%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU781^2 : 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 : n015.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 09:37:09 AM UTC 2026
% Result : Theorem 1.68s 1.34s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 1690 ( 420 equ; 0 cnn)
% Maximal formula atoms : 20 ( 26 avg)
% Number of connectives : 2008 ( 270 ~; 227 |; 128 &;1311 @)
% ( 7 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 17 con; 0-5 aty)
% Number of variables : 207 ( 0 ^; 133 !; 74 ?; 207 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
cartprod: $i > $i > $i ).
thf(func_def_4,type,
breln: $i > $i > $i > $o ).
thf(func_def_6,type,
breln1: $i > $i > $o ).
thf(func_def_7,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_21,type,
sK6: $i > $i > $i > $i > $i > $i ).
thf(f83,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f64,f65,f82]) ).
thf(f82,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f80,f49]) ).
thf(f49,plain,
( $true
= ( in @ sK10 @ sK8 ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( in @ sK11 @ sK8 ) )
& ( $true != sK12 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK11 ) @ sK9 ) )
| ( $true = sK12 ) )
& ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
= $true )
& ( $true
= ( in @ sK10 @ sK8 ) )
& ( $true
= ( breln1 @ sK8 @ sK9 ) )
& ( $true
= ( breln1 @ sK8 @ sK7 ) )
& ( breln1compE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12])],[f17,f33,f32,f31,f30,f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ X1 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ X0 ) )
| ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
!= $true )
| ( $true = X5 ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK8 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ sK7 ) )
| ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
!= $true )
| ( $true = X5 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK8 @ sK7 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK8 ) ) )
& ( ( breln1 @ sK8 @ X2 )
= $true ) )
& ( $true
= ( breln1 @ sK8 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK8 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ sK7 ) )
| ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
!= $true )
| ( $true = X5 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK8 @ sK7 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK8 ) ) )
& ( ( breln1 @ sK8 @ X2 )
= $true ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK8 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ sK9 ) )
| ( $true = X5 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) ) ) )
& ( $true
= ( in @ X3 @ sK8 ) ) )
& ( $true
= ( breln1 @ sK8 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK8 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ sK9 ) )
| ( $true = X5 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) ) ) )
& ( $true
= ( in @ X3 @ sK8 ) ) )
=> ( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK8 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ sK9 ) )
| ( $true = X5 ) ) )
& ( $true
= ( in @ ( kpair @ sK10 @ X4 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) ) ) )
& ( $true
= ( in @ sK10 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK8 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ sK9 ) )
| ( $true = X5 ) ) )
& ( $true
= ( in @ ( kpair @ sK10 @ X4 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) ) ) )
=> ( ( $true
= ( in @ sK11 @ sK8 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK11 ) @ sK9 ) )
| ( $true = X5 ) ) )
& ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK11 ) @ sK9 ) )
| ( $true = X5 ) ) )
=> ( ( $true != sK12 )
& ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK11 ) @ sK9 ) )
| ( $true = sK12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( ( in @ X6 @ X1 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ X0 ) )
| ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
!= $true )
| ( $true = X5 ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( breln1compE = $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ X0 ) )
| ( ( in @ X6 @ X1 )
!= $true ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X4 @ X1 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( breln1compE = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( breln1compE = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true )
=> ! [X5: $o] :
( ! [X6: $i] :
( ( ( in @ X6 @ X1 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X6 ) @ X0 ) )
=> ( ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
= $true )
=> ( $true = X5 ) ) ) )
=> ( $true = X5 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( breln1compE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
=> ! [X5: $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X6 ) @ X0 )
=> ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
=> X5 ) ) )
=> X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( breln1compE
=> ! [X3: $i,X0: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X4: $i] :
( ( breln1 @ X0 @ X4 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X0 @ X3 @ X4 ) )
=> ! [X8: $o] :
( ! [X7: $i] :
( ( in @ X7 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X7 ) @ X3 )
=> ( ( in @ ( kpair @ X7 @ X6 ) @ X4 )
=> X8 ) ) )
=> X8 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( breln1compE
=> ! [X3: $i,X0: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X4: $i] :
( ( breln1 @ X0 @ X4 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X0 @ X3 @ X4 ) )
=> ! [X8: $o] :
( ! [X7: $i] :
( ( in @ X7 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X7 ) @ X3 )
=> ( ( in @ ( kpair @ X7 @ X6 ) @ X4 )
=> X8 ) ) )
=> X8 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sYxiJQxlj4/DTF2THF_20814.p',breln1compEex) ).
thf(f80,plain,
( ( $true
!= ( in @ sK10 @ sK8 ) )
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f79,f48]) ).
thf(f48,plain,
( $true
= ( breln1 @ sK8 @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f79,plain,
( ( $true
!= ( breln1 @ sK8 @ sK9 ) )
| ( $true
!= ( in @ sK10 @ sK8 ) )
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f78,f50]) ).
thf(f50,plain,
( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f78,plain,
( ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( breln1 @ sK8 @ sK9 ) )
| ( $true
!= ( in @ sK10 @ sK8 ) )
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f77,f47]) ).
thf(f47,plain,
( $true
= ( breln1 @ sK8 @ sK7 ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f77,plain,
( ( $true
!= ( breln1 @ sK8 @ sK7 ) )
| ( $true
!= ( in @ sK10 @ sK8 ) )
| ( $true
!= ( breln1 @ sK8 @ sK9 ) )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
!= $true )
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f76,f56]) ).
thf(f56,plain,
$true = sP0,
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true = sP0 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f44,f46]) ).
thf(f46,plain,
breln1compE = $true,
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f44,plain,
( ( $true = sP0 )
| ( breln1compE != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( breln1compE = $true )
| ( $true != sP0 ) )
& ( ( $true = sP0 )
| ( breln1compE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( breln1compE = $true )
<=> ( $true = sP0 ) ),
inference(definition_folding,[status(thm)],[f15,f18]) ).
thf(f18,plain,
( ( $true = sP0 )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( ( in @ X5 @ X0 )
= $true ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f15,plain,
( ( breln1compE = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( ( in @ X5 @ X0 )
= $true ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( breln1compE = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( ( in @ X5 @ X0 )
= $true ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( breln1 @ X0 @ X2 ) ) )
| ( $true
!= ( breln1 @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( breln1compE = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) )
=> ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( ( in @ X5 @ X0 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) )
=> ? [X5: $i] :
( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
& ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ X5 @ X0 ) ) ) ) ) ) )
= breln1compE ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X3: $i] :
( ( ( breln1 @ X0 @ X3 )
=> ! [X4: $i] :
( ( breln1 @ X0 @ X4 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X0 @ X3 @ X4 ) )
=> ? [X7: $i] :
( ( in @ ( kpair @ X5 @ X7 ) @ X3 )
& ( in @ ( kpair @ X7 @ X6 ) @ X4 )
& ( in @ X7 @ X0 ) ) ) ) ) ) )
= breln1compE ),
file('/export/starexec/sandbox/tmp/tmp.sYxiJQxlj4/DTF2THF_20814.p',breln1compE) ).
thf(f76,plain,
( ( $true != sP0 )
| ( $true
!= ( breln1 @ sK8 @ sK7 ) )
| ( $true
!= ( breln1 @ sK8 @ sK9 ) )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( in @ sK10 @ sK8 ) )
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f75,f53]) ).
thf(f53,plain,
( $true
= ( in @ sK11 @ sK8 ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f75,plain,
( ( $true
!= ( in @ sK11 @ sK8 ) )
| ( $true
!= ( in @ sK10 @ sK8 ) )
| ( $true != sP0 )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( breln1 @ sK8 @ sK9 ) )
| ( $true
!= ( breln1 @ sK8 @ sK7 ) )
| ~ spl13_1 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( $true
!= ( breln1 @ sK8 @ sK7 ) )
| ( $true != $true )
| ( $true
!= ( in @ sK11 @ sK8 ) )
| ( $true
!= ( in @ sK10 @ sK8 ) )
| ( $true != sP0 )
| ( $true
!= ( breln1 @ sK8 @ sK9 ) )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
!= $true )
| ~ spl13_1 ),
inference(duplicate_literal_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true
!= ( in @ sK10 @ sK8 ) )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
!= $true )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ sK8 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( in @ sK11 @ sK8 ) )
| ( $true
!= ( breln1 @ sK8 @ sK9 ) )
| ( $true != $true )
| ( $true != sP0 )
| ( $true
!= ( breln1 @ sK8 @ sK7 ) )
| ( $true
!= ( breln1 @ sK8 @ sK9 ) )
| ( $true
!= ( in @ sK10 @ sK8 ) )
| ( $true
!= ( in @ sK11 @ sK8 ) )
| ( $true
!= ( breln1 @ sK8 @ sK7 ) )
| ~ spl13_1 ),
inference(superposition,[status(thm)],[f72,f35]) ).
thf(f35,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
= ( in @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( breln1 @ X6 @ X7 ) )
| ( $true != sP0 )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( breln1 @ X6 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( $true = sP0 )
| ( ( ( breln1 @ sK1 @ sK2 )
= $true )
& ( $true
= ( breln1 @ sK1 @ sK3 ) )
& ( $true
= ( in @ sK5 @ sK1 ) )
& ! [X5: $i] :
( ( ( in @ ( kpair @ sK4 @ X5 ) @ sK2 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X5 @ sK5 ) @ sK3 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( ( in @ ( kpair @ sK4 @ sK5 ) @ ( breln1compset @ sK1 @ sK2 @ sK3 ) )
= $true )
& ( ( in @ sK4 @ sK1 )
= $true ) ) )
& ( ! [X6: $i,X7: $i] :
( ( $true
!= ( breln1 @ X6 @ X7 ) )
| ! [X8: $i] :
( ( $true
!= ( breln1 @ X6 @ X8 ) )
| ! [X9: $i] :
( ! [X10: $i] :
( ( $true
!= ( in @ X10 @ X6 ) )
| ( ( $true
= ( in @ ( kpair @ X9 @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
& ( ( in @ ( kpair @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 )
= $true )
& ( $true
= ( in @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) ) )
| ( $true
!= ( in @ X9 @ X6 ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f21,f26,f25,f24,f23,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
| ( ( in @ X5 @ X0 )
!= $true ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) ) )
=> ( ( ( breln1 @ sK1 @ sK2 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ sK1 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK2 @ X2 ) ) ) )
& ( ( in @ X3 @ sK1 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X2: $i] :
( ( ( breln1 @ sK1 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK2 @ X2 ) ) ) )
& ( ( in @ X3 @ sK1 )
= $true ) ) )
=> ( ( $true
= ( breln1 @ sK1 @ sK3 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ sK3 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK2 @ sK3 ) ) ) )
& ( ( in @ X3 @ sK1 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ sK3 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK2 @ sK3 ) ) ) )
& ( ( in @ X3 @ sK1 )
= $true ) )
=> ( ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ! [X5: $i] :
( ( ( in @ ( kpair @ sK4 @ X5 ) @ sK2 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ sK3 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( $true
= ( in @ ( kpair @ sK4 @ X4 ) @ ( breln1compset @ sK1 @ sK2 @ sK3 ) ) ) )
& ( ( in @ sK4 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ! [X5: $i] :
( ( ( in @ ( kpair @ sK4 @ X5 ) @ sK2 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ sK3 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( $true
= ( in @ ( kpair @ sK4 @ X4 ) @ ( breln1compset @ sK1 @ sK2 @ sK3 ) ) ) )
=> ( ( $true
= ( in @ sK5 @ sK1 ) )
& ! [X5: $i] :
( ( ( in @ ( kpair @ sK4 @ X5 ) @ sK2 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X5 @ sK5 ) @ sK3 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( ( in @ ( kpair @ sK4 @ sK5 ) @ ( breln1compset @ sK1 @ sK2 @ sK3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
( ? [X11: $i] :
( ( ( in @ ( kpair @ X9 @ X11 ) @ X7 )
= $true )
& ( $true
= ( in @ ( kpair @ X11 @ X10 ) @ X8 ) )
& ( $true
= ( in @ X11 @ X6 ) ) )
=> ( ( $true
= ( in @ ( kpair @ X9 @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
& ( ( in @ ( kpair @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 )
= $true )
& ( $true
= ( in @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ( $true = sP0 )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
| ( ( in @ X5 @ X0 )
!= $true ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) ) ) )
& ( ! [X6: $i,X7: $i] :
( ( $true
!= ( breln1 @ X6 @ X7 ) )
| ! [X8: $i] :
( ( $true
!= ( breln1 @ X6 @ X8 ) )
| ! [X9: $i] :
( ! [X10: $i] :
( ( $true
!= ( in @ X10 @ X6 ) )
| ? [X11: $i] :
( ( ( in @ ( kpair @ X9 @ X11 ) @ X7 )
= $true )
& ( $true
= ( in @ ( kpair @ X11 @ X10 ) @ X8 ) )
& ( $true
= ( in @ X11 @ X6 ) ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) ) )
| ( $true
!= ( in @ X9 @ X6 ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( $true = sP0 )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
| ( ( in @ X5 @ X0 )
!= $true ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( ( in @ X5 @ X0 )
= $true ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f72,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK6 @ sK11 @ sK10 @ sK9 @ sK7 @ X0 ) @ sK8 ) )
| ( $true
!= ( in @ sK11 @ X0 ) )
| ( $true
!= ( breln1 @ X0 @ sK7 ) )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ X0 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( in @ sK10 @ X0 ) )
| ( $true
!= ( breln1 @ X0 @ sK9 ) ) )
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f71,f56]) ).
thf(f71,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ X0 @ sK7 ) )
| ( $true
!= ( in @ sK10 @ X0 ) )
| ( $true != sP0 )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ X0 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( breln1 @ X0 @ sK9 ) )
| ( $true
!= ( in @ ( sK6 @ sK11 @ sK10 @ sK9 @ sK7 @ X0 ) @ sK8 ) )
| ( $true
!= ( in @ sK11 @ X0 ) ) )
| ~ spl13_1 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X0: $i] :
( ( $true != sP0 )
| ( $true
!= ( breln1 @ X0 @ sK9 ) )
| ( $true
!= ( breln1 @ X0 @ sK7 ) )
| ( $true
!= ( in @ sK10 @ X0 ) )
| ( $true
!= ( in @ ( sK6 @ sK11 @ sK10 @ sK9 @ sK7 @ X0 ) @ sK8 ) )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ X0 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( in @ sK11 @ X0 ) )
| ( $true != $true ) )
| ~ spl13_1 ),
inference(duplicate_literal_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ sK10 @ X0 ) )
| ( $true
!= ( in @ sK11 @ X0 ) )
| ( $true
!= ( in @ sK10 @ X0 ) )
| ( $true
!= ( in @ sK11 @ X0 ) )
| ( $true != sP0 )
| ( $true
!= ( breln1 @ X0 @ sK7 ) )
| ( $true
!= ( breln1 @ X0 @ sK9 ) )
| ( $true
!= ( breln1 @ X0 @ sK9 ) )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ X0 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( in @ ( sK6 @ sK11 @ sK10 @ sK9 @ sK7 @ X0 ) @ sK8 ) )
| ( ( in @ ( kpair @ sK10 @ sK11 ) @ ( breln1compset @ X0 @ sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( breln1 @ X0 @ sK7 ) ) )
| ~ spl13_1 ),
inference(superposition,[status(thm)],[f68,f36]) ).
thf(f36,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( ( in @ ( kpair @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 )
= $true )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( breln1 @ X6 @ X7 ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( breln1 @ X6 @ X8 ) )
| ( $true != sP0 )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f68,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2 ) @ sK11 ) @ sK9 )
!= $true )
| ( $true
!= ( in @ sK10 @ X2 ) )
| ( $true
!= ( breln1 @ X2 @ sK7 ) )
| ( ( breln1 @ X2 @ X1 )
!= $true )
| ( ( in @ ( sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2 ) @ sK8 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK10 @ X0 ) @ ( breln1compset @ X2 @ sK7 @ X1 ) ) ) )
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f67,f56]) ).
thf(f67,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ sK10 @ X0 ) @ ( breln1compset @ X2 @ sK7 @ X1 ) ) )
| ( ( in @ ( kpair @ ( sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2 ) @ sK11 ) @ sK9 )
!= $true )
| ( ( in @ ( sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2 ) @ sK8 )
!= $true )
| ( ( breln1 @ X2 @ X1 )
!= $true )
| ( $true
!= ( breln1 @ X2 @ sK7 ) )
| ( $true != sP0 )
| ( ( in @ X0 @ X2 )
!= $true )
| ( $true
!= ( in @ sK10 @ X2 ) ) )
| ~ spl13_1 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
!= $true )
| ( ( in @ ( kpair @ ( sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2 ) @ sK11 ) @ sK9 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ ( sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2 ) @ sK8 )
!= $true )
| ( $true
!= ( in @ sK10 @ X2 ) )
| ( $true
!= ( in @ ( kpair @ sK10 @ X0 ) @ ( breln1compset @ X2 @ sK7 @ X1 ) ) )
| ( $true != $true )
| ( $true
!= ( breln1 @ X2 @ sK7 ) )
| ( $true != sP0 ) )
| ~ spl13_1 ),
inference(superposition,[status(thm)],[f59,f37]) ).
thf(f37,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
= ( in @ ( kpair @ X9 @ ( sK6 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( breln1 @ X6 @ X8 ) )
| ( $true != sP0 )
| ( $true
!= ( breln1 @ X6 @ X7 ) )
| ( $true
!= ( in @ X9 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f59,plain,
( ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) )
| ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ sK11 ) @ sK9 ) ) )
| ~ spl13_1 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl13_1
<=> ! [X6: $i] :
( ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK11 ) @ sK9 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition]) ).
thf(f65,plain,
~ spl13_2,
inference(avatar_split_clause,[status(thm)],[f52,f61]) ).
thf(f61,definition,
( spl13_2
<=> ( $true = sK12 ) ),
introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition]) ).
thf(f52,plain,
$true != sK12,
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f64,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[status(thm)],[f51,f61,f58]) ).
thf(f51,plain,
! [X6: $i] :
( ( $true = sK12 )
| ( ( in @ X6 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ sK11 ) @ sK9 ) )
| ( $true
!= ( in @ ( kpair @ sK10 @ X6 ) @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU781^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:34:01 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SEU781^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.47 % Domain : Set Theory
% 0.30/0.47 % Problem : Binary Relations on a Set
% 0.30/0.47 % Version : Especial > Reduced > Especial.
% 0.30/0.47 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.30/0.47 % (! y:i.in y A -> in (kpair x y) (breln1compset A R S) ->
% 0.30/0.47 % (! phi:o.(! z:i.in z A -> in (kpair x z) R -> in (kpair z y) S ->
% 0.30/0.47 % phi) -> phi)))))
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.47 % Source : [Bro08]
% 0.30/0.47 % Names : ZFC283l [Bro08]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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, 0.00 v3.7.0
% 0.30/0.47 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 3 def)
% 0.30/0.47 % Number of atoms : 25 ( 3 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 9 ( 6 avg)
% 0.30/0.47 % Number of connectives : 74 ( 0 ~; 0 |; 2 &; 57 @)
% 0.30/0.47 % ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 22 ( 6 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 9 ( 8 usr; 1 con; 0-3 aty)
% 0.30/0.47 % Number of variables : 18 ( 5 ^; 12 !; 1 ?; 18 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : http://mathgate.info/detsetitem.php?id=376
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(in_type,type,
% 0.30/0.47 in: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(subset_type,type,
% 0.30/0.47 subset: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(kpair_type,type,
% 0.30/0.47 kpair: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(cartprod_type,type,
% 0.30/0.47 cartprod: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(breln_type,type,
% 0.30/0.47 breln: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln,definition,
% 0.30/0.47 ( breln
% 0.30/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1_type,type,
% 0.30/0.47 breln1: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1,definition,
% 0.30/0.47 ( breln1
% 0.30/0.47 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compset_type,type,
% 0.30/0.47 breln1compset: $i > $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compE_type,type,
% 0.30/0.47 breln1compE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compE,definition,
% 0.30/0.47 ( breln1compE
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.30/0.47 => ? [Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ A )
% 0.30/0.47 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.30/0.47 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compEex,conjecture,
% 0.30/0.47 ( breln1compE
% 0.30/0.47 => ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ! [Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.30/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.30/0.47 => Xphi ) ) )
% 0.30/0.47 => Xphi ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.48/1.29 ---- Embedded in THF ---
% 1.48/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.30 %%% Generated on Tue Feb 24 12:34:02 EST 2026
% 1.48/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.30 %%% Logic specification used:
% 1.48/1.30 %%% thf(spec, logic, $$dhol).
% 1.48/1.30
% 1.48/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.sYxiJQxlj4/DTF2DTF20814.p
% See solution above
% 1.48/1.30 ------------------------
% 1.68/1.31 ---- Cleaned THF ---
% 1.68/1.31 thf(in_type,type,
% 1.68/1.31 in: $i > $i > $o ).
% 1.68/1.31
% 1.68/1.31 thf(subset_type,type,
% 1.68/1.31 subset: $i > $i > $o ).
% 1.68/1.31
% 1.68/1.31 thf(kpair_type,type,
% 1.68/1.31 kpair: $i > $i > $i ).
% 1.68/1.31
% 1.68/1.31 thf(cartprod_type,type,
% 1.68/1.31 cartprod: $i > $i > $i ).
% 1.68/1.31
% 1.68/1.31 thf(breln_type,type,
% 1.68/1.31 breln: $i > $i > $i > $o ).
% 1.68/1.31
% 1.68/1.31 thf(breln,definition,
% 1.68/1.31 ( breln
% 1.68/1.31 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(breln1_type,type,
% 1.68/1.31 breln1: $i > $i > $o ).
% 1.68/1.31
% 1.68/1.31 thf(breln1,definition,
% 1.68/1.31 ( breln1
% 1.68/1.31 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(breln1compset_type,type,
% 1.68/1.31 breln1compset: $i > $i > $i > $i ).
% 1.68/1.31
% 1.68/1.31 thf(breln1compE_type,type,
% 1.68/1.31 breln1compE: $o ).
% 1.68/1.31
% 1.68/1.31 thf(breln1compE,definition,
% 1.68/1.31 ( breln1compE
% 1.68/1.31 = ( ! [A: $i,R: $i] :
% 1.68/1.31 ( ( breln1 @ A @ R )
% 1.68/1.31 => ! [S: $i] :
% 1.68/1.31 ( ( breln1 @ A @ S )
% 1.68/1.31 => ! [Xx: $i] :
% 1.68/1.31 ( ( in @ Xx @ A )
% 1.68/1.31 => ! [Xy: $i] :
% 1.68/1.31 ( ( in @ Xy @ A )
% 1.68/1.31 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 1.68/1.31 => ? [Xz: $i] :
% 1.68/1.31 ( ( in @ Xz @ A )
% 1.68/1.31 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 1.68/1.31 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(breln1compEex,conjecture,
% 1.68/1.31 ( breln1compE
% 1.68/1.31 => ! [A: $i,R: $i] :
% 1.68/1.31 ( ( breln1 @ A @ R )
% 1.68/1.31 => ! [S: $i] :
% 1.68/1.31 ( ( breln1 @ A @ S )
% 1.68/1.31 => ! [Xx: $i] :
% 1.68/1.31 ( ( in @ Xx @ A )
% 1.68/1.31 => ! [Xy: $i] :
% 1.68/1.31 ( ( in @ Xy @ A )
% 1.68/1.31 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 1.68/1.31 => ! [Xphi: $o] :
% 1.68/1.31 ( ! [Xz: $i] :
% 1.68/1.31 ( ( in @ Xz @ A )
% 1.68/1.31 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 1.68/1.31 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 1.68/1.31 => Xphi ) ) )
% 1.68/1.31 => Xphi ) ) ) ) ) ) ) ).
% 1.68/1.31 ------------------------
% 1.68/1.32 % (21176)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_20814 for (2999ds/2Mi)
% 1.68/1.32 % (21173)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_20814 for (2999ds/4Mi)
% 1.68/1.32 % (21176)Instruction limit reached!
% 1.68/1.32 % (21176)------------------------------
% 1.68/1.32 % (21176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (21176)Termination reason: Unknown
% 1.68/1.32 % (21176)Termination phase: Property scanning
% 1.68/1.32
% 1.68/1.32 % (21176)Memory used [KB]: 1023
% 1.68/1.32 % (21176)Time elapsed: 0.002 s
% 1.68/1.32 % (21176)Instructions burned: 3 (million)
% 1.68/1.32 % (21176)------------------------------
% 1.68/1.32 % (21176)------------------------------
% 1.68/1.32 % (21173)Instruction limit reached!
% 1.68/1.32 % (21173)------------------------------
% 1.68/1.32 % (21173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (21173)Termination reason: Unknown
% 1.68/1.32 % (21173)Termination phase: Saturation
% 1.68/1.32
% 1.68/1.32 % (21173)Memory used [KB]: 5500
% 1.68/1.32 % (21173)Time elapsed: 0.003 s
% 1.68/1.32 % (21173)Instructions burned: 6 (million)
% 1.68/1.32 % (21173)------------------------------
% 1.68/1.32 % (21173)------------------------------
% 1.68/1.33 % (21172)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20814 for (2999ds/183Mi)
% 1.68/1.33 % (21174)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_20814 for (2999ds/27Mi)
% 1.68/1.33 % (21175)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20814 for (2999ds/2Mi)
% 1.68/1.33 % (21177)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_20814 for (2999ds/275Mi)
% 1.68/1.33 % (21179)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20814 for (2999ds/18Mi)
% 1.68/1.33 % (21175)Instruction limit reached!
% 1.68/1.33 % (21175)------------------------------
% 1.68/1.33 % (21175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (21175)Termination reason: Unknown
% 1.68/1.33 % (21175)Termination phase: shuffling
% 1.68/1.33
% 1.68/1.33 % (21175)Memory used [KB]: 1023
% 1.68/1.33 % (21175)Time elapsed: 0.003 s
% 1.68/1.33 % (21175)Instructions burned: 2 (million)
% 1.68/1.33 % (21175)------------------------------
% 1.68/1.33 % (21175)------------------------------
% 1.68/1.33 % (21180)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20814 for (2999ds/3Mi)
% 1.68/1.33 % (21180)Instruction limit reached!
% 1.68/1.33 % (21180)------------------------------
% 1.68/1.33 % (21180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (21180)Termination reason: Unknown
% 1.68/1.33 % (21180)Termination phase: Property scanning
% 1.68/1.33
% 1.68/1.33 % (21180)Memory used [KB]: 1023
% 1.68/1.33 % (21180)Time elapsed: 0.002 s
% 1.68/1.33 % (21180)Instructions burned: 3 (million)
% 1.68/1.33 % (21180)------------------------------
% 1.68/1.33 % (21180)------------------------------
% 1.68/1.33 % (21181)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_20814 for (2999ds/37Mi)
% 1.68/1.34 % (21177)First to succeed.
% 1.68/1.34 % (21179)Instruction limit reached!
% 1.68/1.34 % (21179)------------------------------
% 1.68/1.34 % (21179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (21179)Termination reason: Unknown
% 1.68/1.34 % (21179)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (21179)Memory used [KB]: 5628
% 1.68/1.34 % (21179)Time elapsed: 0.013 s
% 1.68/1.34 % (21179)Instructions burned: 18 (million)
% 1.68/1.34 % (21179)------------------------------
% 1.68/1.34 % (21179)------------------------------
% 1.68/1.34 % (21172)Also succeeded, but the first one will report.
% 1.68/1.34 % (21183)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_20814 for (2999ds/3Mi)
% 1.68/1.34 % (21183)Instruction limit reached!
% 1.68/1.34 % (21183)------------------------------
% 1.68/1.34 % (21183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (21183)Termination reason: Unknown
% 1.68/1.34 % (21183)Termination phase: Property scanning
% 1.68/1.34
% 1.68/1.34 % (21183)Memory used [KB]: 1023
% 1.68/1.34 % (21183)Time elapsed: 0.002 s
% 1.68/1.34 % (21183)Instructions burned: 3 (million)
% 1.68/1.34 % (21183)------------------------------
% 1.68/1.34 % (21183)------------------------------
% 1.68/1.34 % (21177)Refutation found. Thanks to Tanya!
% 1.68/1.34 % SZS status Theorem for DTF2THF_20814
% 1.68/1.34 % SZS output start Proof for DTF2THF_20814
% 1.68/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.68/1.34 thf(func_def_1, type, subset: $i > $i > $o).
% 1.68/1.34 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.68/1.34 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.68/1.34 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.68/1.34 thf(func_def_6, type, breln1: $i > $i > $o).
% 1.68/1.34 thf(func_def_7, type, breln1compset: $i > $i > $i > $i).
% 1.68/1.34 thf(func_def_21, type, sK6: $i > $i > $i > $i > $i > $i).
% 1.68/1.34 thf(f83,plain,(
% 1.68/1.34 $false),
% 1.68/1.34 inference(avatar_sat_refutation,[status(thm)],[f64,f65,f82])).
% 1.68/1.34 thf(f82,plain,(
% 1.68/1.34 ~spl13_1),
% 1.68/1.34 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.68/1.34 thf(f81,plain,(
% 1.68/1.34 $false | ~spl13_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f80,f49])).
% 1.68/1.34 thf(f49,plain,(
% 1.68/1.34 ($true = (in @ sK10 @ sK8))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.68/1.34 thf(f34,plain,(
% 1.68/1.34 ((((($true = (in @ sK11 @ sK8)) & (($true != sK12) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ sK10 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ sK11) @ sK9)) | ($true = sK12))) & ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) = $true)) & ($true = (in @ sK10 @ sK8))) & ($true = (breln1 @ sK8 @ sK9))) & ($true = (breln1 @ sK8 @ sK7))) & (breln1compE = $true)),
% 1.68/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12])],[f17,f33,f32,f31,f30,f29])).
% 1.68/1.34 thf(f29,plain,(
% 1.68/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X1)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ X1) != $true) | ($true != (in @ (kpair @ X3 @ X6) @ X0)) | ((in @ (kpair @ X6 @ X4) @ X2) != $true) | ($true = X5))) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)) & ($true = (in @ X3 @ X1))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))) => (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK8)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ X3 @ X6) @ sK7)) | ((in @ (kpair @ X6 @ X4) @ X2) != $true) | ($true = X5))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK8 @ sK7 @ X2)))) & ($true = (in @ X3 @ sK8))) & ((breln1 @ sK8 @ X2) = $true)) & ($true = (breln1 @ sK8 @ sK7)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f30,plain,(
% 1.68/1.34 ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK8)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ X3 @ X6) @ sK7)) | ((in @ (kpair @ X6 @ X4) @ X2) != $true) | ($true = X5))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK8 @ sK7 @ X2)))) & ($true = (in @ X3 @ sK8))) & ((breln1 @ sK8 @ X2) = $true)) => (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK8)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ X3 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ X4) @ sK9)) | ($true = X5))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK8 @ sK7 @ sK9)))) & ($true = (in @ X3 @ sK8))) & ($true = (breln1 @ sK8 @ sK9)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f31,plain,(
% 1.68/1.34 ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK8)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ X3 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ X4) @ sK9)) | ($true = X5))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK8 @ sK7 @ sK9)))) & ($true = (in @ X3 @ sK8))) => (? [X4 : $i] : (($true = (in @ X4 @ sK8)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ sK10 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ X4) @ sK9)) | ($true = X5))) & ($true = (in @ (kpair @ sK10 @ X4) @ (breln1compset @ sK8 @ sK7 @ sK9)))) & ($true = (in @ sK10 @ sK8)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f32,plain,(
% 1.68/1.34 ? [X4 : $i] : (($true = (in @ X4 @ sK8)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ sK10 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ X4) @ sK9)) | ($true = X5))) & ($true = (in @ (kpair @ sK10 @ X4) @ (breln1compset @ sK8 @ sK7 @ sK9)))) => (($true = (in @ sK11 @ sK8)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ sK10 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ sK11) @ sK9)) | ($true = X5))) & ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) = $true))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f33,plain,(
% 1.68/1.34 ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ sK10 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ sK11) @ sK9)) | ($true = X5))) => (($true != sK12) & ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ sK10 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ sK11) @ sK9)) | ($true = sK12)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f17,plain,(
% 1.68/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X1)) & ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((in @ X6 @ X1) != $true) | ($true != (in @ (kpair @ X3 @ X6) @ X0)) | ((in @ (kpair @ X6 @ X4) @ X2) != $true) | ($true = X5))) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)) & ($true = (in @ X3 @ X1))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))) & (breln1compE = $true)),
% 1.68/1.34 inference(flattening,[status(thm)],[f16])).
% 1.68/1.34 thf(f16,plain,(
% 1.68/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((($true = X5) | ((in @ (kpair @ X6 @ X4) @ X2) != $true)) | ($true != (in @ (kpair @ X3 @ X6) @ X0))) | ((in @ X6 @ X1) != $true))) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)) & ($true = (in @ X4 @ X1))) & ($true = (in @ X3 @ X1))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))) & (breln1compE = $true)),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f10])).
% 1.68/1.34 thf(f10,plain,(
% 1.68/1.34 ~((breln1compE = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X1 @ X0)) => ! [X2 : $i] : (($true = (breln1 @ X1 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ! [X4 : $i] : (($true = (in @ X4 @ X1)) => (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) => ! [X5 : $o] : (! [X6 : $i] : (((in @ X6 @ X1) = $true) => (($true = (in @ (kpair @ X3 @ X6) @ X0)) => (((in @ (kpair @ X6 @ X4) @ X2) = $true) => ($true = X5)))) => ($true = X5))))))))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f9])).
% 1.68/1.34 thf(f9,plain,(
% 1.68/1.34 ~(breln1compE => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) => ! [X5 : $o] : (! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X3 @ X6) @ X0) => ((in @ (kpair @ X6 @ X4) @ X2) => X5))) => X5)))))))),
% 1.68/1.34 inference(rectify,[status(thm)],[f5])).
% 1.68/1.34 thf(f5,negated_conjecture,(
% 1.68/1.34 ~(breln1compE => ! [X3 : $i,X0 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i] : ((breln1 @ X0 @ X4) => ! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ (breln1compset @ X0 @ X3 @ X4)) => ! [X8 : $o] : (! [X7 : $i] : ((in @ X7 @ X0) => ((in @ (kpair @ X5 @ X7) @ X3) => ((in @ (kpair @ X7 @ X6) @ X4) => X8))) => X8)))))))),
% 1.68/1.34 inference(negated_conjecture,[status(cth)],[f4])).
% 1.68/1.34 thf(f4,conjecture,(
% 1.68/1.34 breln1compE => ! [X3 : $i,X0 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i] : ((breln1 @ X0 @ X4) => ! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ (breln1compset @ X0 @ X3 @ X4)) => ! [X8 : $o] : (! [X7 : $i] : ((in @ X7 @ X0) => ((in @ (kpair @ X5 @ X7) @ X3) => ((in @ (kpair @ X7 @ X6) @ X4) => X8))) => X8))))))),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.sYxiJQxlj4/DTF2THF_20814.p',breln1compEex)).
% 1.68/1.34 thf(f80,plain,(
% 1.68/1.34 ($true != (in @ sK10 @ sK8)) | ~spl13_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f79,f48])).
% 1.68/1.34 thf(f48,plain,(
% 1.68/1.34 ($true = (breln1 @ sK8 @ sK9))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.68/1.34 thf(f79,plain,(
% 1.68/1.34 ($true != (breln1 @ sK8 @ sK9)) | ($true != (in @ sK10 @ sK8)) | ~spl13_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f78,f50])).
% 1.68/1.34 thf(f50,plain,(
% 1.68/1.34 ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) = $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.68/1.34 thf(f78,plain,(
% 1.68/1.34 ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) != $true) | ($true != (breln1 @ sK8 @ sK9)) | ($true != (in @ sK10 @ sK8)) | ~spl13_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f77,f47])).
% 1.68/1.34 thf(f47,plain,(
% 1.68/1.34 ($true = (breln1 @ sK8 @ sK7))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.68/1.34 thf(f77,plain,(
% 1.68/1.34 ($true != (breln1 @ sK8 @ sK7)) | ($true != (in @ sK10 @ sK8)) | ($true != (breln1 @ sK8 @ sK9)) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) != $true) | ~spl13_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f76,f56])).
% 1.68/1.34 thf(f56,plain,(
% 1.68/1.34 ($true = sP0)),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.68/1.34 thf(f55,plain,(
% 1.68/1.34 ($true = sP0) | ($true != $true)),
% 1.68/1.34 inference(definition_unfolding,[status(thm)],[f44,f46])).
% 1.68/1.34 thf(f46,plain,(
% 1.68/1.34 (breln1compE = $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.68/1.34 thf(f44,plain,(
% 1.68/1.34 ($true = sP0) | (breln1compE != $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f28])).
% 1.68/1.34 thf(f28,plain,(
% 1.68/1.34 ((breln1compE = $true) | ($true != sP0)) & (($true = sP0) | (breln1compE != $true))),
% 1.68/1.34 inference(nnf_transformation,[status(thm)],[f19])).
% 1.68/1.34 thf(f19,plain,(
% 1.68/1.34 (breln1compE = $true) <=> ($true = sP0)),
% 1.68/1.34 inference(definition_folding,[status(thm)],[f15,f18])).
% 1.68/1.34 thf(f18,plain,(
% 1.68/1.34 ($true = sP0) <=> ! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X0) != $true) | ? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ X1)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ X0) = $true)) | ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (in @ X3 @ X0)))))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.68/1.34 thf(f15,plain,(
% 1.68/1.34 (breln1compE = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X0) != $true) | ? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ X1)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ X0) = $true)) | ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (in @ X3 @ X0)))))),
% 1.68/1.34 inference(flattening,[status(thm)],[f14])).
% 1.68/1.34 thf(f14,plain,(
% 1.68/1.34 (breln1compE = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ X1)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ X0) = $true)) | ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) | ((in @ X4 @ X0) != $true)) | ($true != (in @ X3 @ X0))) | ($true != (breln1 @ X0 @ X2))) | ($true != (breln1 @ X0 @ X1)))),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f8])).
% 1.68/1.34 thf(f8,plain,(
% 1.68/1.34 (breln1compE = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => ! [X4 : $i] : (((in @ X4 @ X0) = $true) => (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) => ? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ X1)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ X0) = $true)))))))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f7])).
% 1.68/1.34 thf(f7,plain,(
% 1.68/1.34 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ? [X5 : $i] : ((in @ (kpair @ X3 @ X5) @ X1) & (in @ (kpair @ X5 @ X4) @ X2) & (in @ X5 @ X0))))))) = breln1compE)),
% 1.68/1.34 inference(rectify,[status(thm)],[f3])).
% 1.68/1.34 thf(f3,axiom,(
% 1.68/1.34 (! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i] : ((breln1 @ X0 @ X4) => ! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ (breln1compset @ X0 @ X3 @ X4)) => ? [X7 : $i] : ((in @ (kpair @ X5 @ X7) @ X3) & (in @ (kpair @ X7 @ X6) @ X4) & (in @ X7 @ X0))))))) = breln1compE)),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.sYxiJQxlj4/DTF2THF_20814.p',breln1compE)).
% 1.68/1.34 thf(f76,plain,(
% 1.68/1.34 ($true != sP0) | ($true != (breln1 @ sK8 @ sK7)) | ($true != (breln1 @ sK8 @ sK9)) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) != $true) | ($true != (in @ sK10 @ sK8)) | ~spl13_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f75,f53])).
% 1.68/1.34 thf(f53,plain,(
% 1.68/1.34 ($true = (in @ sK11 @ sK8))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.68/1.34 thf(f75,plain,(
% 1.68/1.34 ($true != (in @ sK11 @ sK8)) | ($true != (in @ sK10 @ sK8)) | ($true != sP0) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) != $true) | ($true != (breln1 @ sK8 @ sK9)) | ($true != (breln1 @ sK8 @ sK7)) | ~spl13_1),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.68/1.34 thf(f74,plain,(
% 1.68/1.34 ($true != (breln1 @ sK8 @ sK7)) | ($true != $true) | ($true != (in @ sK11 @ sK8)) | ($true != (in @ sK10 @ sK8)) | ($true != sP0) | ($true != (breln1 @ sK8 @ sK9)) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) != $true) | ~spl13_1),
% 1.68/1.34 inference(duplicate_literal_removal,[status(thm)],[f73])).
% 1.68/1.34 thf(f73,plain,(
% 1.68/1.34 ($true != (in @ sK10 @ sK8)) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) != $true) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9)) != $true) | ($true != (in @ sK11 @ sK8)) | ($true != (breln1 @ sK8 @ sK9)) | ($true != $true) | ($true != sP0) | ($true != (breln1 @ sK8 @ sK7)) | ($true != (breln1 @ sK8 @ sK9)) | ($true != (in @ sK10 @ sK8)) | ($true != (in @ sK11 @ sK8)) | ($true != (breln1 @ sK8 @ sK7)) | ~spl13_1),
% 1.68/1.34 inference(superposition,[status(thm)],[f72,f35])).
% 1.68/1.34 thf(f35,plain,(
% 1.68/1.34 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = (in @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X9 @ X6)) | ($true != (breln1 @ X6 @ X7)) | ($true != sP0) | ($true != (in @ X10 @ X6)) | ($true != (breln1 @ X6 @ X8))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f27])).
% 1.68/1.34 thf(f27,plain,(
% 1.68/1.34 (($true = sP0) | (((breln1 @ sK1 @ sK2) = $true) & (($true = (breln1 @ sK1 @ sK3)) & ((($true = (in @ sK5 @ sK1)) & ! [X5 : $i] : (((in @ (kpair @ sK4 @ X5) @ sK2) != $true) | ($true != (in @ (kpair @ X5 @ sK5) @ sK3)) | ($true != (in @ X5 @ sK1))) & ((in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3)) = $true)) & ((in @ sK4 @ sK1) = $true))))) & (! [X6 : $i,X7 : $i] : (($true != (breln1 @ X6 @ X7)) | ! [X8 : $i] : (($true != (breln1 @ X6 @ X8)) | ! [X9 : $i] : (! [X10 : $i] : (($true != (in @ X10 @ X6)) | (($true = (in @ (kpair @ X9 @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) & ((in @ (kpair @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8) = $true) & ($true = (in @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6))) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8)))) | ($true != (in @ X9 @ X6))))) | ($true != sP0))),
% 1.68/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f21,f26,f25,f24,f23,f22])).
% 1.68/1.34 thf(f22,plain,(
% 1.68/1.34 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X0) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ X1)) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ((in @ X5 @ X0) != $true)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (in @ X3 @ X0))))) => (((breln1 @ sK1 @ sK2) = $true) & ? [X2 : $i] : (((breln1 @ sK1 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ sK2)) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ($true != (in @ X5 @ sK1))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK2 @ X2)))) & ((in @ X3 @ sK1) = $true))))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f23,plain,(
% 1.68/1.34 ? [X2 : $i] : (((breln1 @ sK1 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ sK2)) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ($true != (in @ X5 @ sK1))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK2 @ X2)))) & ((in @ X3 @ sK1) = $true))) => (($true = (breln1 @ sK1 @ sK3)) & ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ sK2)) | ($true != (in @ (kpair @ X5 @ X4) @ sK3)) | ($true != (in @ X5 @ sK1))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK2 @ sK3)))) & ((in @ X3 @ sK1) = $true)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f24,plain,(
% 1.68/1.34 ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ sK2)) | ($true != (in @ (kpair @ X5 @ X4) @ sK3)) | ($true != (in @ X5 @ sK1))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK2 @ sK3)))) & ((in @ X3 @ sK1) = $true)) => (? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ! [X5 : $i] : (((in @ (kpair @ sK4 @ X5) @ sK2) != $true) | ($true != (in @ (kpair @ X5 @ X4) @ sK3)) | ($true != (in @ X5 @ sK1))) & ($true = (in @ (kpair @ sK4 @ X4) @ (breln1compset @ sK1 @ sK2 @ sK3)))) & ((in @ sK4 @ sK1) = $true))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f25,plain,(
% 1.68/1.34 ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ! [X5 : $i] : (((in @ (kpair @ sK4 @ X5) @ sK2) != $true) | ($true != (in @ (kpair @ X5 @ X4) @ sK3)) | ($true != (in @ X5 @ sK1))) & ($true = (in @ (kpair @ sK4 @ X4) @ (breln1compset @ sK1 @ sK2 @ sK3)))) => (($true = (in @ sK5 @ sK1)) & ! [X5 : $i] : (((in @ (kpair @ sK4 @ X5) @ sK2) != $true) | ($true != (in @ (kpair @ X5 @ sK5) @ sK3)) | ($true != (in @ X5 @ sK1))) & ((in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3)) = $true))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f26,plain,(
% 1.68/1.34 ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i,X10 : $i] : (? [X11 : $i] : (((in @ (kpair @ X9 @ X11) @ X7) = $true) & ($true = (in @ (kpair @ X11 @ X10) @ X8)) & ($true = (in @ X11 @ X6))) => (($true = (in @ (kpair @ X9 @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) & ((in @ (kpair @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8) = $true) & ($true = (in @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6))))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f21,plain,(
% 1.68/1.34 (($true = sP0) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X0) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ X1)) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ((in @ X5 @ X0) != $true)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (in @ X3 @ X0)))))) & (! [X6 : $i,X7 : $i] : (($true != (breln1 @ X6 @ X7)) | ! [X8 : $i] : (($true != (breln1 @ X6 @ X8)) | ! [X9 : $i] : (! [X10 : $i] : (($true != (in @ X10 @ X6)) | ? [X11 : $i] : (((in @ (kpair @ X9 @ X11) @ X7) = $true) & ($true = (in @ (kpair @ X11 @ X10) @ X8)) & ($true = (in @ X11 @ X6))) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8)))) | ($true != (in @ X9 @ X6))))) | ($true != sP0))),
% 1.68/1.34 inference(rectify,[status(thm)],[f20])).
% 1.68/1.34 thf(f20,plain,(
% 1.68/1.34 (($true = sP0) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X0) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ X1)) | ($true != (in @ (kpair @ X5 @ X4) @ X2)) | ((in @ X5 @ X0) != $true)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (in @ X3 @ X0)))))) & (! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X0) != $true) | ? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ X1)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ X0) = $true)) | ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (in @ X3 @ X0))))) | ($true != sP0))),
% 1.68/1.34 inference(nnf_transformation,[status(thm)],[f18])).
% 1.68/1.34 thf(f72,plain,(
% 1.68/1.34 ( ! [X0 : $i] : (($true != (in @ (sK6 @ sK11 @ sK10 @ sK9 @ sK7 @ X0) @ sK8)) | ($true != (in @ sK11 @ X0)) | ($true != (breln1 @ X0 @ sK7)) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ X0 @ sK7 @ sK9)) != $true) | ($true != (in @ sK10 @ X0)) | ($true != (breln1 @ X0 @ sK9))) ) | ~spl13_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f71,f56])).
% 1.68/1.34 thf(f71,plain,(
% 1.68/1.34 ( ! [X0 : $i] : (($true != (breln1 @ X0 @ sK7)) | ($true != (in @ sK10 @ X0)) | ($true != sP0) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ X0 @ sK7 @ sK9)) != $true) | ($true != (breln1 @ X0 @ sK9)) | ($true != (in @ (sK6 @ sK11 @ sK10 @ sK9 @ sK7 @ X0) @ sK8)) | ($true != (in @ sK11 @ X0))) ) | ~spl13_1),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.68/1.34 thf(f70,plain,(
% 1.68/1.34 ( ! [X0 : $i] : (($true != sP0) | ($true != (breln1 @ X0 @ sK9)) | ($true != (breln1 @ X0 @ sK7)) | ($true != (in @ sK10 @ X0)) | ($true != (in @ (sK6 @ sK11 @ sK10 @ sK9 @ sK7 @ X0) @ sK8)) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ X0 @ sK7 @ sK9)) != $true) | ($true != (in @ sK11 @ X0)) | ($true != $true)) ) | ~spl13_1),
% 1.68/1.34 inference(duplicate_literal_removal,[status(thm)],[f69])).
% 1.68/1.34 thf(f69,plain,(
% 1.68/1.34 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ sK10 @ X0)) | ($true != (in @ sK11 @ X0)) | ($true != (in @ sK10 @ X0)) | ($true != (in @ sK11 @ X0)) | ($true != sP0) | ($true != (breln1 @ X0 @ sK7)) | ($true != (breln1 @ X0 @ sK9)) | ($true != (breln1 @ X0 @ sK9)) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ X0 @ sK7 @ sK9)) != $true) | ($true != (in @ (sK6 @ sK11 @ sK10 @ sK9 @ sK7 @ X0) @ sK8)) | ((in @ (kpair @ sK10 @ sK11) @ (breln1compset @ X0 @ sK7 @ sK9)) != $true) | ($true != (breln1 @ X0 @ sK7))) ) | ~spl13_1),
% 1.68/1.34 inference(superposition,[status(thm)],[f68,f36])).
% 1.68/1.34 thf(f36,plain,(
% 1.68/1.34 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((in @ (kpair @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8) = $true) | ($true != (in @ X10 @ X6)) | ($true != (breln1 @ X6 @ X7)) | ($true != (in @ X9 @ X6)) | ($true != (breln1 @ X6 @ X8)) | ($true != sP0) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8)))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f27])).
% 1.68/1.34 thf(f68,plain,(
% 1.68/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2) @ sK11) @ sK9) != $true) | ($true != (in @ sK10 @ X2)) | ($true != (breln1 @ X2 @ sK7)) | ((breln1 @ X2 @ X1) != $true) | ((in @ (sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2) @ sK8) != $true) | ((in @ X0 @ X2) != $true) | ($true != (in @ (kpair @ sK10 @ X0) @ (breln1compset @ X2 @ sK7 @ X1)))) ) | ~spl13_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f67,f56])).
% 1.68/1.34 thf(f67,plain,(
% 1.68/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ sK10 @ X0) @ (breln1compset @ X2 @ sK7 @ X1))) | ((in @ (kpair @ (sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2) @ sK11) @ sK9) != $true) | ((in @ (sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2) @ sK8) != $true) | ((breln1 @ X2 @ X1) != $true) | ($true != (breln1 @ X2 @ sK7)) | ($true != sP0) | ((in @ X0 @ X2) != $true) | ($true != (in @ sK10 @ X2))) ) | ~spl13_1),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.68/1.34 thf(f66,plain,(
% 1.68/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((breln1 @ X2 @ X1) != $true) | ((in @ (kpair @ (sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2) @ sK11) @ sK9) != $true) | ((in @ X0 @ X2) != $true) | ((in @ (sK6 @ X0 @ sK10 @ X1 @ sK7 @ X2) @ sK8) != $true) | ($true != (in @ sK10 @ X2)) | ($true != (in @ (kpair @ sK10 @ X0) @ (breln1compset @ X2 @ sK7 @ X1))) | ($true != $true) | ($true != (breln1 @ X2 @ sK7)) | ($true != sP0)) ) | ~spl13_1),
% 1.68/1.34 inference(superposition,[status(thm)],[f59,f37])).
% 1.68/1.34 thf(f37,plain,(
% 1.68/1.34 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = (in @ (kpair @ X9 @ (sK6 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X10 @ X6)) | ($true != (breln1 @ X6 @ X8)) | ($true != sP0) | ($true != (breln1 @ X6 @ X7)) | ($true != (in @ X9 @ X6))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f27])).
% 1.68/1.34 thf(f59,plain,(
% 1.68/1.34 ( ! [X6 : $i] : (($true != (in @ (kpair @ sK10 @ X6) @ sK7)) | ((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ X6 @ sK11) @ sK9))) ) | ~spl13_1),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.68/1.34 thf(f58,definition,(
% 1.68/1.34 spl13_1 <=> ! [X6 : $i] : (((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ sK10 @ X6) @ sK7)) | ($true != (in @ (kpair @ X6 @ sK11) @ sK9)))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition])).
% 1.68/1.34 thf(f65,plain,(
% 1.68/1.34 ~spl13_2),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f52,f61])).
% 1.68/1.34 thf(f61,definition,(
% 1.68/1.34 spl13_2 <=> ($true = sK12)),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition])).
% 1.68/1.34 thf(f52,plain,(
% 1.68/1.34 ($true != sK12)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.68/1.34 thf(f64,plain,(
% 1.68/1.34 spl13_1 | spl13_2),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f51,f61,f58])).
% 1.68/1.34 thf(f51,plain,(
% 1.68/1.34 ( ! [X6 : $i] : (($true = sK12) | ((in @ X6 @ sK8) != $true) | ($true != (in @ (kpair @ X6 @ sK11) @ sK9)) | ($true != (in @ (kpair @ sK10 @ X6) @ sK7))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.68/1.34 % SZS output end Proof for DTF2THF_20814
% 1.68/1.34 % (21177)------------------------------
% 1.68/1.34 % (21177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (21177)Termination reason: Refutation
% 1.68/1.34
% 1.68/1.34 % (21177)Memory used [KB]: 5628
% 1.68/1.34 % (21177)Time elapsed: 0.014 s
% 1.68/1.34 % (21177)Instructions burned: 13 (million)
% 1.68/1.34 % (21177)------------------------------
% 1.68/1.34 % (21177)------------------------------
% 1.68/1.34 % (21171)Success in time 0.029 s
%------------------------------------------------------------------------------