%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU711^2 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:35 AM UTC 2026
% Result : Theorem 1.04s 0.91s
% Output : Refutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 81 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 1009 ( 283 equ; 0 cnn)
% Maximal formula atoms : 14 ( 12 avg)
% Number of connectives : 1027 ( 128 ~; 120 |; 76 &; 640 @)
% ( 10 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 19 con; 0-2 aty)
% Number of variables : 174 ( 0 ^; 132 !; 42 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_5,type,
binunion: $i > $i > $i ).
thf(func_def_11,type,
sK2: $i > $i > $i ).
thf(f118,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f105,f111,f117]) ).
thf(f117,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[status(thm)],[f116]) ).
thf(f116,plain,
( $false
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f115,f45]) ).
thf(f45,plain,
( ( in @ ( binunion @ sK3 @ sK5 ) @ ( powerset @ sK4 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ ( binunion @ sK3 @ sK5 ) @ ( powerset @ sK4 ) )
!= $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( powersetI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f16,f28,f27]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
!= $true ) ) )
=> ( ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ ( binunion @ sK3 @ X2 ) @ ( powerset @ sK4 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ ( binunion @ sK3 @ X2 ) @ ( powerset @ sK4 ) )
!= $true ) )
=> ( ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ ( binunion @ sK3 @ sK5 ) @ ( powerset @ sK4 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
!= $true ) ) )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( powersetI = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
!= $true ) ) )
& ( binunionEcases = $true )
& ( powersetE = $true )
& ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( powersetI = $true )
=> ( ( powersetE = $true )
=> ( ( binunionEcases = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [X4: $i,X0: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X4 @ X5 ) @ ( powerset @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [X4: $i,X0: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X4 @ X5 ) @ ( powerset @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2THF_14574.p',binunionT_lem) ).
thf(f115,plain,
( ( ( in @ ( binunion @ sK3 @ sK5 ) @ ( powerset @ sK4 ) )
= $true )
| ~ spl13_1 ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ( ( in @ ( binunion @ sK3 @ sK5 ) @ ( powerset @ sK4 ) )
= $true )
| ( $true != $true )
| ~ spl13_1 ),
inference(superposition,[status(thm)],[f79,f113]) ).
thf(f113,plain,
( ( $true
= ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK4 ) )
| ~ spl13_1 ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true
= ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK4 ) )
| ( $true != $true )
| ~ spl13_1 ),
inference(superposition,[status(thm)],[f93,f100]) ).
thf(f100,plain,
( ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK5 )
= $true )
| ~ spl13_1 ),
inference(avatar_component_clause,[status(thm)],[f98]) ).
thf(f98,definition,
( spl13_1
<=> ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition]) ).
thf(f93,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK5 )
!= $true )
| ( ( in @ X0 @ sK4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ sK4 )
= $true )
| ( ( in @ X0 @ sK5 )
!= $true ) ),
inference(superposition,[status(thm)],[f82,f46]) ).
thf(f46,plain,
( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f82,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( $true != $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f56,f44]) ).
thf(f44,plain,
powersetE = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f56,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( powersetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( powersetE = $true )
| ( ( ( in @ sK11 @ sK12 )
= $true )
& ( ( in @ sK11 @ sK10 )
!= $true )
& ( ( in @ sK12 @ ( powerset @ sK10 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true ) )
| ( powersetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f35,f36]) ).
thf(f36,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
=> ( ( ( in @ sK11 @ sK12 )
= $true )
& ( ( in @ sK11 @ sK10 )
!= $true )
& ( ( in @ sK12 @ ( powerset @ sK10 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ( ( powersetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true ) )
| ( powersetE != $true ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( powersetE = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X2 ) )
= $true ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) )
| ( powersetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( powersetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ( powersetE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( powersetE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) )
= powersetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= powersetE ),
file('/export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2THF_14574.p',powersetE) ).
thf(f79,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f39,f42]) ).
thf(f42,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f39,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( powersetI = $true )
| ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
| ( ( in @ X2 @ sK1 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
& ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ) )
| ( powersetI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f25,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) )
=> ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
| ( ( in @ X2 @ sK1 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( ( in @ X5 @ X4 )
= $true ) )
=> ( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
& ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ? [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( ( in @ X5 @ X4 )
= $true ) ) )
| ( powersetI != $true ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( powersetI = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( powersetI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( powersetI = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
<=> ( powersetI = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( powersetI
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2THF_14574.p',powersetI) ).
thf(f111,plain,
~ spl13_2,
inference(avatar_contradiction_clause,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
| ~ spl13_2 ),
inference(subsumption_resolution,[status(thm)],[f109,f45]) ).
thf(f109,plain,
( ( ( in @ ( binunion @ sK3 @ sK5 ) @ ( powerset @ sK4 ) )
= $true )
| ~ spl13_2 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( in @ ( binunion @ sK3 @ sK5 ) @ ( powerset @ sK4 ) )
= $true )
| ( $true != $true )
| ~ spl13_2 ),
inference(superposition,[status(thm)],[f79,f107]) ).
thf(f107,plain,
( ( $true
= ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK4 ) )
| ~ spl13_2 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true
= ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK4 ) )
| ( $true != $true )
| ~ spl13_2 ),
inference(superposition,[status(thm)],[f94,f104]) ).
thf(f104,plain,
( ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK3 )
= $true )
| ~ spl13_2 ),
inference(avatar_component_clause,[status(thm)],[f102]) ).
thf(f102,definition,
( spl13_2
<=> ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition]) ).
thf(f94,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK3 )
!= $true )
| ( ( in @ X0 @ sK4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ sK3 )
!= $true )
| ( ( in @ X0 @ sK4 )
= $true ) ),
inference(superposition,[status(thm)],[f82,f47]) ).
thf(f47,plain,
( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f105,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[status(thm)],[f96,f102,f98]) ).
thf(f96,plain,
( ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK3 )
= $true )
| ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $true != $true )
| ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK5 )
= $true )
| ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f84,f87]) ).
thf(f87,plain,
( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ ( binunion @ sK3 @ sK5 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ( in @ ( sK2 @ ( binunion @ sK3 @ sK5 ) @ sK4 ) @ ( binunion @ sK3 @ sK5 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f45,f81]) ).
thf(f81,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( $true != $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f42]) ).
thf(f38,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f84,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(condensation,[status(thm)],[f83]) ).
thf(f83,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ X5 )
= $true )
| ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ ( binunion @ X5 @ X4 ) )
!= $true )
| ( $true = X6 ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( binunion @ X5 @ X4 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ X5 )
= $true )
| ( $true = X6 ) ),
inference(definition_unfolding,[status(thm)],[f48,f43]) ).
thf(f43,plain,
binunionEcases = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f48,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( binunion @ X5 @ X4 ) )
!= $true )
| ( ( in @ X7 @ X5 )
= $true )
| ( ( in @ X7 @ X4 )
= $true )
| ( $true = X6 )
| ( binunionEcases != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( binunionEcases = $true )
| ( ( ( in @ sK9 @ ( binunion @ sK7 @ sK6 ) )
= $true )
& ( ( sK8 = $true )
| ( ( in @ sK9 @ sK7 )
!= $true ) )
& ( ( sK8 = $true )
| ( ( in @ sK9 @ sK6 )
!= $true ) )
& ( sK8 != $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $o,X7: $i] :
( ( ( in @ X7 @ ( binunion @ X5 @ X4 ) )
!= $true )
| ( ( $true != X6 )
& ( ( in @ X7 @ X5 )
= $true ) )
| ( ( $true != X6 )
& ( ( in @ X7 @ X4 )
= $true ) )
| ( $true = X6 ) )
| ( binunionEcases != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f31,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i,X2: $o,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X1 @ X0 ) )
= $true )
& ( ( $true = X2 )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( ( $true = X2 )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( $true != X2 ) )
=> ( ( ( in @ sK9 @ ( binunion @ sK7 @ sK6 ) )
= $true )
& ( ( sK8 = $true )
| ( ( in @ sK9 @ sK7 )
!= $true ) )
& ( ( sK8 = $true )
| ( ( in @ sK9 @ sK6 )
!= $true ) )
& ( sK8 != $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( binunionEcases = $true )
| ? [X0: $i,X1: $i,X2: $o,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X1 @ X0 ) )
= $true )
& ( ( $true = X2 )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( ( $true = X2 )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( $true != X2 ) ) )
& ( ! [X4: $i,X5: $i,X6: $o,X7: $i] :
( ( ( in @ X7 @ ( binunion @ X5 @ X4 ) )
!= $true )
| ( ( $true != X6 )
& ( ( in @ X7 @ X5 )
= $true ) )
| ( ( $true != X6 )
& ( ( in @ X7 @ X4 )
= $true ) )
| ( $true = X6 ) )
| ( binunionEcases != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( binunionEcases = $true )
| ? [X2: $i,X0: $i,X1: $o,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
& ( ( $true = X1 )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( ( $true = X1 )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( $true != X1 ) ) )
& ( ! [X2: $i,X0: $i,X1: $o,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( ( $true != X1 )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( $true != X1 )
& ( ( in @ X3 @ X2 )
= $true ) )
| ( $true = X1 ) )
| ( binunionEcases != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( binunionEcases = $true )
<=> ! [X2: $i,X0: $i,X1: $o,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( ( $true != X1 )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( $true != X1 )
& ( ( in @ X3 @ X2 )
= $true ) )
| ( $true = X1 ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ( binunionEcases = $true )
<=> ! [X2: $i,X0: $i,X1: $o,X3: $i] :
( ( $true = X1 )
| ( ( $true != X1 )
& ( ( in @ X3 @ X2 )
= $true ) )
| ( ( $true != X1 )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( binunionEcases = $true )
<=> ! [X2: $i,X0: $i,X1: $o,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
=> ( ( ( ( in @ X3 @ X0 )
= $true )
=> ( $true = X1 ) )
=> ( ( ( ( in @ X3 @ X2 )
= $true )
=> ( $true = X1 ) )
=> ( $true = X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ( ( ( in @ X3 @ X0 )
=> X1 )
=> ( ( ( in @ X3 @ X2 )
=> X1 )
=> X1 ) ) )
= binunionEcases ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X3: $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= binunionEcases ),
file('/export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2THF_14574.p',binunionEcases) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU711^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:31:30 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU711^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.32 % Domain : Set Theory
% 0.07/0.32 % Problem : Typed Set Theory - Types of Set Operators
% 0.07/0.32 % Version : Especial > Reduced > Especial.
% 0.07/0.32 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.07/0.32 % in (binunion X Y) (powerset A)))
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.32 % Source : [Bro08]
% 0.07/0.32 % Names : ZFC213l [Bro08]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.67 v3.7.0
% 0.07/0.32 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.07/0.32 % Number of atoms : 21 ( 3 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 6 ( 5 avg)
% 0.07/0.32 % Number of connectives : 47 ( 0 ~; 0 |; 0 &; 33 @)
% 0.07/0.32 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 13 ( 4 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.07/0.32 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : http://mathgate.info/detsetitem.php?id=268
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(in_type,type,
% 0.07/0.32 in: $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(powerset_type,type,
% 0.07/0.32 powerset: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(powersetI_type,type,
% 0.07/0.32 powersetI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(powersetI,definition,
% 0.07/0.32 ( powersetI
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) )
% 0.07/0.32 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(powersetE_type,type,
% 0.07/0.32 powersetE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(powersetE,definition,
% 0.07/0.32 ( powersetE
% 0.07/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.07/0.32 => ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(binunion_type,type,
% 0.07/0.32 binunion: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(binunionEcases_type,type,
% 0.07/0.32 binunionEcases: $o ).
% 0.07/0.32
% 0.07/0.32 thf(binunionEcases,definition,
% 0.07/0.32 ( binunionEcases
% 0.07/0.32 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.07/0.32 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.07/0.32 => ( ( ( in @ Xx @ A )
% 0.07/0.32 => Xphi )
% 0.07/0.32 => ( ( ( in @ Xx @ B )
% 0.07/0.32 => Xphi )
% 0.07/0.32 => Xphi ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(binunionT_lem,conjecture,
% 0.07/0.32 ( powersetI
% 0.07/0.32 => ( powersetE
% 0.07/0.32 => ( binunionEcases
% 0.07/0.32 => ! [A: $i,X: $i] :
% 0.07/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.07/0.32 => ! [Y: $i] :
% 0.07/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.07/0.32 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.85/0.88 ---- Embedded in THF ---
% 0.85/0.89 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.85/0.89 %%% Generated on Tue Feb 24 12:31:31 EST 2026
% 0.85/0.89 %%% using '$$dhol' embedding, version 1.3.0.
% 0.85/0.89 %%% Logic specification used:
% 0.85/0.89 %%% thf(spec, logic, $$dhol).
% 0.85/0.89
% 0.85/0.89 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2DTF14574.p
% See solution above
% 0.85/0.89 ------------------------
% 0.85/0.89 ---- Cleaned THF ---
% 0.85/0.89 thf(in_type,type,
% 0.85/0.89 in: $i > $i > $o ).
% 0.85/0.89
% 0.85/0.89 thf(powerset_type,type,
% 0.85/0.89 powerset: $i > $i ).
% 0.85/0.89
% 0.85/0.89 thf(powersetI_type,type,
% 0.85/0.89 powersetI: $o ).
% 0.85/0.89
% 0.85/0.89 thf(powersetI,definition,
% 0.85/0.89 ( powersetI
% 0.85/0.89 = ( ! [A: $i,B: $i] :
% 0.85/0.89 ( ! [Xx: $i] :
% 0.85/0.89 ( ( in @ Xx @ B )
% 0.85/0.89 => ( in @ Xx @ A ) )
% 0.85/0.89 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.85/0.89
% 0.85/0.89 thf(powersetE_type,type,
% 0.85/0.89 powersetE: $o ).
% 0.85/0.89
% 0.85/0.89 thf(powersetE,definition,
% 0.85/0.89 ( powersetE
% 0.85/0.89 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.85/0.89 ( ( in @ B @ ( powerset @ A ) )
% 0.85/0.89 => ( ( in @ Xx @ B )
% 0.85/0.89 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.85/0.89
% 0.85/0.89 thf(binunion_type,type,
% 0.85/0.89 binunion: $i > $i > $i ).
% 0.85/0.89
% 0.85/0.89 thf(binunionEcases_type,type,
% 0.85/0.89 binunionEcases: $o ).
% 0.85/0.89
% 0.85/0.89 thf(binunionEcases,definition,
% 0.85/0.89 ( binunionEcases
% 0.85/0.89 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.85/0.89 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.85/0.89 => ( ( ( in @ Xx @ A )
% 0.85/0.89 => Xphi )
% 0.85/0.89 => ( ( ( in @ Xx @ B )
% 0.85/0.89 => Xphi )
% 0.85/0.89 => Xphi ) ) ) ) ) ).
% 0.85/0.89
% 0.85/0.89 thf(binunionT_lem,conjecture,
% 0.85/0.89 ( powersetI
% 0.85/0.89 => ( powersetE
% 0.85/0.89 => ( binunionEcases
% 0.85/0.89 => ! [A: $i,X: $i] :
% 0.85/0.89 ( ( in @ X @ ( powerset @ A ) )
% 0.85/0.89 => ! [Y: $i] :
% 0.85/0.89 ( ( in @ Y @ ( powerset @ A ) )
% 0.85/0.89 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ) ).
% 0.85/0.89 ------------------------
% 1.04/0.90 % (14842)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14574 for (3000ds/183Mi)
% 1.04/0.90 % (14843)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_14574 for (3000ds/4Mi)
% 1.04/0.90 % (14844)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_14574 for (3000ds/27Mi)
% 1.04/0.90 % (14845)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14574 for (3000ds/2Mi)
% 1.04/0.90 % (14846)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_14574 for (3000ds/2Mi)
% 1.04/0.90 % (14847)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_14574 for (3000ds/275Mi)
% 1.04/0.90 % (14848)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14574 for (3000ds/18Mi)
% 1.04/0.90 % (14845)Instruction limit reached!
% 1.04/0.90 % (14845)------------------------------
% 1.04/0.90 % (14845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.90 % (14845)Termination reason: Unknown
% 1.04/0.90 % (14845)Termination phase: Saturation
% 1.04/0.90
% 1.04/0.90 % (14845)Memory used [KB]: 1023
% 1.04/0.90 % (14845)Time elapsed: 0.002 s
% 1.04/0.90 % (14845)Instructions burned: 3 (million)
% 1.04/0.90 % (14845)------------------------------
% 1.04/0.90 % (14845)------------------------------
% 1.04/0.90 % (14846)Instruction limit reached!
% 1.04/0.90 % (14846)------------------------------
% 1.04/0.90 % (14846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.90 % (14846)Termination reason: Unknown
% 1.04/0.90 % (14846)Termination phase: Saturation
% 1.04/0.90
% 1.04/0.90 % (14846)Memory used [KB]: 1023
% 1.04/0.90 % (14846)Time elapsed: 0.002 s
% 1.04/0.90 % (14846)Instructions burned: 3 (million)
% 1.04/0.90 % (14846)------------------------------
% 1.04/0.90 % (14846)------------------------------
% 1.04/0.91 % (14843)Instruction limit reached!
% 1.04/0.91 % (14843)------------------------------
% 1.04/0.91 % (14843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.91 % (14843)Termination reason: Unknown
% 1.04/0.91 % (14843)Termination phase: Saturation
% 1.04/0.91
% 1.04/0.91 % (14843)Memory used [KB]: 5500
% 1.04/0.91 % (14843)Time elapsed: 0.003 s
% 1.04/0.91 % (14843)Instructions burned: 6 (million)
% 1.04/0.91 % (14843)------------------------------
% 1.04/0.91 % (14843)------------------------------
% 1.04/0.91 % (14848)First to succeed.
% 1.04/0.91 % (14848)Refutation found. Thanks to Tanya!
% 1.04/0.91 % SZS status Theorem for DTF2THF_14574
% 1.04/0.91 % SZS output start Proof for DTF2THF_14574
% 1.04/0.91 thf(func_def_0, type, in: $i > $i > $o).
% 1.04/0.91 thf(func_def_1, type, powerset: $i > $i).
% 1.04/0.91 thf(func_def_5, type, binunion: $i > $i > $i).
% 1.04/0.91 thf(func_def_11, type, sK2: $i > $i > $i).
% 1.04/0.91 thf(f118,plain,(
% 1.04/0.91 $false),
% 1.04/0.91 inference(avatar_sat_refutation,[status(thm)],[f105,f111,f117])).
% 1.04/0.91 thf(f117,plain,(
% 1.04/0.91 ~spl13_1),
% 1.04/0.91 inference(avatar_contradiction_clause,[status(thm)],[f116])).
% 1.04/0.91 thf(f116,plain,(
% 1.04/0.91 $false | ~spl13_1),
% 1.04/0.91 inference(subsumption_resolution,[status(thm)],[f115,f45])).
% 1.04/0.91 thf(f45,plain,(
% 1.04/0.91 ((in @ (binunion @ sK3 @ sK5) @ (powerset @ sK4)) != $true)),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f29])).
% 1.04/0.91 thf(f29,plain,(
% 1.04/0.91 (((in @ sK3 @ (powerset @ sK4)) = $true) & (((in @ sK5 @ (powerset @ sK4)) = $true) & ((in @ (binunion @ sK3 @ sK5) @ (powerset @ sK4)) != $true))) & (powersetE = $true) & (binunionEcases = $true) & (powersetI = $true)),
% 1.04/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f16,f28,f27])).
% 1.04/0.91 thf(f27,plain,(
% 1.04/0.91 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) != $true))) => (((in @ sK3 @ (powerset @ sK4)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ sK4)) = $true) & ((in @ (binunion @ sK3 @ X2) @ (powerset @ sK4)) != $true)))),
% 1.04/0.91 introduced(definition,[],[choice_axiom])).
% 1.04/0.91 thf(f28,plain,(
% 1.04/0.91 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK4)) = $true) & ((in @ (binunion @ sK3 @ X2) @ (powerset @ sK4)) != $true)) => (((in @ sK5 @ (powerset @ sK4)) = $true) & ((in @ (binunion @ sK3 @ sK5) @ (powerset @ sK4)) != $true))),
% 1.04/0.91 introduced(definition,[],[choice_axiom])).
% 1.04/0.91 thf(f16,plain,(
% 1.04/0.91 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) != $true))) & (powersetE = $true) & (binunionEcases = $true) & (powersetI = $true)),
% 1.04/0.91 inference(flattening,[status(thm)],[f15])).
% 1.04/0.91 thf(f15,plain,(
% 1.04/0.91 ((? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) != $true))) & (binunionEcases = $true)) & (powersetE = $true)) & (powersetI = $true)),
% 1.04/0.91 inference(ennf_transformation,[status(thm)],[f14])).
% 1.04/0.91 thf(f14,plain,(
% 1.04/0.91 ~((powersetI = $true) => ((powersetE = $true) => ((binunionEcases = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ((in @ (binunion @ X0 @ X2) @ (powerset @ X1)) = $true))))))),
% 1.04/0.91 inference(fool_elimination,[status(thm)],[f13])).
% 1.04/0.91 thf(f13,plain,(
% 1.04/0.91 ~(powersetI => (powersetE => (binunionEcases => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))))))),
% 1.04/0.91 inference(rectify,[status(thm)],[f5])).
% 1.04/0.91 thf(f5,negated_conjecture,(
% 1.04/0.91 ~(powersetI => (powersetE => (binunionEcases => ! [X4 : $i,X0 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => (in @ (binunion @ X4 @ X5) @ (powerset @ X0)))))))),
% 1.04/0.91 inference(negated_conjecture,[status(cth)],[f4])).
% 1.04/0.91 thf(f4,conjecture,(
% 1.04/0.91 powersetI => (powersetE => (binunionEcases => ! [X4 : $i,X0 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => (in @ (binunion @ X4 @ X5) @ (powerset @ X0))))))),
% 1.04/0.91 file('/export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2THF_14574.p',binunionT_lem)).
% 1.04/0.91 thf(f115,plain,(
% 1.04/0.91 ((in @ (binunion @ sK3 @ sK5) @ (powerset @ sK4)) = $true) | ~spl13_1),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.04/0.91 thf(f114,plain,(
% 1.04/0.91 ((in @ (binunion @ sK3 @ sK5) @ (powerset @ sK4)) = $true) | ($true != $true) | ~spl13_1),
% 1.04/0.91 inference(superposition,[status(thm)],[f79,f113])).
% 1.04/0.91 thf(f113,plain,(
% 1.04/0.91 ($true = (in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK4)) | ~spl13_1),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.04/0.91 thf(f112,plain,(
% 1.04/0.91 ($true = (in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK4)) | ($true != $true) | ~spl13_1),
% 1.04/0.91 inference(superposition,[status(thm)],[f93,f100])).
% 1.04/0.91 thf(f100,plain,(
% 1.04/0.91 ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK5) = $true) | ~spl13_1),
% 1.04/0.91 inference(avatar_component_clause,[status(thm)],[f98])).
% 1.04/0.91 thf(f98,definition,(
% 1.04/0.91 spl13_1 <=> ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK5) = $true)),
% 1.04/0.91 introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition])).
% 1.04/0.91 thf(f93,plain,(
% 1.04/0.91 ( ! [X0 : $i] : (((in @ X0 @ sK5) != $true) | ((in @ X0 @ sK4) = $true)) )),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.04/0.91 thf(f89,plain,(
% 1.04/0.91 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK4) = $true) | ((in @ X0 @ sK5) != $true)) )),
% 1.04/0.91 inference(superposition,[status(thm)],[f82,f46])).
% 1.04/0.91 thf(f46,plain,(
% 1.04/0.91 ((in @ sK5 @ (powerset @ sK4)) = $true)),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f29])).
% 1.04/0.91 thf(f82,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X3)) != $true) | ((in @ X4 @ X3) = $true) | ((in @ X4 @ X5) != $true)) )),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.04/0.91 thf(f75,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true) | ($true != $true) | ((in @ X5 @ (powerset @ X3)) != $true)) )),
% 1.04/0.91 inference(definition_unfolding,[status(thm)],[f56,f44])).
% 1.04/0.91 thf(f44,plain,(
% 1.04/0.91 (powersetE = $true)),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f29])).
% 1.04/0.91 thf(f56,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true) | ((in @ X5 @ (powerset @ X3)) != $true) | (powersetE != $true)) )),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f37])).
% 1.04/0.91 thf(f37,plain,(
% 1.04/0.91 ((powersetE = $true) | (((in @ sK11 @ sK12) = $true) & ((in @ sK11 @ sK10) != $true) & ((in @ sK12 @ (powerset @ sK10)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true) | ((in @ X5 @ (powerset @ X3)) != $true)) | (powersetE != $true))),
% 1.04/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f35,f36])).
% 1.04/0.91 thf(f36,plain,(
% 1.04/0.91 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ X0) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) => (((in @ sK11 @ sK12) = $true) & ((in @ sK11 @ sK10) != $true) & ((in @ sK12 @ (powerset @ sK10)) = $true))),
% 1.04/0.91 introduced(definition,[],[choice_axiom])).
% 1.04/0.91 thf(f35,plain,(
% 1.04/0.91 ((powersetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ X0) != $true) & ((in @ X2 @ (powerset @ X0)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true) | ((in @ X5 @ (powerset @ X3)) != $true)) | (powersetE != $true))),
% 1.04/0.91 inference(rectify,[status(thm)],[f34])).
% 1.04/0.91 thf(f34,plain,(
% 1.04/0.91 ((powersetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) & ((in @ X0 @ X2) != $true) & ((in @ X1 @ (powerset @ X2)) = $true))) & (! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ((in @ X0 @ X2) = $true) | ((in @ X1 @ (powerset @ X2)) != $true)) | (powersetE != $true))),
% 1.04/0.91 inference(nnf_transformation,[status(thm)],[f18])).
% 1.04/0.91 thf(f18,plain,(
% 1.04/0.91 (powersetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ((in @ X0 @ X2) = $true) | ((in @ X1 @ (powerset @ X2)) != $true))),
% 1.04/0.91 inference(flattening,[status(thm)],[f17])).
% 1.04/0.91 thf(f17,plain,(
% 1.04/0.91 (powersetE = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) | ((in @ X1 @ (powerset @ X2)) != $true))),
% 1.04/0.91 inference(ennf_transformation,[status(thm)],[f12])).
% 1.04/0.91 thf(f12,plain,(
% 1.04/0.91 (powersetE = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X2)) = $true) => (((in @ X0 @ X1) = $true) => ((in @ X0 @ X2) = $true)))),
% 1.04/0.91 inference(fool_elimination,[status(thm)],[f11])).
% 1.04/0.91 thf(f11,plain,(
% 1.04/0.91 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X2)) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = powersetE)),
% 1.04/0.91 inference(rectify,[status(thm)],[f2])).
% 1.04/0.91 thf(f2,axiom,(
% 1.04/0.91 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 1.04/0.91 file('/export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2THF_14574.p',powersetE)).
% 1.04/0.91 thf(f79,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.04/0.91 thf(f62,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true) | ($true != $true)) )),
% 1.04/0.91 inference(definition_unfolding,[status(thm)],[f39,f42])).
% 1.04/0.91 thf(f42,plain,(
% 1.04/0.91 (powersetI = $true)),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f29])).
% 1.04/0.91 thf(f39,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ((in @ (sK2 @ X4 @ X3) @ X3) != $true) | (powersetI != $true)) )),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f26])).
% 1.04/0.91 thf(f26,plain,(
% 1.04/0.91 ((powersetI = $true) | (((in @ sK1 @ (powerset @ sK0)) != $true) & ! [X2 : $i] : (((in @ X2 @ sK0) = $true) | ((in @ X2 @ sK1) != $true)))) & (! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | (((in @ (sK2 @ X4 @ X3) @ X3) != $true) & ((in @ (sK2 @ X4 @ X3) @ X4) = $true))) | (powersetI != $true))),
% 1.04/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f25,f24])).
% 1.04/0.91 thf(f24,plain,(
% 1.04/0.91 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true))) => (((in @ sK1 @ (powerset @ sK0)) != $true) & ! [X2 : $i] : (((in @ X2 @ sK0) = $true) | ((in @ X2 @ sK1) != $true)))),
% 1.04/0.91 introduced(definition,[],[choice_axiom])).
% 1.04/0.91 thf(f25,plain,(
% 1.04/0.91 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X3) != $true) & ((in @ X5 @ X4) = $true)) => (((in @ (sK2 @ X4 @ X3) @ X3) != $true) & ((in @ (sK2 @ X4 @ X3) @ X4) = $true)))),
% 1.04/0.91 introduced(definition,[],[choice_axiom])).
% 1.04/0.91 thf(f23,plain,(
% 1.04/0.91 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)))) & (! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ? [X5 : $i] : (((in @ X5 @ X3) != $true) & ((in @ X5 @ X4) = $true))) | (powersetI != $true))),
% 1.04/0.91 inference(rectify,[status(thm)],[f22])).
% 1.04/0.91 thf(f22,plain,(
% 1.04/0.91 ((powersetI = $true) | ? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)))) & (! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (powersetI != $true))),
% 1.04/0.91 inference(nnf_transformation,[status(thm)],[f19])).
% 1.04/0.91 thf(f19,plain,(
% 1.04/0.91 (powersetI = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)))),
% 1.04/0.91 inference(ennf_transformation,[status(thm)],[f8])).
% 1.04/0.91 thf(f8,plain,(
% 1.04/0.91 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((in @ X0 @ (powerset @ X1)) = $true)) <=> (powersetI = $true)),
% 1.04/0.91 inference(fool_elimination,[status(thm)],[f7])).
% 1.04/0.91 thf(f7,plain,(
% 1.04/0.91 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 1.04/0.91 inference(rectify,[status(thm)],[f1])).
% 1.04/0.91 thf(f1,axiom,(
% 1.04/0.91 (powersetI = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 1.04/0.91 file('/export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2THF_14574.p',powersetI)).
% 1.04/0.91 thf(f111,plain,(
% 1.04/0.91 ~spl13_2),
% 1.04/0.91 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.04/0.91 thf(f110,plain,(
% 1.04/0.91 $false | ~spl13_2),
% 1.04/0.91 inference(subsumption_resolution,[status(thm)],[f109,f45])).
% 1.04/0.91 thf(f109,plain,(
% 1.04/0.91 ((in @ (binunion @ sK3 @ sK5) @ (powerset @ sK4)) = $true) | ~spl13_2),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.04/0.91 thf(f108,plain,(
% 1.04/0.91 ((in @ (binunion @ sK3 @ sK5) @ (powerset @ sK4)) = $true) | ($true != $true) | ~spl13_2),
% 1.04/0.91 inference(superposition,[status(thm)],[f79,f107])).
% 1.04/0.91 thf(f107,plain,(
% 1.04/0.91 ($true = (in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK4)) | ~spl13_2),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.04/0.91 thf(f106,plain,(
% 1.04/0.91 ($true = (in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK4)) | ($true != $true) | ~spl13_2),
% 1.04/0.91 inference(superposition,[status(thm)],[f94,f104])).
% 1.04/0.91 thf(f104,plain,(
% 1.04/0.91 ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK3) = $true) | ~spl13_2),
% 1.04/0.91 inference(avatar_component_clause,[status(thm)],[f102])).
% 1.04/0.91 thf(f102,definition,(
% 1.04/0.91 spl13_2 <=> ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK3) = $true)),
% 1.04/0.91 introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition])).
% 1.04/0.91 thf(f94,plain,(
% 1.04/0.91 ( ! [X0 : $i] : (((in @ X0 @ sK3) != $true) | ((in @ X0 @ sK4) = $true)) )),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.04/0.91 thf(f90,plain,(
% 1.04/0.91 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK3) != $true) | ((in @ X0 @ sK4) = $true)) )),
% 1.04/0.91 inference(superposition,[status(thm)],[f82,f47])).
% 1.04/0.91 thf(f47,plain,(
% 1.04/0.91 ((in @ sK3 @ (powerset @ sK4)) = $true)),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f29])).
% 1.04/0.91 thf(f105,plain,(
% 1.04/0.91 spl13_1 | spl13_2),
% 1.04/0.91 inference(avatar_split_clause,[status(thm)],[f96,f102,f98])).
% 1.04/0.91 thf(f96,plain,(
% 1.04/0.91 ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK3) = $true) | ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK5) = $true)),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.04/0.91 thf(f95,plain,(
% 1.04/0.91 ($true != $true) | ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK5) = $true) | ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ sK3) = $true)),
% 1.04/0.91 inference(superposition,[status(thm)],[f84,f87])).
% 1.04/0.91 thf(f87,plain,(
% 1.04/0.91 ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ (binunion @ sK3 @ sK5)) = $true)),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.04/0.91 thf(f85,plain,(
% 1.04/0.91 ((in @ (sK2 @ (binunion @ sK3 @ sK5) @ sK4) @ (binunion @ sK3 @ sK5)) = $true) | ($true != $true)),
% 1.04/0.91 inference(superposition,[status(thm)],[f45,f81])).
% 1.04/0.91 thf(f81,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true)) )),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.04/0.91 thf(f63,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ($true != $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true)) )),
% 1.04/0.91 inference(definition_unfolding,[status(thm)],[f38,f42])).
% 1.04/0.91 thf(f38,plain,(
% 1.04/0.91 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true) | (powersetI != $true)) )),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f26])).
% 1.04/0.91 thf(f84,plain,(
% 1.04/0.91 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binunion @ X1 @ X2)) != $true) | ((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) = $true)) )),
% 1.04/0.91 inference(condensation,[status(thm)],[f83])).
% 1.04/0.91 thf(f83,plain,(
% 1.04/0.91 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ X5) = $true) | ((in @ X7 @ X4) = $true) | ((in @ X7 @ (binunion @ X5 @ X4)) != $true) | ($true = X6)) )),
% 1.04/0.91 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.04/0.91 thf(f71,plain,(
% 1.04/0.91 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (binunion @ X5 @ X4)) != $true) | ($true != $true) | ((in @ X7 @ X4) = $true) | ((in @ X7 @ X5) = $true) | ($true = X6)) )),
% 1.04/0.91 inference(definition_unfolding,[status(thm)],[f48,f43])).
% 1.04/0.91 thf(f43,plain,(
% 1.04/0.91 (binunionEcases = $true)),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f29])).
% 1.04/0.91 thf(f48,plain,(
% 1.04/0.91 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (binunion @ X5 @ X4)) != $true) | ((in @ X7 @ X5) = $true) | ((in @ X7 @ X4) = $true) | ($true = X6) | (binunionEcases != $true)) )),
% 1.04/0.91 inference(cnf_transformation,[status(thm)],[f33])).
% 1.04/0.91 thf(f33,plain,(
% 1.04/0.91 ((binunionEcases = $true) | (((in @ sK9 @ (binunion @ sK7 @ sK6)) = $true) & ((sK8 = $true) | ((in @ sK9 @ sK7) != $true)) & ((sK8 = $true) | ((in @ sK9 @ sK6) != $true)) & (sK8 != $true))) & (! [X4 : $i,X5 : $i,X6 : $o,X7 : $i] : (((in @ X7 @ (binunion @ X5 @ X4)) != $true) | (($true != X6) & ((in @ X7 @ X5) = $true)) | (($true != X6) & ((in @ X7 @ X4) = $true)) | ($true = X6)) | (binunionEcases != $true))),
% 1.04/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f31,f32])).
% 1.04/0.91 thf(f32,plain,(
% 1.04/0.91 ? [X0 : $i,X1 : $i,X2 : $o,X3 : $i] : (((in @ X3 @ (binunion @ X1 @ X0)) = $true) & (($true = X2) | ((in @ X3 @ X1) != $true)) & (($true = X2) | ((in @ X3 @ X0) != $true)) & ($true != X2)) => (((in @ sK9 @ (binunion @ sK7 @ sK6)) = $true) & ((sK8 = $true) | ((in @ sK9 @ sK7) != $true)) & ((sK8 = $true) | ((in @ sK9 @ sK6) != $true)) & (sK8 != $true))),
% 1.04/0.91 introduced(definition,[],[choice_axiom])).
% 1.04/0.91 thf(f31,plain,(
% 1.04/0.91 ((binunionEcases = $true) | ? [X0 : $i,X1 : $i,X2 : $o,X3 : $i] : (((in @ X3 @ (binunion @ X1 @ X0)) = $true) & (($true = X2) | ((in @ X3 @ X1) != $true)) & (($true = X2) | ((in @ X3 @ X0) != $true)) & ($true != X2))) & (! [X4 : $i,X5 : $i,X6 : $o,X7 : $i] : (((in @ X7 @ (binunion @ X5 @ X4)) != $true) | (($true != X6) & ((in @ X7 @ X5) = $true)) | (($true != X6) & ((in @ X7 @ X4) = $true)) | ($true = X6)) | (binunionEcases != $true))),
% 1.04/0.91 inference(rectify,[status(thm)],[f30])).
% 1.04/0.91 thf(f30,plain,(
% 1.04/0.91 ((binunionEcases = $true) | ? [X2 : $i,X0 : $i,X1 : $o,X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) & (($true = X1) | ((in @ X3 @ X0) != $true)) & (($true = X1) | ((in @ X3 @ X2) != $true)) & ($true != X1))) & (! [X2 : $i,X0 : $i,X1 : $o,X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | (($true != X1) & ((in @ X3 @ X0) = $true)) | (($true != X1) & ((in @ X3 @ X2) = $true)) | ($true = X1)) | (binunionEcases != $true))),
% 1.04/0.91 inference(nnf_transformation,[status(thm)],[f21])).
% 1.04/0.91 thf(f21,plain,(
% 1.04/0.91 (binunionEcases = $true) <=> ! [X2 : $i,X0 : $i,X1 : $o,X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | (($true != X1) & ((in @ X3 @ X0) = $true)) | (($true != X1) & ((in @ X3 @ X2) = $true)) | ($true = X1))),
% 1.04/0.91 inference(flattening,[status(thm)],[f20])).
% 1.04/0.91 thf(f20,plain,(
% 1.04/0.91 (binunionEcases = $true) <=> ! [X2 : $i,X0 : $i,X1 : $o,X3 : $i] : (((($true = X1) | (($true != X1) & ((in @ X3 @ X2) = $true))) | (($true != X1) & ((in @ X3 @ X0) = $true))) | ((in @ X3 @ (binunion @ X0 @ X2)) != $true))),
% 1.04/0.91 inference(ennf_transformation,[status(thm)],[f10])).
% 1.04/0.91 thf(f10,plain,(
% 1.04/0.91 (binunionEcases = $true) <=> ! [X2 : $i,X0 : $i,X1 : $o,X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) => ((((in @ X3 @ X0) = $true) => ($true = X1)) => ((((in @ X3 @ X2) = $true) => ($true = X1)) => ($true = X1))))),
% 1.04/0.91 inference(fool_elimination,[status(thm)],[f9])).
% 1.04/0.91 thf(f9,plain,(
% 1.04/0.91 (! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((in @ X3 @ (binunion @ X0 @ X2)) => (((in @ X3 @ X0) => X1) => (((in @ X3 @ X2) => X1) => X1))) = binunionEcases)),
% 1.04/0.91 inference(rectify,[status(thm)],[f3])).
% 1.04/0.91 thf(f3,axiom,(
% 1.04/0.91 (! [X0 : $i,X3 : $o,X1 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => (((in @ X2 @ X0) => X3) => (((in @ X2 @ X1) => X3) => X3))) = binunionEcases)),
% 1.04/0.91 file('/export/starexec/sandbox/tmp/tmp.h1FSCmxZ5U/DTF2THF_14574.p',binunionEcases)).
% 1.04/0.91 % SZS output end Proof for DTF2THF_14574
% 1.04/0.91 % (14848)------------------------------
% 1.04/0.91 % (14848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.91 % (14848)Termination reason: Refutation
% 1.04/0.91
% 1.04/0.91 % (14848)Memory used [KB]: 5628
% 1.04/0.91 % (14848)Time elapsed: 0.006 s
% 1.04/0.91 % (14848)Instructions burned: 11 (million)
% 1.04/0.91 % (14848)------------------------------
% 1.04/0.91 % (14848)------------------------------
% 1.04/0.91 % (14841)Success in time 0.014 s
%------------------------------------------------------------------------------