f13,plain,(
% 1.71/1.33 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f12])).
% 1.71/1.33 thf(f12,plain,(
% 1.71/1.33 ((^[X0 : $i, X1 : $i] : (setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = binunion)),
% 1.71/1.33 inference(rectify,[status(thm)],[f4])).
% 1.71/1.33 thf(f4,axiom,(
% 1.71/1.33 ((^[X0 : $i, X2 : $i] : (setunion @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)))) = binunion)),
% 1.71/1.33 file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',binunion)).
% 1.71/1.33 thf(f60,plain,(
% 1.71/1.33 ($true = (in @ sK11 @ (binunion @ sK13 @ sK10)))),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.33 thf(f41,plain,(
% 1.71/1.33 (setadjoinE = $true) & (uniqinunit = $true) & (setunionE = $true) & ((($true != (in @ sK11 @ sK10)) | ($true = sK12)) & (($true != (in @ sK11 @ sK13)) | ($true = sK12)) & ($true != sK12) & ($true = (in @ sK11 @ (binunion @ sK13 @ sK10))))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f21,f40])).
% 1.71/1.33 thf(f40,plain,(
% 1.71/1.33 ? [X0 : $i,X1 : $i,X2 : $o,X3 : $i] : ((($true != (in @ X1 @ X0)) | ($true = X2)) & (($true != (in @ X1 @ X3)) | ($true = X2)) & ($true != X2) & ($true = (in @ X1 @ (binunion @ X3 @ X0)))) => ((($true != (in @ sK11 @ sK10)) | ($true = sK12)) & (($true != (in @ sK11 @ sK13)) | ($true = sK12)) & ($true != sK12) & ($true = (in @ sK11 @ (binunion @ sK13 @ sK10))))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f21,plain,(
% 1.71/1.33 (setadjoinE = $true) & (uniqinunit = $true) & (setunionE = $true) & ? [X0 : $i,X1 : $i,X2 : $o,X3 : $i] : ((($true != (in @ X1 @ X0)) | ($true = X2)) & (($true != (in @ X1 @ X3)) | ($true = X2)) & ($true != X2) & ($true = (in @ X1 @ (binunion @ X3 @ X0))))),
% 1.71/1.33 inference(flattening,[status(thm)],[f20])).
% 1.71/1.33 thf(f20,plain,(
% 1.71/1.33 ((? [X0 : $i,X1 : $i,X2 : $o,X3 : $i] : (((($true != X2) & (($true != (in @ X1 @ X0)) | ($true = X2))) & (($true != (in @ X1 @ X3)) | ($true = X2))) & ($true = (in @ X1 @ (binunion @ X3 @ X0)))) & (uniqinunit = $true)) & (setunionE = $true)) & (setadjoinE = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f9])).
% 1.71/1.33 thf(f9,plain,(
% 1.71/1.33 ~((setadjoinE = $true) => ((setunionE = $true) => ((uniqinunit = $true) => ! [X0 : $i,X1 : $i,X2 : $o,X3 : $i] : (($true = (in @ X1 @ (binunion @ X3 @ X0))) => ((($true = (in @ X1 @ X3)) => ($true = X2)) => ((($true = (in @ X1 @ X0)) => ($true = X2)) => ($true = X2)))))))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.71/1.33 thf(f8,plain,(
% 1.71/1.33 ~(setadjoinE => (setunionE => (uniqinunit => ! [X0 : $i,X1 : $i,X2 : $o,X3 : $i] : ((in @ X1 @ (binunion @ X3 @ X0)) => (((in @ X1 @ X3) => X2) => (((in @ X1 @ X0) => X2) => X2))))))),
% 1.71/1.33 inference(rectify,[status(thm)],[f6])).
% 1.71/1.33 thf(f6,negated_conjecture,(
% 1.71/1.33 ~(setadjoinE => (setunionE => (uniqinunit => ! [X4 : $i,X0 : $i,X3 : $o,X1 : $i] : ((in @ X0 @ (binunion @ X1 @ X4)) => (((in @ X0 @ X1) => X3) => (((in @ X0 @ X4) => X3) => X3))))))),
% 1.71/1.33 inference(negated_conjecture,[status(cth)],[f5])).
% 1.71/1.33 thf(f5,conjecture,(
% 1.71/1.33 setadjoinE => (setunionE => (uniqinunit => ! [X4 : $i,X0 : $i,X3 : $o,X1 : $i] : ((in @ X0 @ (binunion @ X1 @ X4)) => (((in @ X0 @ X1) => X3) => (((in @ X0 @ X4) => X3) => X3)))))),
% 1.71/1.33 file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',binunionEcases)).
% 1.71/1.33 thf(f89,plain,(
% 1.71/1.33 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ($true = (in @ (sK6 @ X2 @ X1 @ X0) @ X1)) | ($true = X2)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.71/1.33 thf(f79,plain,(
% 1.71/1.33 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (in @ (sK6 @ X2 @ X1 @ X0) @ X1)) | ($true != $true) | ((in @ X0 @ (setunion @ X1)) != $true) | ($true = X2)) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f57,f64])).
% 1.71/1.33 thf(f64,plain,(
% 1.71/1.33 (setunionE = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.33 thf(f57,plain,(
% 1.71/1.33 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ($true = (in @ (sK6 @ X2 @ X1 @ X0) @ X1)) | ((in @ X0 @ (setunion @ X1)) != $true) | (setunionE != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.33 thf(f39,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | (($true != X2) & ($true = (in @ (sK6 @ X2 @ X1 @ X0) @ X1)) & ((in @ X0 @ (sK6 @ X2 @ X1 @ X0)) = $true))) | ((in @ X0 @ (setunion @ X1)) != $true)) | (setunionE != $true)) & ((setunionE = $true) | ((($true != sK9) & ! [X7 : $i] : (($true = sK9) | ($true != (in @ X7 @ sK8)) | ($true != (in @ sK7 @ X7)))) & ($true = (in @ sK7 @ (setunion @ sK8)))))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f35,f38,f37,f36])).
% 1.71/1.33 thf(f36,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i,X2 : $o] : (? [X3 : $i] : (($true != X2) & ($true = (in @ X3 @ X1)) & ($true = (in @ X0 @ X3))) => (($true != X2) & ($true = (in @ (sK6 @ X2 @ X1 @ X0) @ X1)) & ((in @ X0 @ (sK6 @ X2 @ X1 @ X0)) = $true)))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f37,plain,(
% 1.71/1.33 ? [X4 : $i,X5 : $i] : (? [X6 : $o] : (($true != X6) & ! [X7 : $i] : (($true = X6) | ($true != (in @ X7 @ X5)) | ($true != (in @ X4 @ X7)))) & ($true = (in @ X4 @ (setunion @ X5)))) => (? [X6 : $o] : (($true != X6) & ! [X7 : $i] : (($true = X6) | ($true != (in @ X7 @ sK8)) | ($true != (in @ sK7 @ X7)))) & ($true = (in @ sK7 @ (setunion @ sK8))))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f38,plain,(
% 1.71/1.33 ? [X6 : $o] : (($true != X6) & ! [X7 : $i] : (($true = X6) | ($true != (in @ X7 @ sK8)) | ($true != (in @ sK7 @ X7)))) => (($true != sK9) & ! [X7 : $i] : (($true = sK9) | ($true != (in @ X7 @ sK8)) | ($true != (in @ sK7 @ X7))))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f35,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : (($true != X2) & ($true = (in @ X3 @ X1)) & ($true = (in @ X0 @ X3)))) | ((in @ X0 @ (setunion @ X1)) != $true)) | (setunionE != $true)) & ((setunionE = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $o] : (($true != X6) & ! [X7 : $i] : (($true = X6) | ($true != (in @ X7 @ X5)) | ($true != (in @ X4 @ X7)))) & ($true = (in @ X4 @ (setunion @ X5)))))),
% 1.71/1.33 inference(rectify,[status(thm)],[f34])).
% 1.71/1.33 thf(f34,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : (($true != X2) & ($true = (in @ X3 @ X1)) & ($true = (in @ X0 @ X3)))) | ((in @ X0 @ (setunion @ X1)) != $true)) | (setunionE != $true)) & ((setunionE = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $o] : (($true != X2) & ! [X3 : $i] : (($true = X2) | ($true != (in @ X3 @ X1)) | ($true != (in @ X0 @ X3)))) & ((in @ X0 @ (setunion @ X1)) = $true)))),
% 1.71/1.33 inference(nnf_transformation,[status(thm)],[f23])).
% 1.71/1.33 thf(f23,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : (($true != X2) & ($true = (in @ X3 @ X1)) & ($true = (in @ X0 @ X3)))) | ((in @ X0 @ (setunion @ X1)) != $true)) <=> (setunionE = $true)),
% 1.71/1.33 inference(flattening,[status(thm)],[f22])).
% 1.71/1.33 thf(f22,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : ((($true != X2) & ($true = (in @ X3 @ X1))) & ($true = (in @ X0 @ X3)))) | ((in @ X0 @ (setunion @ X1)) != $true)) <=> (setunionE = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f17])).
% 1.71/1.33 thf(f17,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) = $true) => ! [X2 : $o] : (! [X3 : $i] : (($true = (in @ X0 @ X3)) => (($true = (in @ X3 @ X1)) => ($true = X2))) => ($true = X2))) <=> (setunionE = $true)),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f16])).
% 1.71/1.33 thf(f16,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X0 @ X3) => ((in @ X3 @ X1) => X2)) => X2)) = setunionE)),
% 1.71/1.33 inference(rectify,[status(thm)],[f2])).
% 1.71/1.33 thf(f2,axiom,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ! [X3 : $o] : (! [X4 : $i] : ((in @ X0 @ X4) => ((in @ X4 @ X1) => X3)) => X3)) = setunionE)),
% 1.71/1.33 file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',setunionE)).
% 1.71/1.33 thf(f94,plain,(
% 1.71/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X2 @ X1))) | (X0 = X2) | ((in @ X0 @ X1) = $true)) )),
% 1.71/1.33 inference(condensation,[status(thm)],[f93])).
% 1.71/1.33 thf(f93,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : ((X0 = X1) | ($true = (in @ X1 @ X2)) | ($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ($true = X3)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.71/1.33 thf(f69,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true != $true) | ($true = X3) | ($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ($true = (in @ X1 @ X2)) | (X0 = X1)) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f47,f66])).
% 1.71/1.33 thf(f66,plain,(
% 1.71/1.33 (setadjoinE = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.33 thf(f47,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ($true = (in @ X1 @ X2)) | ($true = X3) | (X0 = X1) | (setadjoinE != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f29])).
% 1.71/1.33 thf(f29,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ! [X3 : $o] : ((($true != X3) & ($true = (in @ X1 @ X2))) | ($true = X3) | ((X0 = X1) & ($true != X3)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | (($true = (in @ sK1 @ (setadjoin @ sK0 @ sK2))) & ((($true = sK3) | ($true != (in @ sK1 @ sK2))) & ($true != sK3) & ((sK1 != sK0) | ($true = sK3)))))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f26,f28,f27])).
% 1.71/1.33 thf(f27,plain,(
% 1.71/1.33 ? [X4 : $i,X5 : $i,X6 : $i] : (($true = (in @ X5 @ (setadjoin @ X4 @ X6))) & ? [X7 : $o] : ((($true = X7) | ($true != (in @ X5 @ X6))) & ($true != X7) & ((X4 != X5) | ($true = X7)))) => (($true = (in @ sK1 @ (setadjoin @ sK0 @ sK2))) & ? [X7 : $o] : ((($true = X7) | ($true != (in @ sK1 @ sK2))) & ($true != X7) & ((sK1 != sK0) | ($true = X7))))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f28,plain,(
% 1.71/1.33 ? [X7 : $o] : ((($true = X7) | ($true != (in @ sK1 @ sK2))) & ($true != X7) & ((sK1 != sK0) | ($true = X7))) => ((($true = sK3) | ($true != (in @ sK1 @ sK2))) & ($true != sK3) & ((sK1 != sK0) | ($true = sK3)))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f26,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ! [X3 : $o] : ((($true != X3) & ($true = (in @ X1 @ X2))) | ($true = X3) | ((X0 = X1) & ($true != X3)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (($true = (in @ X5 @ (setadjoin @ X4 @ X6))) & ? [X7 : $o] : ((($true = X7) | ($true != (in @ X5 @ X6))) & ($true != X7) & ((X4 != X5) | ($true = X7)))))),
% 1.71/1.33 inference(rectify,[status(thm)],[f25])).
% 1.71/1.33 thf(f25,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ! [X3 : $o] : ((($true != X3) & ($true = (in @ X1 @ X2))) | ($true = X3) | ((X0 = X1) & ($true != X3)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) & ? [X3 : $o] : ((($true = X3) | ($true != (in @ X1 @ X2))) & ($true != X3) & ((X0 != X1) | ($true = X3)))))),
% 1.71/1.33 inference(nnf_transformation,[status(thm)],[f19])).
% 1.71/1.33 thf(f19,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ! [X3 : $o] : ((($true != X3) & ($true = (in @ X1 @ X2))) | ($true = X3) | ((X0 = X1) & ($true != X3)))) <=> (setadjoinE = $true)),
% 1.71/1.33 inference(flattening,[status(thm)],[f18])).
% 1.71/1.33 thf(f18,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((($true = X3) | (($true != X3) & ($true = (in @ X1 @ X2)))) | ((X0 = X1) & ($true != X3))) | ($true != (in @ X1 @ (setadjoin @ X0 @ X2)))) <=> (setadjoinE = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f15])).
% 1.71/1.33 thf(f15,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) => ! [X3 : $o] : (((X0 = X1) => ($true = X3)) => ((($true = (in @ X1 @ X2)) => ($true = X3)) => ($true = X3)))) <=> (setadjoinE = $true)),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f14])).
% 1.71/1.33 thf(f14,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X0 @ X2)) => ! [X3 : $o] : (((X0 = X1) => X3) => (((in @ X1 @ X2) => X3) => X3))) = setadjoinE)),
% 1.71/1.33 inference(rectify,[status(thm)],[f1])).
% 1.71/1.33 thf(f1,axiom,(
% 1.71/1.33 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ! [X3 : $o] : (((X0 = X2) => X3) => (((in @ X2 @ X1) => X3) => X3))) = setadjoinE)),
% 1.71/1.33 file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',setadjoinE)).
% 1.71/1.33 thf(f90,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $i] : (($true != (in @ X3 @ (setadjoin @ X2 @ emptyset))) | (X2 = X3)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.71/1.33 thf(f77,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != $true) | ($true != (in @ X3 @ (setadjoin @ X2 @ emptyset)))) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f50,f65])).
% 1.71/1.33 thf(f65,plain,(
% 1.71/1.33 (uniqinunit = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.33 thf(f50,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != (in @ X3 @ (setadjoin @ X2 @ emptyset))) | (uniqinunit != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f33,plain,(
% 1.71/1.33 ((uniqinunit = $true) | ((sK5 != sK4) & ($true = (in @ sK5 @ (setadjoin @ sK4 @ emptyset))))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != (in @ X3 @ (setadjoin @ X2 @ emptyset)))) | (uniqinunit != $true))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f31,f32])).
% 1.71/1.33 thf(f32,plain,(
% 1.71/1.33 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ($true = (in @ X1 @ (setadjoin @ X0 @ emptyset)))) => ((sK5 != sK4) & ($true = (in @ sK5 @ (setadjoin @ sK4 @ emptyset))))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f31,plain,(
% 1.71/1.33 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != (in @ X3 @ (setadjoin @ X2 @ emptyset)))) | (uniqinunit != $true))),
% 1.71/1.33 inference(rectify,[status(thm)],[f30])).
% 1.71/1.33 thf(f30,plain,(
% 1.71/1.33 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))))) & (! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset)))) | (uniqinunit != $true))),
% 1.71/1.33 inference(nnf_transformation,[status(thm)],[f24])).
% 1.71/1.33 thf(f24,plain,(
% 1.71/1.33 (uniqinunit = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.71/1.33 thf(f11,plain,(
% 1.71/1.33 (uniqinunit = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))) => (X0 = X1))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.71/1.33 thf(f10,plain,(
% 1.71/1.33 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)))),
% 1.71/1.33 inference(rectify,[status(thm)],[f3])).
% 1.71/1.33 thf(f3,axiom,(
% 1.71/1.33 (uniqinunit = ! [X2 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X2 @ emptyset)) => (X0 = X2)))),
% 1.71/1.33 file('/export/starexec/sandbox2/tmp/tmp.VcBZNunSpO/DTF2THF_22508.p',uniqinunit)).
% 1.71/1.33 thf(f114,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true = (in @ sK11 @ (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11))) | ($true = X0)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.71/1.33 thf(f113,plain,(
% 1.71/1.33 ( ! [X0 : $o] : (($true = (in @ sK11 @ (sK6 @ X0 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)) @ sK11))) | ($true != $true) | ($true = X0)) )),
% 1.71/1.33 inference(superposition,[status(thm)],[f95,f91])).
% 1.71/1.33 thf(f95,plain,(
% 1.71/1.33 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ($true = X2) | ((in @ X0 @ (sK6 @ X2 @ X1 @ X0)) = $true)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.71/1.33 thf(f80,plain,(
% 1.71/1.33 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true != $true) | ($true = X2) | ((in @ X0 @ (sK6 @ X2 @ X1 @ X0)) = $true) | ((in @ X0 @ (setunion @ X1)) != $true)) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f56,f64])).
% 1.71/1.33 thf(f56,plain,(
% 1.71/1.33 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ((in @ X0 @ (sK6 @ X2 @ X1 @ X0)) = $true) | ((in @ X0 @ (setunion @ X1)) != $true) | (setunionE != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f39])).
% 1.71/1.33 thf(f110,plain,(
% 1.71/1.33 ~spl14_3 | spl14_1),
% 1.71/1.33 inference(avatar_split_clause,[status(thm)],[f63,f97,f107])).
% 1.71/1.33 thf(f97,definition,(
% 1.71/1.33 spl14_1 <=> ($true = sK12)),
% 1.71/1.33 introduced(definition,[new_symbols(naming,[spl14_1])],[avatar_definition])).
% 1.71/1.33 thf(f63,plain,(
% 1.71/1.33 ($true != (in @ sK11 @ sK10)) | ($true = sK12)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.33 thf(f105,plain,(
% 1.71/1.33 ~spl14_1),
% 1.71/1.33 inference(avatar_split_clause,[status(thm)],[f61,f97])).
% 1.71/1.33 thf(f61,plain,(
% 1.71/1.33 ($true != sK12)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.33 thf(f104,plain,(
% 1.71/1.33 spl14_1 | ~spl14_2),
% 1.71/1.33 inference(avatar_split_clause,[status(thm)],[f62,f101,f97])).
% 1.71/1.33 thf(f62,plain,(
% 1.71/1.33 ($true = sK12) | ($true != (in @ sK11 @ sK13))),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.33 % SZS output end Proof for DTF2THF_22508
% 1.71/1.33 % (22628)------------------------------
% 1.71/1.33 % (22628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (22628)Termination reason: Refutation
% 1.71/1.33
% 1.71/1.33 % (22628)Memory used [KB]: 5628
% 1.71/1.33 % (22628)Time elapsed: 0.007 s
% 1.71/1.33 % (22628)Instructions burned: 12 (million)
% 1.71/1.33 % (22628)------------------------------
% 1.71/1.33 % (22628)------------------------------
% 1.71/1.33 % (22621)Success in time 0.004 s
%------------------------------------------------------------------------------