%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU689^2 : 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 : n027.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 09:36:25 AM UTC 2026
% Result : Theorem 1.41s 1.21s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 83 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 1560 ( 481 equ; 0 cnn)
% Maximal formula atoms : 16 ( 18 avg)
% Number of connectives : 1912 ( 299 ~; 273 |; 88 &;1181 @)
% ( 6 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 15 con; 0-4 aty)
% Number of variables : 345 ( 16 ^; 272 !; 57 ?; 345 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
cartprod: $i > $i > $i ).
thf(func_def_6,type,
breln: $i > $i > $i > $o ).
thf(func_def_17,type,
sK3: $i > $o ).
thf(func_def_19,type,
sK5: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_20,type,
sK6: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_25,type,
sK11: $i > $i > $i ).
thf(func_def_30,type,
ph15:
!>[X0: $tType] : X0 ).
thf(f190,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f170,f189]) ).
thf(f189,plain,
~ spl14_3,
inference(avatar_contradiction_clause,[status(thm)],[f188]) ).
thf(f188,plain,
( $false
| ~ spl14_3 ),
inference(subsumption_resolution,[status(thm)],[f187,f46]) ).
thf(f46,plain,
( $true
!= ( subset @ sK7 @ sK10 ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
= ( breln @ sK8 @ sK9 @ sK7 ) )
& ( $true
= ( breln @ sK8 @ sK9 @ sK10 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK8 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK7 )
!= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ sK10 )
= $true )
| ( ( in @ X5 @ sK9 )
!= $true ) ) )
& ( $true
!= ( subset @ sK7 @ sK10 ) )
& ( brelnall1 = $true )
& ( subsetI1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f19,f29,f28]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X1 @ X2 @ X0 ) )
& ? [X3: $i] :
( ( $true
= ( breln @ X1 @ X2 @ X3 ) )
& ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true )
| ( ( in @ X5 @ X2 )
!= $true ) ) )
& ( $true
!= ( subset @ X0 @ X3 ) ) ) )
=> ( ( $true
= ( breln @ sK8 @ sK9 @ sK7 ) )
& ? [X3: $i] :
( ( $true
= ( breln @ sK8 @ sK9 @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK8 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK7 )
!= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true )
| ( ( in @ X5 @ sK9 )
!= $true ) ) )
& ( $true
!= ( subset @ sK7 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X3: $i] :
( ( $true
= ( breln @ sK8 @ sK9 @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK8 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK7 )
!= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true )
| ( ( in @ X5 @ sK9 )
!= $true ) ) )
& ( $true
!= ( subset @ sK7 @ X3 ) ) )
=> ( ( $true
= ( breln @ sK8 @ sK9 @ sK10 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK8 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK7 )
!= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ sK10 )
= $true )
| ( ( in @ X5 @ sK9 )
!= $true ) ) )
& ( $true
!= ( subset @ sK7 @ sK10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X1 @ X2 @ X0 ) )
& ? [X3: $i] :
( ( $true
= ( breln @ X1 @ X2 @ X3 ) )
& ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true )
| ( ( in @ X5 @ X2 )
!= $true ) ) )
& ( $true
!= ( subset @ X0 @ X3 ) ) ) )
& ( brelnall1 = $true )
& ( subsetI1 = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( subset @ X0 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
| ( ( in @ X5 @ X2 )
!= $true ) )
| ( ( in @ X4 @ X1 )
!= $true ) )
& ( $true
= ( breln @ X1 @ X2 @ X3 ) ) )
& ( $true
= ( breln @ X1 @ X2 @ X0 ) ) )
& ( brelnall1 = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( subsetI1 = $true )
=> ( ( brelnall1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X1 @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( breln @ X1 @ X2 @ X3 ) )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ! [X5: $i] :
( ( ( in @ X5 @ X2 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true ) ) ) )
=> ( $true
= ( subset @ X0 @ X3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( subsetI1
=> ( brelnall1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( breln @ X1 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X0 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( subset @ X0 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( subsetI1
=> ( brelnall1
=> ! [X4: $i,X0: $i,X1: $i] :
( ( breln @ X0 @ X1 @ X4 )
=> ! [X7: $i] :
( ( breln @ X0 @ X1 @ X7 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X2 @ X6 ) @ X4 )
=> ( in @ ( kpair @ X2 @ X6 ) @ X7 ) ) ) )
=> ( subset @ X4 @ X7 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( subsetI1
=> ( brelnall1
=> ! [X4: $i,X0: $i,X1: $i] :
( ( breln @ X0 @ X1 @ X4 )
=> ! [X7: $i] :
( ( breln @ X0 @ X1 @ X7 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X2 @ X6 ) @ X4 )
=> ( in @ ( kpair @ X2 @ X6 ) @ X7 ) ) ) )
=> ( subset @ X4 @ X7 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.z13JXQQSqE/DTF2THF_17594.p',subbreln) ).
thf(f187,plain,
( ( $true
= ( subset @ sK7 @ sK10 ) )
| ~ spl14_3 ),
inference(equality_resolution,[status(thm)],[f182]) ).
thf(f182,plain,
( ! [X0: $i] :
( ( ( sK11 @ sK7 @ X0 )
!= ( sK11 @ sK7 @ sK10 ) )
| ( ( subset @ sK7 @ X0 )
= $true ) )
| ~ spl14_3 ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ! [X0: $i] :
( ( ( sK11 @ sK7 @ X0 )
!= ( sK11 @ sK7 @ sK10 ) )
| ( $true != $true )
| ( ( subset @ sK7 @ X0 )
= $true ) )
| ~ spl14_3 ),
inference(superposition,[status(thm)],[f169,f70]) ).
thf(f70,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
= $true )
| ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( $true != $true )
| ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f52,f44]) ).
thf(f44,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f52,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( $true
!= ( in @ ( sK11 @ X1 @ X0 ) @ X0 ) )
& ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ( ( $true
!= ( subset @ sK13 @ sK12 ) )
& ! [X5: $i] :
( ( $true
= ( in @ X5 @ sK12 ) )
| ( $true
!= ( in @ X5 @ sK13 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f32,f34,f33]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( $true
!= ( in @ ( sK11 @ X1 @ X0 ) @ X0 ) )
& ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
& ! [X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
| ( $true
!= ( in @ X5 @ X4 ) ) ) )
=> ( ( $true
!= ( subset @ sK13 @ sK12 ) )
& ! [X5: $i] :
( ( $true
= ( in @ X5 @ sK12 ) )
| ( $true
!= ( in @ X5 @ sK13 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
& ! [X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
| ( $true
!= ( in @ X5 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
<=> ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( $true
= ( subset @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
file('/export/starexec/sandbox/tmp/tmp.z13JXQQSqE/DTF2THF_17594.p',subsetI1) ).
thf(f169,plain,
( ! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK7 ) )
| ( ( sK11 @ sK7 @ sK10 )
!= X1 ) )
| ~ spl14_3 ),
inference(avatar_component_clause,[status(thm)],[f168]) ).
thf(f168,definition,
( spl14_3
<=> ! [X1: $i] :
( ( ( sK11 @ sK7 @ sK10 )
!= X1 )
| ( $true
!= ( in @ X1 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl14_3])],[avatar_definition]) ).
thf(f170,plain,
( spl14_3
| spl14_3 ),
inference(avatar_split_clause,[status(thm)],[f166,f168,f168]) ).
thf(f166,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ sK7 ) )
| ( ( sK11 @ sK7 @ sK10 )
!= X1 )
| ( ( sK11 @ sK7 @ sK10 )
!= X0 )
| ( $true
!= ( in @ X1 @ sK7 ) ) ),
inference(subsumption_resolution,[status(thm)],[f165,f46]) ).
thf(f165,plain,
! [X0: $i,X1: $i] :
( ( ( sK11 @ sK7 @ sK10 )
!= X1 )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
= ( subset @ sK7 @ sK10 ) )
| ( $true
!= ( in @ X1 @ sK7 ) )
| ( ( sK11 @ sK7 @ sK10 )
!= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f164]) ).
thf(f164,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ sK7 @ sK10 ) )
| ( $true != $true )
| ( $true
!= ( in @ X1 @ sK7 ) )
| ( ( sK11 @ sK7 @ sK10 )
!= X0 )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( ( sK11 @ sK7 @ sK10 )
!= X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f163]) ).
thf(f163,plain,
! [X0: $i,X1: $i] :
( ( ( sK11 @ sK7 @ sK10 )
!= X1 )
| ( $true != $true )
| ( $true
= ( subset @ sK7 @ sK10 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ X1 @ sK7 ) )
| ( $true
= ( subset @ sK7 @ sK10 ) )
| ( ( sK11 @ sK7 @ sK10 )
!= X0 ) ),
inference(superposition,[status(thm)],[f154,f70]) ).
thf(f154,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK11 @ X0 @ sK10 ) @ sK7 ) )
| ( ( sK11 @ X0 @ sK10 )
!= X2 )
| ( $true
!= ( in @ X1 @ sK7 ) )
| ( $true
!= ( in @ X2 @ sK7 ) )
| ( ( subset @ X0 @ sK10 )
= $true )
| ( ( sK11 @ X0 @ sK10 )
!= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X2 @ sK7 ) )
| ( ( sK11 @ X0 @ sK10 )
!= X1 )
| ( $true
!= ( in @ X1 @ sK7 ) )
| ( $true
!= ( in @ ( sK11 @ X0 @ sK10 ) @ sK7 ) )
| ( ( subset @ X0 @ sK10 )
= $true )
| ( ( sK11 @ X0 @ sK10 )
!= X2 ) ),
inference(superposition,[status(thm)],[f69,f152]) ).
thf(f152,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ sK10 ) )
| ( $true
!= ( in @ X2 @ sK7 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ X1 @ sK7 ) )
| ( X0 != X1 )
| ( X1 != X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f151]) ).
thf(f151,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ sK7 ) )
| ( $true
!= ( in @ X2 @ sK7 ) )
| ( X0 != X1 )
| ( $true
= ( in @ X1 @ sK10 ) )
| ( X1 != X2 )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f147]) ).
thf(f147,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X1 != X2 )
| ( $true
!= ( in @ X1 @ sK7 ) )
| ( X0 != X1 )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ X2 @ sK7 ) )
| ( $true
!= ( in @ X1 @ sK7 ) )
| ( $true
= ( in @ X1 @ sK10 ) ) ),
inference(superposition,[status(thm)],[f145,f49]) ).
thf(f49,plain,
( $true
= ( breln @ sK8 @ sK9 @ sK7 ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( breln @ sK8 @ sK9 @ X1 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( X0 != X3 )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( X0 = X3 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( X0 != X2 )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( breln @ sK8 @ sK9 @ X1 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( ( X0 != X3 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( breln @ sK8 @ sK9 @ X1 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( X0 != X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ X3 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( X0 != X2 )
| ( $true
!= ( breln @ sK8 @ sK9 @ X1 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( in @ X0 @ sK7 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f141]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( breln @ sK8 @ sK9 @ X1 ) )
| ( $true != $true )
| ( X0 != X2 )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ X3 ) )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f140]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( breln @ sK8 @ sK9 @ X1 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( breln @ sK8 @ sK9 @ X1 ) )
| ( X0 != X2 )
| ( $true
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ X3 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(superposition,[status(thm)],[f139,f71]) ).
thf(f71,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
= ( in @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) @ X8 ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true )
| ( $true
= ( X10 @ X13 ) )
| ( $true
!= ( in @ X13 @ X9 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
= ( X10 @ X13 ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true )
| ( $true != $true )
| ( $true
= ( in @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) @ X8 ) )
| ( $true
!= ( in @ X13 @ X9 ) ) ),
inference(definition_unfolding,[status(thm)],[f36,f45]) ).
thf(f45,plain,
brelnall1 = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f36,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
= ( in @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) @ X8 ) )
| ( $true
= ( X10 @ X13 ) )
| ( $true
!= ( in @ X13 @ X9 ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true )
| ( brelnall1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( brelnall1 = $true )
| ( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ! [X5: $i] :
( ( $true
= ( sK3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) ) )
& ( ( sK3 @ sK4 )
!= $true )
& ( $true
= ( in @ sK4 @ sK2 ) )
& ( ( breln @ sK0 @ sK1 @ sK2 )
= $true ) ) )
& ( ! [X7: $i,X8: $i,X9: $i] :
( ! [X10: $i > $o] :
( ( ( $true
= ( in @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X7 ) )
& ( $true
!= ( X10 @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) ) ) )
& ( ( in @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) ) @ X9 )
= $true )
& ( $true
= ( in @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) @ X8 ) ) )
| ! [X13: $i] :
( ( $true
= ( X10 @ X13 ) )
| ( $true
!= ( in @ X13 @ X9 ) ) ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true ) )
| ( brelnall1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f21,f26,f25,f24,f23,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) ) )
& ? [X6: $i] :
( ( ( X3 @ X6 )
!= $true )
& ( $true
= ( in @ X6 @ X2 ) ) ) )
& ( $true
= ( breln @ X0 @ X1 @ X2 ) ) )
=> ( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) ) )
& ? [X6: $i] :
( ( ( X3 @ X6 )
!= $true )
& ( $true
= ( in @ X6 @ sK2 ) ) ) )
& ( ( breln @ sK0 @ sK1 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) ) )
& ? [X6: $i] :
( ( ( X3 @ X6 )
!= $true )
& ( $true
= ( in @ X6 @ sK2 ) ) ) )
=> ( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ! [X5: $i] :
( ( $true
= ( sK3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( sK3 @ X6 ) )
& ( $true
= ( in @ X6 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X6: $i] :
( ( $true
!= ( sK3 @ X6 ) )
& ( $true
= ( in @ X6 @ sK2 ) ) )
=> ( ( ( sK3 @ sK4 )
!= $true )
& ( $true
= ( in @ sK4 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X7: $i,X8: $i,X9: $i,X10: $i > $o] :
( ? [X11: $i] :
( ( $true
= ( in @ X11 @ X7 ) )
& ? [X12: $i] :
( ( $true
!= ( X10 @ ( kpair @ X11 @ X12 ) ) )
& ( $true
= ( in @ ( kpair @ X11 @ X12 ) @ X9 ) )
& ( ( in @ X12 @ X8 )
= $true ) ) )
=> ( ( $true
= ( in @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X7 ) )
& ? [X12: $i] :
( ( $true
!= ( X10 @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X12 ) ) )
& ( ( in @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X12 ) @ X9 )
= $true )
& ( ( in @ X12 @ X8 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
! [X7: $i,X8: $i,X9: $i,X10: $i > $o] :
( ? [X12: $i] :
( ( $true
!= ( X10 @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X12 ) ) )
& ( ( in @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X12 ) @ X9 )
= $true )
& ( ( in @ X12 @ X8 )
= $true ) )
=> ( ( $true
!= ( X10 @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) ) ) )
& ( ( in @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) ) @ X9 )
= $true )
& ( $true
= ( in @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) @ X8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ( brelnall1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) ) )
& ? [X6: $i] :
( ( ( X3 @ X6 )
!= $true )
& ( $true
= ( in @ X6 @ X2 ) ) ) )
& ( $true
= ( breln @ X0 @ X1 @ X2 ) ) ) )
& ( ! [X7: $i,X8: $i,X9: $i] :
( ! [X10: $i > $o] :
( ? [X11: $i] :
( ( $true
= ( in @ X11 @ X7 ) )
& ? [X12: $i] :
( ( $true
!= ( X10 @ ( kpair @ X11 @ X12 ) ) )
& ( $true
= ( in @ ( kpair @ X11 @ X12 ) @ X9 ) )
& ( ( in @ X12 @ X8 )
= $true ) ) )
| ! [X13: $i] :
( ( $true
= ( X10 @ X13 ) )
| ( $true
!= ( in @ X13 @ X9 ) ) ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true ) )
| ( brelnall1 != $true ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( brelnall1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) ) )
& ? [X6: $i] :
( ( ( X3 @ X6 )
!= $true )
& ( $true
= ( in @ X6 @ X2 ) ) ) )
& ( $true
= ( breln @ X0 @ X1 @ X2 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i > $o] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
& ? [X5: $i] :
( ( $true
!= ( X3 @ ( kpair @ X4 @ X5 ) ) )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
& ( ( in @ X5 @ X1 )
= $true ) ) )
| ! [X6: $i] :
( ( ( X3 @ X6 )
= $true )
| ( $true
!= ( in @ X6 @ X2 ) ) ) )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) ) )
| ( brelnall1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( brelnall1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i > $o] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
& ? [X5: $i] :
( ( $true
!= ( X3 @ ( kpair @ X4 @ X5 ) ) )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
& ( ( in @ X5 @ X1 )
= $true ) ) )
| ! [X6: $i] :
( ( ( X3 @ X6 )
= $true )
| ( $true
!= ( in @ X6 @ X2 ) ) ) )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i > $o] :
( ! [X6: $i] :
( ( ( X3 @ X6 )
= $true )
| ( $true
!= ( in @ X6 @ X2 ) ) )
| ? [X4: $i] :
( ? [X5: $i] :
( ( $true
!= ( X3 @ ( kpair @ X4 @ X5 ) ) )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
& ( ( in @ X5 @ X1 )
= $true ) )
& ( $true
= ( in @ X4 @ X0 ) ) ) )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) ) )
<=> ( brelnall1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X2 ) )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
=> ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) ) )
=> ! [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
=> ( ( X3 @ X6 )
= $true ) ) ) )
<=> ( brelnall1 = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( brelnall1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( X3 @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( brelnall1
= ( ! [X0: $i,X1: $i,X4: $i] :
( ( breln @ X0 @ X1 @ X4 )
=> ! [X5: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X2 @ X6 ) @ X4 )
=> ( X5 @ ( kpair @ X2 @ X6 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X5 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.z13JXQQSqE/DTF2THF_17594.p',brelnall1) ).
thf(f139,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in
@ ( sK6
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ sK8 )
@ sK9 )
!= $true )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( breln @ sK8 @ X2 @ X1 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( X0 != X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in
@ ( sK6
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ sK8 )
@ sK9 )
!= $true )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $false
= ( X0 = X3 ) )
| ( $true
!= ( breln @ sK8 @ X2 @ X1 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ sK7 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( breln @ sK8 @ X2 @ X1 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in
@ ( sK6
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ sK8 )
@ sK9 )
!= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( X0 != X3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f136]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in
@ ( sK6
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ sK8 )
@ sK9 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( breln @ sK8 @ X2 @ X1 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true != $true )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( breln @ sK8 @ X2 @ X1 ) )
| ( ( in
@ ( sK6
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ sK8 )
@ sK9 )
!= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ X3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f134]) ).
thf(f134,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ X3 ) )
| ( $true
!= ( breln @ sK8 @ X2 @ X1 ) )
| ( $true
!= ( breln @ sK8 @ X2 @ X1 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( ( in
@ ( sK6
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ sK8 )
@ sK9 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ sK10 )
= $true ) ),
inference(superposition,[status(thm)],[f107,f67]) ).
thf(f67,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
= ( in @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X7 ) )
| ( $true
= ( X10 @ X13 ) )
| ( $true
!= ( in @ X13 @ X9 ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
!= ( in @ X13 @ X9 ) )
| ( $true != $true )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true )
| ( $true
= ( in @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X7 ) )
| ( $true
= ( X10 @ X13 ) ) ),
inference(definition_unfolding,[status(thm)],[f39,f45]) ).
thf(f39,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
= ( in @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ X7 ) )
| ( $true
= ( X10 @ X13 ) )
| ( $true
!= ( in @ X13 @ X9 ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true )
| ( brelnall1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in
@ ( sK5
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ X3 )
@ sK8 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( breln @ X3 @ X2 @ X1 ) )
| ( ( in @ X0 @ sK10 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in
@ ( sK6
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ X3 )
@ sK9 )
!= $true ) ),
inference(superposition,[status(thm)],[f47,f75]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair
@ ( sK5
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ X3 )
@ ( sK6
@ ^ [Y0: $i] : ( X0 != Y0 )
@ X1
@ X2
@ X3 ) )
= X0 )
| ( $true
!= ( breln @ X3 @ X2 @ X1 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f66]) ).
thf(f66,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
!= ( X10 @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) ) ) )
| ( $true
!= ( in @ X13 @ X9 ) )
| ( $true
= ( X10 @ X13 ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
!= ( in @ X13 @ X9 ) )
| ( $true
= ( X10 @ X13 ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true )
| ( $true
!= ( X10 @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f45]) ).
thf(f38,plain,
! [X10: $i > $o,X8: $i,X9: $i,X7: $i,X13: $i] :
( ( $true
!= ( X10 @ ( kpair @ ( sK5 @ X10 @ X9 @ X8 @ X7 ) @ ( sK6 @ X10 @ X9 @ X8 @ X7 ) ) ) )
| ( $true
= ( X10 @ X13 ) )
| ( $true
!= ( in @ X13 @ X9 ) )
| ( ( breln @ X7 @ X8 @ X9 )
!= $true )
| ( brelnall1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f47,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK10 )
= $true )
| ( $true
!= ( in @ X4 @ sK8 ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ sK7 )
!= $true )
| ( ( in @ X5 @ sK9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f69,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK11 @ X1 @ X0 ) @ X0 ) )
| ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( $true
!= ( in @ ( sK11 @ X1 @ X0 ) @ X0 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f53,f44]) ).
thf(f53,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( $true
!= ( in @ ( sK11 @ X1 @ X0 ) @ X0 ) )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU689^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n027.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:31:22 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU689^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Functions - Extensionality and Beta Reduction
% 0.16/0.39 % Version : Especial > Reduced > Especial.
% 0.16/0.39 % English : (! A:i.! B:i.! R:i.breln A B R -> (! S:i.breln A B S ->
% 0.16/0.39 % (! x:i.in x A -> (! y:i.in y B -> in (kpair x y) R ->
% 0.16/0.39 % in (kpair x y) S)) -> subset R S))
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC191l [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 1.00 v5.2.0, 0.60 v4.1.0, 0.67 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.16/0.39 % Number of atoms : 24 ( 3 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 9 ( 6 avg)
% 0.16/0.39 % Number of connectives : 63 ( 0 ~; 0 |; 0 &; 47 @)
% 0.16/0.39 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 19 ( 6 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 8 ( 7 usr; 2 con; 0-3 aty)
% 0.16/0.39 % Number of variables : 19 ( 3 ^; 16 !; 0 ?; 19 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=243
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(subset_type,type,
% 0.16/0.39 subset: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1_type,type,
% 0.16/0.39 subsetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1,definition,
% 0.16/0.39 ( subsetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kpair_type,type,
% 0.16/0.39 kpair: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(cartprod_type,type,
% 0.16/0.39 cartprod: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(breln_type,type,
% 0.16/0.39 breln: $i > $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(breln,definition,
% 0.16/0.39 ( breln
% 0.16/0.39 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(brelnall1_type,type,
% 0.16/0.39 brelnall1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(brelnall1,definition,
% 0.16/0.39 ( brelnall1
% 0.16/0.39 = ( ! [A: $i,B: $i,R: $i] :
% 0.16/0.39 ( ( breln @ A @ B @ R )
% 0.16/0.39 => ! [Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.16/0.39 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ R )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subbreln,conjecture,
% 0.16/0.39 ( subsetI1
% 0.16/0.39 => ( brelnall1
% 0.16/0.39 => ! [A: $i,B: $i,R: $i] :
% 0.16/0.39 ( ( breln @ A @ B @ R )
% 0.16/0.39 => ! [S: $i] :
% 0.16/0.39 ( ( breln @ A @ B @ S )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.16/0.39 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.38/1.14 ---- Embedded in THF ---
% 1.38/1.14 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.14 %%% Generated on Tue Feb 24 12:31:22 EST 2026
% 1.38/1.14 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.14 %%% Logic specification used:
% 1.38/1.14 %%% thf(spec, logic, $$dhol).
% 1.38/1.14
% 1.38/1.14 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.z13JXQQSqE/DTF2DTF17594.p
% See solution above
% 1.38/1.14 ------------------------
% 1.38/1.15 ---- Cleaned THF ---
% 1.38/1.15 thf(in_type,type,
% 1.38/1.15 in: $i > $i > $o ).
% 1.38/1.15
% 1.38/1.15 thf(subset_type,type,
% 1.38/1.15 subset: $i > $i > $o ).
% 1.38/1.15
% 1.38/1.15 thf(subsetI1_type,type,
% 1.38/1.15 subsetI1: $o ).
% 1.38/1.15
% 1.38/1.15 thf(subsetI1,definition,
% 1.38/1.15 ( subsetI1
% 1.38/1.15 = ( ! [A: $i,B: $i] :
% 1.38/1.15 ( ! [Xx: $i] :
% 1.38/1.15 ( ( in @ Xx @ A )
% 1.38/1.15 => ( in @ Xx @ B ) )
% 1.38/1.15 => ( subset @ A @ B ) ) ) ) ).
% 1.38/1.15
% 1.38/1.15 thf(kpair_type,type,
% 1.38/1.15 kpair: $i > $i > $i ).
% 1.38/1.15
% 1.38/1.15 thf(cartprod_type,type,
% 1.38/1.15 cartprod: $i > $i > $i ).
% 1.38/1.15
% 1.38/1.15 thf(breln_type,type,
% 1.38/1.15 breln: $i > $i > $i > $o ).
% 1.38/1.15
% 1.38/1.15 thf(breln,definition,
% 1.38/1.15 ( breln
% 1.38/1.15 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.38/1.15
% 1.38/1.15 thf(brelnall1_type,type,
% 1.38/1.15 brelnall1: $o ).
% 1.38/1.15
% 1.38/1.15 thf(brelnall1,definition,
% 1.38/1.15 ( brelnall1
% 1.38/1.15 = ( ! [A: $i,B: $i,R: $i] :
% 1.38/1.15 ( ( breln @ A @ B @ R )
% 1.38/1.15 => ! [Xphi: $i > $o] :
% 1.38/1.15 ( ! [Xx: $i] :
% 1.38/1.15 ( ( in @ Xx @ A )
% 1.38/1.15 => ! [Xy: $i] :
% 1.38/1.15 ( ( in @ Xy @ B )
% 1.38/1.15 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.38/1.15 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 1.38/1.15 => ! [Xx: $i] :
% 1.38/1.15 ( ( in @ Xx @ R )
% 1.38/1.15 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.38/1.15
% 1.38/1.15 thf(subbreln,conjecture,
% 1.38/1.15 ( subsetI1
% 1.38/1.15 => ( brelnall1
% 1.38/1.15 => ! [A: $i,B: $i,R: $i] :
% 1.38/1.15 ( ( breln @ A @ B @ R )
% 1.38/1.15 => ! [S: $i] :
% 1.38/1.15 ( ( breln @ A @ B @ S )
% 1.38/1.15 => ( ! [Xx: $i] :
% 1.38/1.15 ( ( in @ Xx @ A )
% 1.38/1.15 => ! [Xy: $i] :
% 1.38/1.15 ( ( in @ Xy @ B )
% 1.38/1.15 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.38/1.15 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 1.38/1.15 => ( subset @ R @ S ) ) ) ) ) ) ).
% 1.38/1.15 ------------------------
% 1.38/1.16 % (17695)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17594 for (3000ds/183Mi)
% 1.38/1.17 % (17697)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_17594 for (3000ds/27Mi)
% 1.38/1.17 % (17698)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17594 for (3000ds/2Mi)
% 1.38/1.17 % (17696)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_17594 for (3000ds/4Mi)
% 1.38/1.17 % (17699)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_17594 for (3000ds/2Mi)
% 1.38/1.17 % (17701)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17594 for (3000ds/18Mi)
% 1.38/1.17 % (17700)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_17594 for (3000ds/275Mi)
% 1.38/1.17 % (17699)Instruction limit reached!
% 1.38/1.17 % (17699)------------------------------
% 1.38/1.17 % (17699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.17 % (17699)Termination reason: Unknown
% 1.38/1.17 % (17699)Termination phase: shuffling
% 1.38/1.17
% 1.38/1.17 % (17699)Memory used [KB]: 895
% 1.38/1.17 % (17699)Time elapsed: 0.002 s
% 1.38/1.17 % (17699)Instructions burned: 2 (million)
% 1.38/1.17 % (17699)------------------------------
% 1.38/1.17 % (17699)------------------------------
% 1.38/1.17 % (17698)Instruction limit reached!
% 1.38/1.17 % (17698)------------------------------
% 1.38/1.17 % (17698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.17 % (17698)Termination reason: Unknown
% 1.38/1.17 % (17698)Termination phase: Property scanning
% 1.38/1.17
% 1.38/1.17 % (17698)Memory used [KB]: 1023
% 1.38/1.17 % (17698)Time elapsed: 0.003 s
% 1.38/1.17 % (17698)Instructions burned: 3 (million)
% 1.38/1.17 % (17698)------------------------------
% 1.38/1.17 % (17698)------------------------------
% 1.38/1.17 % (17696)Instruction limit reached!
% 1.38/1.17 % (17696)------------------------------
% 1.38/1.17 % (17696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.17 % (17696)Termination reason: Unknown
% 1.38/1.17 % (17696)Termination phase: Saturation
% 1.38/1.17
% 1.38/1.17 % (17696)Memory used [KB]: 5500
% 1.38/1.17 % (17696)Time elapsed: 0.004 s
% 1.38/1.17 % (17696)Instructions burned: 5 (million)
% 1.38/1.17 % (17696)------------------------------
% 1.38/1.17 % (17696)------------------------------
% 1.38/1.18 % (17701)Instruction limit reached!
% 1.38/1.18 % (17701)------------------------------
% 1.38/1.18 % (17701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.18 % (17701)Termination reason: Unknown
% 1.38/1.18 % (17701)Termination phase: Saturation
% 1.38/1.18
% 1.38/1.18 % (17701)Memory used [KB]: 5628
% 1.38/1.18 % (17701)Time elapsed: 0.011 s
% 1.38/1.18 % (17701)Instructions burned: 18 (million)
% 1.38/1.18 % (17701)------------------------------
% 1.38/1.18 % (17701)------------------------------
% 1.38/1.18 % (17697)Refutation not found, incomplete strategy
% 1.38/1.18 % (17697)------------------------------
% 1.38/1.18 % (17697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.18 % (17697)Termination reason: Refutation not found, incomplete strategy
% 1.38/1.18
% 1.38/1.18
% 1.38/1.18 % (17697)Memory used [KB]: 5628
% 1.38/1.18 % (17697)Time elapsed: 0.011 s
% 1.38/1.18 % (17697)Instructions burned: 19 (million)
% 1.38/1.18 % (17697)------------------------------
% 1.38/1.18 % (17697)------------------------------
% 1.38/1.19 % (17702)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17594 for (2999ds/3Mi)
% 1.38/1.19 % (17702)Instruction limit reached!
% 1.38/1.19 % (17702)------------------------------
% 1.38/1.19 % (17702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.19 % (17702)Termination reason: Unknown
% 1.38/1.19 % (17702)Termination phase: Property scanning
% 1.38/1.19
% 1.38/1.19 % (17702)Memory used [KB]: 1023
% 1.38/1.19 % (17702)Time elapsed: 0.003 s
% 1.38/1.19 % (17702)Instructions burned: 4 (million)
% 1.38/1.19 % (17704)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_17594 for (2999ds/15Mi)
% 1.38/1.19 % (17702)------------------------------
% 1.38/1.19 % (17702)------------------------------
% 1.38/1.19 % (17703)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_17594 for (2999ds/37Mi)
% 1.38/1.20 % (17704)Instruction limit reached!
% 1.38/1.20 % (17704)------------------------------
% 1.38/1.20 % (17704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.20 % (17704)Termination reason: Unknown
% 1.38/1.20 % (17704)Termination phase: Saturation
% 1.38/1.20
% 1.38/1.20 % (17704)Memory used [KB]: 5628
% 1.38/1.20 % (17704)Time elapsed: 0.009 s
% 1.38/1.20 % (17704)Instructions burned: 15 (million)
% 1.38/1.20 % (17704)------------------------------
% 1.38/1.20 % (17704)------------------------------
% 1.38/1.20 % (17705)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17594 for (2999ds/3Mi)
% 1.41/1.20 % (17706)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_17594 for (2999ds/1041Mi)
% 1.41/1.20 % (17705)Instruction limit reached!
% 1.41/1.20 % (17705)------------------------------
% 1.41/1.20 % (17705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.20 % (17705)Termination reason: Unknown
% 1.41/1.20 % (17705)Termination phase: Saturation
% 1.41/1.20
% 1.41/1.20 % (17705)Memory used [KB]: 1023
% 1.41/1.20 % (17705)Time elapsed: 0.003 s
% 1.41/1.20 % (17705)Instructions burned: 4 (million)
% 1.41/1.20 % (17705)------------------------------
% 1.41/1.20 % (17705)------------------------------
% 1.41/1.20 % (17700)First to succeed.
% 1.41/1.20 % (17707)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17594 for (2999ds/7Mi)
% 1.41/1.21 % (17703)Instruction limit reached!
% 1.41/1.21 % (17703)------------------------------
% 1.41/1.21 % (17703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.21 % (17703)Termination reason: Unknown
% 1.41/1.21 % (17703)Termination phase: Saturation
% 1.41/1.21
% 1.41/1.21 % (17703)Memory used [KB]: 5756
% 1.41/1.21 % (17703)Time elapsed: 0.019 s
% 1.41/1.21 % (17703)Instructions burned: 37 (million)
% 1.41/1.21 % (17703)------------------------------
% 1.41/1.21 % (17703)------------------------------
% 1.41/1.21 % (17700)Refutation found. Thanks to Tanya!
% 1.41/1.21 % SZS status Theorem for DTF2THF_17594
% 1.41/1.21 % SZS output start Proof for DTF2THF_17594
% 1.41/1.21 thf(func_def_0, type, in: $i > $i > $o).
% 1.41/1.21 thf(func_def_1, type, subset: $i > $i > $o).
% 1.41/1.21 thf(func_def_4, type, kpair: $i > $i > $i).
% 1.41/1.21 thf(func_def_5, type, cartprod: $i > $i > $i).
% 1.41/1.21 thf(func_def_6, type, breln: $i > $i > $i > $o).
% 1.41/1.21 thf(func_def_17, type, sK3: $i > $o).
% 1.41/1.21 thf(func_def_19, type, sK5: ($i > $o) > $i > $i > $i > $i).
% 1.41/1.21 thf(func_def_20, type, sK6: ($i > $o) > $i > $i > $i > $i).
% 1.41/1.21 thf(func_def_25, type, sK11: $i > $i > $i).
% 1.41/1.21 thf(func_def_30, type, ph15: !>[X0: $tType]:(X0)).
% 1.41/1.21 thf(f190,plain,(
% 1.41/1.21 $false),
% 1.41/1.21 inference(avatar_sat_refutation,[status(thm)],[f170,f189])).
% 1.41/1.21 thf(f189,plain,(
% 1.41/1.21 ~spl14_3),
% 1.41/1.21 inference(avatar_contradiction_clause,[status(thm)],[f188])).
% 1.41/1.21 thf(f188,plain,(
% 1.41/1.21 $false | ~spl14_3),
% 1.41/1.21 inference(subsumption_resolution,[status(thm)],[f187,f46])).
% 1.41/1.21 thf(f46,plain,(
% 1.41/1.21 ($true != (subset @ sK7 @ sK10))),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f30])).
% 1.41/1.21 thf(f30,plain,(
% 1.41/1.21 (($true = (breln @ sK8 @ sK9 @ sK7)) & (($true = (breln @ sK8 @ sK9 @ sK10)) & ! [X4 : $i] : (($true != (in @ X4 @ sK8)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK7) != $true) | ((in @ (kpair @ X4 @ X5) @ sK10) = $true) | ((in @ X5 @ sK9) != $true))) & ($true != (subset @ sK7 @ sK10)))) & (brelnall1 = $true) & (subsetI1 = $true)),
% 1.41/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f19,f29,f28])).
% 1.41/1.21 thf(f28,plain,(
% 1.41/1.21 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X1 @ X2 @ X0)) & ? [X3 : $i] : (($true = (breln @ X1 @ X2 @ X3)) & ! [X4 : $i] : (((in @ X4 @ X1) != $true) | ! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ X0)) | ((in @ (kpair @ X4 @ X5) @ X3) = $true) | ((in @ X5 @ X2) != $true))) & ($true != (subset @ X0 @ X3)))) => (($true = (breln @ sK8 @ sK9 @ sK7)) & ? [X3 : $i] : (($true = (breln @ sK8 @ sK9 @ X3)) & ! [X4 : $i] : (($true != (in @ X4 @ sK8)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK7) != $true) | ((in @ (kpair @ X4 @ X5) @ X3) = $true) | ((in @ X5 @ sK9) != $true))) & ($true != (subset @ sK7 @ X3))))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f29,plain,(
% 1.41/1.21 ? [X3 : $i] : (($true = (breln @ sK8 @ sK9 @ X3)) & ! [X4 : $i] : (($true != (in @ X4 @ sK8)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK7) != $true) | ((in @ (kpair @ X4 @ X5) @ X3) = $true) | ((in @ X5 @ sK9) != $true))) & ($true != (subset @ sK7 @ X3))) => (($true = (breln @ sK8 @ sK9 @ sK10)) & ! [X4 : $i] : (($true != (in @ X4 @ sK8)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK7) != $true) | ((in @ (kpair @ X4 @ X5) @ sK10) = $true) | ((in @ X5 @ sK9) != $true))) & ($true != (subset @ sK7 @ sK10)))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f19,plain,(
% 1.41/1.21 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X1 @ X2 @ X0)) & ? [X3 : $i] : (($true = (breln @ X1 @ X2 @ X3)) & ! [X4 : $i] : (((in @ X4 @ X1) != $true) | ! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ X0)) | ((in @ (kpair @ X4 @ X5) @ X3) = $true) | ((in @ X5 @ X2) != $true))) & ($true != (subset @ X0 @ X3)))) & (brelnall1 = $true) & (subsetI1 = $true)),
% 1.41/1.21 inference(flattening,[status(thm)],[f18])).
% 1.41/1.21 thf(f18,plain,(
% 1.41/1.21 (? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((($true != (subset @ X0 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3) = $true) | ($true != (in @ (kpair @ X4 @ X5) @ X0))) | ((in @ X5 @ X2) != $true)) | ((in @ X4 @ X1) != $true))) & ($true = (breln @ X1 @ X2 @ X3))) & ($true = (breln @ X1 @ X2 @ X0))) & (brelnall1 = $true)) & (subsetI1 = $true)),
% 1.41/1.21 inference(ennf_transformation,[status(thm)],[f8])).
% 1.41/1.21 thf(f8,plain,(
% 1.41/1.21 ~((subsetI1 = $true) => ((brelnall1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X1 @ X2 @ X0)) => ! [X3 : $i] : (($true = (breln @ X1 @ X2 @ X3)) => (! [X4 : $i] : (((in @ X4 @ X1) = $true) => ! [X5 : $i] : (((in @ X5 @ X2) = $true) => (($true = (in @ (kpair @ X4 @ X5) @ X0)) => ((in @ (kpair @ X4 @ X5) @ X3) = $true)))) => ($true = (subset @ X0 @ X3)))))))),
% 1.41/1.21 inference(fool_elimination,[status(thm)],[f7])).
% 1.41/1.21 thf(f7,plain,(
% 1.41/1.21 ~(subsetI1 => (brelnall1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X2 @ X0) => ! [X3 : $i] : ((breln @ X1 @ X2 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X0) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X0 @ X3))))))),
% 1.41/1.21 inference(rectify,[status(thm)],[f5])).
% 1.41/1.21 thf(f5,negated_conjecture,(
% 1.41/1.21 ~(subsetI1 => (brelnall1 => ! [X4 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X4) => ! [X7 : $i] : ((breln @ X0 @ X1 @ X7) => (! [X2 : $i] : ((in @ X2 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X2 @ X6) @ X4) => (in @ (kpair @ X2 @ X6) @ X7)))) => (subset @ X4 @ X7))))))),
% 1.41/1.21 inference(negated_conjecture,[status(cth)],[f4])).
% 1.41/1.21 thf(f4,conjecture,(
% 1.41/1.21 subsetI1 => (brelnall1 => ! [X4 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X4) => ! [X7 : $i] : ((breln @ X0 @ X1 @ X7) => (! [X2 : $i] : ((in @ X2 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X2 @ X6) @ X4) => (in @ (kpair @ X2 @ X6) @ X7)))) => (subset @ X4 @ X7)))))),
% 1.41/1.21 file('/export/starexec/sandbox/tmp/tmp.z13JXQQSqE/DTF2THF_17594.p',subbreln)).
% 1.41/1.21 thf(f187,plain,(
% 1.41/1.21 ($true = (subset @ sK7 @ sK10)) | ~spl14_3),
% 1.41/1.21 inference(equality_resolution,[status(thm)],[f182])).
% 1.41/1.21 thf(f182,plain,(
% 1.41/1.21 ( ! [X0 : $i] : (((sK11 @ sK7 @ X0) != (sK11 @ sK7 @ sK10)) | ((subset @ sK7 @ X0) = $true)) ) | ~spl14_3),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 1.41/1.21 thf(f177,plain,(
% 1.41/1.21 ( ! [X0 : $i] : (((sK11 @ sK7 @ X0) != (sK11 @ sK7 @ sK10)) | ($true != $true) | ((subset @ sK7 @ X0) = $true)) ) | ~spl14_3),
% 1.41/1.21 inference(superposition,[status(thm)],[f169,f70])).
% 1.41/1.21 thf(f70,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (((in @ (sK11 @ X1 @ X0) @ X1) = $true) | ($true = (subset @ X1 @ X0))) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.41/1.21 thf(f63,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ($true != $true) | ((in @ (sK11 @ X1 @ X0) @ X1) = $true)) )),
% 1.41/1.21 inference(definition_unfolding,[status(thm)],[f52,f44])).
% 1.41/1.21 thf(f44,plain,(
% 1.41/1.21 (subsetI1 = $true)),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f30])).
% 1.41/1.21 thf(f52,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ((in @ (sK11 @ X1 @ X0) @ X1) = $true) | (subsetI1 != $true)) )),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f35])).
% 1.41/1.21 thf(f35,plain,(
% 1.41/1.21 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | (($true != (in @ (sK11 @ X1 @ X0) @ X0)) & ((in @ (sK11 @ X1 @ X0) @ X1) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != (subset @ sK13 @ sK12)) & ! [X5 : $i] : (($true = (in @ X5 @ sK12)) | ($true != (in @ X5 @ sK13)))))),
% 1.41/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f32,f34,f33])).
% 1.41/1.21 thf(f33,plain,(
% 1.41/1.21 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) => (($true != (in @ (sK11 @ X1 @ X0) @ X0)) & ((in @ (sK11 @ X1 @ X0) @ X1) = $true)))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f34,plain,(
% 1.41/1.21 ? [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) != $true) & ! [X5 : $i] : (($true = (in @ X5 @ X3)) | ($true != (in @ X5 @ X4)))) => (($true != (subset @ sK13 @ sK12)) & ! [X5 : $i] : (($true = (in @ X5 @ sK12)) | ($true != (in @ X5 @ sK13))))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f32,plain,(
% 1.41/1.21 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) != $true) & ! [X5 : $i] : (($true = (in @ X5 @ X3)) | ($true != (in @ X5 @ X4)))))),
% 1.41/1.21 inference(rectify,[status(thm)],[f31])).
% 1.41/1.21 thf(f31,plain,(
% 1.41/1.21 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true))))),
% 1.41/1.21 inference(nnf_transformation,[status(thm)],[f17])).
% 1.41/1.21 thf(f17,plain,(
% 1.41/1.21 ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) <=> (subsetI1 = $true)),
% 1.41/1.21 inference(ennf_transformation,[status(thm)],[f10])).
% 1.41/1.21 thf(f10,plain,(
% 1.41/1.21 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ($true = (subset @ X1 @ X0)))),
% 1.41/1.21 inference(fool_elimination,[status(thm)],[f9])).
% 1.41/1.21 thf(f9,plain,(
% 1.41/1.21 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 1.41/1.21 inference(rectify,[status(thm)],[f1])).
% 1.41/1.21 thf(f1,axiom,(
% 1.41/1.21 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.41/1.21 file('/export/starexec/sandbox/tmp/tmp.z13JXQQSqE/DTF2THF_17594.p',subsetI1)).
% 1.41/1.21 thf(f169,plain,(
% 1.41/1.21 ( ! [X1 : $i] : (($true != (in @ X1 @ sK7)) | ((sK11 @ sK7 @ sK10) != X1)) ) | ~spl14_3),
% 1.41/1.21 inference(avatar_component_clause,[status(thm)],[f168])).
% 1.41/1.21 thf(f168,definition,(
% 1.41/1.21 spl14_3 <=> ! [X1 : $i] : (((sK11 @ sK7 @ sK10) != X1) | ($true != (in @ X1 @ sK7)))),
% 1.41/1.21 introduced(definition,[new_symbols(naming,[spl14_3])],[avatar_definition])).
% 1.41/1.21 thf(f170,plain,(
% 1.41/1.21 spl14_3 | spl14_3),
% 1.41/1.21 inference(avatar_split_clause,[status(thm)],[f166,f168,f168])).
% 1.41/1.21 thf(f166,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ sK7)) | ((sK11 @ sK7 @ sK10) != X1) | ((sK11 @ sK7 @ sK10) != X0) | ($true != (in @ X1 @ sK7))) )),
% 1.41/1.21 inference(subsumption_resolution,[status(thm)],[f165,f46])).
% 1.41/1.21 thf(f165,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (((sK11 @ sK7 @ sK10) != X1) | ($true != (in @ X0 @ sK7)) | ($true = (subset @ sK7 @ sK10)) | ($true != (in @ X1 @ sK7)) | ((sK11 @ sK7 @ sK10) != X0)) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f164])).
% 1.41/1.21 thf(f164,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ sK7 @ sK10)) | ($true != $true) | ($true != (in @ X1 @ sK7)) | ((sK11 @ sK7 @ sK10) != X0) | ($true != (in @ X0 @ sK7)) | ((sK11 @ sK7 @ sK10) != X1)) )),
% 1.41/1.21 inference(duplicate_literal_removal,[status(thm)],[f163])).
% 1.41/1.21 thf(f163,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (((sK11 @ sK7 @ sK10) != X1) | ($true != $true) | ($true = (subset @ sK7 @ sK10)) | ($true != (in @ X0 @ sK7)) | ($true != (in @ X1 @ sK7)) | ($true = (subset @ sK7 @ sK10)) | ((sK11 @ sK7 @ sK10) != X0)) )),
% 1.41/1.21 inference(superposition,[status(thm)],[f154,f70])).
% 1.41/1.21 thf(f154,plain,(
% 1.41/1.21 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK11 @ X0 @ sK10) @ sK7)) | ((sK11 @ X0 @ sK10) != X2) | ($true != (in @ X1 @ sK7)) | ($true != (in @ X2 @ sK7)) | ((subset @ X0 @ sK10) = $true) | ((sK11 @ X0 @ sK10) != X1)) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.41/1.21 thf(f153,plain,(
% 1.41/1.21 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X2 @ sK7)) | ((sK11 @ X0 @ sK10) != X1) | ($true != (in @ X1 @ sK7)) | ($true != (in @ (sK11 @ X0 @ sK10) @ sK7)) | ((subset @ X0 @ sK10) = $true) | ((sK11 @ X0 @ sK10) != X2)) )),
% 1.41/1.21 inference(superposition,[status(thm)],[f69,f152])).
% 1.41/1.21 thf(f152,plain,(
% 1.41/1.21 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ sK10)) | ($true != (in @ X2 @ sK7)) | ($true != (in @ X0 @ sK7)) | ($true != (in @ X1 @ sK7)) | (X0 != X1) | (X1 != X2)) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f151])).
% 1.41/1.21 thf(f151,plain,(
% 1.41/1.21 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ sK7)) | ($true != (in @ X2 @ sK7)) | (X0 != X1) | ($true = (in @ X1 @ sK10)) | (X1 != X2) | ($true != (in @ X0 @ sK7)) | ($true != $true)) )),
% 1.41/1.21 inference(duplicate_literal_removal,[status(thm)],[f147])).
% 1.41/1.21 thf(f147,plain,(
% 1.41/1.21 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X1 != X2) | ($true != (in @ X1 @ sK7)) | (X0 != X1) | ($true != $true) | ($true != (in @ X0 @ sK7)) | ($true != (in @ X2 @ sK7)) | ($true != (in @ X1 @ sK7)) | ($true = (in @ X1 @ sK10))) )),
% 1.41/1.21 inference(superposition,[status(thm)],[f145,f49])).
% 1.41/1.21 thf(f49,plain,(
% 1.41/1.21 ($true = (breln @ sK8 @ sK9 @ sK7))),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f30])).
% 1.41/1.21 thf(f145,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (breln @ sK8 @ sK9 @ X1)) | ($true != (in @ X3 @ X1)) | ($true != (in @ X0 @ X1)) | ((in @ X2 @ X1) != $true) | ($true != (in @ X0 @ sK7)) | ((in @ X0 @ sK10) = $true) | (X0 != X3) | (X0 != X2)) )),
% 1.41/1.21 inference(equality_proxy_clausification,[status(thm)],[f144])).
% 1.41/1.21 thf(f144,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (X0 = X3)) | ((in @ X2 @ X1) != $true) | ($true != (in @ X3 @ X1)) | (X0 != X2) | ((in @ X0 @ sK10) = $true) | ($true != (in @ X0 @ sK7)) | ($true != (breln @ sK8 @ sK9 @ X1)) | ($true != (in @ X0 @ X1))) )),
% 1.41/1.21 inference(not_proxy_clausification,[status(thm)],[f143])).
% 1.41/1.21 thf(f143,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ((~ (X0 = X3)) = $true) | ($true != (in @ X0 @ X1)) | ($true != (in @ X0 @ sK7)) | ((in @ X0 @ sK10) = $true) | ($true != (breln @ sK8 @ sK9 @ X1)) | ((in @ X2 @ X1) != $true) | (X0 != X2)) )),
% 1.41/1.21 inference(beta_eta_normalization,[status(thm)],[f142])).
% 1.41/1.21 thf(f142,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ($true != (in @ X0 @ X1)) | ($true != (in @ X3 @ X1)) | ((in @ X2 @ X1) != $true) | (X0 != X2) | ($true != (breln @ sK8 @ sK9 @ X1)) | ((in @ X0 @ sK10) = $true) | ($true != (in @ X0 @ sK7))) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f141])).
% 1.41/1.21 thf(f141,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ((in @ X0 @ sK10) = $true) | ($true != (breln @ sK8 @ sK9 @ X1)) | ($true != $true) | (X0 != X2) | ($true != (in @ X0 @ sK7)) | ($true != (in @ X0 @ X1)) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ((in @ X2 @ X1) != $true)) )),
% 1.41/1.21 inference(duplicate_literal_removal,[status(thm)],[f140])).
% 1.41/1.21 thf(f140,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X0 @ X1)) | ($true != (in @ X0 @ sK7)) | ((in @ X0 @ sK10) = $true) | ($true != (breln @ sK8 @ sK9 @ X1)) | ((in @ X2 @ X1) != $true) | ($true != (breln @ sK8 @ sK9 @ X1)) | (X0 != X2) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ($true != (in @ X3 @ X1))) )),
% 1.41/1.21 inference(superposition,[status(thm)],[f139,f71])).
% 1.41/1.21 thf(f71,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true = (in @ (sK6 @ X10 @ X9 @ X8 @ X7) @ X8)) | ((breln @ X7 @ X8 @ X9) != $true) | ($true = (X10 @ X13)) | ($true != (in @ X13 @ X9))) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.41/1.21 thf(f61,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true = (X10 @ X13)) | ((breln @ X7 @ X8 @ X9) != $true) | ($true != $true) | ($true = (in @ (sK6 @ X10 @ X9 @ X8 @ X7) @ X8)) | ($true != (in @ X13 @ X9))) )),
% 1.41/1.21 inference(definition_unfolding,[status(thm)],[f36,f45])).
% 1.41/1.21 thf(f45,plain,(
% 1.41/1.21 (brelnall1 = $true)),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f30])).
% 1.41/1.21 thf(f36,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true = (in @ (sK6 @ X10 @ X9 @ X8 @ X7) @ X8)) | ($true = (X10 @ X13)) | ($true != (in @ X13 @ X9)) | ((breln @ X7 @ X8 @ X9) != $true) | (brelnall1 != $true)) )),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f27])).
% 1.41/1.21 thf(f27,plain,(
% 1.41/1.21 ((brelnall1 = $true) | ((! [X4 : $i] : (($true != (in @ X4 @ sK0)) | ! [X5 : $i] : (($true = (sK3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK1)))) & (((sK3 @ sK4) != $true) & ($true = (in @ sK4 @ sK2)))) & ((breln @ sK0 @ sK1 @ sK2) = $true))) & (! [X7 : $i,X8 : $i,X9 : $i] : (! [X10 : $i > $o] : ((($true = (in @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X7)) & (($true != (X10 @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ (sK6 @ X10 @ X9 @ X8 @ X7)))) & ((in @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ (sK6 @ X10 @ X9 @ X8 @ X7)) @ X9) = $true) & ($true = (in @ (sK6 @ X10 @ X9 @ X8 @ X7) @ X8)))) | ! [X13 : $i] : (($true = (X10 @ X13)) | ($true != (in @ X13 @ X9)))) | ((breln @ X7 @ X8 @ X9) != $true)) | (brelnall1 != $true))),
% 1.41/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f21,f26,f25,f24,f23,f22])).
% 1.41/1.21 thf(f22,plain,(
% 1.41/1.21 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X2) != $true) | ((in @ X5 @ X1) != $true))) & ? [X6 : $i] : (((X3 @ X6) != $true) & ($true = (in @ X6 @ X2)))) & ($true = (breln @ X0 @ X1 @ X2))) => (? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ sK0)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK1)))) & ? [X6 : $i] : (((X3 @ X6) != $true) & ($true = (in @ X6 @ sK2)))) & ((breln @ sK0 @ sK1 @ sK2) = $true))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f23,plain,(
% 1.41/1.21 ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ sK0)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK1)))) & ? [X6 : $i] : (((X3 @ X6) != $true) & ($true = (in @ X6 @ sK2)))) => (! [X4 : $i] : (($true != (in @ X4 @ sK0)) | ! [X5 : $i] : (($true = (sK3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK1)))) & ? [X6 : $i] : (($true != (sK3 @ X6)) & ($true = (in @ X6 @ sK2))))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f24,plain,(
% 1.41/1.21 ? [X6 : $i] : (($true != (sK3 @ X6)) & ($true = (in @ X6 @ sK2))) => (((sK3 @ sK4) != $true) & ($true = (in @ sK4 @ sK2)))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f25,plain,(
% 1.41/1.21 ! [X7 : $i,X8 : $i,X9 : $i,X10 : $i > $o] : (? [X11 : $i] : (($true = (in @ X11 @ X7)) & ? [X12 : $i] : (($true != (X10 @ (kpair @ X11 @ X12))) & ($true = (in @ (kpair @ X11 @ X12) @ X9)) & ((in @ X12 @ X8) = $true))) => (($true = (in @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X7)) & ? [X12 : $i] : (($true != (X10 @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X12))) & ((in @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X12) @ X9) = $true) & ((in @ X12 @ X8) = $true))))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f26,plain,(
% 1.41/1.21 ! [X7 : $i,X8 : $i,X9 : $i,X10 : $i > $o] : (? [X12 : $i] : (($true != (X10 @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X12))) & ((in @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X12) @ X9) = $true) & ((in @ X12 @ X8) = $true)) => (($true != (X10 @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ (sK6 @ X10 @ X9 @ X8 @ X7)))) & ((in @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ (sK6 @ X10 @ X9 @ X8 @ X7)) @ X9) = $true) & ($true = (in @ (sK6 @ X10 @ X9 @ X8 @ X7) @ X8))))),
% 1.41/1.21 introduced(definition,[],[choice_axiom])).
% 1.41/1.21 thf(f21,plain,(
% 1.41/1.21 ((brelnall1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X2) != $true) | ((in @ X5 @ X1) != $true))) & ? [X6 : $i] : (((X3 @ X6) != $true) & ($true = (in @ X6 @ X2)))) & ($true = (breln @ X0 @ X1 @ X2)))) & (! [X7 : $i,X8 : $i,X9 : $i] : (! [X10 : $i > $o] : (? [X11 : $i] : (($true = (in @ X11 @ X7)) & ? [X12 : $i] : (($true != (X10 @ (kpair @ X11 @ X12))) & ($true = (in @ (kpair @ X11 @ X12) @ X9)) & ((in @ X12 @ X8) = $true))) | ! [X13 : $i] : (($true = (X10 @ X13)) | ($true != (in @ X13 @ X9)))) | ((breln @ X7 @ X8 @ X9) != $true)) | (brelnall1 != $true))),
% 1.41/1.21 inference(rectify,[status(thm)],[f20])).
% 1.41/1.21 thf(f20,plain,(
% 1.41/1.21 ((brelnall1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X2) != $true) | ((in @ X5 @ X1) != $true))) & ? [X6 : $i] : (((X3 @ X6) != $true) & ($true = (in @ X6 @ X2)))) & ($true = (breln @ X0 @ X1 @ X2)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i > $o] : (? [X4 : $i] : (($true = (in @ X4 @ X0)) & ? [X5 : $i] : (($true != (X3 @ (kpair @ X4 @ X5))) & ((in @ (kpair @ X4 @ X5) @ X2) = $true) & ((in @ X5 @ X1) = $true))) | ! [X6 : $i] : (((X3 @ X6) = $true) | ($true != (in @ X6 @ X2)))) | ($true != (breln @ X0 @ X1 @ X2))) | (brelnall1 != $true))),
% 1.41/1.21 inference(nnf_transformation,[status(thm)],[f16])).
% 1.41/1.21 thf(f16,plain,(
% 1.41/1.21 (brelnall1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i > $o] : (? [X4 : $i] : (($true = (in @ X4 @ X0)) & ? [X5 : $i] : (($true != (X3 @ (kpair @ X4 @ X5))) & ((in @ (kpair @ X4 @ X5) @ X2) = $true) & ((in @ X5 @ X1) = $true))) | ! [X6 : $i] : (((X3 @ X6) = $true) | ($true != (in @ X6 @ X2)))) | ($true != (breln @ X0 @ X1 @ X2)))),
% 1.41/1.21 inference(flattening,[status(thm)],[f15])).
% 1.41/1.21 thf(f15,plain,(
% 1.41/1.21 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i > $o] : (! [X6 : $i] : (((X3 @ X6) = $true) | ($true != (in @ X6 @ X2))) | ? [X4 : $i] : (? [X5 : $i] : ((($true != (X3 @ (kpair @ X4 @ X5))) & ((in @ (kpair @ X4 @ X5) @ X2) = $true)) & ((in @ X5 @ X1) = $true)) & ($true = (in @ X4 @ X0)))) | ($true != (breln @ X0 @ X1 @ X2))) <=> (brelnall1 = $true)),
% 1.41/1.21 inference(ennf_transformation,[status(thm)],[f12])).
% 1.41/1.21 thf(f12,plain,(
% 1.41/1.21 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X0 @ X1 @ X2)) => ! [X3 : $i > $o] : (! [X4 : $i] : (($true = (in @ X4 @ X0)) => ! [X5 : $i] : (((in @ X5 @ X1) = $true) => (((in @ (kpair @ X4 @ X5) @ X2) = $true) => ($true = (X3 @ (kpair @ X4 @ X5)))))) => ! [X6 : $i] : (($true = (in @ X6 @ X2)) => ((X3 @ X6) = $true)))) <=> (brelnall1 = $true)),
% 1.41/1.21 inference(fool_elimination,[status(thm)],[f11])).
% 1.41/1.21 thf(f11,plain,(
% 1.41/1.21 (brelnall1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i > $o] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X2) => (X3 @ X6)))))),
% 1.41/1.21 inference(rectify,[status(thm)],[f3])).
% 1.41/1.21 thf(f3,axiom,(
% 1.41/1.21 (brelnall1 = ! [X0 : $i,X1 : $i,X4 : $i] : ((breln @ X0 @ X1 @ X4) => ! [X5 : $i > $o] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X2 @ X6) @ X4) => (X5 @ (kpair @ X2 @ X6))))) => ! [X2 : $i] : ((in @ X2 @ X4) => (X5 @ X2)))))),
% 1.41/1.21 file('/export/starexec/sandbox/tmp/tmp.z13JXQQSqE/DTF2THF_17594.p',brelnall1)).
% 1.41/1.21 thf(f139,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK6 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ sK8) @ sK9) != $true) | ($true != (in @ X0 @ sK7)) | ($true != (in @ X3 @ X1)) | ($true != (in @ X0 @ X1)) | ($true != (breln @ sK8 @ X2 @ X1)) | ((in @ X0 @ sK10) = $true) | (X0 != X3)) )),
% 1.41/1.21 inference(equality_proxy_clausification,[status(thm)],[f138])).
% 1.41/1.21 thf(f138,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK6 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ sK8) @ sK9) != $true) | ($true != (in @ X0 @ sK7)) | ($true != (in @ X0 @ X1)) | ($false = (X0 = X3)) | ($true != (breln @ sK8 @ X2 @ X1)) | ((in @ X0 @ sK10) = $true) | ($true != (in @ X3 @ X1))) )),
% 1.41/1.21 inference(not_proxy_clausification,[status(thm)],[f137])).
% 1.41/1.21 thf(f137,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ sK7)) | ((in @ X0 @ sK10) = $true) | ($true != (breln @ sK8 @ X2 @ X1)) | ($true != (in @ X3 @ X1)) | ((in @ (sK6 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ sK8) @ sK9) != $true) | ($true != (in @ X0 @ X1)) | ((~ (X0 = X3)) = $true)) )),
% 1.41/1.21 inference(beta_eta_normalization,[status(thm)],[f136])).
% 1.41/1.21 thf(f136,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK6 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ sK8) @ sK9) != $true) | ($true != (in @ X3 @ X1)) | ((in @ X0 @ sK10) = $true) | ($true != (in @ X0 @ X1)) | ($true != (breln @ sK8 @ X2 @ X1)) | ($true != (in @ X0 @ sK7)) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3))) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.41/1.21 thf(f135,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ($true != $true) | ((in @ X0 @ sK10) = $true) | ($true != (breln @ sK8 @ X2 @ X1)) | ((in @ (sK6 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ sK8) @ sK9) != $true) | ($true != (in @ X0 @ X1)) | ($true != (in @ X0 @ sK7)) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3))) )),
% 1.41/1.21 inference(duplicate_literal_removal,[status(thm)],[f134])).
% 1.41/1.21 thf(f134,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true != (in @ X3 @ X1)) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ($true != (breln @ sK8 @ X2 @ X1)) | ($true != (breln @ sK8 @ X2 @ X1)) | ($true != (in @ X0 @ sK7)) | ((in @ (sK6 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ sK8) @ sK9) != $true) | ($true != $true) | ((in @ X0 @ sK10) = $true)) )),
% 1.41/1.21 inference(superposition,[status(thm)],[f107,f67])).
% 1.41/1.21 thf(f67,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true = (in @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X7)) | ($true = (X10 @ X13)) | ($true != (in @ X13 @ X9)) | ((breln @ X7 @ X8 @ X9) != $true)) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.41/1.21 thf(f58,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != (in @ X13 @ X9)) | ($true != $true) | ((breln @ X7 @ X8 @ X9) != $true) | ($true = (in @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X7)) | ($true = (X10 @ X13))) )),
% 1.41/1.21 inference(definition_unfolding,[status(thm)],[f39,f45])).
% 1.41/1.21 thf(f39,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true = (in @ (sK5 @ X10 @ X9 @ X8 @ X7) @ X7)) | ($true = (X10 @ X13)) | ($true != (in @ X13 @ X9)) | ((breln @ X7 @ X8 @ X9) != $true) | (brelnall1 != $true)) )),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f27])).
% 1.41/1.21 thf(f107,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK5 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ X3) @ sK8)) | ($true != (in @ X0 @ sK7)) | ($true != (breln @ X3 @ X2 @ X1)) | ((in @ X0 @ sK10) = $true) | ($true != (in @ X0 @ X1)) | ((in @ (sK6 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ X3) @ sK9) != $true)) )),
% 1.41/1.21 inference(superposition,[status(thm)],[f47,f75])).
% 1.41/1.21 thf(f75,plain,(
% 1.41/1.21 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ (sK5 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ X3) @ (sK6 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ X3)) = X0) | ($true != (breln @ X3 @ X2 @ X1)) | ($true != (in @ X0 @ X1))) )),
% 1.41/1.21 inference(leibniz_equality_elimination,[status(thm)],[f66])).
% 1.41/1.21 thf(f66,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != (X10 @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ (sK6 @ X10 @ X9 @ X8 @ X7)))) | ($true != (in @ X13 @ X9)) | ($true = (X10 @ X13)) | ((breln @ X7 @ X8 @ X9) != $true)) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.41/1.21 thf(f59,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != (in @ X13 @ X9)) | ($true = (X10 @ X13)) | ((breln @ X7 @ X8 @ X9) != $true) | ($true != (X10 @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ (sK6 @ X10 @ X9 @ X8 @ X7)))) | ($true != $true)) )),
% 1.41/1.21 inference(definition_unfolding,[status(thm)],[f38,f45])).
% 1.41/1.21 thf(f38,plain,(
% 1.41/1.21 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != (X10 @ (kpair @ (sK5 @ X10 @ X9 @ X8 @ X7) @ (sK6 @ X10 @ X9 @ X8 @ X7)))) | ($true = (X10 @ X13)) | ($true != (in @ X13 @ X9)) | ((breln @ X7 @ X8 @ X9) != $true) | (brelnall1 != $true)) )),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f27])).
% 1.41/1.21 thf(f47,plain,(
% 1.41/1.21 ( ! [X4 : $i,X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK10) = $true) | ($true != (in @ X4 @ sK8)) | ((in @ (kpair @ X4 @ X5) @ sK7) != $true) | ((in @ X5 @ sK9) != $true)) )),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f30])).
% 1.41/1.21 thf(f69,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK11 @ X1 @ X0) @ X0)) | ($true = (subset @ X1 @ X0))) )),
% 1.41/1.21 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.41/1.21 thf(f62,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ($true != (in @ (sK11 @ X1 @ X0) @ X0)) | ($true != $true)) )),
% 1.41/1.21 inference(definition_unfolding,[status(thm)],[f53,f44])).
% 1.41/1.21 thf(f53,plain,(
% 1.41/1.21 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ($true != (in @ (sK11 @ X1 @ X0) @ X0)) | (subsetI1 != $true)) )),
% 1.41/1.21 inference(cnf_transformation,[status(thm)],[f35])).
% 1.41/1.21 % SZS output end Proof for DTF2THF_17594
% 1.41/1.21 % (17700)------------------------------
% 1.41/1.21 % (17700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.21 % (17700)Termination reason: Refutation
% 1.41/1.21
% 1.41/1.21 % (17700)Memory used [KB]: 5756
% 1.41/1.21 % (17700)Time elapsed: 0.036 s
% 1.41/1.21 % (17700)Instructions burned: 65 (million)
% 1.41/1.21 % (17700)------------------------------
% 1.41/1.21 % (17700)------------------------------
% 1.41/1.21 % (17694)Success in time 0.046 s
%------------------------------------------------------------------------------