%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU715^2 : 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 : n004.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 09:36:37 AM UTC 2026
% Result : Theorem 1.31s 1.15s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 95 ( 12 unt; 0 typ; 5 def)
% Number of atoms : 1250 ( 354 equ; 0 cnn)
% Maximal formula atoms : 18 ( 13 avg)
% Number of connectives : 1273 ( 178 ~; 186 |; 78 &; 756 @)
% ( 11 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 17 con; 0-2 aty)
% Number of variables : 179 ( 0 ^; 140 !; 39 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_15,type,
sK8: $i > $i > $i ).
thf(func_def_16,type,
sK9: $i > $i > $i ).
thf(f147,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f104,f113,f114,f134,f135,f146]) ).
thf(f146,plain,
( ~ spl10_2
| ~ spl10_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f145]) ).
thf(f145,plain,
( $false
| ~ spl10_2
| ~ spl10_4 ),
inference(subsumption_resolution,[status(thm)],[f144,f34]) ).
thf(f34,plain,
sK2 != sK1,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( setext = $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK0 )
!= $true )
| ( $true
= ( in @ X3 @ sK1 ) )
| ( ( in @ X3 @ sK2 )
!= $true ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( sK2 != sK1 )
& ! [X4: $i] :
( ( $true
= ( in @ X4 @ sK2 ) )
| ( $true
!= ( in @ X4 @ sK1 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) )
& ( powersetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f20,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ( X1 != X2 )
& ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ X0 ) ) ) ) )
=> ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ? [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ sK0 )
!= $true )
| ( $true
= ( in @ X3 @ sK1 ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true )
& ( sK1 != X2 )
& ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
| ( $true
!= ( in @ X4 @ sK1 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ sK0 )
!= $true )
| ( $true
= ( in @ X3 @ sK1 ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true )
& ( sK1 != X2 )
& ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
| ( $true
!= ( in @ X4 @ sK1 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) ) )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ sK0 )
!= $true )
| ( $true
= ( in @ X3 @ sK1 ) )
| ( ( in @ X3 @ sK2 )
!= $true ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( sK2 != sK1 )
& ! [X4: $i] :
( ( $true
= ( in @ X4 @ sK2 ) )
| ( $true
!= ( in @ X4 @ sK1 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( setext = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ( X1 != X2 )
& ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ X0 ) ) ) ) )
& ( powersetE = $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setext = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( $true
= ( in @ X4 @ X0 ) )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( X0 != X2 )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) ) ) )
& ( powersetE = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( X0 != X2 )
& ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
| ( $true
!= ( in @ X4 @ X2 ) )
| ( ( in @ X4 @ X1 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( powersetE = $true )
& ( setext = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setext = $true )
=> ( ( powersetE = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( $true
= ( in @ X4 @ X2 ) )
=> ( $true
= ( in @ X4 @ X0 ) ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setext
=> ( powersetE
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X0 ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setext
=> ( powersetE
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X4 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X3 ) ) )
=> ( X3 = X4 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setext
=> ( powersetE
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X4 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X3 ) ) )
=> ( X3 = X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hBT4Y3P8o9/DTF2THF_16002.p',setextT) ).
thf(f144,plain,
( ( sK2 = sK1 )
| ~ spl10_2
| ~ spl10_4 ),
inference(subsumption_resolution,[status(thm)],[f142,f100]) ).
thf(f100,plain,
( ( $true
= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK2 ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl10_2
<=> ( $true
= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition]) ).
thf(f142,plain,
( ( $true
!= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK2 ) )
| ( sK2 = sK1 )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $true
!= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK2 ) )
| ( $true != $true )
| ( sK2 = sK1 )
| ~ spl10_4 ),
inference(superposition,[status(thm)],[f61,f129]) ).
thf(f129,plain,
( ( $true
= ( in @ ( sK9 @ sK1 @ sK2 ) @ sK1 ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[status(thm)],[f127]) ).
thf(f127,definition,
( spl10_4
<=> ( $true
= ( in @ ( sK9 @ sK1 @ sK2 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition]) ).
thf(f61,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( in @ ( sK9 @ X5 @ X4 ) @ X5 ) )
| ( ( in @ ( sK8 @ X5 @ X4 ) @ X4 )
!= $true )
| ( X4 = X5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( sK8 @ X5 @ X4 ) @ X4 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( sK9 @ X5 @ X4 ) @ X5 ) )
| ( X4 = X5 ) ),
inference(definition_unfolding,[status(thm)],[f44,f38]) ).
thf(f38,plain,
setext = $true,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f44,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( sK8 @ X5 @ X4 ) @ X4 )
!= $true )
| ( X4 = X5 )
| ( $true
!= ( in @ ( sK9 @ X5 @ X4 ) @ X5 ) )
| ( setext != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( setext = $true )
| ( ! [X2: $i] :
( ( ( in @ X2 @ sK7 )
!= $true )
| ( $true
= ( in @ X2 @ sK6 ) ) )
& ( sK6 != sK7 )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ sK7 ) )
| ( $true
!= ( in @ X3 @ sK6 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( $true
= ( in @ ( sK8 @ X5 @ X4 ) @ X5 ) )
& ( ( in @ ( sK8 @ X5 @ X4 ) @ X4 )
!= $true ) )
| ( X4 = X5 )
| ( ( $true
!= ( in @ ( sK9 @ X5 @ X4 ) @ X5 ) )
& ( $true
= ( in @ ( sK9 @ X5 @ X4 ) @ X4 ) ) ) )
| ( setext != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f27,f30,f29,f28]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( X0 != X1 )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK7 )
!= $true )
| ( $true
= ( in @ X2 @ sK6 ) ) )
& ( sK6 != sK7 )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ sK7 ) )
| ( $true
!= ( in @ X3 @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
! [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ( $true
!= ( in @ X6 @ X4 ) ) )
=> ( ( $true
= ( in @ ( sK8 @ X5 @ X4 ) @ X5 ) )
& ( ( in @ ( sK8 @ X5 @ X4 ) @ X4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
! [X4: $i,X5: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ X5 ) )
& ( $true
= ( in @ X7 @ X4 ) ) )
=> ( ( $true
!= ( in @ ( sK9 @ X5 @ X4 ) @ X5 ) )
& ( $true
= ( in @ ( sK9 @ X5 @ X4 ) @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ( setext = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( X0 != X1 )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ( $true
!= ( in @ X6 @ X4 ) ) )
| ( X4 = X5 )
| ? [X7: $i] :
( ( $true
!= ( in @ X7 @ X5 ) )
& ( $true
= ( in @ X7 @ X4 ) ) ) )
| ( setext != $true ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( setext = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( X0 != X1 )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( X0 = X1 )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
| ( setext != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( setext = $true )
<=> ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( X0 = X1 )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X1: $i,X0: $i] :
( ( X0 = X1 )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( setext = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( in @ X3 @ X1 ) ) )
=> ( X0 = X1 ) ) )
<=> ( setext = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ X1 ) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setext
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hBT4Y3P8o9/DTF2THF_16002.p',setext) ).
thf(f135,plain,
( spl10_5
| ~ spl10_2 ),
inference(avatar_split_clause,[status(thm)],[f124,f99,f131]) ).
thf(f131,definition,
( spl10_5
<=> ( ( in @ ( sK9 @ sK1 @ sK2 ) @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_5])],[avatar_definition]) ).
thf(f124,plain,
( ( ( in @ ( sK9 @ sK1 @ sK2 ) @ sK0 )
= $true )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ( in @ ( sK9 @ sK1 @ sK2 ) @ sK0 )
= $true )
| ( $true != $true )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f69,f121]) ).
thf(f121,plain,
( ( $true
= ( in @ ( sK9 @ sK1 @ sK2 ) @ sK2 ) )
| ~ spl10_2 ),
inference(subsumption_resolution,[status(thm)],[f118,f34]) ).
thf(f118,plain,
( ( $true
= ( in @ ( sK9 @ sK1 @ sK2 ) @ sK2 ) )
| ( sK2 = sK1 )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $true
= ( in @ ( sK9 @ sK1 @ sK2 ) @ sK2 ) )
| ( $true != $true )
| ( sK2 = sK1 )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f64,f100]) ).
thf(f64,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( sK8 @ X5 @ X4 ) @ X4 )
!= $true )
| ( $true
= ( in @ ( sK9 @ X5 @ X4 ) @ X4 ) )
| ( X4 = X5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X4: $i,X5: $i] :
( ( $true != $true )
| ( X4 = X5 )
| ( $true
= ( in @ ( sK9 @ X5 @ X4 ) @ X4 ) )
| ( ( in @ ( sK8 @ X5 @ X4 ) @ X4 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f43,f38]) ).
thf(f43,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( sK8 @ X5 @ X4 ) @ X4 )
!= $true )
| ( X4 = X5 )
| ( $true
= ( in @ ( sK9 @ X5 @ X4 ) @ X4 ) )
| ( setext != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f69,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK2 ) )
| ( $true
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK0 ) )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f62,f35]) ).
thf(f35,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f42,f32]) ).
thf(f32,plain,
powersetE = $true,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( powersetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ( ( $true
!= ( in @ sK4 @ sK3 ) )
& ( ( in @ sK4 @ sK5 )
= $true )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f23,f24]) ).
thf(f24,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
& ( $true
= ( in @ X4 @ X5 ) )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) )
=> ( ( $true
!= ( in @ sK4 @ sK3 ) )
& ( ( in @ sK4 @ sK5 )
= $true )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
& ( $true
= ( in @ X4 @ X5 ) )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X2 ) ) ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) )
& ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X2 ) ) ) )
<=> ( powersetE = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( powersetE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( powersetE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
=> ( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,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.hBT4Y3P8o9/DTF2THF_16002.p',powersetE) ).
thf(f134,plain,
( spl10_4
| ~ spl10_5
| ~ spl10_2 ),
inference(avatar_split_clause,[status(thm)],[f125,f99,f131,f127]) ).
thf(f125,plain,
( ( $true
= ( in @ ( sK9 @ sK1 @ sK2 ) @ sK1 ) )
| ( ( in @ ( sK9 @ sK1 @ sK2 ) @ sK0 )
!= $true )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( ( in @ ( sK9 @ sK1 @ sK2 ) @ sK0 )
!= $true )
| ( $true
= ( in @ ( sK9 @ sK1 @ sK2 ) @ sK1 ) )
| ( $true != $true )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f36,f121]) ).
thf(f36,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK2 )
!= $true )
| ( ( in @ X3 @ sK0 )
!= $true )
| ( $true
= ( in @ X3 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f114,plain,
( spl10_3
| ~ spl10_1 ),
inference(avatar_split_clause,[status(thm)],[f107,f95,f110]) ).
thf(f110,definition,
( spl10_3
<=> ( $true
= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl10_3])],[avatar_definition]) ).
thf(f95,definition,
( spl10_1
<=> ( ( in @ ( sK8 @ sK1 @ sK2 ) @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition]) ).
thf(f107,plain,
( ( $true
= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK0 ) )
| ~ spl10_1 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $true != $true )
| ( $true
= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK0 ) )
| ~ spl10_1 ),
inference(superposition,[status(thm)],[f68,f97]) ).
thf(f97,plain,
( ( ( in @ ( sK8 @ sK1 @ sK2 ) @ sK1 )
= $true )
| ~ spl10_1 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f68,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK1 ) )
| ( $true != $true )
| ( $true
= ( in @ X0 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f62,f37]) ).
thf(f37,plain,
( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f113,plain,
( spl10_2
| ~ spl10_3
| ~ spl10_1 ),
inference(avatar_split_clause,[status(thm)],[f108,f95,f110,f99]) ).
thf(f108,plain,
( ( $true
!= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK0 ) )
| ( $true
= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK2 ) )
| ~ spl10_1 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true
= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK2 ) )
| ( $true != $true )
| ( $true
!= ( in @ ( sK8 @ sK1 @ sK2 ) @ sK0 ) )
| ~ spl10_1 ),
inference(superposition,[status(thm)],[f33,f97]) ).
thf(f33,plain,
! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK1 ) )
| ( $true
= ( in @ X4 @ sK2 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f104,plain,
spl10_1,
inference(avatar_split_clause,[status(thm)],[f103,f95]) ).
thf(f103,plain,
( ( in @ ( sK8 @ sK1 @ sK2 ) @ sK1 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f89,f34]) ).
thf(f89,plain,
( ( sK2 = sK1 )
| ( ( in @ ( sK8 @ sK1 @ sK2 ) @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( sK2 = sK1 )
| ( ( in @ ( sK8 @ sK1 @ sK2 ) @ sK1 )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( sK2 = sK1 )
| ( ( in @ ( sK8 @ sK1 @ sK2 ) @ sK1 )
= $true )
| ( $true != $true )
| ( sK2 = sK1 )
| ( ( in @ ( sK8 @ sK1 @ sK2 ) @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f65,f81]) ).
thf(f81,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK9 @ X0 @ sK2 ) @ sK1 ) )
| ( ( in @ ( sK8 @ X0 @ sK2 ) @ X0 )
= $true )
| ( sK2 = X0 ) ),
inference(subsumption_resolution,[status(thm)],[f78,f79]) ).
thf(f79,plain,
! [X0: $i] :
( ( ( in @ ( sK8 @ X0 @ sK2 ) @ X0 )
= $true )
| ( sK2 = X0 )
| ( $true
= ( in @ ( sK9 @ X0 @ sK2 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X0: $i] :
( ( ( in @ ( sK8 @ X0 @ sK2 ) @ X0 )
= $true )
| ( $true
= ( in @ ( sK9 @ X0 @ sK2 ) @ sK0 ) )
| ( sK2 = X0 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f69,f63]) ).
thf(f63,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK9 @ X5 @ X4 ) @ X4 ) )
| ( X4 = X5 )
| ( $true
= ( in @ ( sK8 @ X5 @ X4 ) @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK8 @ X5 @ X4 ) @ X5 ) )
| ( $true
= ( in @ ( sK9 @ X5 @ X4 ) @ X4 ) )
| ( $true != $true )
| ( X4 = X5 ) ),
inference(definition_unfolding,[status(thm)],[f45,f38]) ).
thf(f45,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK8 @ X5 @ X4 ) @ X5 ) )
| ( X4 = X5 )
| ( $true
= ( in @ ( sK9 @ X5 @ X4 ) @ X4 ) )
| ( setext != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f78,plain,
! [X0: $i] :
( ( sK2 = X0 )
| ( $true
= ( in @ ( sK9 @ X0 @ sK2 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK9 @ X0 @ sK2 ) @ sK0 ) )
| ( ( in @ ( sK8 @ X0 @ sK2 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK9 @ X0 @ sK2 ) @ sK0 ) )
| ( sK2 = X0 )
| ( $true != $true )
| ( $true
= ( in @ ( sK9 @ X0 @ sK2 ) @ sK1 ) )
| ( ( in @ ( sK8 @ X0 @ sK2 ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f36,f63]) ).
thf(f65,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( in @ ( sK9 @ X5 @ X4 ) @ X5 ) )
| ( $true
= ( in @ ( sK8 @ X5 @ X4 ) @ X5 ) )
| ( X4 = X5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
! [X4: $i,X5: $i] :
( ( X4 = X5 )
| ( $true
= ( in @ ( sK8 @ X5 @ X4 ) @ X5 ) )
| ( $true
!= ( in @ ( sK9 @ X5 @ X4 ) @ X5 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f46,f38]) ).
thf(f46,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK8 @ X5 @ X4 ) @ X5 ) )
| ( X4 = X5 )
| ( $true
!= ( in @ ( sK9 @ X5 @ X4 ) @ X5 ) )
| ( setext != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU715^2 : TPTP v9.2.1. Released v3.7.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:31:26 EST 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.43 ---- Original DTF file ---
% 0.15/0.43 thf(spec,logic,$$dhol).
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 % File : SEU715^2 : TPTP v9.2.1. Released v3.7.0.
% 0.15/0.43 % Domain : Set Theory
% 0.15/0.43 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.15/0.43 % Version : Especial > Reduced > Especial.
% 0.15/0.43 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.15/0.43 % (! x:i.in x A -> in x X -> in x Y) -> (! x:i.in x A -> in x Y ->
% 0.15/0.43 % in x X) -> X = Y))
% 0.15/0.43
% 0.15/0.43 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.15/0.43 % Source : [Bro08]
% 0.15/0.43 % Names : ZFC217l [Bro08]
% 0.15/0.43
% 0.15/0.43 % Status : Theorem
% 0.15/0.43 % Rating : 0.00 v8.2.0, 0.08 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, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v3.7.0
% 0.15/0.43 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.15/0.43 % Number of atoms : 23 ( 4 equ; 0 cnn)
% 0.15/0.43 % Maximal formula atoms : 11 ( 7 avg)
% 0.15/0.43 % Number of connectives : 49 ( 0 ~; 0 |; 0 &; 33 @)
% 0.15/0.43 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.15/0.43 % Maximal formula depth : 15 ( 6 avg)
% 0.15/0.43 % Number of types : 2 ( 0 usr)
% 0.15/0.43 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.15/0.43 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.15/0.43 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.15/0.43 % SPC : TH0_THM_EQU_NAR
% 0.15/0.43
% 0.15/0.43 % Comments : http://mathgate.info/detsetitem.php?id=273
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 thf(in_type,type,
% 0.15/0.43 in: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(powerset_type,type,
% 0.15/0.43 powerset: $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(setext_type,type,
% 0.15/0.43 setext: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setext,definition,
% 0.15/0.43 ( setext
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xx @ B ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ A ) )
% 0.15/0.43 => ( A = B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetE_type,type,
% 0.15/0.43 powersetE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetE,definition,
% 0.15/0.43 ( powersetE
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ B @ ( powerset @ A ) )
% 0.15/0.43 => ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setextT,conjecture,
% 0.15/0.43 ( setext
% 0.15/0.43 => ( powersetE
% 0.15/0.43 => ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ X )
% 0.15/0.43 => ( in @ Xx @ Y ) ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ Y )
% 0.15/0.43 => ( in @ Xx @ X ) ) )
% 0.15/0.43 => ( X = Y ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.44 ------------------------
% 1.12/1.11 ---- Embedded in THF ---
% 1.12/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.11 %%% Generated on Tue Feb 24 12:31:27 EST 2026
% 1.12/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.11 %%% Logic specification used:
% 1.12/1.11 %%% thf(spec, logic, $$dhol).
% 1.12/1.11
% 1.12/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.hBT4Y3P8o9/DTF2DTF16002.p
% See solution above
% 1.12/1.11 ------------------------
% 1.31/1.11 ---- Cleaned THF ---
% 1.31/1.11 thf(in_type,type,
% 1.31/1.11 in: $i > $i > $o ).
% 1.31/1.11
% 1.31/1.11 thf(powerset_type,type,
% 1.31/1.11 powerset: $i > $i ).
% 1.31/1.11
% 1.31/1.11 thf(setext_type,type,
% 1.31/1.11 setext: $o ).
% 1.31/1.11
% 1.31/1.11 thf(setext,definition,
% 1.31/1.11 ( setext
% 1.31/1.11 = ( ! [A: $i,B: $i] :
% 1.31/1.11 ( ! [Xx: $i] :
% 1.31/1.11 ( ( in @ Xx @ A )
% 1.31/1.11 => ( in @ Xx @ B ) )
% 1.31/1.11 => ( ! [Xx: $i] :
% 1.31/1.11 ( ( in @ Xx @ B )
% 1.31/1.11 => ( in @ Xx @ A ) )
% 1.31/1.11 => ( A = B ) ) ) ) ) ).
% 1.31/1.11
% 1.31/1.11 thf(powersetE_type,type,
% 1.31/1.11 powersetE: $o ).
% 1.31/1.11
% 1.31/1.11 thf(powersetE,definition,
% 1.31/1.11 ( powersetE
% 1.31/1.11 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.31/1.11 ( ( in @ B @ ( powerset @ A ) )
% 1.31/1.11 => ( ( in @ Xx @ B )
% 1.31/1.11 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.31/1.11
% 1.31/1.11 thf(setextT,conjecture,
% 1.31/1.11 ( setext
% 1.31/1.11 => ( powersetE
% 1.31/1.11 => ! [A: $i,X: $i] :
% 1.31/1.11 ( ( in @ X @ ( powerset @ A ) )
% 1.31/1.11 => ! [Y: $i] :
% 1.31/1.11 ( ( in @ Y @ ( powerset @ A ) )
% 1.31/1.11 => ( ! [Xx: $i] :
% 1.31/1.11 ( ( in @ Xx @ A )
% 1.31/1.11 => ( ( in @ Xx @ X )
% 1.31/1.11 => ( in @ Xx @ Y ) ) )
% 1.31/1.11 => ( ! [Xx: $i] :
% 1.31/1.11 ( ( in @ Xx @ A )
% 1.31/1.11 => ( ( in @ Xx @ Y )
% 1.31/1.11 => ( in @ Xx @ X ) ) )
% 1.31/1.11 => ( X = Y ) ) ) ) ) ) ) ).
% 1.31/1.11 ------------------------
% 1.31/1.13 % (16101)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16002 for (3000ds/183Mi)
% 1.31/1.13 % (16102)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_16002 for (3000ds/4Mi)
% 1.31/1.13 % (16104)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16002 for (3000ds/2Mi)
% 1.31/1.13 % (16103)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_16002 for (3000ds/27Mi)
% 1.31/1.13 % (16105)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_16002 for (3000ds/2Mi)
% 1.31/1.13 % (16106)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_16002 for (3000ds/275Mi)
% 1.31/1.13 % (16107)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16002 for (3000ds/18Mi)
% 1.31/1.13 % (16104)Instruction limit reached!
% 1.31/1.13 % (16104)------------------------------
% 1.31/1.13 % (16104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.13 % (16105)Instruction limit reached!
% 1.31/1.13 % (16105)------------------------------
% 1.31/1.13 % (16105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.13 % (16104)Termination reason: Unknown
% 1.31/1.13 % (16104)Termination phase: Property scanning
% 1.31/1.13
% 1.31/1.13 % (16104)Memory used [KB]: 895
% 1.31/1.13 % (16104)Time elapsed: 0.002 s
% 1.31/1.13 % (16104)Instructions burned: 2 (million)
% 1.31/1.13 % (16104)------------------------------
% 1.31/1.13 % (16104)------------------------------
% 1.31/1.13 % (16105)Termination reason: Unknown
% 1.31/1.13 % (16105)Termination phase: shuffling
% 1.31/1.13
% 1.31/1.13 % (16105)Memory used [KB]: 895
% 1.31/1.13 % (16105)Time elapsed: 0.002 s
% 1.31/1.13 % (16105)Instructions burned: 2 (million)
% 1.31/1.13 % (16105)------------------------------
% 1.31/1.13 % (16105)------------------------------
% 1.31/1.14 % (16102)Instruction limit reached!
% 1.31/1.14 % (16102)------------------------------
% 1.31/1.14 % (16102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (16102)Termination reason: Unknown
% 1.31/1.14 % (16102)Termination phase: Saturation
% 1.31/1.14
% 1.31/1.14 % (16102)Memory used [KB]: 5500
% 1.31/1.14 % (16102)Time elapsed: 0.004 s
% 1.31/1.14 % (16102)Instructions burned: 5 (million)
% 1.31/1.14 % (16102)------------------------------
% 1.31/1.14 % (16102)------------------------------
% 1.31/1.14 % (16107)First to succeed.
% 1.31/1.15 % (16107)Refutation found. Thanks to Tanya!
% 1.31/1.15 % SZS status Theorem for DTF2THF_16002
% 1.31/1.15 % SZS output start Proof for DTF2THF_16002
% 1.31/1.15 thf(func_def_0, type, in: $i > $i > $o).
% 1.31/1.15 thf(func_def_1, type, powerset: $i > $i).
% 1.31/1.15 thf(func_def_15, type, sK8: $i > $i > $i).
% 1.31/1.15 thf(func_def_16, type, sK9: $i > $i > $i).
% 1.31/1.15 thf(f147,plain,(
% 1.31/1.15 $false),
% 1.31/1.15 inference(avatar_sat_refutation,[status(thm)],[f104,f113,f114,f134,f135,f146])).
% 1.31/1.15 thf(f146,plain,(
% 1.31/1.15 ~spl10_2 | ~spl10_4),
% 1.31/1.15 inference(avatar_contradiction_clause,[status(thm)],[f145])).
% 1.31/1.15 thf(f145,plain,(
% 1.31/1.15 $false | (~spl10_2 | ~spl10_4)),
% 1.31/1.15 inference(subsumption_resolution,[status(thm)],[f144,f34])).
% 1.31/1.15 thf(f34,plain,(
% 1.31/1.15 (sK2 != sK1)),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f21])).
% 1.31/1.15 thf(f21,plain,(
% 1.31/1.15 (setext = $true) & (((in @ sK1 @ (powerset @ sK0)) = $true) & (! [X3 : $i] : (((in @ X3 @ sK0) != $true) | ($true = (in @ X3 @ sK1)) | ((in @ X3 @ sK2) != $true)) & ($true = (in @ sK2 @ (powerset @ sK0))) & (sK2 != sK1) & ! [X4 : $i] : (($true = (in @ X4 @ sK2)) | ($true != (in @ X4 @ sK1)) | ($true != (in @ X4 @ sK0))))) & (powersetE = $true)),
% 1.31/1.15 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f20,f19])).
% 1.31/1.15 thf(f19,plain,(
% 1.31/1.15 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = (in @ X3 @ X1)) | ((in @ X3 @ X2) != $true)) & ($true = (in @ X2 @ (powerset @ X0))) & (X1 != X2) & ! [X4 : $i] : (($true = (in @ X4 @ X2)) | ((in @ X4 @ X1) != $true) | ($true != (in @ X4 @ X0))))) => (((in @ sK1 @ (powerset @ sK0)) = $true) & ? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ sK0) != $true) | ($true = (in @ X3 @ sK1)) | ((in @ X3 @ X2) != $true)) & ((in @ X2 @ (powerset @ sK0)) = $true) & (sK1 != X2) & ! [X4 : $i] : (($true = (in @ X4 @ X2)) | ($true != (in @ X4 @ sK1)) | ($true != (in @ X4 @ sK0)))))),
% 1.31/1.15 introduced(definition,[],[choice_axiom])).
% 1.31/1.15 thf(f20,plain,(
% 1.31/1.15 ? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ sK0) != $true) | ($true = (in @ X3 @ sK1)) | ((in @ X3 @ X2) != $true)) & ((in @ X2 @ (powerset @ sK0)) = $true) & (sK1 != X2) & ! [X4 : $i] : (($true = (in @ X4 @ X2)) | ($true != (in @ X4 @ sK1)) | ($true != (in @ X4 @ sK0)))) => (! [X3 : $i] : (((in @ X3 @ sK0) != $true) | ($true = (in @ X3 @ sK1)) | ((in @ X3 @ sK2) != $true)) & ($true = (in @ sK2 @ (powerset @ sK0))) & (sK2 != sK1) & ! [X4 : $i] : (($true = (in @ X4 @ sK2)) | ($true != (in @ X4 @ sK1)) | ($true != (in @ X4 @ sK0))))),
% 1.31/1.15 introduced(definition,[],[choice_axiom])).
% 1.31/1.15 thf(f18,plain,(
% 1.31/1.15 (setext = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = (in @ X3 @ X1)) | ((in @ X3 @ X2) != $true)) & ($true = (in @ X2 @ (powerset @ X0))) & (X1 != X2) & ! [X4 : $i] : (($true = (in @ X4 @ X2)) | ((in @ X4 @ X1) != $true) | ($true != (in @ X4 @ X0))))) & (powersetE = $true)),
% 1.31/1.15 inference(rectify,[status(thm)],[f13])).
% 1.31/1.15 thf(f13,plain,(
% 1.31/1.15 (setext = $true) & ? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (! [X4 : $i] : (((in @ X4 @ X1) != $true) | ($true = (in @ X4 @ X0)) | ($true != (in @ X4 @ X2))) & ((in @ X2 @ (powerset @ X1)) = $true) & (X0 != X2) & ! [X3 : $i] : (((in @ X3 @ X2) = $true) | ($true != (in @ X3 @ X0)) | ($true != (in @ X3 @ X1))))) & (powersetE = $true)),
% 1.31/1.15 inference(flattening,[status(thm)],[f12])).
% 1.31/1.15 thf(f12,plain,(
% 1.31/1.15 (? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((X0 != X2) & ! [X4 : $i] : ((($true = (in @ X4 @ X0)) | ($true != (in @ X4 @ X2))) | ((in @ X4 @ X1) != $true))) & ! [X3 : $i] : ((((in @ X3 @ X2) = $true) | ($true != (in @ X3 @ X0))) | ($true != (in @ X3 @ X1)))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (powersetE = $true)) & (setext = $true)),
% 1.31/1.15 inference(ennf_transformation,[status(thm)],[f11])).
% 1.31/1.15 thf(f11,plain,(
% 1.31/1.15 ~((setext = $true) => ((powersetE = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => (! [X3 : $i] : (($true = (in @ X3 @ X1)) => (($true = (in @ X3 @ X0)) => ((in @ X3 @ X2) = $true))) => (! [X4 : $i] : (((in @ X4 @ X1) = $true) => (($true = (in @ X4 @ X2)) => ($true = (in @ X4 @ X0)))) => (X0 = X2)))))))),
% 1.31/1.15 inference(fool_elimination,[status(thm)],[f10])).
% 1.31/1.15 thf(f10,plain,(
% 1.31/1.15 ~(setext => (powersetE => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (! [X4 : $i] : ((in @ X4 @ X1) => ((in @ X4 @ X2) => (in @ X4 @ X0))) => (X0 = X2)))))))),
% 1.31/1.15 inference(rectify,[status(thm)],[f4])).
% 1.31/1.15 thf(f4,negated_conjecture,(
% 1.31/1.15 ~(setext => (powersetE => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => (! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X3) => (in @ X2 @ X4))) => (! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X4) => (in @ X2 @ X3))) => (X3 = X4)))))))),
% 1.31/1.15 inference(negated_conjecture,[status(cth)],[f3])).
% 1.31/1.15 thf(f3,conjecture,(
% 1.31/1.15 setext => (powersetE => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => (! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X3) => (in @ X2 @ X4))) => (! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X4) => (in @ X2 @ X3))) => (X3 = X4))))))),
% 1.31/1.15 file('/export/starexec/sandbox/tmp/tmp.hBT4Y3P8o9/DTF2THF_16002.p',setextT)).
% 1.31/1.15 thf(f144,plain,(
% 1.31/1.15 (sK2 = sK1) | (~spl10_2 | ~spl10_4)),
% 1.31/1.15 inference(subsumption_resolution,[status(thm)],[f142,f100])).
% 1.31/1.15 thf(f100,plain,(
% 1.31/1.15 ($true = (in @ (sK8 @ sK1 @ sK2) @ sK2)) | ~spl10_2),
% 1.31/1.15 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.31/1.15 thf(f99,definition,(
% 1.31/1.15 spl10_2 <=> ($true = (in @ (sK8 @ sK1 @ sK2) @ sK2))),
% 1.31/1.15 introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition])).
% 1.31/1.15 thf(f142,plain,(
% 1.31/1.15 ($true != (in @ (sK8 @ sK1 @ sK2) @ sK2)) | (sK2 = sK1) | ~spl10_4),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.31/1.15 thf(f139,plain,(
% 1.31/1.15 ($true != (in @ (sK8 @ sK1 @ sK2) @ sK2)) | ($true != $true) | (sK2 = sK1) | ~spl10_4),
% 1.31/1.15 inference(superposition,[status(thm)],[f61,f129])).
% 1.31/1.15 thf(f129,plain,(
% 1.31/1.15 ($true = (in @ (sK9 @ sK1 @ sK2) @ sK1)) | ~spl10_4),
% 1.31/1.15 inference(avatar_component_clause,[status(thm)],[f127])).
% 1.31/1.15 thf(f127,definition,(
% 1.31/1.15 spl10_4 <=> ($true = (in @ (sK9 @ sK1 @ sK2) @ sK1))),
% 1.31/1.15 introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition])).
% 1.31/1.15 thf(f61,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (($true != (in @ (sK9 @ X5 @ X4) @ X5)) | ((in @ (sK8 @ X5 @ X4) @ X4) != $true) | (X4 = X5)) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.31/1.15 thf(f59,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (((in @ (sK8 @ X5 @ X4) @ X4) != $true) | ($true != $true) | ($true != (in @ (sK9 @ X5 @ X4) @ X5)) | (X4 = X5)) )),
% 1.31/1.15 inference(definition_unfolding,[status(thm)],[f44,f38])).
% 1.31/1.15 thf(f38,plain,(
% 1.31/1.15 (setext = $true)),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f21])).
% 1.31/1.15 thf(f44,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (((in @ (sK8 @ X5 @ X4) @ X4) != $true) | (X4 = X5) | ($true != (in @ (sK9 @ X5 @ X4) @ X5)) | (setext != $true)) )),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f31])).
% 1.31/1.15 thf(f31,plain,(
% 1.31/1.15 ((setext = $true) | (! [X2 : $i] : (((in @ X2 @ sK7) != $true) | ($true = (in @ X2 @ sK6))) & (sK6 != sK7) & ! [X3 : $i] : (($true = (in @ X3 @ sK7)) | ($true != (in @ X3 @ sK6))))) & (! [X4 : $i,X5 : $i] : ((($true = (in @ (sK8 @ X5 @ X4) @ X5)) & ((in @ (sK8 @ X5 @ X4) @ X4) != $true)) | (X4 = X5) | (($true != (in @ (sK9 @ X5 @ X4) @ X5)) & ($true = (in @ (sK9 @ X5 @ X4) @ X4)))) | (setext != $true))),
% 1.31/1.15 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f27,f30,f29,f28])).
% 1.31/1.15 thf(f28,plain,(
% 1.31/1.15 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & (X0 != X1) & ! [X3 : $i] : (($true = (in @ X3 @ X1)) | ($true != (in @ X3 @ X0)))) => (! [X2 : $i] : (((in @ X2 @ sK7) != $true) | ($true = (in @ X2 @ sK6))) & (sK6 != sK7) & ! [X3 : $i] : (($true = (in @ X3 @ sK7)) | ($true != (in @ X3 @ sK6))))),
% 1.31/1.15 introduced(definition,[],[choice_axiom])).
% 1.31/1.15 thf(f29,plain,(
% 1.31/1.15 ! [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ X5) = $true) & ($true != (in @ X6 @ X4))) => (($true = (in @ (sK8 @ X5 @ X4) @ X5)) & ((in @ (sK8 @ X5 @ X4) @ X4) != $true)))),
% 1.31/1.15 introduced(definition,[],[choice_axiom])).
% 1.31/1.15 thf(f30,plain,(
% 1.31/1.15 ! [X4 : $i,X5 : $i] : (? [X7 : $i] : (($true != (in @ X7 @ X5)) & ($true = (in @ X7 @ X4))) => (($true != (in @ (sK9 @ X5 @ X4) @ X5)) & ($true = (in @ (sK9 @ X5 @ X4) @ X4))))),
% 1.31/1.15 introduced(definition,[],[choice_axiom])).
% 1.31/1.15 thf(f27,plain,(
% 1.31/1.15 ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & (X0 != X1) & ! [X3 : $i] : (($true = (in @ X3 @ X1)) | ($true != (in @ X3 @ X0))))) & (! [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ X5) = $true) & ($true != (in @ X6 @ X4))) | (X4 = X5) | ? [X7 : $i] : (($true != (in @ X7 @ X5)) & ($true = (in @ X7 @ X4)))) | (setext != $true))),
% 1.31/1.15 inference(rectify,[status(thm)],[f26])).
% 1.31/1.15 thf(f26,plain,(
% 1.31/1.15 ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & (X0 != X1) & ! [X3 : $i] : (($true = (in @ X3 @ X1)) | ($true != (in @ X3 @ X0))))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | (X0 = X1) | ? [X3 : $i] : (($true != (in @ X3 @ X1)) & ($true = (in @ X3 @ X0)))) | (setext != $true))),
% 1.31/1.15 inference(nnf_transformation,[status(thm)],[f17])).
% 1.31/1.15 thf(f17,plain,(
% 1.31/1.15 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | (X0 = X1) | ? [X3 : $i] : (($true != (in @ X3 @ X1)) & ($true = (in @ X3 @ X0))))),
% 1.31/1.15 inference(flattening,[status(thm)],[f16])).
% 1.31/1.15 thf(f16,plain,(
% 1.31/1.15 ! [X1 : $i,X0 : $i] : (((X0 = X1) | ? [X3 : $i] : (($true != (in @ X3 @ X1)) & ($true = (in @ X3 @ X0)))) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) <=> (setext = $true)),
% 1.31/1.15 inference(ennf_transformation,[status(thm)],[f9])).
% 1.31/1.15 thf(f9,plain,(
% 1.31/1.15 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => (! [X3 : $i] : (($true = (in @ X3 @ X0)) => ($true = (in @ X3 @ X1))) => (X0 = X1))) <=> (setext = $true)),
% 1.31/1.15 inference(fool_elimination,[status(thm)],[f8])).
% 1.31/1.15 thf(f8,plain,(
% 1.31/1.15 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))),
% 1.31/1.15 inference(rectify,[status(thm)],[f1])).
% 1.31/1.15 thf(f1,axiom,(
% 1.31/1.15 (setext = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 1.31/1.15 file('/export/starexec/sandbox/tmp/tmp.hBT4Y3P8o9/DTF2THF_16002.p',setext)).
% 1.31/1.15 thf(f135,plain,(
% 1.31/1.15 spl10_5 | ~spl10_2),
% 1.31/1.15 inference(avatar_split_clause,[status(thm)],[f124,f99,f131])).
% 1.31/1.15 thf(f131,definition,(
% 1.31/1.15 spl10_5 <=> ((in @ (sK9 @ sK1 @ sK2) @ sK0) = $true)),
% 1.31/1.15 introduced(definition,[new_symbols(naming,[spl10_5])],[avatar_definition])).
% 1.31/1.15 thf(f124,plain,(
% 1.31/1.15 ((in @ (sK9 @ sK1 @ sK2) @ sK0) = $true) | ~spl10_2),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.31/1.15 thf(f122,plain,(
% 1.31/1.15 ((in @ (sK9 @ sK1 @ sK2) @ sK0) = $true) | ($true != $true) | ~spl10_2),
% 1.31/1.15 inference(superposition,[status(thm)],[f69,f121])).
% 1.31/1.15 thf(f121,plain,(
% 1.31/1.15 ($true = (in @ (sK9 @ sK1 @ sK2) @ sK2)) | ~spl10_2),
% 1.31/1.15 inference(subsumption_resolution,[status(thm)],[f118,f34])).
% 1.31/1.15 thf(f118,plain,(
% 1.31/1.15 ($true = (in @ (sK9 @ sK1 @ sK2) @ sK2)) | (sK2 = sK1) | ~spl10_2),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.31/1.15 thf(f117,plain,(
% 1.31/1.15 ($true = (in @ (sK9 @ sK1 @ sK2) @ sK2)) | ($true != $true) | (sK2 = sK1) | ~spl10_2),
% 1.31/1.15 inference(superposition,[status(thm)],[f64,f100])).
% 1.31/1.15 thf(f64,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (((in @ (sK8 @ X5 @ X4) @ X4) != $true) | ($true = (in @ (sK9 @ X5 @ X4) @ X4)) | (X4 = X5)) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.31/1.15 thf(f60,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (($true != $true) | (X4 = X5) | ($true = (in @ (sK9 @ X5 @ X4) @ X4)) | ((in @ (sK8 @ X5 @ X4) @ X4) != $true)) )),
% 1.31/1.15 inference(definition_unfolding,[status(thm)],[f43,f38])).
% 1.31/1.15 thf(f43,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (((in @ (sK8 @ X5 @ X4) @ X4) != $true) | (X4 = X5) | ($true = (in @ (sK9 @ X5 @ X4) @ X4)) | (setext != $true)) )),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f31])).
% 1.31/1.15 thf(f69,plain,(
% 1.31/1.15 ( ! [X0 : $i] : (($true != (in @ X0 @ sK2)) | ($true = (in @ X0 @ sK0))) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.31/1.15 thf(f66,plain,(
% 1.31/1.15 ( ! [X0 : $i] : (($true = (in @ X0 @ sK0)) | ($true != $true) | ($true != (in @ X0 @ sK2))) )),
% 1.31/1.15 inference(superposition,[status(thm)],[f62,f35])).
% 1.31/1.15 thf(f35,plain,(
% 1.31/1.15 ($true = (in @ sK2 @ (powerset @ sK0)))),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f21])).
% 1.31/1.15 thf(f62,plain,(
% 1.31/1.15 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X0))) | ($true = (in @ X1 @ X0)) | ((in @ X1 @ X2) != $true)) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.31/1.15 thf(f50,plain,(
% 1.31/1.15 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X2 @ (powerset @ X0))) | ($true = (in @ X1 @ X0)) | ((in @ X1 @ X2) != $true)) )),
% 1.31/1.15 inference(definition_unfolding,[status(thm)],[f42,f32])).
% 1.31/1.15 thf(f32,plain,(
% 1.31/1.15 (powersetE = $true)),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f21])).
% 1.31/1.15 thf(f42,plain,(
% 1.31/1.15 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) | ((in @ X1 @ X2) != $true) | ($true != (in @ X2 @ (powerset @ X0))) | (powersetE != $true)) )),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f25])).
% 1.31/1.15 thf(f25,plain,(
% 1.31/1.15 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ((in @ X1 @ X2) != $true) | ($true != (in @ X2 @ (powerset @ X0)))) | (powersetE != $true)) & ((powersetE = $true) | (($true != (in @ sK4 @ sK3)) & ((in @ sK4 @ sK5) = $true) & ($true = (in @ sK5 @ (powerset @ sK3)))))),
% 1.31/1.15 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f23,f24])).
% 1.31/1.15 thf(f24,plain,(
% 1.31/1.15 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) & ($true = (in @ X4 @ X5)) & ($true = (in @ X5 @ (powerset @ X3)))) => (($true != (in @ sK4 @ sK3)) & ((in @ sK4 @ sK5) = $true) & ($true = (in @ sK5 @ (powerset @ sK3))))),
% 1.31/1.15 introduced(definition,[],[choice_axiom])).
% 1.31/1.15 thf(f23,plain,(
% 1.31/1.15 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ((in @ X1 @ X2) != $true) | ($true != (in @ X2 @ (powerset @ X0)))) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) & ($true = (in @ X4 @ X5)) & ($true = (in @ X5 @ (powerset @ X3)))))),
% 1.31/1.15 inference(rectify,[status(thm)],[f22])).
% 1.31/1.15 thf(f22,plain,(
% 1.31/1.15 (! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) = $true) | ($true != (in @ X0 @ X1)) | ($true != (in @ X1 @ (powerset @ X2)))) | (powersetE != $true)) & ((powersetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) & ($true = (in @ X0 @ X1)) & ($true = (in @ X1 @ (powerset @ X2)))))),
% 1.31/1.15 inference(nnf_transformation,[status(thm)],[f15])).
% 1.31/1.15 thf(f15,plain,(
% 1.31/1.15 ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) = $true) | ($true != (in @ X0 @ X1)) | ($true != (in @ X1 @ (powerset @ X2)))) <=> (powersetE = $true)),
% 1.31/1.15 inference(flattening,[status(thm)],[f14])).
% 1.31/1.15 thf(f14,plain,(
% 1.31/1.15 (powersetE = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2) = $true) | ($true != (in @ X0 @ X1))) | ($true != (in @ X1 @ (powerset @ X2))))),
% 1.31/1.15 inference(ennf_transformation,[status(thm)],[f7])).
% 1.31/1.15 thf(f7,plain,(
% 1.31/1.15 (powersetE = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X1 @ (powerset @ X2))) => (($true = (in @ X0 @ X1)) => ((in @ X0 @ X2) = $true)))),
% 1.31/1.15 inference(fool_elimination,[status(thm)],[f6])).
% 1.31/1.15 thf(f6,plain,(
% 1.31/1.15 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X2)) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = powersetE)),
% 1.31/1.15 inference(rectify,[status(thm)],[f2])).
% 1.31/1.15 thf(f2,axiom,(
% 1.31/1.15 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 1.31/1.15 file('/export/starexec/sandbox/tmp/tmp.hBT4Y3P8o9/DTF2THF_16002.p',powersetE)).
% 1.31/1.15 thf(f134,plain,(
% 1.31/1.15 spl10_4 | ~spl10_5 | ~spl10_2),
% 1.31/1.15 inference(avatar_split_clause,[status(thm)],[f125,f99,f131,f127])).
% 1.31/1.15 thf(f125,plain,(
% 1.31/1.15 ($true = (in @ (sK9 @ sK1 @ sK2) @ sK1)) | ((in @ (sK9 @ sK1 @ sK2) @ sK0) != $true) | ~spl10_2),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.31/1.15 thf(f123,plain,(
% 1.31/1.15 ((in @ (sK9 @ sK1 @ sK2) @ sK0) != $true) | ($true = (in @ (sK9 @ sK1 @ sK2) @ sK1)) | ($true != $true) | ~spl10_2),
% 1.31/1.15 inference(superposition,[status(thm)],[f36,f121])).
% 1.31/1.15 thf(f36,plain,(
% 1.31/1.15 ( ! [X3 : $i] : (((in @ X3 @ sK2) != $true) | ((in @ X3 @ sK0) != $true) | ($true = (in @ X3 @ sK1))) )),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f21])).
% 1.31/1.15 thf(f114,plain,(
% 1.31/1.15 spl10_3 | ~spl10_1),
% 1.31/1.15 inference(avatar_split_clause,[status(thm)],[f107,f95,f110])).
% 1.31/1.15 thf(f110,definition,(
% 1.31/1.15 spl10_3 <=> ($true = (in @ (sK8 @ sK1 @ sK2) @ sK0))),
% 1.31/1.15 introduced(definition,[new_symbols(naming,[spl10_3])],[avatar_definition])).
% 1.31/1.15 thf(f95,definition,(
% 1.31/1.15 spl10_1 <=> ((in @ (sK8 @ sK1 @ sK2) @ sK1) = $true)),
% 1.31/1.15 introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition])).
% 1.31/1.15 thf(f107,plain,(
% 1.31/1.15 ($true = (in @ (sK8 @ sK1 @ sK2) @ sK0)) | ~spl10_1),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.31/1.15 thf(f105,plain,(
% 1.31/1.15 ($true != $true) | ($true = (in @ (sK8 @ sK1 @ sK2) @ sK0)) | ~spl10_1),
% 1.31/1.15 inference(superposition,[status(thm)],[f68,f97])).
% 1.31/1.15 thf(f97,plain,(
% 1.31/1.15 ((in @ (sK8 @ sK1 @ sK2) @ sK1) = $true) | ~spl10_1),
% 1.31/1.15 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.31/1.15 thf(f68,plain,(
% 1.31/1.15 ( ! [X0 : $i] : (($true != (in @ X0 @ sK1)) | ($true = (in @ X0 @ sK0))) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.31/1.15 thf(f67,plain,(
% 1.31/1.15 ( ! [X0 : $i] : (($true != (in @ X0 @ sK1)) | ($true != $true) | ($true = (in @ X0 @ sK0))) )),
% 1.31/1.15 inference(superposition,[status(thm)],[f62,f37])).
% 1.31/1.15 thf(f37,plain,(
% 1.31/1.15 ((in @ sK1 @ (powerset @ sK0)) = $true)),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f21])).
% 1.31/1.15 thf(f113,plain,(
% 1.31/1.15 spl10_2 | ~spl10_3 | ~spl10_1),
% 1.31/1.15 inference(avatar_split_clause,[status(thm)],[f108,f95,f110,f99])).
% 1.31/1.15 thf(f108,plain,(
% 1.31/1.15 ($true != (in @ (sK8 @ sK1 @ sK2) @ sK0)) | ($true = (in @ (sK8 @ sK1 @ sK2) @ sK2)) | ~spl10_1),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.31/1.15 thf(f106,plain,(
% 1.31/1.15 ($true = (in @ (sK8 @ sK1 @ sK2) @ sK2)) | ($true != $true) | ($true != (in @ (sK8 @ sK1 @ sK2) @ sK0)) | ~spl10_1),
% 1.31/1.15 inference(superposition,[status(thm)],[f33,f97])).
% 1.31/1.15 thf(f33,plain,(
% 1.31/1.15 ( ! [X4 : $i] : (($true != (in @ X4 @ sK1)) | ($true = (in @ X4 @ sK2)) | ($true != (in @ X4 @ sK0))) )),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f21])).
% 1.31/1.15 thf(f104,plain,(
% 1.31/1.15 spl10_1),
% 1.31/1.15 inference(avatar_split_clause,[status(thm)],[f103,f95])).
% 1.31/1.15 thf(f103,plain,(
% 1.31/1.15 ((in @ (sK8 @ sK1 @ sK2) @ sK1) = $true)),
% 1.31/1.15 inference(subsumption_resolution,[status(thm)],[f89,f34])).
% 1.31/1.15 thf(f89,plain,(
% 1.31/1.15 (sK2 = sK1) | ((in @ (sK8 @ sK1 @ sK2) @ sK1) = $true)),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.31/1.15 thf(f88,plain,(
% 1.31/1.15 (sK2 = sK1) | ((in @ (sK8 @ sK1 @ sK2) @ sK1) = $true) | ($true != $true)),
% 1.31/1.15 inference(duplicate_literal_removal,[status(thm)],[f85])).
% 1.31/1.15 thf(f85,plain,(
% 1.31/1.15 (sK2 = sK1) | ((in @ (sK8 @ sK1 @ sK2) @ sK1) = $true) | ($true != $true) | (sK2 = sK1) | ((in @ (sK8 @ sK1 @ sK2) @ sK1) = $true)),
% 1.31/1.15 inference(superposition,[status(thm)],[f65,f81])).
% 1.31/1.15 thf(f81,plain,(
% 1.31/1.15 ( ! [X0 : $i] : (($true = (in @ (sK9 @ X0 @ sK2) @ sK1)) | ((in @ (sK8 @ X0 @ sK2) @ X0) = $true) | (sK2 = X0)) )),
% 1.31/1.15 inference(subsumption_resolution,[status(thm)],[f78,f79])).
% 1.31/1.15 thf(f79,plain,(
% 1.31/1.15 ( ! [X0 : $i] : (((in @ (sK8 @ X0 @ sK2) @ X0) = $true) | (sK2 = X0) | ($true = (in @ (sK9 @ X0 @ sK2) @ sK0))) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.31/1.15 thf(f74,plain,(
% 1.31/1.15 ( ! [X0 : $i] : (((in @ (sK8 @ X0 @ sK2) @ X0) = $true) | ($true = (in @ (sK9 @ X0 @ sK2) @ sK0)) | (sK2 = X0) | ($true != $true)) )),
% 1.31/1.15 inference(superposition,[status(thm)],[f69,f63])).
% 1.31/1.15 thf(f63,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (($true = (in @ (sK9 @ X5 @ X4) @ X4)) | (X4 = X5) | ($true = (in @ (sK8 @ X5 @ X4) @ X5))) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.31/1.15 thf(f58,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (($true = (in @ (sK8 @ X5 @ X4) @ X5)) | ($true = (in @ (sK9 @ X5 @ X4) @ X4)) | ($true != $true) | (X4 = X5)) )),
% 1.31/1.15 inference(definition_unfolding,[status(thm)],[f45,f38])).
% 1.31/1.15 thf(f45,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (($true = (in @ (sK8 @ X5 @ X4) @ X5)) | (X4 = X5) | ($true = (in @ (sK9 @ X5 @ X4) @ X4)) | (setext != $true)) )),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f31])).
% 1.31/1.15 thf(f78,plain,(
% 1.31/1.15 ( ! [X0 : $i] : ((sK2 = X0) | ($true = (in @ (sK9 @ X0 @ sK2) @ sK1)) | ($true != (in @ (sK9 @ X0 @ sK2) @ sK0)) | ((in @ (sK8 @ X0 @ sK2) @ X0) = $true)) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.31/1.15 thf(f75,plain,(
% 1.31/1.15 ( ! [X0 : $i] : (($true != (in @ (sK9 @ X0 @ sK2) @ sK0)) | (sK2 = X0) | ($true != $true) | ($true = (in @ (sK9 @ X0 @ sK2) @ sK1)) | ((in @ (sK8 @ X0 @ sK2) @ X0) = $true)) )),
% 1.31/1.15 inference(superposition,[status(thm)],[f36,f63])).
% 1.31/1.15 thf(f65,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (($true != (in @ (sK9 @ X5 @ X4) @ X5)) | ($true = (in @ (sK8 @ X5 @ X4) @ X5)) | (X4 = X5)) )),
% 1.31/1.15 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.31/1.15 thf(f57,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | ($true = (in @ (sK8 @ X5 @ X4) @ X5)) | ($true != (in @ (sK9 @ X5 @ X4) @ X5)) | ($true != $true)) )),
% 1.31/1.15 inference(definition_unfolding,[status(thm)],[f46,f38])).
% 1.31/1.15 thf(f46,plain,(
% 1.31/1.15 ( ! [X4 : $i,X5 : $i] : (($true = (in @ (sK8 @ X5 @ X4) @ X5)) | (X4 = X5) | ($true != (in @ (sK9 @ X5 @ X4) @ X5)) | (setext != $true)) )),
% 1.31/1.15 inference(cnf_transformation,[status(thm)],[f31])).
% 1.31/1.15 % SZS output end Proof for DTF2THF_16002
% 1.31/1.15 % (16107)------------------------------
% 1.31/1.15 % (16107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.15 % (16107)Termination reason: Refutation
% 1.31/1.15
% 1.31/1.15 % (16107)Memory used [KB]: 5628
% 1.31/1.15 % (16107)Time elapsed: 0.013 s
% 1.31/1.15 % (16107)Instructions burned: 16 (million)
% 1.31/1.15 % (16107)------------------------------
% 1.31/1.15 % (16107)------------------------------
% 1.31/1.15 % (16100)Success in time 0.027 s
%------------------------------------------------------------------------------