%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU785^2 : 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 : n016.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 09:37:11 AM UTC 2026
% Result : Theorem 1.61s 1.34s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 74 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 1550 ( 394 equ; 0 cnn)
% Maximal formula atoms : 14 ( 20 avg)
% Number of connectives : 1794 ( 194 ~; 164 |; 148 &;1210 @)
% ( 8 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 21 con; 0-2 aty)
% Number of variables : 222 ( 0 ^; 136 !; 86 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
breln1: $i > $i > $o ).
thf(f103,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f84,f95,f102]) ).
thf(f102,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| ~ spl15_1 ),
inference(subsumption_resolution,[status(thm)],[f100,f38]) ).
thf(f38,plain,
( $true
= ( breln1 @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK0 @ sK2 ) ) )
& ( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) )
& ( $true
= ( breln1 @ sK1 @ sK2 ) )
& ( $true
= ( breln1 @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f18,f22,f21,f20,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
& ( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK0 @ X2 ) ) )
& ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK0 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) )
& ( $true
= ( breln1 @ sK1 @ X2 ) ) )
& ( $true
= ( breln1 @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK0 @ X2 ) ) )
& ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK0 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) )
& ( $true
= ( breln1 @ sK1 @ X2 ) ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK0 @ sK2 ) ) )
& ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK0 ) )
| ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK2 ) ) ) ) )
& ( $true
= ( breln1 @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK0 @ sK2 ) ) )
& ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK0 ) )
| ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK2 ) ) ) ) )
=> ( ( $true
= ( in @ sK3 @ sK1 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ X4 ) @ ( binunion @ sK0 @ sK2 ) ) )
& ( ( $true
= ( in @ ( kpair @ sK3 @ X4 ) @ sK0 ) )
| ( ( in @ ( kpair @ sK3 @ X4 ) @ sK2 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ X4 ) @ ( binunion @ sK0 @ sK2 ) ) )
& ( ( $true
= ( in @ ( kpair @ sK3 @ X4 ) @ sK0 ) )
| ( ( in @ ( kpair @ sK3 @ X4 ) @ sK2 )
= $true ) ) )
=> ( ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK0 @ sK2 ) ) )
& ( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
& ( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( breln1unionIR = $true )
& ( breln1unionIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( breln1unionIL
=> ( breln1unionIR
=> ! [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 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( breln1unionIL
=> ( breln1unionIR
=> ! [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 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( breln1unionIL
=> ( breln1unionIR
=> ! [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 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BWja0DuX9z/DTF2THF_2901.p',breln1unionI) ).
thf(f100,plain,
( ( $true
!= ( breln1 @ sK1 @ sK0 ) )
| ~ spl15_1 ),
inference(subsumption_resolution,[status(thm)],[f99,f43]) ).
thf(f43,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f99,plain,
( ( $true
!= ( in @ sK3 @ sK1 ) )
| ( $true
!= ( breln1 @ sK1 @ sK0 ) )
| ~ spl15_1 ),
inference(subsumption_resolution,[status(thm)],[f98,f42]) ).
thf(f42,plain,
( $true
= ( in @ sK4 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f98,plain,
( ( $true
!= ( in @ sK4 @ sK1 ) )
| ( $true
!= ( in @ sK3 @ sK1 ) )
| ( $true
!= ( breln1 @ sK1 @ sK0 ) )
| ~ spl15_1 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK4 @ sK1 ) )
| ( $true
!= ( breln1 @ sK1 @ sK0 ) )
| ( $true
!= ( in @ sK3 @ sK1 ) )
| ~ spl15_1 ),
inference(superposition,[status(thm)],[f96,f39]) ).
thf(f39,plain,
( $true
= ( breln1 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f96,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ X0 @ sK2 ) )
| ( $true
!= ( in @ sK3 @ X0 ) )
| ( $true
!= ( in @ sK4 @ X0 ) )
| ( $true
!= ( breln1 @ X0 @ sK0 ) ) )
| ~ spl15_1 ),
inference(subsumption_resolution,[status(thm)],[f89,f79]) ).
thf(f79,plain,
( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ~ spl15_1 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl15_1
<=> ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl15_1])],[avatar_definition]) ).
thf(f89,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK4 @ X0 ) )
| ( $true
!= ( in @ sK3 @ X0 ) )
| ( $true
!= ( breln1 @ X0 @ sK2 ) )
| ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ( $true
!= ( breln1 @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ sK4 @ X0 ) )
| ( $true
!= ( breln1 @ X0 @ sK2 ) )
| ( $true
!= ( in @ sK3 @ X0 ) )
| ( $true
!= ( breln1 @ X0 @ sK0 ) )
| ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) ),
inference(superposition,[status(thm)],[f41,f75]) ).
thf(f75,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) ) )
| ( $true
!= ( breln1 @ X6 @ X5 ) )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X7 ) )
| ( $true
!= ( in @ X8 @ X6 ) )
| ( ( breln1 @ X6 @ X7 )
!= $true )
| ( $true
!= ( in @ X9 @ X6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true
!= ( breln1 @ X6 @ X5 ) )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X7 ) )
| ( $true != $true )
| ( $true
!= ( in @ X8 @ X6 ) )
| ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) ) )
| ( ( breln1 @ X6 @ X7 )
!= $true )
| ( $true
!= ( in @ X9 @ X6 ) ) ),
inference(definition_unfolding,[status(thm)],[f53,f45]) ).
thf(f45,plain,
breln1unionIR = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f53,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true
!= ( breln1 @ X6 @ X5 ) )
| ( ( breln1 @ X6 @ X7 )
!= $true )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X7 ) )
| ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) ) )
| ( $true
!= ( in @ X8 @ X6 ) )
| ( breln1unionIR != $true ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( breln1unionIR = $true )
| ( ( $true
= ( breln1 @ sK11 @ sK10 ) )
& ( $true
= ( breln1 @ sK11 @ sK12 ) )
& ( $true
= ( in @ sK14 @ sK11 ) )
& ( $true
= ( in @ ( kpair @ sK13 @ sK14 ) @ sK12 ) )
& ( $true
!= ( in @ ( kpair @ sK13 @ sK14 ) @ ( binunion @ sK10 @ sK12 ) ) )
& ( $true
= ( in @ sK13 @ sK11 ) ) ) )
& ( ! [X5: $i,X6: $i] :
( ( $true
!= ( breln1 @ X6 @ X5 ) )
| ! [X7: $i] :
( ( ( breln1 @ X6 @ X7 )
!= $true )
| ! [X8: $i] :
( ! [X9: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X7 ) )
| ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) ) ) )
| ( $true
!= ( in @ X8 @ X6 ) ) ) ) )
| ( breln1unionIR != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14])],[f32,f36,f35,f34,f33]) ).
thf(f33,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) ) )
=> ( ( $true
= ( breln1 @ sK11 @ sK10 ) )
& ? [X2: $i] :
( ( ( breln1 @ sK11 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK11 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK10 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK11 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X2: $i] :
( ( ( breln1 @ sK11 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK11 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK10 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK11 ) ) ) )
=> ( ( $true
= ( breln1 @ sK11 @ sK12 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK11 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK12 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK10 @ sK12 ) ) ) )
& ( $true
= ( in @ X3 @ sK11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK11 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK12 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK10 @ sK12 ) ) ) )
& ( $true
= ( in @ X3 @ sK11 ) ) )
=> ( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK11 ) )
& ( ( in @ ( kpair @ sK13 @ X4 ) @ sK12 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK13 @ X4 ) @ ( binunion @ sK10 @ sK12 ) ) ) )
& ( $true
= ( in @ sK13 @ sK11 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK11 ) )
& ( ( in @ ( kpair @ sK13 @ X4 ) @ sK12 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK13 @ X4 ) @ ( binunion @ sK10 @ sK12 ) ) ) )
=> ( ( $true
= ( in @ sK14 @ sK11 ) )
& ( $true
= ( in @ ( kpair @ sK13 @ sK14 ) @ sK12 ) )
& ( $true
!= ( in @ ( kpair @ sK13 @ sK14 ) @ ( binunion @ sK10 @ sK12 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ( breln1unionIR = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) ) ) )
& ( ! [X5: $i,X6: $i] :
( ( $true
!= ( breln1 @ X6 @ X5 ) )
| ! [X7: $i] :
( ( ( breln1 @ X6 @ X7 )
!= $true )
| ! [X8: $i] :
( ! [X9: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X7 ) )
| ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) ) ) )
| ( $true
!= ( in @ X8 @ X6 ) ) ) ) )
| ( breln1unionIR != $true ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( breln1unionIR = $true )
| ? [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
!= $true )
| ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
!= $true )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) )
| ( breln1unionIR != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( breln1unionIR = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
!= $true )
| ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
!= $true )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( breln1 @ X0 @ X2 )
!= $true ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) )
<=> ( breln1unionIR = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ) )
<=> ( breln1unionIR = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( breln1unionIR
= ( ! [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 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( breln1unionIR
= ( ! [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 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BWja0DuX9z/DTF2THF_2901.p',breln1unionIR) ).
thf(f41,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f95,plain,
~ spl15_2,
inference(avatar_contradiction_clause,[status(thm)],[f94]) ).
thf(f94,plain,
( $false
| ~ spl15_2 ),
inference(subsumption_resolution,[status(thm)],[f93,f43]) ).
thf(f93,plain,
( ( $true
!= ( in @ sK3 @ sK1 ) )
| ~ spl15_2 ),
inference(subsumption_resolution,[status(thm)],[f92,f38]) ).
thf(f92,plain,
( ( $true
!= ( breln1 @ sK1 @ sK0 ) )
| ( $true
!= ( in @ sK3 @ sK1 ) )
| ~ spl15_2 ),
inference(subsumption_resolution,[status(thm)],[f91,f42]) ).
thf(f91,plain,
( ( $true
!= ( in @ sK4 @ sK1 ) )
| ( $true
!= ( in @ sK3 @ sK1 ) )
| ( $true
!= ( breln1 @ sK1 @ sK0 ) )
| ~ spl15_2 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true
!= ( in @ sK3 @ sK1 ) )
| ( $true
!= ( in @ sK4 @ sK1 ) )
| ( $true != $true )
| ( $true
!= ( breln1 @ sK1 @ sK0 ) )
| ~ spl15_2 ),
inference(superposition,[status(thm)],[f87,f39]) ).
thf(f87,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ X0 @ sK2 ) )
| ( $true
!= ( breln1 @ X0 @ sK0 ) )
| ( $true
!= ( in @ sK4 @ X0 ) )
| ( $true
!= ( in @ sK3 @ X0 ) ) )
| ~ spl15_2 ),
inference(subsumption_resolution,[status(thm)],[f86,f83]) ).
thf(f83,plain,
( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) )
| ~ spl15_2 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl15_2
<=> ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl15_2])],[avatar_definition]) ).
thf(f86,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) )
| ( $true
!= ( breln1 @ X0 @ sK0 ) )
| ( $true
!= ( breln1 @ X0 @ sK2 ) )
| ( $true
!= ( in @ sK3 @ X0 ) )
| ( $true
!= ( in @ sK4 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK4 @ X0 ) )
| ( $true
!= ( in @ sK3 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) )
| ( $true
!= ( breln1 @ X0 @ sK0 ) )
| ( $true
!= ( breln1 @ X0 @ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f41,f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( breln1 @ X0 @ X1 )
!= $true )
| ( ( breln1 @ X0 @ X2 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( breln1 @ X0 @ X2 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( $true != $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( ( breln1 @ X0 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f52,f44]) ).
thf(f44,plain,
breln1unionIL = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true )
| ( ( breln1 @ X0 @ X2 )
!= $true )
| ( ( breln1 @ X0 @ X1 )
!= $true )
| ( breln1unionIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) ) )
| ( ( breln1 @ X0 @ X2 )
!= $true ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) )
| ( breln1unionIL != $true ) )
& ( ( breln1unionIL = $true )
| ( ( $true
= ( in @ sK8 @ sK5 ) )
& ( $true
!= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK6 @ sK7 ) ) )
& ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ sK6 ) )
& ( $true
= ( in @ sK9 @ sK5 ) )
& ( $true
= ( breln1 @ sK5 @ sK7 ) )
& ( $true
= ( breln1 @ sK5 @ sK6 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f25,f29,f28,f27,f26]) ).
thf(f26,plain,
( ? [X5: $i,X6: $i] :
( ? [X7: $i] :
( ? [X8: $i] :
( ( $true
= ( in @ X8 @ X5 ) )
& ? [X9: $i] :
( ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X6 @ X7 ) ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ X6 ) )
& ( $true
= ( in @ X9 @ X5 ) ) ) )
& ( $true
= ( breln1 @ X5 @ X7 ) ) )
& ( $true
= ( breln1 @ X5 @ X6 ) ) )
=> ( ? [X7: $i] :
( ? [X8: $i] :
( ( $true
= ( in @ X8 @ sK5 ) )
& ? [X9: $i] :
( ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ sK6 @ X7 ) ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ sK6 ) )
& ( $true
= ( in @ X9 @ sK5 ) ) ) )
& ( $true
= ( breln1 @ sK5 @ X7 ) ) )
& ( $true
= ( breln1 @ sK5 @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X7: $i] :
( ? [X8: $i] :
( ( $true
= ( in @ X8 @ sK5 ) )
& ? [X9: $i] :
( ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ sK6 @ X7 ) ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ sK6 ) )
& ( $true
= ( in @ X9 @ sK5 ) ) ) )
& ( $true
= ( breln1 @ sK5 @ X7 ) ) )
=> ( ? [X8: $i] :
( ( $true
= ( in @ X8 @ sK5 ) )
& ? [X9: $i] :
( ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ sK6 @ sK7 ) ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ sK6 ) )
& ( $true
= ( in @ X9 @ sK5 ) ) ) )
& ( $true
= ( breln1 @ sK5 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X8: $i] :
( ( $true
= ( in @ X8 @ sK5 ) )
& ? [X9: $i] :
( ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ sK6 @ sK7 ) ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ sK6 ) )
& ( $true
= ( in @ X9 @ sK5 ) ) ) )
=> ( ( $true
= ( in @ sK8 @ sK5 ) )
& ? [X9: $i] :
( ( $true
!= ( in @ ( kpair @ sK8 @ X9 ) @ ( binunion @ sK6 @ sK7 ) ) )
& ( $true
= ( in @ ( kpair @ sK8 @ X9 ) @ sK6 ) )
& ( $true
= ( in @ X9 @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X9: $i] :
( ( $true
!= ( in @ ( kpair @ sK8 @ X9 ) @ ( binunion @ sK6 @ sK7 ) ) )
& ( $true
= ( in @ ( kpair @ sK8 @ X9 ) @ sK6 ) )
& ( $true
= ( in @ X9 @ sK5 ) ) )
=> ( ( $true
!= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK6 @ sK7 ) ) )
& ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ sK6 ) )
& ( $true
= ( in @ sK9 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) ) )
| ( ( breln1 @ X0 @ X2 )
!= $true ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) )
| ( breln1unionIL != $true ) )
& ( ( breln1unionIL = $true )
| ? [X5: $i,X6: $i] :
( ? [X7: $i] :
( ? [X8: $i] :
( ( $true
= ( in @ X8 @ X5 ) )
& ? [X9: $i] :
( ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X6 @ X7 ) ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ X6 ) )
& ( $true
= ( in @ X9 @ X5 ) ) ) )
& ( $true
= ( breln1 @ X5 @ X7 ) ) )
& ( $true
= ( breln1 @ X5 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ! [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true
!= ( in @ X4 @ X1 ) ) ) )
| ( $true
!= ( breln1 @ X1 @ X2 ) ) )
| ( $true
!= ( breln1 @ X1 @ X0 ) ) )
| ( breln1unionIL != $true ) )
& ( ( breln1unionIL = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ? [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
& ( $true
= ( in @ X4 @ X1 ) ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ! [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true
!= ( in @ X4 @ X1 ) ) ) )
| ( $true
!= ( breln1 @ X1 @ X2 ) ) )
| ( $true
!= ( breln1 @ X1 @ X0 ) ) )
<=> ( breln1unionIL = $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ( breln1unionIL = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true
!= ( in @ X4 @ X1 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( breln1 @ X1 @ X2 ) ) )
| ( $true
!= ( breln1 @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( breln1unionIL = $true )
<=> ! [X1: $i,X0: $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 ) @ X0 )
= $true )
=> ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( breln1unionIL
= ( ! [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 ) @ X0 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( breln1unionIL
= ( ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BWja0DuX9z/DTF2THF_2901.p',breln1unionIL) ).
thf(f84,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[status(thm)],[f40,f81,f77]) ).
thf(f40,plain,
( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU785^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n016.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:34:21 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU785^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Binary Relations on a Set
% 0.18/0.38 % Version : Especial > Reduced > Especial.
% 0.18/0.38 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.18/0.38 % (! y:i.in y A -> in (kpair x y) R | in (kpair x y) S ->
% 0.18/0.38 % in (kpair x y) (binunion R S)))))
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC287l [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.18/0.38 % Number of atoms : 25 ( 2 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 9 ( 8 avg)
% 0.18/0.38 % Number of connectives : 76 ( 0 ~; 1 |; 0 &; 58 @)
% 0.18/0.38 % ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 18 ( 7 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.18/0.38 % Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=350
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(in_type,type,
% 0.18/0.38 in: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(binunion_type,type,
% 0.18/0.38 binunion: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(kpair_type,type,
% 0.18/0.38 kpair: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(breln1_type,type,
% 0.18/0.38 breln1: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(breln1unionIL_type,type,
% 0.18/0.38 breln1unionIL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(breln1unionIL,definition,
% 0.18/0.38 ( breln1unionIL
% 0.18/0.38 = ( ! [A: $i,R: $i] :
% 0.18/0.38 ( ( breln1 @ A @ R )
% 0.18/0.38 => ! [S: $i] :
% 0.18/0.38 ( ( breln1 @ A @ S )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ A )
% 0.18/0.38 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.38 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(breln1unionIR_type,type,
% 0.18/0.38 breln1unionIR: $o ).
% 0.18/0.38
% 0.18/0.38 thf(breln1unionIR,definition,
% 0.18/0.38 ( breln1unionIR
% 0.18/0.38 = ( ! [A: $i,R: $i] :
% 0.18/0.38 ( ( breln1 @ A @ R )
% 0.18/0.38 => ! [S: $i] :
% 0.18/0.38 ( ( breln1 @ A @ S )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ A )
% 0.18/0.38 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.18/0.38 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(breln1unionI,conjecture,
% 0.18/0.38 ( breln1unionIL
% 0.18/0.38 => ( breln1unionIR
% 0.18/0.38 => ! [A: $i,R: $i] :
% 0.18/0.38 ( ( breln1 @ A @ R )
% 0.18/0.38 => ! [S: $i] :
% 0.18/0.38 ( ( breln1 @ A @ S )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ A )
% 0.18/0.38 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.38 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.18/0.38 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.61/1.30 ---- Embedded in THF ---
% 1.61/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.30 %%% Generated on Tue Feb 24 12:34:21 EST 2026
% 1.61/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.30 %%% Logic specification used:
% 1.61/1.30 %%% thf(spec, logic, $$dhol).
% 1.61/1.30
% 1.61/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BWja0DuX9z/DTF2DTF2901.p
% See solution above
% 1.61/1.30 ------------------------
% 1.61/1.31 ---- Cleaned THF ---
% 1.61/1.31 thf(in_type,type,
% 1.61/1.31 in: $i > $i > $o ).
% 1.61/1.31
% 1.61/1.31 thf(binunion_type,type,
% 1.61/1.31 binunion: $i > $i > $i ).
% 1.61/1.31
% 1.61/1.31 thf(kpair_type,type,
% 1.61/1.31 kpair: $i > $i > $i ).
% 1.61/1.31
% 1.61/1.31 thf(breln1_type,type,
% 1.61/1.31 breln1: $i > $i > $o ).
% 1.61/1.31
% 1.61/1.31 thf(breln1unionIL_type,type,
% 1.61/1.31 breln1unionIL: $o ).
% 1.61/1.31
% 1.61/1.31 thf(breln1unionIL,definition,
% 1.61/1.31 ( breln1unionIL
% 1.61/1.31 = ( ! [A: $i,R: $i] :
% 1.61/1.31 ( ( breln1 @ A @ R )
% 1.61/1.31 => ! [S: $i] :
% 1.61/1.31 ( ( breln1 @ A @ S )
% 1.61/1.31 => ! [Xx: $i] :
% 1.61/1.31 ( ( in @ Xx @ A )
% 1.61/1.31 => ! [Xy: $i] :
% 1.61/1.31 ( ( in @ Xy @ A )
% 1.61/1.31 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.61/1.31 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 1.61/1.31
% 1.61/1.31 thf(breln1unionIR_type,type,
% 1.61/1.31 breln1unionIR: $o ).
% 1.61/1.31
% 1.61/1.31 thf(breln1unionIR,definition,
% 1.61/1.31 ( breln1unionIR
% 1.61/1.31 = ( ! [A: $i,R: $i] :
% 1.61/1.31 ( ( breln1 @ A @ R )
% 1.61/1.31 => ! [S: $i] :
% 1.61/1.31 ( ( breln1 @ A @ S )
% 1.61/1.31 => ! [Xx: $i] :
% 1.61/1.31 ( ( in @ Xx @ A )
% 1.61/1.31 => ! [Xy: $i] :
% 1.61/1.31 ( ( in @ Xy @ A )
% 1.61/1.31 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 1.61/1.31 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 1.61/1.31
% 1.61/1.31 thf(breln1unionI,conjecture,
% 1.61/1.31 ( breln1unionIL
% 1.61/1.31 => ( breln1unionIR
% 1.61/1.31 => ! [A: $i,R: $i] :
% 1.61/1.31 ( ( breln1 @ A @ R )
% 1.61/1.31 => ! [S: $i] :
% 1.61/1.31 ( ( breln1 @ A @ S )
% 1.61/1.31 => ! [Xx: $i] :
% 1.61/1.31 ( ( in @ Xx @ A )
% 1.61/1.31 => ! [Xy: $i] :
% 1.61/1.31 ( ( in @ Xy @ A )
% 1.61/1.31 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.61/1.31 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 1.61/1.31 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 1.61/1.31 ------------------------
% 1.61/1.33 % (3004)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2901 for (2999ds/18Mi)
% 1.61/1.33 % (3001)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2901 for (2999ds/2Mi)
% 1.61/1.33 % (3002)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_2901 for (2999ds/2Mi)
% 1.61/1.33 % (2999)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_2901 for (2999ds/4Mi)
% 1.61/1.33 % (3000)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_2901 for (2999ds/27Mi)
% 1.61/1.33 % (2998)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2901 for (2999ds/183Mi)
% 1.61/1.33 % (3003)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_2901 for (2999ds/275Mi)
% 1.61/1.33 % (3001)Instruction limit reached!
% 1.61/1.33 % (3001)------------------------------
% 1.61/1.33 % (3001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (3001)Termination reason: Unknown
% 1.61/1.33 % (3001)Termination phase: shuffling
% 1.61/1.33
% 1.61/1.33 % (3002)Instruction limit reached!
% 1.61/1.33 % (3002)------------------------------
% 1.61/1.33 % (3002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (3002)Termination reason: Unknown
% 1.61/1.33 % (3002)Termination phase: shuffling
% 1.61/1.33
% 1.61/1.33 % (3002)Memory used [KB]: 895
% 1.61/1.33 % (3002)Time elapsed: 0.002 s
% 1.61/1.33 % (3002)Instructions burned: 2 (million)
% 1.61/1.33 % (3002)------------------------------
% 1.61/1.33 % (3002)------------------------------
% 1.61/1.33 % (3001)Memory used [KB]: 895
% 1.61/1.33 % (3001)Time elapsed: 0.002 s
% 1.61/1.33 % (3001)Instructions burned: 2 (million)
% 1.61/1.33 % (3001)------------------------------
% 1.61/1.33 % (3001)------------------------------
% 1.61/1.33 % (2999)Instruction limit reached!
% 1.61/1.33 % (2999)------------------------------
% 1.61/1.33 % (2999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (2999)Termination reason: Unknown
% 1.61/1.33 % (2999)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (2999)Memory used [KB]: 5500
% 1.61/1.33 % (2999)Time elapsed: 0.004 s
% 1.61/1.33 % (2999)Instructions burned: 5 (million)
% 1.61/1.33 % (2999)------------------------------
% 1.61/1.33 % (2999)------------------------------
% 1.61/1.33 % (3003)First to succeed.
% 1.61/1.34 % (2998)Also succeeded, but the first one will report.
% 1.61/1.34 % (3004)Instruction limit reached!
% 1.61/1.34 % (3004)------------------------------
% 1.61/1.34 % (3004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (3004)Termination reason: Unknown
% 1.61/1.34 % (3004)Termination phase: Saturation
% 1.61/1.34
% 1.61/1.34 % (3004)Memory used [KB]: 5628
% 1.61/1.34 % (3004)Time elapsed: 0.012 s
% 1.61/1.34 % (3004)Instructions burned: 19 (million)
% 1.61/1.34 % (3004)------------------------------
% 1.61/1.34 % (3004)------------------------------
% 1.61/1.34 % (3000)Also succeeded, but the first one will report.
% 1.61/1.34 % (3003)Refutation found. Thanks to Tanya!
% 1.61/1.34 % SZS status Theorem for DTF2THF_2901
% 1.61/1.34 % SZS output start Proof for DTF2THF_2901
% 1.61/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.61/1.34 thf(func_def_1, type, binunion: $i > $i > $i).
% 1.61/1.34 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.61/1.34 thf(func_def_3, type, breln1: $i > $i > $o).
% 1.61/1.34 thf(f103,plain,(
% 1.61/1.34 $false),
% 1.61/1.34 inference(avatar_sat_refutation,[status(thm)],[f84,f95,f102])).
% 1.61/1.34 thf(f102,plain,(
% 1.61/1.34 ~spl15_1),
% 1.61/1.34 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.61/1.34 thf(f101,plain,(
% 1.61/1.34 $false | ~spl15_1),
% 1.61/1.34 inference(subsumption_resolution,[status(thm)],[f100,f38])).
% 1.61/1.34 thf(f38,plain,(
% 1.61/1.34 ($true = (breln1 @ sK1 @ sK0))),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.34 thf(f23,plain,(
% 1.61/1.34 (breln1unionIR = $true) & (breln1unionIL = $true) & (((($true = (in @ sK3 @ sK1)) & (($true = (in @ sK4 @ sK1)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (binunion @ sK0 @ sK2))) & (($true = (in @ (kpair @ sK3 @ sK4) @ sK0)) | ($true = (in @ (kpair @ sK3 @ sK4) @ sK2))))) & ($true = (breln1 @ sK1 @ sK2))) & ($true = (breln1 @ sK1 @ sK0)))),
% 1.61/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f18,f22,f21,f20,f19])).
% 1.61/1.34 thf(f19,plain,(
% 1.61/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ? [X4 : $i] : (($true = (in @ X4 @ X1)) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))) & (((in @ (kpair @ X3 @ X4) @ X0) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))) => (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (($true = (in @ X4 @ sK1)) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK0 @ X2))) & (($true = (in @ (kpair @ X3 @ X4) @ sK0)) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)))) & ($true = (breln1 @ sK1 @ X2))) & ($true = (breln1 @ sK1 @ sK0)))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f20,plain,(
% 1.61/1.34 ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (($true = (in @ X4 @ sK1)) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK0 @ X2))) & (($true = (in @ (kpair @ X3 @ X4) @ sK0)) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)))) & ($true = (breln1 @ sK1 @ X2))) => (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (($true = (in @ X4 @ sK1)) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK0 @ sK2))) & (($true = (in @ (kpair @ X3 @ X4) @ sK0)) | ($true = (in @ (kpair @ X3 @ X4) @ sK2))))) & ($true = (breln1 @ sK1 @ sK2)))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f21,plain,(
% 1.61/1.34 ? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (($true = (in @ X4 @ sK1)) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK0 @ sK2))) & (($true = (in @ (kpair @ X3 @ X4) @ sK0)) | ($true = (in @ (kpair @ X3 @ X4) @ sK2))))) => (($true = (in @ sK3 @ sK1)) & ? [X4 : $i] : (($true = (in @ X4 @ sK1)) & ($true != (in @ (kpair @ sK3 @ X4) @ (binunion @ sK0 @ sK2))) & (($true = (in @ (kpair @ sK3 @ X4) @ sK0)) | ((in @ (kpair @ sK3 @ X4) @ sK2) = $true))))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f22,plain,(
% 1.61/1.34 ? [X4 : $i] : (($true = (in @ X4 @ sK1)) & ($true != (in @ (kpair @ sK3 @ X4) @ (binunion @ sK0 @ sK2))) & (($true = (in @ (kpair @ sK3 @ X4) @ sK0)) | ((in @ (kpair @ sK3 @ X4) @ sK2) = $true))) => (($true = (in @ sK4 @ sK1)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (binunion @ sK0 @ sK2))) & (($true = (in @ (kpair @ sK3 @ sK4) @ sK0)) | ($true = (in @ (kpair @ sK3 @ sK4) @ sK2))))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f18,plain,(
% 1.61/1.34 (breln1unionIR = $true) & (breln1unionIL = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ? [X4 : $i] : (($true = (in @ X4 @ X1)) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))) & (((in @ (kpair @ X3 @ X4) @ X0) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0)))),
% 1.61/1.34 inference(rectify,[status(thm)],[f13])).
% 1.61/1.34 thf(f13,plain,(
% 1.61/1.34 (breln1unionIR = $true) & (breln1unionIL = $true) & ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true) & (((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)))) & ((breln1 @ X0 @ X2) = $true)) & ((breln1 @ X0 @ X1) = $true))),
% 1.61/1.34 inference(flattening,[status(thm)],[f12])).
% 1.61/1.34 thf(f12,plain,(
% 1.61/1.34 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true) & (((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) & ((in @ X4 @ X0) = $true)) & ((in @ X3 @ X0) = $true)) & ((breln1 @ X0 @ X2) = $true)) & ((breln1 @ X0 @ X1) = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)),
% 1.61/1.34 inference(ennf_transformation,[status(thm)],[f9])).
% 1.61/1.34 thf(f9,plain,(
% 1.61/1.34 ~((breln1unionIL = $true) => ((breln1unionIR = $true) => ! [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) => ! [X2 : $i] : (((breln1 @ X0 @ X2) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ! [X4 : $i] : (((in @ X4 @ X0) = $true) => ((((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true))))))))),
% 1.61/1.34 inference(fool_elimination,[status(thm)],[f8])).
% 1.61/1.34 thf(f8,plain,(
% 1.61/1.34 ~(breln1unionIL => (breln1unionIR => ! [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) @ X2) | (in @ (kpair @ X3 @ X4) @ X1)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)))))))))),
% 1.61/1.34 inference(rectify,[status(thm)],[f4])).
% 1.61/1.34 thf(f4,negated_conjecture,(
% 1.61/1.34 ~(breln1unionIL => (breln1unionIR => ! [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) @ X2) | (in @ (kpair @ X3 @ X4) @ X1)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)))))))))),
% 1.61/1.34 inference(negated_conjecture,[status(cth)],[f3])).
% 1.61/1.34 thf(f3,conjecture,(
% 1.61/1.34 breln1unionIL => (breln1unionIR => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => (((in @ (kpair @ X3 @ X4) @ X2) | (in @ (kpair @ X3 @ X4) @ X1)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 1.61/1.34 file('/export/starexec/sandbox/tmp/tmp.BWja0DuX9z/DTF2THF_2901.p',breln1unionI)).
% 1.61/1.34 thf(f100,plain,(
% 1.61/1.34 ($true != (breln1 @ sK1 @ sK0)) | ~spl15_1),
% 1.61/1.34 inference(subsumption_resolution,[status(thm)],[f99,f43])).
% 1.61/1.34 thf(f43,plain,(
% 1.61/1.34 ($true = (in @ sK3 @ sK1))),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.34 thf(f99,plain,(
% 1.61/1.34 ($true != (in @ sK3 @ sK1)) | ($true != (breln1 @ sK1 @ sK0)) | ~spl15_1),
% 1.61/1.34 inference(subsumption_resolution,[status(thm)],[f98,f42])).
% 1.61/1.34 thf(f42,plain,(
% 1.61/1.34 ($true = (in @ sK4 @ sK1))),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.34 thf(f98,plain,(
% 1.61/1.34 ($true != (in @ sK4 @ sK1)) | ($true != (in @ sK3 @ sK1)) | ($true != (breln1 @ sK1 @ sK0)) | ~spl15_1),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.61/1.34 thf(f97,plain,(
% 1.61/1.34 ($true != $true) | ($true != (in @ sK4 @ sK1)) | ($true != (breln1 @ sK1 @ sK0)) | ($true != (in @ sK3 @ sK1)) | ~spl15_1),
% 1.61/1.34 inference(superposition,[status(thm)],[f96,f39])).
% 1.61/1.34 thf(f39,plain,(
% 1.61/1.34 ($true = (breln1 @ sK1 @ sK2))),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.34 thf(f96,plain,(
% 1.61/1.34 ( ! [X0 : $i] : (($true != (breln1 @ X0 @ sK2)) | ($true != (in @ sK3 @ X0)) | ($true != (in @ sK4 @ X0)) | ($true != (breln1 @ X0 @ sK0))) ) | ~spl15_1),
% 1.61/1.34 inference(subsumption_resolution,[status(thm)],[f89,f79])).
% 1.61/1.34 thf(f79,plain,(
% 1.61/1.34 ($true = (in @ (kpair @ sK3 @ sK4) @ sK2)) | ~spl15_1),
% 1.61/1.34 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.61/1.34 thf(f77,definition,(
% 1.61/1.34 spl15_1 <=> ($true = (in @ (kpair @ sK3 @ sK4) @ sK2))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl15_1])],[avatar_definition])).
% 1.61/1.34 thf(f89,plain,(
% 1.61/1.34 ( ! [X0 : $i] : (($true != (in @ sK4 @ X0)) | ($true != (in @ sK3 @ X0)) | ($true != (breln1 @ X0 @ sK2)) | ($true != (in @ (kpair @ sK3 @ sK4) @ sK2)) | ($true != (breln1 @ X0 @ sK0))) )),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.61/1.34 thf(f88,plain,(
% 1.61/1.34 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ sK4 @ X0)) | ($true != (breln1 @ X0 @ sK2)) | ($true != (in @ sK3 @ X0)) | ($true != (breln1 @ X0 @ sK0)) | ($true != (in @ (kpair @ sK3 @ sK4) @ sK2))) )),
% 1.61/1.34 inference(superposition,[status(thm)],[f41,f75])).
% 1.61/1.34 thf(f75,plain,(
% 1.61/1.34 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true = (in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7))) | ($true != (breln1 @ X6 @ X5)) | ($true != (in @ (kpair @ X8 @ X9) @ X7)) | ($true != (in @ X8 @ X6)) | ((breln1 @ X6 @ X7) != $true) | ($true != (in @ X9 @ X6))) )),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.61/1.34 thf(f73,plain,(
% 1.61/1.34 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true != (breln1 @ X6 @ X5)) | ($true != (in @ (kpair @ X8 @ X9) @ X7)) | ($true != $true) | ($true != (in @ X8 @ X6)) | ($true = (in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7))) | ((breln1 @ X6 @ X7) != $true) | ($true != (in @ X9 @ X6))) )),
% 1.61/1.34 inference(definition_unfolding,[status(thm)],[f53,f45])).
% 1.61/1.34 thf(f45,plain,(
% 1.61/1.34 (breln1unionIR = $true)),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.34 thf(f53,plain,(
% 1.61/1.34 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true != (breln1 @ X6 @ X5)) | ((breln1 @ X6 @ X7) != $true) | ($true != (in @ X9 @ X6)) | ($true != (in @ (kpair @ X8 @ X9) @ X7)) | ($true = (in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7))) | ($true != (in @ X8 @ X6)) | (breln1unionIR != $true)) )),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f37])).
% 1.61/1.34 thf(f37,plain,(
% 1.61/1.34 ((breln1unionIR = $true) | (($true = (breln1 @ sK11 @ sK10)) & (($true = (breln1 @ sK11 @ sK12)) & ((($true = (in @ sK14 @ sK11)) & ($true = (in @ (kpair @ sK13 @ sK14) @ sK12)) & ($true != (in @ (kpair @ sK13 @ sK14) @ (binunion @ sK10 @ sK12)))) & ($true = (in @ sK13 @ sK11)))))) & (! [X5 : $i,X6 : $i] : (($true != (breln1 @ X6 @ X5)) | ! [X7 : $i] : (((breln1 @ X6 @ X7) != $true) | ! [X8 : $i] : (! [X9 : $i] : (($true != (in @ X9 @ X6)) | ($true != (in @ (kpair @ X8 @ X9) @ X7)) | ($true = (in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7)))) | ($true != (in @ X8 @ X6))))) | (breln1unionIR != $true))),
% 1.61/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14])],[f32,f36,f35,f34,f33])).
% 1.61/1.34 thf(f33,plain,(
% 1.61/1.34 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X1 @ X0)) & ? [X2 : $i] : (($true = (breln1 @ X1 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X1)) & ((in @ (kpair @ X3 @ X4) @ X2) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)))) & ($true = (in @ X3 @ X1))))) => (($true = (breln1 @ sK11 @ sK10)) & ? [X2 : $i] : (((breln1 @ sK11 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK11)) & ((in @ (kpair @ X3 @ X4) @ X2) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK10 @ X2)))) & ($true = (in @ X3 @ sK11)))))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f34,plain,(
% 1.61/1.34 ? [X2 : $i] : (((breln1 @ sK11 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK11)) & ((in @ (kpair @ X3 @ X4) @ X2) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK10 @ X2)))) & ($true = (in @ X3 @ sK11)))) => (($true = (breln1 @ sK11 @ sK12)) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK11)) & ((in @ (kpair @ X3 @ X4) @ sK12) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK10 @ sK12)))) & ($true = (in @ X3 @ sK11))))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f35,plain,(
% 1.61/1.34 ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK11)) & ((in @ (kpair @ X3 @ X4) @ sK12) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK10 @ sK12)))) & ($true = (in @ X3 @ sK11))) => (? [X4 : $i] : (($true = (in @ X4 @ sK11)) & ((in @ (kpair @ sK13 @ X4) @ sK12) = $true) & ($true != (in @ (kpair @ sK13 @ X4) @ (binunion @ sK10 @ sK12)))) & ($true = (in @ sK13 @ sK11)))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f36,plain,(
% 1.61/1.34 ? [X4 : $i] : (($true = (in @ X4 @ sK11)) & ((in @ (kpair @ sK13 @ X4) @ sK12) = $true) & ($true != (in @ (kpair @ sK13 @ X4) @ (binunion @ sK10 @ sK12)))) => (($true = (in @ sK14 @ sK11)) & ($true = (in @ (kpair @ sK13 @ sK14) @ sK12)) & ($true != (in @ (kpair @ sK13 @ sK14) @ (binunion @ sK10 @ sK12))))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f32,plain,(
% 1.61/1.34 ((breln1unionIR = $true) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X1 @ X0)) & ? [X2 : $i] : (($true = (breln1 @ X1 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X1)) & ((in @ (kpair @ X3 @ X4) @ X2) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)))) & ($true = (in @ X3 @ X1)))))) & (! [X5 : $i,X6 : $i] : (($true != (breln1 @ X6 @ X5)) | ! [X7 : $i] : (((breln1 @ X6 @ X7) != $true) | ! [X8 : $i] : (! [X9 : $i] : (($true != (in @ X9 @ X6)) | ($true != (in @ (kpair @ X8 @ X9) @ X7)) | ($true = (in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7)))) | ($true != (in @ X8 @ X6))))) | (breln1unionIR != $true))),
% 1.61/1.34 inference(rectify,[status(thm)],[f31])).
% 1.61/1.34 thf(f31,plain,(
% 1.61/1.34 ((breln1unionIR = $true) | ? [X1 : $i,X0 : $i] : (((breln1 @ X0 @ X1) = $true) & ? [X2 : $i] : (((breln1 @ X0 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ X2) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true)) & ((in @ X3 @ X0) = $true))))) & (! [X1 : $i,X0 : $i] : (((breln1 @ X0 @ X1) != $true) | ! [X2 : $i] : (((breln1 @ X0 @ X2) != $true) | ! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true)) | ((in @ X3 @ X0) != $true)))) | (breln1unionIR != $true))),
% 1.61/1.34 inference(nnf_transformation,[status(thm)],[f15])).
% 1.61/1.34 thf(f15,plain,(
% 1.61/1.34 (breln1unionIR = $true) <=> ! [X1 : $i,X0 : $i] : (((breln1 @ X0 @ X1) != $true) | ! [X2 : $i] : (((breln1 @ X0 @ X2) != $true) | ! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true)) | ((in @ X3 @ X0) != $true))))),
% 1.61/1.34 inference(flattening,[status(thm)],[f14])).
% 1.61/1.34 thf(f14,plain,(
% 1.61/1.34 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true)) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X0) != $true)) | ((breln1 @ X0 @ X2) != $true)) | ((breln1 @ X0 @ X1) != $true)) <=> (breln1unionIR = $true)),
% 1.61/1.34 inference(ennf_transformation,[status(thm)],[f11])).
% 1.61/1.34 thf(f11,plain,(
% 1.61/1.34 ! [X1 : $i,X0 : $i] : (((breln1 @ X0 @ X1) = $true) => ! [X2 : $i] : (((breln1 @ X0 @ X2) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ! [X4 : $i] : (((in @ X4 @ X0) = $true) => (((in @ (kpair @ X3 @ X4) @ X2) = $true) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true)))))) <=> (breln1unionIR = $true)),
% 1.61/1.34 inference(fool_elimination,[status(thm)],[f10])).
% 1.61/1.34 thf(f10,plain,(
% 1.61/1.34 (breln1unionIR = ! [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) @ X2) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 1.61/1.34 inference(rectify,[status(thm)],[f2])).
% 1.61/1.34 thf(f2,axiom,(
% 1.61/1.34 (breln1unionIR = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 1.61/1.34 file('/export/starexec/sandbox/tmp/tmp.BWja0DuX9z/DTF2THF_2901.p',breln1unionIR)).
% 1.61/1.34 thf(f41,plain,(
% 1.61/1.34 ($true != (in @ (kpair @ sK3 @ sK4) @ (binunion @ sK0 @ sK2)))),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.34 thf(f95,plain,(
% 1.61/1.34 ~spl15_2),
% 1.61/1.34 inference(avatar_contradiction_clause,[status(thm)],[f94])).
% 1.61/1.34 thf(f94,plain,(
% 1.61/1.34 $false | ~spl15_2),
% 1.61/1.34 inference(subsumption_resolution,[status(thm)],[f93,f43])).
% 1.61/1.34 thf(f93,plain,(
% 1.61/1.34 ($true != (in @ sK3 @ sK1)) | ~spl15_2),
% 1.61/1.34 inference(subsumption_resolution,[status(thm)],[f92,f38])).
% 1.61/1.34 thf(f92,plain,(
% 1.61/1.34 ($true != (breln1 @ sK1 @ sK0)) | ($true != (in @ sK3 @ sK1)) | ~spl15_2),
% 1.61/1.34 inference(subsumption_resolution,[status(thm)],[f91,f42])).
% 1.61/1.34 thf(f91,plain,(
% 1.61/1.34 ($true != (in @ sK4 @ sK1)) | ($true != (in @ sK3 @ sK1)) | ($true != (breln1 @ sK1 @ sK0)) | ~spl15_2),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.61/1.34 thf(f90,plain,(
% 1.61/1.34 ($true != (in @ sK3 @ sK1)) | ($true != (in @ sK4 @ sK1)) | ($true != $true) | ($true != (breln1 @ sK1 @ sK0)) | ~spl15_2),
% 1.61/1.34 inference(superposition,[status(thm)],[f87,f39])).
% 1.61/1.34 thf(f87,plain,(
% 1.61/1.34 ( ! [X0 : $i] : (($true != (breln1 @ X0 @ sK2)) | ($true != (breln1 @ X0 @ sK0)) | ($true != (in @ sK4 @ X0)) | ($true != (in @ sK3 @ X0))) ) | ~spl15_2),
% 1.61/1.34 inference(subsumption_resolution,[status(thm)],[f86,f83])).
% 1.61/1.34 thf(f83,plain,(
% 1.61/1.34 ($true = (in @ (kpair @ sK3 @ sK4) @ sK0)) | ~spl15_2),
% 1.61/1.34 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.61/1.34 thf(f81,definition,(
% 1.61/1.34 spl15_2 <=> ($true = (in @ (kpair @ sK3 @ sK4) @ sK0))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl15_2])],[avatar_definition])).
% 1.61/1.34 thf(f86,plain,(
% 1.61/1.34 ( ! [X0 : $i] : (($true != (in @ (kpair @ sK3 @ sK4) @ sK0)) | ($true != (breln1 @ X0 @ sK0)) | ($true != (breln1 @ X0 @ sK2)) | ($true != (in @ sK3 @ X0)) | ($true != (in @ sK4 @ X0))) )),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.61/1.34 thf(f85,plain,(
% 1.61/1.34 ( ! [X0 : $i] : (($true != (in @ sK4 @ X0)) | ($true != (in @ sK3 @ X0)) | ($true != (in @ (kpair @ sK3 @ sK4) @ sK0)) | ($true != (breln1 @ X0 @ sK0)) | ($true != (breln1 @ X0 @ sK2)) | ($true != $true)) )),
% 1.61/1.34 inference(superposition,[status(thm)],[f41,f74])).
% 1.61/1.34 thf(f74,plain,(
% 1.61/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((in @ X3 @ X0) != $true) | ((breln1 @ X0 @ X1) != $true) | ((breln1 @ X0 @ X2) != $true) | ((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ X1) != $true)) )),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.61/1.34 thf(f60,plain,(
% 1.61/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((breln1 @ X0 @ X2) != $true) | ((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ($true != $true) | ((in @ (kpair @ X3 @ X4) @ X1) != $true) | ((breln1 @ X0 @ X1) != $true) | ((in @ X3 @ X0) != $true)) )),
% 1.61/1.34 inference(definition_unfolding,[status(thm)],[f52,f44])).
% 1.61/1.34 thf(f44,plain,(
% 1.61/1.34 (breln1unionIL = $true)),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.34 thf(f52,plain,(
% 1.61/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X3 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((in @ (kpair @ X3 @ X4) @ X1) != $true) | ((in @ X4 @ X0) != $true) | ((breln1 @ X0 @ X2) != $true) | ((breln1 @ X0 @ X1) != $true) | (breln1unionIL != $true)) )),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f30])).
% 1.61/1.34 thf(f30,plain,(
% 1.61/1.34 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((in @ (kpair @ X3 @ X4) @ X1) != $true) | ((in @ X4 @ X0) != $true))) | ((breln1 @ X0 @ X2) != $true)) | ((breln1 @ X0 @ X1) != $true)) | (breln1unionIL != $true)) & ((breln1unionIL = $true) | (((($true = (in @ sK8 @ sK5)) & (($true != (in @ (kpair @ sK8 @ sK9) @ (binunion @ sK6 @ sK7))) & ($true = (in @ (kpair @ sK8 @ sK9) @ sK6)) & ($true = (in @ sK9 @ sK5)))) & ($true = (breln1 @ sK5 @ sK7))) & ($true = (breln1 @ sK5 @ sK6))))),
% 1.61/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f25,f29,f28,f27,f26])).
% 1.61/1.34 thf(f26,plain,(
% 1.61/1.34 ? [X5 : $i,X6 : $i] : (? [X7 : $i] : (? [X8 : $i] : (($true = (in @ X8 @ X5)) & ? [X9 : $i] : (($true != (in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7))) & ($true = (in @ (kpair @ X8 @ X9) @ X6)) & ($true = (in @ X9 @ X5)))) & ($true = (breln1 @ X5 @ X7))) & ($true = (breln1 @ X5 @ X6))) => (? [X7 : $i] : (? [X8 : $i] : (($true = (in @ X8 @ sK5)) & ? [X9 : $i] : (($true != (in @ (kpair @ X8 @ X9) @ (binunion @ sK6 @ X7))) & ($true = (in @ (kpair @ X8 @ X9) @ sK6)) & ($true = (in @ X9 @ sK5)))) & ($true = (breln1 @ sK5 @ X7))) & ($true = (breln1 @ sK5 @ sK6)))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f27,plain,(
% 1.61/1.34 ? [X7 : $i] : (? [X8 : $i] : (($true = (in @ X8 @ sK5)) & ? [X9 : $i] : (($true != (in @ (kpair @ X8 @ X9) @ (binunion @ sK6 @ X7))) & ($true = (in @ (kpair @ X8 @ X9) @ sK6)) & ($true = (in @ X9 @ sK5)))) & ($true = (breln1 @ sK5 @ X7))) => (? [X8 : $i] : (($true = (in @ X8 @ sK5)) & ? [X9 : $i] : (($true != (in @ (kpair @ X8 @ X9) @ (binunion @ sK6 @ sK7))) & ($true = (in @ (kpair @ X8 @ X9) @ sK6)) & ($true = (in @ X9 @ sK5)))) & ($true = (breln1 @ sK5 @ sK7)))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f28,plain,(
% 1.61/1.34 ? [X8 : $i] : (($true = (in @ X8 @ sK5)) & ? [X9 : $i] : (($true != (in @ (kpair @ X8 @ X9) @ (binunion @ sK6 @ sK7))) & ($true = (in @ (kpair @ X8 @ X9) @ sK6)) & ($true = (in @ X9 @ sK5)))) => (($true = (in @ sK8 @ sK5)) & ? [X9 : $i] : (($true != (in @ (kpair @ sK8 @ X9) @ (binunion @ sK6 @ sK7))) & ($true = (in @ (kpair @ sK8 @ X9) @ sK6)) & ($true = (in @ X9 @ sK5))))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f29,plain,(
% 1.61/1.34 ? [X9 : $i] : (($true != (in @ (kpair @ sK8 @ X9) @ (binunion @ sK6 @ sK7))) & ($true = (in @ (kpair @ sK8 @ X9) @ sK6)) & ($true = (in @ X9 @ sK5))) => (($true != (in @ (kpair @ sK8 @ sK9) @ (binunion @ sK6 @ sK7))) & ($true = (in @ (kpair @ sK8 @ sK9) @ sK6)) & ($true = (in @ sK9 @ sK5)))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f25,plain,(
% 1.61/1.34 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((in @ (kpair @ X3 @ X4) @ X1) != $true) | ((in @ X4 @ X0) != $true))) | ((breln1 @ X0 @ X2) != $true)) | ((breln1 @ X0 @ X1) != $true)) | (breln1unionIL != $true)) & ((breln1unionIL = $true) | ? [X5 : $i,X6 : $i] : (? [X7 : $i] : (? [X8 : $i] : (($true = (in @ X8 @ X5)) & ? [X9 : $i] : (($true != (in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7))) & ($true = (in @ (kpair @ X8 @ X9) @ X6)) & ($true = (in @ X9 @ X5)))) & ($true = (breln1 @ X5 @ X7))) & ($true = (breln1 @ X5 @ X6))))),
% 1.61/1.34 inference(rectify,[status(thm)],[f24])).
% 1.61/1.34 thf(f24,plain,(
% 1.61/1.34 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ! [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))) | ((in @ (kpair @ X3 @ X4) @ X0) != $true) | ($true != (in @ X4 @ X1)))) | ($true != (breln1 @ X1 @ X2))) | ($true != (breln1 @ X1 @ X0))) | (breln1unionIL != $true)) & ((breln1unionIL = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ? [X4 : $i] : (($true != (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))) & ((in @ (kpair @ X3 @ X4) @ X0) = $true) & ($true = (in @ X4 @ X1)))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))))),
% 1.61/1.34 inference(nnf_transformation,[status(thm)],[f17])).
% 1.61/1.34 thf(f17,plain,(
% 1.61/1.34 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ! [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))) | ((in @ (kpair @ X3 @ X4) @ X0) != $true) | ($true != (in @ X4 @ X1)))) | ($true != (breln1 @ X1 @ X2))) | ($true != (breln1 @ X1 @ X0))) <=> (breln1unionIL = $true)),
% 1.61/1.34 inference(flattening,[status(thm)],[f16])).
% 1.61/1.34 thf(f16,plain,(
% 1.61/1.34 (breln1unionIL = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((($true = (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))) | ((in @ (kpair @ X3 @ X4) @ X0) != $true)) | ($true != (in @ X4 @ X1))) | ($true != (in @ X3 @ X1))) | ($true != (breln1 @ X1 @ X2))) | ($true != (breln1 @ X1 @ X0)))),
% 1.61/1.34 inference(ennf_transformation,[status(thm)],[f7])).
% 1.61/1.34 thf(f7,plain,(
% 1.61/1.34 (breln1unionIL = $true) <=> ! [X1 : $i,X0 : $i] : (($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) @ X0) = $true) => ($true = (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))))))))),
% 1.61/1.34 inference(fool_elimination,[status(thm)],[f6])).
% 1.61/1.34 thf(f6,plain,(
% 1.61/1.34 (breln1unionIL = ! [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) @ X0) => (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))))))))),
% 1.61/1.34 inference(rectify,[status(thm)],[f1])).
% 1.61/1.34 thf(f1,axiom,(
% 1.61/1.34 (breln1unionIL = ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 1.61/1.34 file('/export/starexec/sandbox/tmp/tmp.BWja0DuX9z/DTF2THF_2901.p',breln1unionIL)).
% 1.61/1.34 thf(f84,plain,(
% 1.61/1.34 spl15_1 | spl15_2),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f40,f81,f77])).
% 1.61/1.34 thf(f40,plain,(
% 1.61/1.34 ($true = (in @ (kpair @ sK3 @ sK4) @ sK2)) | ($true = (in @ (kpair @ sK3 @ sK4) @ sK0))),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.34 % SZS output end Proof for DTF2THF_2901
% 1.61/1.34 % (3003)------------------------------
% 1.61/1.34 % (3003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (3003)Termination reason: Refutation
% 1.61/1.34
% 1.61/1.34 % (3003)Memory used [KB]: 5628
% 1.61/1.34 % (3003)Time elapsed: 0.010 s
% 1.61/1.34 % (3003)Instructions burned: 8 (million)
% 1.61/1.34 % (3003)------------------------------
% 1.61/1.34 % (3003)------------------------------
% 1.61/1.34 % (2997)Success in time 0.025 s
%------------------------------------------------------------------------------