%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU773^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.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 09:37:04 AM UTC 2026
% Result : Theorem 1.66s 1.30s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 1212 ( 316 equ; 0 cnn)
% Maximal formula atoms : 16 ( 19 avg)
% Number of connectives : 1566 ( 180 ~; 167 |; 69 &;1095 @)
% ( 3 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 10 con; 0-4 aty)
% Number of variables : 211 ( 12 ^; 162 !; 37 ?; 211 :)
% 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_7,type,
breln1: $i > $i > $o ).
thf(func_def_14,type,
sK0: $i > $i > $i > $i > $i ).
thf(func_def_15,type,
sK1: $i > $i > $i > $i > $i ).
thf(f80,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f79,f56]) ).
thf(f56,plain,
( ( breln @ sK6 @ sK6 @ sK7 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 )
@ sK6
@ sK7 )
= $true ),
inference(definition_unfolding,[status(thm)],[f38,f36]) ).
thf(f36,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( breln1
= ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( breln1
= ( ^ [X0: $i,X3: $i] : ( breln @ X0 @ X0 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YKdjtdYOOG/DTF2THF_29495.p',breln1) ).
thf(f38,plain,
( ( breln1 @ sK6 @ sK7 )
= $true ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( breln1 @ sK6 @ sK8 )
= $true )
& ( ( subset @ sK7 @ sK8 )
!= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK7 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK8 )
= $true )
| ( ( in @ X4 @ sK6 )
!= $true ) )
| ( ( in @ X3 @ sK6 )
!= $true ) )
& ( ( breln1 @ sK6 @ sK7 )
= $true )
& ( subbreln = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f15,f26,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ( $true
!= ( subset @ X1 @ X2 ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
=> ( ? [X2: $i] :
( ( ( breln1 @ sK6 @ X2 )
= $true )
& ( ( subset @ sK7 @ X2 )
!= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK7 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ X4 @ sK6 )
!= $true ) )
| ( ( in @ X3 @ sK6 )
!= $true ) ) )
& ( ( breln1 @ sK6 @ sK7 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X2: $i] :
( ( ( breln1 @ sK6 @ X2 )
= $true )
& ( ( subset @ sK7 @ X2 )
!= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK7 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ X4 @ sK6 )
!= $true ) )
| ( ( in @ X3 @ sK6 )
!= $true ) ) )
=> ( ( ( breln1 @ sK6 @ sK8 )
= $true )
& ( ( subset @ sK7 @ sK8 )
!= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK7 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK8 )
= $true )
| ( ( in @ X4 @ sK6 )
!= $true ) )
| ( ( in @ X3 @ sK6 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ( $true
!= ( subset @ X1 @ X2 ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( subbreln = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( subbreln = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( subbreln = $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 ) ) ) )
=> ( $true
= ( subset @ X1 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( subbreln
=> ! [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 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) )
=> ( subset @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( subbreln
=> ! [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 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
=> ( subset @ X3 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( subbreln
=> ! [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 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
=> ( subset @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YKdjtdYOOG/DTF2THF_29495.p',subbreln1) ).
thf(f79,plain,
( ( breln @ sK6 @ sK6 @ sK7 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f78,f54]) ).
thf(f54,plain,
( ( breln @ sK6 @ sK6 @ sK8 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 )
@ sK6
@ sK8 )
= $true ),
inference(definition_unfolding,[status(thm)],[f41,f36]) ).
thf(f41,plain,
( ( breln1 @ sK6 @ sK8 )
= $true ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f78,plain,
( ( ( breln @ sK6 @ sK6 @ sK8 )
!= $true )
| ( ( breln @ sK6 @ sK6 @ sK7 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f77,f40]) ).
thf(f40,plain,
( ( subset @ sK7 @ sK8 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f77,plain,
( ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( breln @ sK6 @ sK6 @ sK7 )
!= $true )
| ( ( breln @ sK6 @ sK6 @ sK8 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( breln @ sK6 @ sK6 @ sK8 )
!= $true )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( breln @ sK6 @ sK6 @ sK7 )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( breln @ sK6 @ sK6 @ sK8 )
!= $true )
| ( ( breln @ sK6 @ sK6 @ sK7 )
!= $true )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( breln @ sK6 @ sK6 @ sK8 )
!= $true )
| ( ( breln @ sK6 @ sK6 @ sK7 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f74,f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f34,f37]) ).
thf(f37,plain,
subbreln = $true,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( in @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( subbreln != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( ( in @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( in @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 )
= $true ) ) )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true ) )
| ( subbreln != $true ) )
& ( ( subbreln = $true )
| ( ( $true
!= ( subset @ sK4 @ sK5 ) )
& ( ( breln @ sK2 @ sK3 @ sK5 )
= $true )
& ! [X10: $i] :
( ( ( in @ X10 @ sK2 )
!= $true )
| ! [X11: $i] :
( ( ( in @ X11 @ sK3 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ sK5 )
= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ sK4 )
!= $true ) ) )
& ( ( breln @ sK2 @ sK3 @ sK4 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f19,f23,f22,f21,f20]) ).
thf(f20,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ? [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true ) ) )
=> ( ( ( in @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ? [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
& ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X5 ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X5 ) @ X2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
& ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X5 ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X5 ) @ X2 )
= $true ) )
=> ( ( ( in @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X6: $i,X7: $i,X8: $i] :
( ? [X9: $i] :
( ( ( subset @ X8 @ X9 )
!= $true )
& ( ( breln @ X6 @ X7 @ X9 )
= $true )
& ! [X10: $i] :
( ( ( in @ X10 @ X6 )
!= $true )
| ! [X11: $i] :
( ( ( in @ X11 @ X7 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X8 )
!= $true ) ) ) )
& ( ( breln @ X6 @ X7 @ X8 )
= $true ) )
=> ( ? [X9: $i] :
( ( $true
!= ( subset @ sK4 @ X9 ) )
& ( ( breln @ sK2 @ sK3 @ X9 )
= $true )
& ! [X10: $i] :
( ( ( in @ X10 @ sK2 )
!= $true )
| ! [X11: $i] :
( ( ( in @ X11 @ sK3 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ sK4 )
!= $true ) ) ) )
& ( ( breln @ sK2 @ sK3 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X9: $i] :
( ( $true
!= ( subset @ sK4 @ X9 ) )
& ( ( breln @ sK2 @ sK3 @ X9 )
= $true )
& ! [X10: $i] :
( ( ( in @ X10 @ sK2 )
!= $true )
| ! [X11: $i] :
( ( ( in @ X11 @ sK3 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ sK4 )
!= $true ) ) ) )
=> ( ( $true
!= ( subset @ sK4 @ sK5 ) )
& ( ( breln @ sK2 @ sK3 @ sK5 )
= $true )
& ! [X10: $i] :
( ( ( in @ X10 @ sK2 )
!= $true )
| ! [X11: $i] :
( ( ( in @ X11 @ sK3 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ sK5 )
= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ sK4 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ? [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true ) ) ) )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true ) )
| ( subbreln != $true ) )
& ( ( subbreln = $true )
| ? [X6: $i,X7: $i,X8: $i] :
( ? [X9: $i] :
( ( ( subset @ X8 @ X9 )
!= $true )
& ( ( breln @ X6 @ X7 @ X9 )
= $true )
& ! [X10: $i] :
( ( ( in @ X10 @ X6 )
!= $true )
| ! [X11: $i] :
( ( ( in @ X11 @ X7 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X8 )
!= $true ) ) ) )
& ( ( breln @ X6 @ X7 @ X8 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ? [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true ) ) ) )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true ) )
| ( subbreln != $true ) )
& ( ( subbreln = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
& ( ( breln @ X0 @ X1 @ X3 )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true ) ) ) )
& ( ( breln @ X0 @ X1 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ? [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true ) ) ) )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true ) )
<=> ( subbreln = $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ( subbreln = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ? [X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
!= $true )
& ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
& ( ( in @ X5 @ X1 )
= $true ) )
& ( ( in @ X4 @ X0 )
= $true ) )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true ) )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( subbreln = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( breln @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( breln @ X0 @ X1 @ X3 )
= $true )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true ) ) ) )
=> ( ( subset @ X2 @ X3 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( subset @ X2 @ X3 ) ) ) )
= subbreln ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i,X3: $i] :
( ( ( breln @ X0 @ X1 @ X3 )
=> ! [X4: $i] :
( ( breln @ X0 @ X1 @ X4 )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
=> ( subset @ X3 @ X4 ) ) ) )
= subbreln ),
file('/export/starexec/sandbox2/tmp/tmp.YKdjtdYOOG/DTF2THF_29495.p',subbreln) ).
thf(f74,plain,
! [X0: $i] :
( ( ( in @ ( sK1 @ sK8 @ sK7 @ X0 @ sK6 ) @ sK6 )
!= $true )
| ( $true
!= ( breln @ sK6 @ X0 @ sK7 ) )
| ( ( breln @ sK6 @ X0 @ sK8 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f73,f40]) ).
thf(f73,plain,
! [X0: $i] :
( ( ( in @ ( sK1 @ sK8 @ sK7 @ X0 @ sK6 ) @ sK6 )
!= $true )
| ( ( breln @ sK6 @ X0 @ sK8 )
!= $true )
| ( $true
!= ( breln @ sK6 @ X0 @ sK7 ) )
| ( ( subset @ sK7 @ sK8 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: $i] :
( ( ( in @ ( sK1 @ sK8 @ sK7 @ X0 @ sK6 ) @ sK6 )
!= $true )
| ( $true
!= ( breln @ sK6 @ X0 @ sK7 ) )
| ( ( breln @ sK6 @ X0 @ sK8 )
!= $true )
| ( $true != $true )
| ( ( subset @ sK7 @ sK8 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: $i] :
( ( $true
!= ( breln @ sK6 @ X0 @ sK7 ) )
| ( ( in @ ( sK1 @ sK8 @ sK7 @ X0 @ sK6 ) @ sK6 )
!= $true )
| ( ( breln @ sK6 @ X0 @ sK8 )
!= $true )
| ( ( breln @ sK6 @ X0 @ sK8 )
!= $true )
| ( $true
!= ( breln @ sK6 @ X0 @ sK7 ) )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f70,f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( subset @ X2 @ X3 )
= $true )
| ( ( in @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f35,f37]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( in @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( subbreln != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f70,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK0 @ sK8 @ sK7 @ X0 @ X1 ) @ sK6 ) )
| ( ( breln @ X1 @ X0 @ sK8 )
!= $true )
| ( ( breln @ X1 @ X0 @ sK7 )
!= $true )
| ( ( in @ ( sK1 @ sK8 @ sK7 @ X0 @ X1 ) @ sK6 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f69,f40]) ).
thf(f69,plain,
! [X0: $i,X1: $i] :
( ( ( breln @ X1 @ X0 @ sK8 )
!= $true )
| ( $true
!= ( in @ ( sK0 @ sK8 @ sK7 @ X0 @ X1 ) @ sK6 ) )
| ( ( in @ ( sK1 @ sK8 @ sK7 @ X0 @ X1 ) @ sK6 )
!= $true )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( breln @ X1 @ X0 @ sK7 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK1 @ sK8 @ sK7 @ X0 @ X1 ) @ sK6 )
!= $true )
| ( $true
!= ( in @ ( sK0 @ sK8 @ sK7 @ X0 @ X1 ) @ sK6 ) )
| ( ( breln @ X1 @ X0 @ sK8 )
!= $true )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( breln @ X1 @ X0 @ sK7 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ sK7 @ sK8 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( sK0 @ sK8 @ sK7 @ X0 @ X1 ) @ sK6 ) )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( in @ ( sK1 @ sK8 @ sK7 @ X0 @ X1 ) @ sK6 )
!= $true )
| ( ( breln @ X1 @ X0 @ sK7 )
!= $true )
| ( ( breln @ X1 @ X0 @ sK7 )
!= $true )
| ( ( breln @ X1 @ X0 @ sK8 )
!= $true )
| ( ( breln @ X1 @ X0 @ sK8 )
!= $true ) ),
inference(superposition,[status(thm)],[f59,f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( ( subset @ X2 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( subset @ X2 @ X3 )
= $true )
| ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f37]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 )
= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( subbreln != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f59,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK0 @ sK8 @ X0 @ X1 @ X2 ) @ ( sK1 @ sK8 @ X0 @ X1 @ X2 ) ) @ sK7 )
!= $true )
| ( $true
!= ( in @ ( sK1 @ sK8 @ X0 @ X1 @ X2 ) @ sK6 ) )
| ( ( in @ ( sK0 @ sK8 @ X0 @ X1 @ X2 ) @ sK6 )
!= $true )
| ( ( subset @ X0 @ sK8 )
= $true )
| ( ( breln @ X2 @ X1 @ X0 )
!= $true )
| ( ( breln @ X2 @ X1 @ sK8 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ sK8 @ X0 @ X1 @ X2 ) @ sK6 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( sK1 @ sK8 @ X0 @ X1 @ X2 ) @ sK6 ) )
| ( ( subset @ X0 @ sK8 )
= $true )
| ( ( breln @ X2 @ X1 @ sK8 )
!= $true )
| ( ( in @ ( kpair @ ( sK0 @ sK8 @ X0 @ X1 @ X2 ) @ ( sK1 @ sK8 @ X0 @ X1 @ X2 ) ) @ sK7 )
!= $true )
| ( ( breln @ X2 @ X1 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f52,f39]) ).
thf(f39,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK8 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK7 )
!= $true )
| ( ( in @ X3 @ sK6 )
!= $true )
| ( ( in @ X4 @ sK6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 )
!= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( subset @ X2 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f37]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( ( breln @ X0 @ X1 @ X3 )
!= $true )
| ( ( in @ ( kpair @ ( sK0 @ X3 @ X2 @ X1 @ X0 ) @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 )
!= $true )
| ( ( breln @ X0 @ X1 @ X2 )
!= $true )
| ( subbreln != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU773^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:33:27 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU773^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Binary Relations on a Set
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.18/0.45 % (! y:i.in y A -> in (kpair x y) R -> in (kpair x y) S)) ->
% 0.18/0.45 % subset R S))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC275l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.18/0.45 % Number of atoms : 23 ( 3 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 8 ( 5 avg)
% 0.18/0.45 % Number of connectives : 58 ( 0 ~; 0 |; 0 &; 45 @)
% 0.18/0.45 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 17 ( 5 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 8 ( 7 usr; 1 con; 0-3 aty)
% 0.18/0.45 % Number of variables : 16 ( 5 ^; 11 !; 0 ?; 16 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=331
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(subset_type,type,
% 0.18/0.45 subset: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(kpair_type,type,
% 0.18/0.45 kpair: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(cartprod_type,type,
% 0.18/0.45 cartprod: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(breln_type,type,
% 0.18/0.45 breln: $i > $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(breln,definition,
% 0.18/0.45 ( breln
% 0.18/0.45 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(subbreln_type,type,
% 0.18/0.45 subbreln: $o ).
% 0.18/0.45
% 0.18/0.45 thf(subbreln,definition,
% 0.18/0.45 ( subbreln
% 0.18/0.45 = ( ! [A: $i,B: $i,R: $i] :
% 0.18/0.45 ( ( breln @ A @ B @ R )
% 0.18/0.45 => ! [S: $i] :
% 0.18/0.45 ( ( breln @ A @ B @ S )
% 0.18/0.45 => ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ B )
% 0.18/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.45 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.18/0.45 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(breln1_type,type,
% 0.18/0.45 breln1: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(breln1,definition,
% 0.18/0.45 ( breln1
% 0.18/0.45 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(subbreln1,conjecture,
% 0.18/0.45 ( subbreln
% 0.18/0.45 => ! [A: $i,R: $i] :
% 0.18/0.45 ( ( breln1 @ A @ R )
% 0.18/0.45 => ! [S: $i] :
% 0.18/0.45 ( ( breln1 @ A @ S )
% 0.18/0.45 => ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ A )
% 0.18/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.45 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.18/0.45 => ( subset @ R @ S ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.53/1.26 ---- Embedded in THF ---
% 1.53/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.26 %%% Generated on Tue Feb 24 12:33:28 EST 2026
% 1.53/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.26 %%% Logic specification used:
% 1.53/1.26 %%% thf(spec, logic, $$dhol).
% 1.53/1.26
% 1.53/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YKdjtdYOOG/DTF2DTF29495.p
% See solution above
% 1.53/1.26 ------------------------
% 1.53/1.27 ---- Cleaned THF ---
% 1.53/1.27 thf(in_type,type,
% 1.53/1.27 in: $i > $i > $o ).
% 1.53/1.27
% 1.53/1.27 thf(subset_type,type,
% 1.53/1.27 subset: $i > $i > $o ).
% 1.53/1.27
% 1.53/1.27 thf(kpair_type,type,
% 1.53/1.27 kpair: $i > $i > $i ).
% 1.53/1.27
% 1.53/1.27 thf(cartprod_type,type,
% 1.53/1.27 cartprod: $i > $i > $i ).
% 1.53/1.27
% 1.53/1.27 thf(breln_type,type,
% 1.53/1.27 breln: $i > $i > $i > $o ).
% 1.53/1.27
% 1.53/1.27 thf(breln,definition,
% 1.53/1.27 ( breln
% 1.53/1.27 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.53/1.27
% 1.53/1.27 thf(subbreln_type,type,
% 1.53/1.27 subbreln: $o ).
% 1.53/1.27
% 1.53/1.27 thf(subbreln,definition,
% 1.53/1.27 ( subbreln
% 1.53/1.27 = ( ! [A: $i,B: $i,R: $i] :
% 1.53/1.27 ( ( breln @ A @ B @ R )
% 1.53/1.27 => ! [S: $i] :
% 1.53/1.27 ( ( breln @ A @ B @ S )
% 1.53/1.27 => ( ! [Xx: $i] :
% 1.53/1.27 ( ( in @ Xx @ A )
% 1.53/1.27 => ! [Xy: $i] :
% 1.53/1.27 ( ( in @ Xy @ B )
% 1.53/1.27 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.53/1.27 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 1.53/1.27 => ( subset @ R @ S ) ) ) ) ) ) ).
% 1.53/1.27
% 1.53/1.27 thf(breln1_type,type,
% 1.53/1.27 breln1: $i > $i > $o ).
% 1.53/1.27
% 1.53/1.27 thf(breln1,definition,
% 1.53/1.27 ( breln1
% 1.53/1.27 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.53/1.27
% 1.53/1.27 thf(subbreln1,conjecture,
% 1.53/1.27 ( subbreln
% 1.53/1.27 => ! [A: $i,R: $i] :
% 1.53/1.27 ( ( breln1 @ A @ R )
% 1.53/1.27 => ! [S: $i] :
% 1.53/1.27 ( ( breln1 @ A @ S )
% 1.53/1.27 => ( ! [Xx: $i] :
% 1.53/1.27 ( ( in @ Xx @ A )
% 1.53/1.27 => ! [Xy: $i] :
% 1.53/1.27 ( ( in @ Xy @ A )
% 1.53/1.27 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.53/1.27 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 1.53/1.27 => ( subset @ R @ S ) ) ) ) ) ).
% 1.53/1.27 ------------------------
% 1.53/1.28 % (29716)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29495 for (2999ds/2Mi)
% 1.53/1.28 % (29716)Instruction limit reached!
% 1.53/1.28 % (29716)------------------------------
% 1.53/1.28 % (29716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (29716)Termination reason: Unknown
% 1.53/1.28 % (29716)Termination phase: Preprocessing 3
% 1.53/1.28
% 1.53/1.28 % (29716)Memory used [KB]: 1023
% 1.53/1.28 % (29716)Time elapsed: 0.002 s
% 1.53/1.28 % (29716)Instructions burned: 2 (million)
% 1.53/1.28 % (29716)------------------------------
% 1.53/1.28 % (29716)------------------------------
% 1.53/1.29 % (29713)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29495 for (2999ds/183Mi)
% 1.53/1.29 % (29714)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_29495 for (2999ds/4Mi)
% 1.53/1.29 % (29717)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_29495 for (2999ds/2Mi)
% 1.53/1.29 % (29715)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_29495 for (2999ds/27Mi)
% 1.53/1.29 % (29718)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_29495 for (2999ds/275Mi)
% 1.53/1.29 % (29719)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29495 for (2999ds/18Mi)
% 1.53/1.29 % (29717)Instruction limit reached!
% 1.53/1.29 % (29717)------------------------------
% 1.53/1.29 % (29717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (29717)Termination reason: Unknown
% 1.53/1.29 % (29717)Termination phase: shuffling
% 1.53/1.29
% 1.53/1.29 % (29717)Memory used [KB]: 895
% 1.53/1.29 % (29717)Time elapsed: 0.003 s
% 1.53/1.29 % (29717)Instructions burned: 2 (million)
% 1.53/1.29 % (29717)------------------------------
% 1.53/1.29 % (29717)------------------------------
% 1.53/1.29 % (29720)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29495 for (2999ds/3Mi)
% 1.53/1.29 % (29714)Instruction limit reached!
% 1.53/1.29 % (29714)------------------------------
% 1.53/1.29 % (29714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (29714)Termination reason: Unknown
% 1.53/1.29 % (29714)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (29714)Memory used [KB]: 5500
% 1.53/1.29 % (29714)Time elapsed: 0.005 s
% 1.53/1.29 % (29714)Instructions burned: 5 (million)
% 1.53/1.29 % (29714)------------------------------
% 1.53/1.29 % (29714)------------------------------
% 1.53/1.29 % (29720)Instruction limit reached!
% 1.53/1.29 % (29720)------------------------------
% 1.53/1.29 % (29720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (29720)Termination reason: Unknown
% 1.53/1.29 % (29720)Termination phase: Property scanning
% 1.53/1.29
% 1.53/1.29 % (29720)Memory used [KB]: 1023
% 1.53/1.29 % (29720)Time elapsed: 0.002 s
% 1.53/1.29 % (29720)Instructions burned: 4 (million)
% 1.53/1.29 % (29720)------------------------------
% 1.53/1.29 % (29720)------------------------------
% 1.66/1.30 % (29718)First to succeed.
% 1.66/1.30 % (29719)Instruction limit reached!
% 1.66/1.30 % (29719)------------------------------
% 1.66/1.30 % (29719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (29719)Termination reason: Unknown
% 1.66/1.30 % (29719)Termination phase: Saturation
% 1.66/1.30
% 1.66/1.30 % (29719)Memory used [KB]: 5628
% 1.66/1.30 % (29719)Time elapsed: 0.014 s
% 1.66/1.30 % (29719)Instructions burned: 18 (million)
% 1.66/1.30 % (29719)------------------------------
% 1.66/1.30 % (29719)------------------------------
% 1.66/1.30 % (29713)Also succeeded, but the first one will report.
% 1.66/1.30 % (29723)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_29495 for (2999ds/3Mi)
% 1.66/1.30 % (29718)Refutation found. Thanks to Tanya!
% 1.66/1.30 % SZS status Theorem for DTF2THF_29495
% 1.66/1.30 % SZS output start Proof for DTF2THF_29495
% 1.66/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.30 thf(func_def_1, type, subset: $i > $i > $o).
% 1.66/1.30 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.66/1.30 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.66/1.30 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.66/1.30 thf(func_def_7, type, breln1: $i > $i > $o).
% 1.66/1.30 thf(func_def_14, type, sK0: $i > $i > $i > $i > $i).
% 1.66/1.30 thf(func_def_15, type, sK1: $i > $i > $i > $i > $i).
% 1.66/1.30 thf(f80,plain,(
% 1.66/1.30 $false),
% 1.66/1.30 inference(subsumption_resolution,[status(thm)],[f79,f56])).
% 1.66/1.30 thf(f56,plain,(
% 1.66/1.30 ((breln @ sK6 @ sK6 @ sK7) = $true)),
% 1.66/1.30 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.66/1.30 thf(f51,plain,(
% 1.66/1.30 (((^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))) @ sK6 @ sK7) = $true)),
% 1.66/1.30 inference(definition_unfolding,[status(thm)],[f38,f36])).
% 1.66/1.30 thf(f36,plain,(
% 1.66/1.30 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.66/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.30 thf(f12,plain,(
% 1.66/1.30 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.66/1.30 inference(fool_elimination,[status(thm)],[f11])).
% 1.66/1.30 thf(f11,plain,(
% 1.66/1.30 (breln1 = (^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)))),
% 1.66/1.30 inference(rectify,[status(thm)],[f3])).
% 1.66/1.30 thf(f3,axiom,(
% 1.66/1.30 (breln1 = (^[X0 : $i, X3 : $i] : (breln @ X0 @ X0 @ X3)))),
% 1.66/1.30 file('/export/starexec/sandbox2/tmp/tmp.YKdjtdYOOG/DTF2THF_29495.p',breln1)).
% 1.66/1.30 thf(f38,plain,(
% 1.66/1.30 ((breln1 @ sK6 @ sK7) = $true)),
% 1.66/1.30 inference(cnf_transformation,[status(thm)],[f27])).
% 1.66/1.30 thf(f27,plain,(
% 1.66/1.30 ((((breln1 @ sK6 @ sK8) = $true) & ((subset @ sK7 @ sK8) != $true) & ! [X3 : $i] : (! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK7) != $true) | ((in @ (kpair @ X3 @ X4) @ sK8) = $true) | ((in @ X4 @ sK6) != $true)) | ((in @ X3 @ sK6) != $true))) & ((breln1 @ sK6 @ sK7) = $true)) & (subbreln = $true)),
% 1.66/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f15,f26,f25])).
% 1.66/1.30 thf(f25,plain,(
% 1.66/1.30 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((breln1 @ X0 @ X2) = $true) & ($true != (subset @ X1 @ X2)) & ! [X3 : $i] : (! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X1) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X0) != $true))) & ((breln1 @ X0 @ X1) = $true)) => (? [X2 : $i] : (((breln1 @ sK6 @ X2) = $true) & ((subset @ sK7 @ X2) != $true) & ! [X3 : $i] : (! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK7) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true) | ((in @ X4 @ sK6) != $true)) | ((in @ X3 @ sK6) != $true))) & ((breln1 @ sK6 @ sK7) = $true))),
% 1.66/1.30 introduced(definition,[],[choice_axiom])).
% 1.66/1.30 thf(f26,plain,(
% 1.66/1.30 ? [X2 : $i] : (((breln1 @ sK6 @ X2) = $true) & ((subset @ sK7 @ X2) != $true) & ! [X3 : $i] : (! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK7) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true) | ((in @ X4 @ sK6) != $true)) | ((in @ X3 @ sK6) != $true))) => (((breln1 @ sK6 @ sK8) = $true) & ((subset @ sK7 @ sK8) != $true) & ! [X3 : $i] : (! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK7) != $true) | ((in @ (kpair @ X3 @ X4) @ sK8) = $true) | ((in @ X4 @ sK6) != $true)) | ((in @ X3 @ sK6) != $true)))),
% 1.66/1.30 introduced(definition,[],[choice_axiom])).
% 1.66/1.30 thf(f15,plain,(
% 1.66/1.30 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((breln1 @ X0 @ X2) = $true) & ($true != (subset @ X1 @ X2)) & ! [X3 : $i] : (! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X1) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X0) != $true))) & ((breln1 @ X0 @ X1) = $true)) & (subbreln = $true)),
% 1.66/1.30 inference(flattening,[status(thm)],[f14])).
% 1.66/1.30 thf(f14,plain,(
% 1.66/1.30 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((($true != (subset @ X1 @ X2)) & ! [X3 : $i] : (! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2) = $true) | ((in @ (kpair @ X3 @ X4) @ X1) != $true)) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X0) != $true))) & ((breln1 @ X0 @ X2) = $true)) & ((breln1 @ X0 @ X1) = $true)) & (subbreln = $true)),
% 1.66/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.66/1.30 thf(f8,plain,(
% 1.66/1.30 ~((subbreln = $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) = $true)))) => ($true = (subset @ X1 @ X2))))))),
% 1.66/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.31 thf(f7,plain,(
% 1.66/1.31 ~(subbreln => ! [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) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (subset @ X1 @ X2)))))),
% 1.66/1.31 inference(rectify,[status(thm)],[f5])).
% 1.66/1.31 thf(f5,negated_conjecture,(
% 1.66/1.31 ~(subbreln => ! [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) @ X3) => (in @ (kpair @ X5 @ X6) @ X4)))) => (subset @ X3 @ X4)))))),
% 1.66/1.31 inference(negated_conjecture,[status(cth)],[f4])).
% 1.66/1.31 thf(f4,conjecture,(
% 1.66/1.31 subbreln => ! [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) @ X3) => (in @ (kpair @ X5 @ X6) @ X4)))) => (subset @ X3 @ X4))))),
% 1.66/1.31 file('/export/starexec/sandbox2/tmp/tmp.YKdjtdYOOG/DTF2THF_29495.p',subbreln1)).
% 1.66/1.31 thf(f79,plain,(
% 1.66/1.31 ((breln @ sK6 @ sK6 @ sK7) != $true)),
% 1.66/1.31 inference(subsumption_resolution,[status(thm)],[f78,f54])).
% 1.66/1.31 thf(f54,plain,(
% 1.66/1.31 ((breln @ sK6 @ sK6 @ sK8) = $true)),
% 1.66/1.31 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.66/1.31 thf(f50,plain,(
% 1.66/1.31 (((^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))) @ sK6 @ sK8) = $true)),
% 1.66/1.31 inference(definition_unfolding,[status(thm)],[f41,f36])).
% 1.66/1.31 thf(f41,plain,(
% 1.66/1.31 ((breln1 @ sK6 @ sK8) = $true)),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.66/1.31 thf(f78,plain,(
% 1.66/1.31 ((breln @ sK6 @ sK6 @ sK8) != $true) | ((breln @ sK6 @ sK6 @ sK7) != $true)),
% 1.66/1.31 inference(subsumption_resolution,[status(thm)],[f77,f40])).
% 1.66/1.31 thf(f40,plain,(
% 1.66/1.31 ((subset @ sK7 @ sK8) != $true)),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.66/1.31 thf(f77,plain,(
% 1.66/1.31 ((subset @ sK7 @ sK8) = $true) | ((breln @ sK6 @ sK6 @ sK7) != $true) | ((breln @ sK6 @ sK6 @ sK8) != $true)),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.66/1.31 thf(f76,plain,(
% 1.66/1.31 ((breln @ sK6 @ sK6 @ sK8) != $true) | ((subset @ sK7 @ sK8) = $true) | ((breln @ sK6 @ sK6 @ sK7) != $true) | ($true != $true)),
% 1.66/1.31 inference(duplicate_literal_removal,[status(thm)],[f75])).
% 1.66/1.31 thf(f75,plain,(
% 1.66/1.31 ((breln @ sK6 @ sK6 @ sK8) != $true) | ((breln @ sK6 @ sK6 @ sK7) != $true) | ((subset @ sK7 @ sK8) = $true) | ((breln @ sK6 @ sK6 @ sK8) != $true) | ((breln @ sK6 @ sK6 @ sK7) != $true) | ($true != $true)),
% 1.66/1.31 inference(superposition,[status(thm)],[f74,f55])).
% 1.66/1.31 thf(f55,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X1) = $true) | ((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X2) != $true) | ((breln @ X0 @ X1 @ X3) != $true)) )),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.66/1.31 thf(f43,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X1) = $true) | ((breln @ X0 @ X1 @ X2) != $true) | ((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true)) )),
% 1.66/1.31 inference(definition_unfolding,[status(thm)],[f34,f37])).
% 1.66/1.31 thf(f37,plain,(
% 1.66/1.31 (subbreln = $true)),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.66/1.31 thf(f34,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X1) = $true) | ((breln @ X0 @ X1 @ X2) != $true) | (subbreln != $true)) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.31 thf(f24,plain,(
% 1.66/1.31 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | (((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X0) = $true) & (((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X1) = $true) & ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X3) != $true) & ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) = $true)))) | ((breln @ X0 @ X1 @ X2) != $true)) | (subbreln != $true)) & ((subbreln = $true) | ((($true != (subset @ sK4 @ sK5)) & ((breln @ sK2 @ sK3 @ sK5) = $true) & ! [X10 : $i] : (((in @ X10 @ sK2) != $true) | ! [X11 : $i] : (((in @ X11 @ sK3) != $true) | ((in @ (kpair @ X10 @ X11) @ sK5) = $true) | ((in @ (kpair @ X10 @ X11) @ sK4) != $true)))) & ((breln @ sK2 @ sK3 @ sK4) = $true)))),
% 1.66/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f19,f23,f22,f21,f20])).
% 1.66/1.31 thf(f20,plain,(
% 1.66/1.31 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X0) = $true) & ? [X5 : $i] : (((in @ X5 @ X1) = $true) & ((in @ (kpair @ X4 @ X5) @ X3) != $true) & ((in @ (kpair @ X4 @ X5) @ X2) = $true))) => (((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X0) = $true) & ? [X5 : $i] : (((in @ X5 @ X1) = $true) & ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X5) @ X3) != $true) & ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X5) @ X2) = $true))))),
% 1.66/1.31 introduced(definition,[],[choice_axiom])).
% 1.66/1.31 thf(f21,plain,(
% 1.66/1.31 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (? [X5 : $i] : (((in @ X5 @ X1) = $true) & ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X5) @ X3) != $true) & ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X5) @ X2) = $true)) => (((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X1) = $true) & ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X3) != $true) & ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) = $true)))),
% 1.66/1.31 introduced(definition,[],[choice_axiom])).
% 1.66/1.31 thf(f22,plain,(
% 1.66/1.31 ? [X6 : $i,X7 : $i,X8 : $i] : (? [X9 : $i] : (((subset @ X8 @ X9) != $true) & ((breln @ X6 @ X7 @ X9) = $true) & ! [X10 : $i] : (((in @ X10 @ X6) != $true) | ! [X11 : $i] : (((in @ X11 @ X7) != $true) | ((in @ (kpair @ X10 @ X11) @ X9) = $true) | ((in @ (kpair @ X10 @ X11) @ X8) != $true)))) & ((breln @ X6 @ X7 @ X8) = $true)) => (? [X9 : $i] : (($true != (subset @ sK4 @ X9)) & ((breln @ sK2 @ sK3 @ X9) = $true) & ! [X10 : $i] : (((in @ X10 @ sK2) != $true) | ! [X11 : $i] : (((in @ X11 @ sK3) != $true) | ((in @ (kpair @ X10 @ X11) @ X9) = $true) | ((in @ (kpair @ X10 @ X11) @ sK4) != $true)))) & ((breln @ sK2 @ sK3 @ sK4) = $true))),
% 1.66/1.31 introduced(definition,[],[choice_axiom])).
% 1.66/1.31 thf(f23,plain,(
% 1.66/1.31 ? [X9 : $i] : (($true != (subset @ sK4 @ X9)) & ((breln @ sK2 @ sK3 @ X9) = $true) & ! [X10 : $i] : (((in @ X10 @ sK2) != $true) | ! [X11 : $i] : (((in @ X11 @ sK3) != $true) | ((in @ (kpair @ X10 @ X11) @ X9) = $true) | ((in @ (kpair @ X10 @ X11) @ sK4) != $true)))) => (($true != (subset @ sK4 @ sK5)) & ((breln @ sK2 @ sK3 @ sK5) = $true) & ! [X10 : $i] : (((in @ X10 @ sK2) != $true) | ! [X11 : $i] : (((in @ X11 @ sK3) != $true) | ((in @ (kpair @ X10 @ X11) @ sK5) = $true) | ((in @ (kpair @ X10 @ X11) @ sK4) != $true))))),
% 1.66/1.31 introduced(definition,[],[choice_axiom])).
% 1.66/1.31 thf(f19,plain,(
% 1.66/1.31 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ? [X5 : $i] : (((in @ X5 @ X1) = $true) & ((in @ (kpair @ X4 @ X5) @ X3) != $true) & ((in @ (kpair @ X4 @ X5) @ X2) = $true)))) | ((breln @ X0 @ X1 @ X2) != $true)) | (subbreln != $true)) & ((subbreln = $true) | ? [X6 : $i,X7 : $i,X8 : $i] : (? [X9 : $i] : (((subset @ X8 @ X9) != $true) & ((breln @ X6 @ X7 @ X9) = $true) & ! [X10 : $i] : (((in @ X10 @ X6) != $true) | ! [X11 : $i] : (((in @ X11 @ X7) != $true) | ((in @ (kpair @ X10 @ X11) @ X9) = $true) | ((in @ (kpair @ X10 @ X11) @ X8) != $true)))) & ((breln @ X6 @ X7 @ X8) = $true)))),
% 1.66/1.31 inference(rectify,[status(thm)],[f18])).
% 1.66/1.31 thf(f18,plain,(
% 1.66/1.31 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ? [X5 : $i] : (((in @ X5 @ X1) = $true) & ((in @ (kpair @ X4 @ X5) @ X3) != $true) & ((in @ (kpair @ X4 @ X5) @ X2) = $true)))) | ((breln @ X0 @ X1 @ X2) != $true)) | (subbreln != $true)) & ((subbreln = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((subset @ X2 @ X3) != $true) & ((breln @ X0 @ X1 @ X3) = $true) & ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ! [X5 : $i] : (((in @ X5 @ X1) != $true) | ((in @ (kpair @ X4 @ X5) @ X3) = $true) | ((in @ (kpair @ X4 @ X5) @ X2) != $true)))) & ((breln @ X0 @ X1 @ X2) = $true)))),
% 1.66/1.31 inference(nnf_transformation,[status(thm)],[f17])).
% 1.66/1.31 thf(f17,plain,(
% 1.66/1.31 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ? [X5 : $i] : (((in @ X5 @ X1) = $true) & ((in @ (kpair @ X4 @ X5) @ X3) != $true) & ((in @ (kpair @ X4 @ X5) @ X2) = $true)))) | ((breln @ X0 @ X1 @ X2) != $true)) <=> (subbreln = $true)),
% 1.66/1.31 inference(flattening,[status(thm)],[f16])).
% 1.66/1.31 thf(f16,plain,(
% 1.66/1.31 (subbreln = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((((subset @ X2 @ X3) = $true) | ? [X4 : $i] : (? [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3) != $true) & ((in @ (kpair @ X4 @ X5) @ X2) = $true)) & ((in @ X5 @ X1) = $true)) & ((in @ X4 @ X0) = $true))) | ((breln @ X0 @ X1 @ X3) != $true)) | ((breln @ X0 @ X1 @ X2) != $true))),
% 1.66/1.31 inference(ennf_transformation,[status(thm)],[f10])).
% 1.66/1.31 thf(f10,plain,(
% 1.66/1.31 (subbreln = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((breln @ X0 @ X1 @ X2) = $true) => ! [X3 : $i] : (((breln @ X0 @ X1 @ X3) = $true) => (! [X4 : $i] : (((in @ X4 @ X0) = $true) => ! [X5 : $i] : (((in @ X5 @ X1) = $true) => (((in @ (kpair @ X4 @ X5) @ X2) = $true) => ((in @ (kpair @ X4 @ X5) @ X3) = $true)))) => ((subset @ X2 @ X3) = $true))))),
% 1.66/1.31 inference(fool_elimination,[status(thm)],[f9])).
% 1.66/1.31 thf(f9,plain,(
% 1.66/1.31 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))) = subbreln)),
% 1.66/1.31 inference(rectify,[status(thm)],[f2])).
% 1.66/1.31 thf(f2,axiom,(
% 1.66/1.31 (! [X0 : $i,X1 : $i,X3 : $i] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i] : ((breln @ X0 @ X1 @ X4) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (in @ (kpair @ X5 @ X6) @ X4)))) => (subset @ X3 @ X4)))) = subbreln)),
% 1.66/1.31 file('/export/starexec/sandbox2/tmp/tmp.YKdjtdYOOG/DTF2THF_29495.p',subbreln)).
% 1.66/1.31 thf(f74,plain,(
% 1.66/1.31 ( ! [X0 : $i] : (((in @ (sK1 @ sK8 @ sK7 @ X0 @ sK6) @ sK6) != $true) | ($true != (breln @ sK6 @ X0 @ sK7)) | ((breln @ sK6 @ X0 @ sK8) != $true)) )),
% 1.66/1.31 inference(subsumption_resolution,[status(thm)],[f73,f40])).
% 1.66/1.31 thf(f73,plain,(
% 1.66/1.31 ( ! [X0 : $i] : (((in @ (sK1 @ sK8 @ sK7 @ X0 @ sK6) @ sK6) != $true) | ((breln @ sK6 @ X0 @ sK8) != $true) | ($true != (breln @ sK6 @ X0 @ sK7)) | ((subset @ sK7 @ sK8) = $true)) )),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.66/1.31 thf(f72,plain,(
% 1.66/1.31 ( ! [X0 : $i] : (((in @ (sK1 @ sK8 @ sK7 @ X0 @ sK6) @ sK6) != $true) | ($true != (breln @ sK6 @ X0 @ sK7)) | ((breln @ sK6 @ X0 @ sK8) != $true) | ($true != $true) | ((subset @ sK7 @ sK8) = $true)) )),
% 1.66/1.31 inference(duplicate_literal_removal,[status(thm)],[f71])).
% 1.66/1.31 thf(f71,plain,(
% 1.66/1.31 ( ! [X0 : $i] : (($true != (breln @ sK6 @ X0 @ sK7)) | ((in @ (sK1 @ sK8 @ sK7 @ X0 @ sK6) @ sK6) != $true) | ((breln @ sK6 @ X0 @ sK8) != $true) | ((breln @ sK6 @ X0 @ sK8) != $true) | ($true != (breln @ sK6 @ X0 @ sK7)) | ((subset @ sK7 @ sK8) = $true) | ($true != $true)) )),
% 1.66/1.31 inference(superposition,[status(thm)],[f70,f57])).
% 1.66/1.31 thf(f57,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X0) = $true) | ((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X2) != $true) | ((breln @ X0 @ X1 @ X3) != $true)) )),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.66/1.31 thf(f42,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((breln @ X0 @ X1 @ X2) != $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((subset @ X2 @ X3) = $true) | ((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X0) = $true)) )),
% 1.66/1.31 inference(definition_unfolding,[status(thm)],[f35,f37])).
% 1.66/1.31 thf(f35,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X0) = $true) | ((breln @ X0 @ X1 @ X2) != $true) | (subbreln != $true)) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.31 thf(f70,plain,(
% 1.66/1.31 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK0 @ sK8 @ sK7 @ X0 @ X1) @ sK6)) | ((breln @ X1 @ X0 @ sK8) != $true) | ((breln @ X1 @ X0 @ sK7) != $true) | ((in @ (sK1 @ sK8 @ sK7 @ X0 @ X1) @ sK6) != $true)) )),
% 1.66/1.31 inference(subsumption_resolution,[status(thm)],[f69,f40])).
% 1.66/1.31 thf(f69,plain,(
% 1.66/1.31 ( ! [X0 : $i,X1 : $i] : (((breln @ X1 @ X0 @ sK8) != $true) | ($true != (in @ (sK0 @ sK8 @ sK7 @ X0 @ X1) @ sK6)) | ((in @ (sK1 @ sK8 @ sK7 @ X0 @ X1) @ sK6) != $true) | ((subset @ sK7 @ sK8) = $true) | ((breln @ X1 @ X0 @ sK7) != $true)) )),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.66/1.31 thf(f68,plain,(
% 1.66/1.31 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK1 @ sK8 @ sK7 @ X0 @ X1) @ sK6) != $true) | ($true != (in @ (sK0 @ sK8 @ sK7 @ X0 @ X1) @ sK6)) | ((breln @ X1 @ X0 @ sK8) != $true) | ((subset @ sK7 @ sK8) = $true) | ((breln @ X1 @ X0 @ sK7) != $true)) )),
% 1.66/1.31 inference(duplicate_literal_removal,[status(thm)],[f67])).
% 1.66/1.31 thf(f67,plain,(
% 1.66/1.31 ( ! [X0 : $i,X1 : $i] : (((subset @ sK7 @ sK8) = $true) | ($true != $true) | ($true != (in @ (sK0 @ sK8 @ sK7 @ X0 @ X1) @ sK6)) | ((subset @ sK7 @ sK8) = $true) | ((in @ (sK1 @ sK8 @ sK7 @ X0 @ X1) @ sK6) != $true) | ((breln @ X1 @ X0 @ sK7) != $true) | ((breln @ X1 @ X0 @ sK7) != $true) | ((breln @ X1 @ X0 @ sK8) != $true) | ((breln @ X1 @ X0 @ sK8) != $true)) )),
% 1.66/1.31 inference(superposition,[status(thm)],[f59,f53])).
% 1.66/1.31 thf(f53,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((breln @ X0 @ X1 @ X2) != $true) | ((subset @ X2 @ X3) = $true)) )),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.66/1.31 thf(f45,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((breln @ X0 @ X1 @ X2) != $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((subset @ X2 @ X3) = $true) | ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) = $true) | ($true != $true)) )),
% 1.66/1.31 inference(definition_unfolding,[status(thm)],[f32,f37])).
% 1.66/1.31 thf(f32,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) = $true) | ((breln @ X0 @ X1 @ X2) != $true) | (subbreln != $true)) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.31 thf(f59,plain,(
% 1.66/1.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK0 @ sK8 @ X0 @ X1 @ X2) @ (sK1 @ sK8 @ X0 @ X1 @ X2)) @ sK7) != $true) | ($true != (in @ (sK1 @ sK8 @ X0 @ X1 @ X2) @ sK6)) | ((in @ (sK0 @ sK8 @ X0 @ X1 @ X2) @ sK6) != $true) | ((subset @ X0 @ sK8) = $true) | ((breln @ X2 @ X1 @ X0) != $true) | ((breln @ X2 @ X1 @ sK8) != $true)) )),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.66/1.31 thf(f58,plain,(
% 1.66/1.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK0 @ sK8 @ X0 @ X1 @ X2) @ sK6) != $true) | ($true != $true) | ($true != (in @ (sK1 @ sK8 @ X0 @ X1 @ X2) @ sK6)) | ((subset @ X0 @ sK8) = $true) | ((breln @ X2 @ X1 @ sK8) != $true) | ((in @ (kpair @ (sK0 @ sK8 @ X0 @ X1 @ X2) @ (sK1 @ sK8 @ X0 @ X1 @ X2)) @ sK7) != $true) | ((breln @ X2 @ X1 @ X0) != $true)) )),
% 1.66/1.31 inference(superposition,[status(thm)],[f52,f39])).
% 1.66/1.31 thf(f39,plain,(
% 1.66/1.31 ( ! [X3 : $i,X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK8) = $true) | ((in @ (kpair @ X3 @ X4) @ sK7) != $true) | ((in @ X3 @ sK6) != $true) | ((in @ X4 @ sK6) != $true)) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.66/1.31 thf(f52,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X3) != $true) | ((breln @ X0 @ X1 @ X2) != $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((subset @ X2 @ X3) = $true)) )),
% 1.66/1.31 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.66/1.31 thf(f44,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X3) != $true) | ($true != $true) | ((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((breln @ X0 @ X1 @ X2) != $true)) )),
% 1.66/1.31 inference(definition_unfolding,[status(thm)],[f33,f37])).
% 1.66/1.31 thf(f33,plain,(
% 1.66/1.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X3) = $true) | ((breln @ X0 @ X1 @ X3) != $true) | ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X3) != $true) | ((breln @ X0 @ X1 @ X2) != $true) | (subbreln != $true)) )),
% 1.66/1.31 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.31 % SZS output end Proof for DTF2THF_29495
% 1.66/1.31 % (29718)------------------------------
% 1.66/1.31 % (29718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (29718)Termination reason: Refutation
% 1.66/1.31
% 1.66/1.31 % (29718)Memory used [KB]: 5628
% 1.66/1.31 % (29718)Time elapsed: 0.014 s
% 1.66/1.31 % (29718)Instructions burned: 12 (million)
% 1.66/1.31 % (29718)------------------------------
% 1.66/1.31 % (29718)------------------------------
% 1.66/1.31 % (29712)Success in time 0.03 s
%------------------------------------------------------------------------------