%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU774^2 : 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 : n013.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 09:37:05 AM UTC 2026
% Result : Theorem 1.68s 1.46s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 88 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 1949 ( 524 equ; 0 cnn)
% Maximal formula atoms : 22 ( 22 avg)
% Number of connectives : 2531 ( 292 ~; 277 |; 123 &;1751 @)
% ( 6 <=>; 82 =>; 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 : 23 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 303 ( 12 ^; 235 !; 56 ?; 303 :)
% 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,
sP0: $i > $i > $i > $i > $o ).
thf(func_def_20,type,
sK6: $i > $i > $i > $i > $i ).
thf(func_def_21,type,
sK7: $i > $i > $i > $i > $i ).
thf(func_def_22,type,
sK8: $i > $i > $i > $i > $i ).
thf(func_def_23,type,
sK9: $i > $i > $i > $i > $i ).
thf(f139,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f138,f66]) ).
thf(f66,plain,
$true = sP1,
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true = sP1 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f53,f60]) ).
thf(f60,plain,
eqbreln = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( eqbreln = $true )
& ( sK11 != sK12 )
& ! [X3: $i] :
( ( ( in @ X3 @ sK10 )
!= $true )
| ! [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ sK12 ) )
| ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK11 ) )
| ( $true
!= ( in @ X4 @ sK10 ) ) ) )
& ( $true
= ( breln1 @ sK10 @ sK12 ) )
& ! [X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK11 ) )
| ( $true
!= ( in @ X6 @ sK10 ) )
| ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ sK12 ) ) )
| ( ( in @ X5 @ sK10 )
!= $true ) )
& ( $true
= ( breln1 @ sK10 @ sK11 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f34,f36,f35]) ).
thf(f35,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
| ( $true
!= ( in @ X4 @ X0 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) )
& ! [X5: $i] :
( ! [X6: $i] :
( ( ( in @ ( kpair @ X5 @ X6 ) @ X1 )
!= $true )
| ( ( in @ X6 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
= $true ) )
| ( ( in @ X5 @ X0 )
!= $true ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
=> ( ? [X2: $i] :
( ( sK11 != X2 )
& ! [X3: $i] :
( ( ( in @ X3 @ sK10 )
!= $true )
| ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK11 ) )
| ( $true
!= ( in @ X4 @ sK10 ) ) ) )
& ( $true
= ( breln1 @ sK10 @ X2 ) )
& ! [X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK11 ) )
| ( $true
!= ( in @ X6 @ sK10 ) )
| ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
= $true ) )
| ( ( in @ X5 @ sK10 )
!= $true ) ) )
& ( $true
= ( breln1 @ sK10 @ sK11 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X2: $i] :
( ( sK11 != X2 )
& ! [X3: $i] :
( ( ( in @ X3 @ sK10 )
!= $true )
| ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK11 ) )
| ( $true
!= ( in @ X4 @ sK10 ) ) ) )
& ( $true
= ( breln1 @ sK10 @ X2 ) )
& ! [X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK11 ) )
| ( $true
!= ( in @ X6 @ sK10 ) )
| ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
= $true ) )
| ( ( in @ X5 @ sK10 )
!= $true ) ) )
=> ( ( sK11 != sK12 )
& ! [X3: $i] :
( ( ( in @ X3 @ sK10 )
!= $true )
| ! [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ sK12 ) )
| ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK11 ) )
| ( $true
!= ( in @ X4 @ sK10 ) ) ) )
& ( $true
= ( breln1 @ sK10 @ sK12 ) )
& ! [X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK11 ) )
| ( $true
!= ( in @ X6 @ sK10 ) )
| ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ sK12 ) ) )
| ( ( in @ X5 @ sK10 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ( eqbreln = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
| ( $true
!= ( in @ X4 @ X0 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) )
& ! [X5: $i] :
( ! [X6: $i] :
( ( ( in @ ( kpair @ X5 @ X6 ) @ X1 )
!= $true )
| ( ( in @ X6 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
= $true ) )
| ( ( in @ X5 @ X0 )
!= $true ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
( ( eqbreln = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ! [X5: $i] :
( ( ( in @ X5 @ X0 )
!= $true )
| ! [X6: $i] :
( ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X6 ) @ X1 )
= $true )
| ( ( in @ X6 @ X0 )
!= $true ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( X1 != X2 )
& ! [X5: $i] :
( ! [X6: $i] :
( ( ( in @ ( kpair @ X5 @ X6 ) @ X1 )
= $true )
| ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
!= $true )
| ( ( in @ X6 @ X0 )
!= $true ) )
| ( ( in @ X5 @ X0 )
!= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( $true
!= ( in @ X4 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( eqbreln = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( eqbreln = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) )
=> ( ! [X5: $i] :
( ( ( in @ X5 @ X0 )
= $true )
=> ! [X6: $i] :
( ( ( in @ X6 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
= $true )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X1 )
= $true ) ) ) )
=> ( X1 = X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( eqbreln
=> ! [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 ) ) ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X2 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X1 ) ) ) )
=> ( X1 = X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( eqbreln
=> ! [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 ) ) ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X4 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X3 ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( eqbreln
=> ! [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 ) ) ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X4 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X3 ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4e0JryDwKR/DTF2THF_11646.p',eqbreln1) ).
thf(f53,plain,
( ( $true = sP1 )
| ( eqbreln != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( eqbreln = $true )
| ( $true != sP1 ) )
& ( ( $true = sP1 )
| ( eqbreln != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( eqbreln = $true )
<=> ( $true = sP1 ) ),
inference(definition_folding,[status(thm)],[f17,f19,f18]) ).
thf(f18,plain,
! [X2: $i,X0: $i,X3: $i,X1: $i] :
( ( $true
= ( sP0 @ X1 @ X3 @ X0 @ X2 ) )
<=> ? [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
& ? [X7: $i] :
( ( ( in @ X7 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
& ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
( ( $true = sP1 )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( breln @ X2 @ X0 @ X3 ) )
| ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
& ( ( in @ X5 @ X0 )
= $true )
& ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
& ( $true
= ( in @ X4 @ X2 ) ) )
| ( X1 = X3 )
| ( $true
= ( sP0 @ X1 @ X3 @ X0 @ X2 ) ) )
| ( $true
!= ( breln @ X2 @ X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
( ( eqbreln = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( breln @ X2 @ X0 @ X3 ) )
| ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
& ( ( in @ X5 @ X0 )
= $true )
& ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
& ( $true
= ( in @ X4 @ X2 ) ) )
| ( X1 = X3 )
| ? [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
& ? [X7: $i] :
( ( ( in @ X7 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
& ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X1 ) ) ) ) )
| ( $true
!= ( breln @ X2 @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( X1 = X3 )
| ? [X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X1 ) )
& ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
& ( ( in @ X7 @ X0 )
= $true ) )
& ( $true
= ( in @ X6 @ X2 ) ) )
| ? [X4: $i] :
( ? [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
& ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
& ( ( in @ X5 @ X0 )
= $true ) )
& ( $true
= ( in @ X4 @ X2 ) ) )
| ( $true
!= ( breln @ X2 @ X0 @ X3 ) ) )
| ( $true
!= ( breln @ X2 @ X0 @ X1 ) ) )
<=> ( eqbreln = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X2 @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( breln @ X2 @ X0 @ X3 ) )
=> ( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X0 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
=> ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) )
=> ( ! [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
=> ! [X7: $i] :
( ( ( in @ X7 @ X0 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
=> ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X1 ) ) ) ) )
=> ( X1 = X3 ) ) ) ) )
<=> ( eqbreln = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( eqbreln
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X2 @ X0 @ X1 )
=> ! [X3: $i] :
( ( breln @ X2 @ X0 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ! [X7: $i] :
( ( in @ X7 @ X0 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( eqbreln
= ( ! [X1: $i,X3: $i,X0: $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 ) ) ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X4 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X3 ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4e0JryDwKR/DTF2THF_11646.p',eqbreln) ).
thf(f138,plain,
$true != sP1,
inference(subsumption_resolution,[status(thm)],[f137,f59]) ).
thf(f59,plain,
sK11 != sK12,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f137,plain,
( ( sK11 = sK12 )
| ( $true != sP1 ) ),
inference(subsumption_resolution,[status(thm)],[f136,f119]) ).
thf(f119,plain,
( $true
!= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $true != $true )
| ( $true
!= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $true != $true )
| ( $true
!= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) )
| ( $true
!= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) ) ),
inference(superposition,[status(thm)],[f116,f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ X0 ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( $true
= ( sP0 @ X3 @ X2 @ X1 @ X0 ) )
| ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X2 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) )
& ( ( ( $true
= ( in @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ X0 ) )
& ( $true
= ( in @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true
= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 ) )
& ( $true
!= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 ) ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f29,f31,f30]) ).
thf(f30,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ X0 )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X1 ) )
& ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) ) ) )
=> ( ( $true
= ( in @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ X0 ) )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X1 ) )
& ( $true
= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ X7 ) @ X2 ) )
& ( $true
!= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ X7 ) @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X1 ) )
& ( $true
= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ X7 ) @ X2 ) )
& ( $true
!= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ X7 ) @ X3 ) ) )
=> ( ( $true
= ( in @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true
= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 ) )
& ( $true
!= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( $true
= ( sP0 @ X3 @ X2 @ X1 @ X0 ) )
| ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X2 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) )
& ( ? [X6: $i] :
( ( ( in @ X6 @ X0 )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X1 ) )
& ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) ) ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X0: $i,X3: $i,X1: $i] :
( ( ( $true
= ( sP0 @ X1 @ X3 @ X0 @ X2 ) )
| ! [X6: $i] :
( ( $true
!= ( in @ X6 @ X2 ) )
| ! [X7: $i] :
( ( ( in @ X7 @ X0 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
| ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X1 ) ) ) ) )
& ( ? [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
& ? [X7: $i] :
( ( ( in @ X7 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
& ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X1 ) ) ) )
| ( $true
!= ( sP0 @ X1 @ X3 @ X0 @ X2 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f116,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK8 @ sK11 @ sK12 @ sK10 @ X0 ) @ sK10 ) )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
!= $true )
| ( $true
!= ( in @ ( sK8 @ sK11 @ sK12 @ sK10 @ X0 ) @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f114]) ).
thf(f114,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
!= $true )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
!= $true )
| ( $true
!= ( in @ ( sK8 @ sK11 @ sK12 @ sK10 @ X0 ) @ sK10 ) ) ),
inference(superposition,[status(thm)],[f87,f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f87,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK9 @ sK11 @ sK12 @ X0 @ X1 ) @ sK10 ) )
| ( $true
!= ( in @ ( sK8 @ sK11 @ sK12 @ X0 @ X1 ) @ sK10 ) )
| ( ( sP0 @ sK11 @ sK12 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK9 @ sK11 @ sK12 @ X0 @ X1 ) @ sK10 ) )
| ( ( sP0 @ sK11 @ sK12 @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ ( sK8 @ sK11 @ sK12 @ X0 @ X1 ) @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f84]) ).
thf(f84,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( sP0 @ sK11 @ sK12 @ X0 @ X1 )
!= $true )
| ( ( sP0 @ sK11 @ sK12 @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ ( sK9 @ sK11 @ sK12 @ X0 @ X1 ) @ sK10 ) )
| ( $true
!= ( in @ ( sK8 @ sK11 @ sK12 @ X0 @ X1 ) @ sK10 ) ) ),
inference(superposition,[status(thm)],[f76,f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK8 @ sK11 @ X0 @ X1 @ X2 ) @ ( sK9 @ sK11 @ X0 @ X1 @ X2 ) ) @ sK12 ) )
| ( $true
!= ( in @ ( sK8 @ sK11 @ X0 @ X1 @ X2 ) @ sK10 ) )
| ( $true
!= ( sP0 @ sK11 @ X0 @ X1 @ X2 ) )
| ( $true
!= ( in @ ( sK9 @ sK11 @ X0 @ X1 @ X2 ) @ sK10 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( sP0 @ sK11 @ X0 @ X1 @ X2 ) )
| ( $true
!= ( in @ ( kpair @ ( sK8 @ sK11 @ X0 @ X1 @ X2 ) @ ( sK9 @ sK11 @ X0 @ X1 @ X2 ) ) @ sK12 ) )
| ( $true != $true )
| ( $true
!= ( in @ ( sK9 @ sK11 @ X0 @ X1 @ X2 ) @ sK10 ) )
| ( $true
!= ( in @ ( sK8 @ sK11 @ X0 @ X1 @ X2 ) @ sK10 ) ) ),
inference(superposition,[status(thm)],[f48,f58]) ).
thf(f58,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ sK11 ) )
| ( $true
!= ( in @ X4 @ sK10 ) )
| ( ( in @ X3 @ sK10 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ sK12 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK8 @ X3 @ X2 @ X1 @ X0 ) @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f136,plain,
( ( $true
= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) )
| ( $true != sP1 )
| ( sK11 = sK12 ) ),
inference(subsumption_resolution,[status(thm)],[f135,f67]) ).
thf(f67,plain,
( $true
= ( breln @ sK10 @ sK10 @ sK11 ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 )
@ sK10
@ sK11 ) ),
inference(definition_unfolding,[status(thm)],[f55,f38]) ).
thf(f38,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,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/sandbox/tmp/tmp.4e0JryDwKR/DTF2THF_11646.p',breln1) ).
thf(f55,plain,
( $true
= ( breln1 @ sK10 @ sK11 ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f135,plain,
( ( $true
!= ( breln @ sK10 @ sK10 @ sK11 ) )
| ( $true
= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) )
| ( sK11 = sK12 )
| ( $true != sP1 ) ),
inference(subsumption_resolution,[status(thm)],[f134,f65]) ).
thf(f65,plain,
( $true
= ( breln @ sK10 @ sK10 @ sK12 ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 )
@ sK10
@ sK12 ) ),
inference(definition_unfolding,[status(thm)],[f57,f38]) ).
thf(f57,plain,
( $true
= ( breln1 @ sK10 @ sK12 ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f134,plain,
( ( $true
!= ( breln @ sK10 @ sK10 @ sK12 ) )
| ( sK11 = sK12 )
| ( $true
= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) )
| ( $true != sP1 )
| ( $true
!= ( breln @ sK10 @ sK10 @ sK11 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
( ( sK11 = sK12 )
| ( $true
!= ( breln @ sK10 @ sK10 @ sK12 ) )
| ( $true != $true )
| ( $true
!= ( breln @ sK10 @ sK10 @ sK11 ) )
| ( $true
= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) )
| ( $true != sP1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $true
= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) )
| ( sK11 = sK12 )
| ( $true != sP1 )
| ( $true
!= ( breln @ sK10 @ sK10 @ sK11 ) )
| ( $true
!= ( breln @ sK10 @ sK10 @ sK12 ) )
| ( $true != $true )
| ( $true
!= ( breln @ sK10 @ sK10 @ sK12 ) )
| ( $true
= ( sP0 @ sK11 @ sK12 @ sK10 @ sK10 ) )
| ( $true
!= ( breln @ sK10 @ sK10 @ sK11 ) ) ),
inference(superposition,[status(thm)],[f124,f39]) ).
thf(f39,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
= ( in @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ X8 ) )
| ( X7 = X9 )
| ( ( breln @ X8 @ X6 @ X9 )
!= $true )
| ( $true
!= ( breln @ X8 @ X6 @ X7 ) )
| ( $true
= ( sP0 @ X7 @ X9 @ X6 @ X8 ) )
| ( $true != sP1 ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( $true = sP1 )
| ( ( $true
= ( breln @ sK4 @ sK2 @ sK5 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK3 )
!= $true )
| ( $true
!= ( in @ X5 @ sK2 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK5 ) ) )
| ( $true
!= ( in @ X4 @ sK4 ) ) )
& ( sK5 != sK3 )
& ( $true
!= ( sP0 @ sK3 @ sK5 @ sK2 @ sK4 ) )
& ( ( breln @ sK4 @ sK2 @ sK3 )
= $true ) ) )
& ( ! [X6: $i,X7: $i,X8: $i] :
( ! [X9: $i] :
( ( ( breln @ X8 @ X6 @ X9 )
!= $true )
| ( ( ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 )
= $true )
& ( ( in @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) @ X6 )
= $true )
& ( $true
!= ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) ) @ X9 ) )
& ( $true
= ( in @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ X8 ) ) )
| ( X7 = X9 )
| ( $true
= ( sP0 @ X7 @ X9 @ X6 @ X8 ) ) )
| ( $true
!= ( breln @ X8 @ X6 @ X7 ) ) )
| ( $true != sP1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7])],[f22,f26,f25,f24,f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( breln @ X2 @ X0 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
| ( ( in @ X5 @ X0 )
!= $true )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( X1 != X3 )
& ( $true
!= ( sP0 @ X1 @ X3 @ X0 @ X2 ) ) )
& ( $true
= ( breln @ X2 @ X0 @ X1 ) ) )
=> ( ? [X3: $i] :
( ( $true
= ( breln @ sK4 @ sK2 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK3 )
!= $true )
| ( $true
!= ( in @ X5 @ sK2 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( $true
!= ( in @ X4 @ sK4 ) ) )
& ( sK3 != X3 )
& ( ( sP0 @ sK3 @ X3 @ sK2 @ sK4 )
!= $true ) )
& ( ( breln @ sK4 @ sK2 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X3: $i] :
( ( $true
= ( breln @ sK4 @ sK2 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK3 )
!= $true )
| ( $true
!= ( in @ X5 @ sK2 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( $true
!= ( in @ X4 @ sK4 ) ) )
& ( sK3 != X3 )
& ( ( sP0 @ sK3 @ X3 @ sK2 @ sK4 )
!= $true ) )
=> ( ( $true
= ( breln @ sK4 @ sK2 @ sK5 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK3 )
!= $true )
| ( $true
!= ( in @ X5 @ sK2 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK5 ) ) )
| ( $true
!= ( in @ X4 @ sK4 ) ) )
& ( sK5 != sK3 )
& ( $true
!= ( sP0 @ sK3 @ sK5 @ sK2 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X6: $i,X7: $i,X8: $i,X9: $i] :
( ? [X10: $i] :
( ? [X11: $i] :
( ( $true
= ( in @ ( kpair @ X10 @ X11 ) @ X7 ) )
& ( $true
= ( in @ X11 @ X6 ) )
& ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
!= $true ) )
& ( $true
= ( in @ X10 @ X8 ) ) )
=> ( ? [X11: $i] :
( ( $true
= ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ X11 ) @ X7 ) )
& ( $true
= ( in @ X11 @ X6 ) )
& ( $true
!= ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ X11 ) @ X9 ) ) )
& ( $true
= ( in @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ X8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
! [X6: $i,X7: $i,X8: $i,X9: $i] :
( ? [X11: $i] :
( ( $true
= ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ X11 ) @ X7 ) )
& ( $true
= ( in @ X11 @ X6 ) )
& ( $true
!= ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ X11 ) @ X9 ) ) )
=> ( ( ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 )
= $true )
& ( ( in @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) @ X6 )
= $true )
& ( $true
!= ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) ) @ X9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ( $true = sP1 )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( breln @ X2 @ X0 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
| ( ( in @ X5 @ X0 )
!= $true )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( X1 != X3 )
& ( $true
!= ( sP0 @ X1 @ X3 @ X0 @ X2 ) ) )
& ( $true
= ( breln @ X2 @ X0 @ X1 ) ) ) )
& ( ! [X6: $i,X7: $i,X8: $i] :
( ! [X9: $i] :
( ( ( breln @ X8 @ X6 @ X9 )
!= $true )
| ? [X10: $i] :
( ? [X11: $i] :
( ( $true
= ( in @ ( kpair @ X10 @ X11 ) @ X7 ) )
& ( $true
= ( in @ X11 @ X6 ) )
& ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
!= $true ) )
& ( $true
= ( in @ X10 @ X8 ) ) )
| ( X7 = X9 )
| ( $true
= ( sP0 @ X7 @ X9 @ X6 @ X8 ) ) )
| ( $true
!= ( breln @ X8 @ X6 @ X7 ) ) )
| ( $true != sP1 ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( $true = sP1 )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( breln @ X2 @ X0 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
| ( ( in @ X5 @ X0 )
!= $true )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( X1 != X3 )
& ( $true
!= ( sP0 @ X1 @ X3 @ X0 @ X2 ) ) )
& ( $true
= ( breln @ X2 @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( breln @ X2 @ X0 @ X3 ) )
| ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
& ( ( in @ X5 @ X0 )
= $true )
& ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
& ( $true
= ( in @ X4 @ X2 ) ) )
| ( X1 = X3 )
| ( $true
= ( sP0 @ X1 @ X3 @ X0 @ X2 ) ) )
| ( $true
!= ( breln @ X2 @ X0 @ X1 ) ) )
| ( $true != sP1 ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f124,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ sK10 ) @ sK10 ) )
| ( $true
!= ( breln @ X0 @ sK10 @ sK11 ) )
| ( $true
!= ( breln @ X0 @ sK10 @ sK12 ) )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f123,f59]) ).
thf(f123,plain,
! [X0: $i] :
( ( $true
!= ( breln @ X0 @ sK10 @ sK11 ) )
| ( sK11 = sK12 )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ sK10 ) @ sK10 ) )
| ( $true
!= ( breln @ X0 @ sK10 @ sK12 ) )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f122,f66]) ).
thf(f122,plain,
! [X0: $i] :
( ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
= $true )
| ( $true
!= ( breln @ X0 @ sK10 @ sK11 ) )
| ( $true != sP1 )
| ( sK11 = sK12 )
| ( $true
!= ( breln @ X0 @ sK10 @ sK12 ) )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ sK10 ) @ sK10 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
! [X0: $i] :
( ( $true
!= ( breln @ X0 @ sK10 @ sK11 ) )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ sK10 ) @ sK10 ) )
| ( sK11 = sK12 )
| ( $true
!= ( breln @ X0 @ sK10 @ sK12 ) )
| ( $true != $true )
| ( $true != sP1 )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f120]) ).
thf(f120,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( breln @ X0 @ sK10 @ sK12 ) )
| ( $true
!= ( breln @ X0 @ sK10 @ sK12 ) )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ sK10 ) @ sK10 ) )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
= $true )
| ( sK11 = sK12 )
| ( ( sP0 @ sK11 @ sK12 @ sK10 @ X0 )
= $true )
| ( $true
!= ( breln @ X0 @ sK10 @ sK11 ) )
| ( $true
!= ( breln @ X0 @ sK10 @ sK11 ) )
| ( $true != sP1 ) ),
inference(superposition,[status(thm)],[f100,f41]) ).
thf(f41,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i] :
( ( ( in @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) @ X6 )
= $true )
| ( X7 = X9 )
| ( ( breln @ X8 @ X6 @ X9 )
!= $true )
| ( $true != sP1 )
| ( $true
= ( sP0 @ X7 @ X9 @ X6 @ X8 ) )
| ( $true
!= ( breln @ X8 @ X6 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f100,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK7 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( ( breln @ X0 @ X1 @ sK11 )
!= $true )
| ( ( sP0 @ sK11 @ sK12 @ X1 @ X0 )
= $true )
| ( $true
!= ( breln @ X0 @ X1 @ sK12 ) ) ),
inference(subsumption_resolution,[status(thm)],[f99,f66]) ).
thf(f99,plain,
! [X0: $i,X1: $i] :
( ( ( sP0 @ sK11 @ sK12 @ X1 @ X0 )
= $true )
| ( $true
!= ( breln @ X0 @ X1 @ sK12 ) )
| ( $true != sP1 )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( ( breln @ X0 @ X1 @ sK11 )
!= $true )
| ( $true
!= ( in @ ( sK7 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) ) ),
inference(subsumption_resolution,[status(thm)],[f96,f59]) ).
thf(f96,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( breln @ X0 @ X1 @ sK12 ) )
| ( $true
!= ( in @ ( sK7 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( sK11 = sK12 )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( ( breln @ X0 @ X1 @ sK11 )
!= $true )
| ( ( sP0 @ sK11 @ sK12 @ X1 @ X0 )
= $true )
| ( $true != sP1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK7 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( $true
!= ( breln @ X0 @ X1 @ sK12 ) )
| ( ( sP0 @ sK11 @ sK12 @ X1 @ X0 )
= $true )
| ( ( breln @ X0 @ X1 @ sK11 )
!= $true )
| ( $true != sP1 )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( sK11 = sK12 )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( breln @ X0 @ X1 @ sK12 ) )
| ( $true
!= ( breln @ X0 @ X1 @ sK12 ) )
| ( ( sP0 @ sK11 @ sK12 @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ ( sK7 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( ( sP0 @ sK11 @ sK12 @ X1 @ X0 )
= $true )
| ( $true != $true )
| ( sK11 = sK12 )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ sK11 @ X1 ) @ sK10 ) )
| ( $true != sP1 )
| ( ( breln @ X0 @ X1 @ sK11 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK11 )
!= $true )
| ( sK11 = sK12 ) ),
inference(superposition,[status(thm)],[f72,f42]) ).
thf(f42,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i] :
( ( ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 )
= $true )
| ( $true
!= ( breln @ X8 @ X6 @ X7 ) )
| ( ( breln @ X8 @ X6 @ X9 )
!= $true )
| ( $true
= ( sP0 @ X7 @ X9 @ X6 @ X8 ) )
| ( $true != sP1 )
| ( X7 = X9 ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f72,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK6 @ sK12 @ X0 @ X1 @ X2 ) @ ( sK7 @ sK12 @ X0 @ X1 @ X2 ) ) @ sK11 )
!= $true )
| ( ( breln @ X0 @ X2 @ X1 )
!= $true )
| ( $true
!= ( breln @ X0 @ X2 @ sK12 ) )
| ( sK12 = X1 )
| ( $true
!= ( in @ ( sK7 @ sK12 @ X0 @ X1 @ X2 ) @ sK10 ) )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ X1 @ X2 ) @ sK10 ) )
| ( $true
= ( sP0 @ X1 @ sK12 @ X2 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f71,f66]) ).
thf(f71,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != sP1 )
| ( $true
!= ( in @ ( sK7 @ sK12 @ X0 @ X1 @ X2 ) @ sK10 ) )
| ( ( in @ ( kpair @ ( sK6 @ sK12 @ X0 @ X1 @ X2 ) @ ( sK7 @ sK12 @ X0 @ X1 @ X2 ) ) @ sK11 )
!= $true )
| ( sK12 = X1 )
| ( $true
= ( sP0 @ X1 @ sK12 @ X2 @ X0 ) )
| ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ X1 @ X2 ) @ sK10 ) )
| ( $true
!= ( breln @ X0 @ X2 @ sK12 ) )
| ( ( breln @ X0 @ X2 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK6 @ sK12 @ X0 @ X1 @ X2 ) @ sK10 ) )
| ( ( breln @ X0 @ X2 @ X1 )
!= $true )
| ( sK12 = X1 )
| ( $true
!= ( in @ ( sK7 @ sK12 @ X0 @ X1 @ X2 ) @ sK10 ) )
| ( $true != $true )
| ( ( in @ ( kpair @ ( sK6 @ sK12 @ X0 @ X1 @ X2 ) @ ( sK7 @ sK12 @ X0 @ X1 @ X2 ) ) @ sK11 )
!= $true )
| ( $true != sP1 )
| ( $true
!= ( breln @ X0 @ X2 @ sK12 ) )
| ( $true
= ( sP0 @ X1 @ sK12 @ X2 @ X0 ) ) ),
inference(superposition,[status(thm)],[f40,f56]) ).
thf(f56,plain,
! [X6: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ sK12 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK11 ) )
| ( $true
!= ( in @ X6 @ sK10 ) )
| ( ( in @ X5 @ sK10 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f40,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK6 @ X9 @ X8 @ X7 @ X6 ) @ ( sK7 @ X9 @ X8 @ X7 @ X6 ) ) @ X9 ) )
| ( ( breln @ X8 @ X6 @ X9 )
!= $true )
| ( $true
= ( sP0 @ X7 @ X9 @ X6 @ X8 ) )
| ( $true != sP1 )
| ( X7 = X9 )
| ( $true
!= ( breln @ X8 @ X6 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU774^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:33:23 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.49 ---- Original DTF file ---
% 0.28/0.49 thf(spec,logic,$$dhol).
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 % File : SEU774^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.49 % Domain : Set Theory
% 0.28/0.49 % Problem : Binary Relations on a Set
% 0.28/0.49 % Version : Especial > Reduced > Especial.
% 0.28/0.49 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.28/0.49 % (! y:i.in y A -> in (kpair x y) R -> in (kpair x y) S)) ->
% 0.28/0.49 % (! x:i.in x A -> (! y:i.in y A -> in (kpair x y) S ->
% 0.28/0.49 % in (kpair x y) R)) -> R = S))
% 0.28/0.49
% 0.28/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.49 % Source : [Bro08]
% 0.28/0.49 % Names : ZFC276l [Bro08]
% 0.28/0.49
% 0.28/0.49 % Status : Theorem
% 0.28/0.49 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.28/0.49 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.28/0.49 % Number of atoms : 31 ( 5 equ; 0 cnn)
% 0.28/0.49 % Maximal formula atoms : 12 ( 7 avg)
% 0.28/0.49 % Number of connectives : 86 ( 0 ~; 0 |; 0 &; 65 @)
% 0.28/0.49 % ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% 0.28/0.49 % Maximal formula depth : 18 ( 5 avg)
% 0.28/0.49 % Number of types : 2 ( 0 usr)
% 0.28/0.49 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.28/0.49 % Number of symbols : 8 ( 7 usr; 1 con; 0-3 aty)
% 0.28/0.49 % Number of variables : 20 ( 5 ^; 15 !; 0 ?; 20 :)
% 0.28/0.49 % SPC : TH0_THM_EQU_NAR
% 0.28/0.49
% 0.28/0.49 % Comments : http://mathgate.info/detsetitem.php?id=332
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 thf(in_type,type,
% 0.28/0.49 in: $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(subset_type,type,
% 0.28/0.49 subset: $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(kpair_type,type,
% 0.28/0.49 kpair: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(cartprod_type,type,
% 0.28/0.49 cartprod: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(breln_type,type,
% 0.28/0.49 breln: $i > $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(breln,definition,
% 0.28/0.49 ( breln
% 0.28/0.49 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(eqbreln_type,type,
% 0.28/0.49 eqbreln: $o ).
% 0.28/0.49
% 0.28/0.49 thf(eqbreln,definition,
% 0.28/0.49 ( eqbreln
% 0.28/0.49 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.49 ( ( breln @ A @ B @ R )
% 0.28/0.49 => ! [S: $i] :
% 0.28/0.49 ( ( breln @ A @ B @ S )
% 0.28/0.49 => ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.49 => ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.28/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.28/0.49 => ( R = S ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(breln1_type,type,
% 0.28/0.49 breln1: $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(breln1,definition,
% 0.28/0.49 ( breln1
% 0.28/0.49 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(eqbreln1,conjecture,
% 0.28/0.49 ( eqbreln
% 0.28/0.49 => ! [A: $i,R: $i] :
% 0.28/0.49 ( ( breln1 @ A @ R )
% 0.28/0.49 => ! [S: $i] :
% 0.28/0.49 ( ( breln1 @ A @ S )
% 0.28/0.49 => ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ A )
% 0.28/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.49 => ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ A )
% 0.28/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.28/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.28/0.49 => ( R = S ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 ------------------------
% 1.68/1.41 ---- Embedded in THF ---
% 1.68/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.41 %%% Generated on Tue Feb 24 12:33:24 EST 2026
% 1.68/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.41 %%% Logic specification used:
% 1.68/1.41 %%% thf(spec, logic, $$dhol).
% 1.68/1.41
% 1.68/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4e0JryDwKR/DTF2DTF11646.p
% See solution above
% 1.68/1.41 ------------------------
% 1.68/1.42 ---- Cleaned THF ---
% 1.68/1.42 thf(in_type,type,
% 1.68/1.42 in: $i > $i > $o ).
% 1.68/1.42
% 1.68/1.42 thf(subset_type,type,
% 1.68/1.42 subset: $i > $i > $o ).
% 1.68/1.42
% 1.68/1.42 thf(kpair_type,type,
% 1.68/1.42 kpair: $i > $i > $i ).
% 1.68/1.42
% 1.68/1.42 thf(cartprod_type,type,
% 1.68/1.42 cartprod: $i > $i > $i ).
% 1.68/1.42
% 1.68/1.42 thf(breln_type,type,
% 1.68/1.42 breln: $i > $i > $i > $o ).
% 1.68/1.42
% 1.68/1.42 thf(breln,definition,
% 1.68/1.42 ( breln
% 1.68/1.42 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.68/1.42
% 1.68/1.42 thf(eqbreln_type,type,
% 1.68/1.42 eqbreln: $o ).
% 1.68/1.42
% 1.68/1.42 thf(eqbreln,definition,
% 1.68/1.42 ( eqbreln
% 1.68/1.42 = ( ! [A: $i,B: $i,R: $i] :
% 1.68/1.42 ( ( breln @ A @ B @ R )
% 1.68/1.42 => ! [S: $i] :
% 1.68/1.42 ( ( breln @ A @ B @ S )
% 1.68/1.42 => ( ! [Xx: $i] :
% 1.68/1.42 ( ( in @ Xx @ A )
% 1.68/1.42 => ! [Xy: $i] :
% 1.68/1.42 ( ( in @ Xy @ B )
% 1.68/1.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.68/1.42 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 1.68/1.42 => ( ! [Xx: $i] :
% 1.68/1.42 ( ( in @ Xx @ A )
% 1.68/1.42 => ! [Xy: $i] :
% 1.68/1.42 ( ( in @ Xy @ B )
% 1.68/1.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 1.68/1.42 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 1.68/1.42 => ( R = S ) ) ) ) ) ) ) ).
% 1.68/1.42
% 1.68/1.42 thf(breln1_type,type,
% 1.68/1.42 breln1: $i > $i > $o ).
% 1.68/1.42
% 1.68/1.42 thf(breln1,definition,
% 1.68/1.42 ( breln1
% 1.68/1.42 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.68/1.42
% 1.68/1.42 thf(eqbreln1,conjecture,
% 1.68/1.42 ( eqbreln
% 1.68/1.42 => ! [A: $i,R: $i] :
% 1.68/1.42 ( ( breln1 @ A @ R )
% 1.68/1.42 => ! [S: $i] :
% 1.68/1.42 ( ( breln1 @ A @ S )
% 1.68/1.42 => ( ! [Xx: $i] :
% 1.68/1.42 ( ( in @ Xx @ A )
% 1.68/1.42 => ! [Xy: $i] :
% 1.68/1.42 ( ( in @ Xy @ A )
% 1.68/1.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.68/1.42 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 1.68/1.42 => ( ! [Xx: $i] :
% 1.68/1.42 ( ( in @ Xx @ A )
% 1.68/1.42 => ! [Xy: $i] :
% 1.68/1.42 ( ( in @ Xy @ A )
% 1.68/1.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 1.68/1.42 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 1.68/1.42 => ( R = S ) ) ) ) ) ) ).
% 1.68/1.42 ------------------------
% 1.68/1.44 % (11748)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_11646 for (2999ds/275Mi)
% 1.68/1.44 % (11743)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11646 for (2999ds/183Mi)
% 1.68/1.44 % (11747)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_11646 for (2999ds/2Mi)
% 1.68/1.44 % (11746)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11646 for (2999ds/2Mi)
% 1.68/1.44 % (11745)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_11646 for (2999ds/27Mi)
% 1.68/1.44 % (11749)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11646 for (2999ds/18Mi)
% 1.68/1.44 % (11744)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_11646 for (2999ds/4Mi)
% 1.68/1.44 % (11746)Instruction limit reached!
% 1.68/1.44 % (11746)------------------------------
% 1.68/1.44 % (11746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (11746)Termination reason: Unknown
% 1.68/1.44 % (11746)Termination phase: Property scanning
% 1.68/1.44 % (11747)Instruction limit reached!
% 1.68/1.44 % (11747)------------------------------
% 1.68/1.44 % (11747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (11747)Termination reason: Unknown
% 1.68/1.44 % (11747)Termination phase: Property scanning
% 1.68/1.44
% 1.68/1.44 % (11747)Memory used [KB]: 1023
% 1.68/1.44 % (11747)Time elapsed: 0.003 s
% 1.68/1.44 % (11747)Instructions burned: 2 (million)
% 1.68/1.44 % (11747)------------------------------
% 1.68/1.44 % (11747)------------------------------
% 1.68/1.44
% 1.68/1.44 % (11746)Memory used [KB]: 1023
% 1.68/1.44 % (11746)Time elapsed: 0.003 s
% 1.68/1.44 % (11746)Instructions burned: 2 (million)
% 1.68/1.44 % (11746)------------------------------
% 1.68/1.44 % (11746)------------------------------
% 1.68/1.44 % (11744)Instruction limit reached!
% 1.68/1.44 % (11744)------------------------------
% 1.68/1.44 % (11744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (11744)Termination reason: Unknown
% 1.68/1.44 % (11744)Termination phase: Function definition elimination
% 1.68/1.44
% 1.68/1.44 % (11744)Memory used [KB]: 1023
% 1.68/1.44 % (11744)Time elapsed: 0.004 s
% 1.68/1.44 % (11744)Instructions burned: 4 (million)
% 1.68/1.44 % (11744)------------------------------
% 1.68/1.44 % (11744)------------------------------
% 1.68/1.45 % (11749)Instruction limit reached!
% 1.68/1.45 % (11749)------------------------------
% 1.68/1.45 % (11749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (11749)Termination reason: Unknown
% 1.68/1.45 % (11749)Termination phase: Saturation
% 1.68/1.45
% 1.68/1.45 % (11749)Memory used [KB]: 5628
% 1.68/1.45 % (11749)Time elapsed: 0.011 s
% 1.68/1.45 % (11749)Instructions burned: 18 (million)
% 1.68/1.45 % (11749)------------------------------
% 1.68/1.45 % (11749)------------------------------
% 1.68/1.45 % (11745)Instruction limit reached!
% 1.68/1.45 % (11745)------------------------------
% 1.68/1.45 % (11745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (11745)Termination reason: Unknown
% 1.68/1.45 % (11745)Termination phase: Saturation
% 1.68/1.45
% 1.68/1.45 % (11745)Memory used [KB]: 5756
% 1.68/1.45 % (11745)Time elapsed: 0.016 s
% 1.68/1.45 % (11745)Instructions burned: 28 (million)
% 1.68/1.45 % (11745)------------------------------
% 1.68/1.45 % (11745)------------------------------
% 1.68/1.46 % (11748)First to succeed.
% 1.68/1.46 % (11751)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_11646 for (2999ds/37Mi)
% 1.68/1.46 % (11750)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11646 for (2999ds/3Mi)
% 1.68/1.46 % (11752)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_11646 for (2999ds/15Mi)
% 1.68/1.46 % (11750)Instruction limit reached!
% 1.68/1.46 % (11750)------------------------------
% 1.68/1.46 % (11750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.46 % (11750)Termination reason: Unknown
% 1.68/1.46 % (11750)Termination phase: Property scanning
% 1.68/1.46
% 1.68/1.46 % (11750)Memory used [KB]: 1023
% 1.68/1.46 % (11750)Time elapsed: 0.003 s
% 1.68/1.46 % (11750)Instructions burned: 3 (million)
% 1.68/1.46 % (11750)------------------------------
% 1.68/1.46 % (11750)------------------------------
% 1.68/1.46 % (11748)Refutation found. Thanks to Tanya!
% 1.68/1.46 % SZS status Theorem for DTF2THF_11646
% 1.68/1.46 % SZS output start Proof for DTF2THF_11646
% 1.68/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.68/1.46 thf(func_def_1, type, subset: $i > $i > $o).
% 1.68/1.46 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.68/1.46 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.68/1.46 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.68/1.46 thf(func_def_7, type, breln1: $i > $i > $o).
% 1.68/1.46 thf(func_def_14, type, sP0: $i > $i > $i > $i > $o).
% 1.68/1.46 thf(func_def_20, type, sK6: $i > $i > $i > $i > $i).
% 1.68/1.46 thf(func_def_21, type, sK7: $i > $i > $i > $i > $i).
% 1.68/1.46 thf(func_def_22, type, sK8: $i > $i > $i > $i > $i).
% 1.68/1.46 thf(func_def_23, type, sK9: $i > $i > $i > $i > $i).
% 1.68/1.46 thf(f139,plain,(
% 1.68/1.46 $false),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f138,f66])).
% 1.68/1.46 thf(f66,plain,(
% 1.68/1.46 ($true = sP1)),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.68/1.46 thf(f62,plain,(
% 1.68/1.46 ($true = sP1) | ($true != $true)),
% 1.68/1.46 inference(definition_unfolding,[status(thm)],[f53,f60])).
% 1.68/1.46 thf(f60,plain,(
% 1.68/1.46 (eqbreln = $true)),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f37])).
% 1.68/1.46 thf(f37,plain,(
% 1.68/1.46 (eqbreln = $true) & (((sK11 != sK12) & ! [X3 : $i] : (((in @ X3 @ sK10) != $true) | ! [X4 : $i] : (($true != (in @ (kpair @ X3 @ X4) @ sK12)) | ($true = (in @ (kpair @ X3 @ X4) @ sK11)) | ($true != (in @ X4 @ sK10)))) & ($true = (breln1 @ sK10 @ sK12)) & ! [X5 : $i] : (! [X6 : $i] : (($true != (in @ (kpair @ X5 @ X6) @ sK11)) | ($true != (in @ X6 @ sK10)) | ($true = (in @ (kpair @ X5 @ X6) @ sK12))) | ((in @ X5 @ sK10) != $true))) & ($true = (breln1 @ sK10 @ sK11)))),
% 1.68/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f34,f36,f35])).
% 1.68/1.46 thf(f35,plain,(
% 1.68/1.46 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X2) != $true) | ((in @ (kpair @ X3 @ X4) @ X1) = $true) | ($true != (in @ X4 @ X0)))) & ($true = (breln1 @ X0 @ X2)) & ! [X5 : $i] : (! [X6 : $i] : (((in @ (kpair @ X5 @ X6) @ X1) != $true) | ((in @ X6 @ X0) != $true) | ((in @ (kpair @ X5 @ X6) @ X2) = $true)) | ((in @ X5 @ X0) != $true))) & ($true = (breln1 @ X0 @ X1))) => (? [X2 : $i] : ((sK11 != X2) & ! [X3 : $i] : (((in @ X3 @ sK10) != $true) | ! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X2) != $true) | ($true = (in @ (kpair @ X3 @ X4) @ sK11)) | ($true != (in @ X4 @ sK10)))) & ($true = (breln1 @ sK10 @ X2)) & ! [X5 : $i] : (! [X6 : $i] : (($true != (in @ (kpair @ X5 @ X6) @ sK11)) | ($true != (in @ X6 @ sK10)) | ((in @ (kpair @ X5 @ X6) @ X2) = $true)) | ((in @ X5 @ sK10) != $true))) & ($true = (breln1 @ sK10 @ sK11)))),
% 1.68/1.46 introduced(definition,[],[choice_axiom])).
% 1.68/1.46 thf(f36,plain,(
% 1.68/1.46 ? [X2 : $i] : ((sK11 != X2) & ! [X3 : $i] : (((in @ X3 @ sK10) != $true) | ! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X2) != $true) | ($true = (in @ (kpair @ X3 @ X4) @ sK11)) | ($true != (in @ X4 @ sK10)))) & ($true = (breln1 @ sK10 @ X2)) & ! [X5 : $i] : (! [X6 : $i] : (($true != (in @ (kpair @ X5 @ X6) @ sK11)) | ($true != (in @ X6 @ sK10)) | ((in @ (kpair @ X5 @ X6) @ X2) = $true)) | ((in @ X5 @ sK10) != $true))) => ((sK11 != sK12) & ! [X3 : $i] : (((in @ X3 @ sK10) != $true) | ! [X4 : $i] : (($true != (in @ (kpair @ X3 @ X4) @ sK12)) | ($true = (in @ (kpair @ X3 @ X4) @ sK11)) | ($true != (in @ X4 @ sK10)))) & ($true = (breln1 @ sK10 @ sK12)) & ! [X5 : $i] : (! [X6 : $i] : (($true != (in @ (kpair @ X5 @ X6) @ sK11)) | ($true != (in @ X6 @ sK10)) | ($true = (in @ (kpair @ X5 @ X6) @ sK12))) | ((in @ X5 @ sK10) != $true)))),
% 1.68/1.46 introduced(definition,[],[choice_axiom])).
% 1.68/1.46 thf(f34,plain,(
% 1.68/1.46 (eqbreln = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X2) != $true) | ((in @ (kpair @ X3 @ X4) @ X1) = $true) | ($true != (in @ X4 @ X0)))) & ($true = (breln1 @ X0 @ X2)) & ! [X5 : $i] : (! [X6 : $i] : (((in @ (kpair @ X5 @ X6) @ X1) != $true) | ((in @ X6 @ X0) != $true) | ((in @ (kpair @ X5 @ X6) @ X2) = $true)) | ((in @ X5 @ X0) != $true))) & ($true = (breln1 @ X0 @ X1)))),
% 1.68/1.46 inference(rectify,[status(thm)],[f15])).
% 1.68/1.46 thf(f15,plain,(
% 1.68/1.46 (eqbreln = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ! [X5 : $i] : (((in @ X5 @ X0) != $true) | ! [X6 : $i] : (((in @ (kpair @ X5 @ X6) @ X2) != $true) | ((in @ (kpair @ X5 @ X6) @ X1) = $true) | ((in @ X6 @ X0) != $true))) & ($true = (breln1 @ X0 @ X2)) & ! [X3 : $i] : (! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X1) != $true) | ($true != (in @ X4 @ X0)) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)) | ($true != (in @ X3 @ X0)))) & ($true = (breln1 @ X0 @ X1)))),
% 1.68/1.46 inference(flattening,[status(thm)],[f14])).
% 1.68/1.46 thf(f14,plain,(
% 1.68/1.46 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((X1 != X2) & ! [X5 : $i] : (! [X6 : $i] : ((((in @ (kpair @ X5 @ X6) @ X1) = $true) | ((in @ (kpair @ X5 @ X6) @ X2) != $true)) | ((in @ X6 @ X0) != $true)) | ((in @ X5 @ X0) != $true))) & ! [X3 : $i] : (! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2) = $true) | ((in @ (kpair @ X3 @ X4) @ X1) != $true)) | ($true != (in @ X4 @ X0))) | ($true != (in @ X3 @ X0)))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1))) & (eqbreln = $true)),
% 1.68/1.46 inference(ennf_transformation,[status(thm)],[f11])).
% 1.68/1.46 thf(f11,plain,(
% 1.68/1.46 ~((eqbreln = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => (! [X3 : $i] : (($true = (in @ X3 @ X0)) => ! [X4 : $i] : (($true = (in @ X4 @ X0)) => (((in @ (kpair @ X3 @ X4) @ X1) = $true) => ((in @ (kpair @ X3 @ X4) @ X2) = $true)))) => (! [X5 : $i] : (((in @ X5 @ X0) = $true) => ! [X6 : $i] : (((in @ X6 @ X0) = $true) => (((in @ (kpair @ X5 @ X6) @ X2) = $true) => ((in @ (kpair @ X5 @ X6) @ X1) = $true)))) => (X1 = X2))))))),
% 1.68/1.46 inference(fool_elimination,[status(thm)],[f10])).
% 1.68/1.46 thf(f10,plain,(
% 1.68/1.46 ~(eqbreln => ! [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)))) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X2) => (in @ (kpair @ X5 @ X6) @ X1)))) => (X1 = X2))))))),
% 1.68/1.46 inference(rectify,[status(thm)],[f5])).
% 1.68/1.46 thf(f5,negated_conjecture,(
% 1.68/1.46 ~(eqbreln => ! [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)))) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X4) => (in @ (kpair @ X5 @ X6) @ X3)))) => (X3 = X4))))))),
% 1.68/1.46 inference(negated_conjecture,[status(cth)],[f4])).
% 1.68/1.46 thf(f4,conjecture,(
% 1.68/1.46 eqbreln => ! [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)))) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X4) => (in @ (kpair @ X5 @ X6) @ X3)))) => (X3 = X4)))))),
% 1.68/1.46 file('/export/starexec/sandbox/tmp/tmp.4e0JryDwKR/DTF2THF_11646.p',eqbreln1)).
% 1.68/1.46 thf(f53,plain,(
% 1.68/1.46 ($true = sP1) | (eqbreln != $true)),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f33])).
% 1.68/1.46 thf(f33,plain,(
% 1.68/1.46 ((eqbreln = $true) | ($true != sP1)) & (($true = sP1) | (eqbreln != $true))),
% 1.68/1.46 inference(nnf_transformation,[status(thm)],[f20])).
% 1.68/1.46 thf(f20,plain,(
% 1.68/1.46 (eqbreln = $true) <=> ($true = sP1)),
% 1.68/1.46 inference(definition_folding,[status(thm)],[f17,f19,f18])).
% 1.68/1.46 thf(f18,plain,(
% 1.68/1.46 ! [X2 : $i,X0 : $i,X3 : $i,X1 : $i] : (($true = (sP0 @ X1 @ X3 @ X0 @ X2)) <=> ? [X6 : $i] : (($true = (in @ X6 @ X2)) & ? [X7 : $i] : (((in @ X7 @ X0) = $true) & ($true = (in @ (kpair @ X6 @ X7) @ X3)) & ($true != (in @ (kpair @ X6 @ X7) @ X1)))))),
% 1.68/1.46 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.68/1.46 thf(f19,plain,(
% 1.68/1.46 ($true = sP1) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true != (breln @ X2 @ X0 @ X3)) | ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X1)) & ((in @ X5 @ X0) = $true) & ($true != (in @ (kpair @ X4 @ X5) @ X3))) & ($true = (in @ X4 @ X2))) | (X1 = X3) | ($true = (sP0 @ X1 @ X3 @ X0 @ X2))) | ($true != (breln @ X2 @ X0 @ X1)))),
% 1.68/1.46 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.68/1.46 thf(f17,plain,(
% 1.68/1.46 (eqbreln = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true != (breln @ X2 @ X0 @ X3)) | ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X1)) & ((in @ X5 @ X0) = $true) & ($true != (in @ (kpair @ X4 @ X5) @ X3))) & ($true = (in @ X4 @ X2))) | (X1 = X3) | ? [X6 : $i] : (($true = (in @ X6 @ X2)) & ? [X7 : $i] : (((in @ X7 @ X0) = $true) & ($true = (in @ (kpair @ X6 @ X7) @ X3)) & ($true != (in @ (kpair @ X6 @ X7) @ X1))))) | ($true != (breln @ X2 @ X0 @ X1)))),
% 1.68/1.46 inference(flattening,[status(thm)],[f16])).
% 1.68/1.46 thf(f16,plain,(
% 1.68/1.46 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((((X1 = X3) | ? [X6 : $i] : (? [X7 : $i] : ((($true != (in @ (kpair @ X6 @ X7) @ X1)) & ($true = (in @ (kpair @ X6 @ X7) @ X3))) & ((in @ X7 @ X0) = $true)) & ($true = (in @ X6 @ X2)))) | ? [X4 : $i] : (? [X5 : $i] : ((($true != (in @ (kpair @ X4 @ X5) @ X3)) & ($true = (in @ (kpair @ X4 @ X5) @ X1))) & ((in @ X5 @ X0) = $true)) & ($true = (in @ X4 @ X2)))) | ($true != (breln @ X2 @ X0 @ X3))) | ($true != (breln @ X2 @ X0 @ X1))) <=> (eqbreln = $true)),
% 1.68/1.46 inference(ennf_transformation,[status(thm)],[f9])).
% 1.68/1.46 thf(f9,plain,(
% 1.68/1.46 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X2 @ X0 @ X1)) => ! [X3 : $i] : (($true = (breln @ X2 @ X0 @ X3)) => (! [X4 : $i] : (($true = (in @ X4 @ X2)) => ! [X5 : $i] : (((in @ X5 @ X0) = $true) => (($true = (in @ (kpair @ X4 @ X5) @ X1)) => ($true = (in @ (kpair @ X4 @ X5) @ X3))))) => (! [X6 : $i] : (($true = (in @ X6 @ X2)) => ! [X7 : $i] : (((in @ X7 @ X0) = $true) => (($true = (in @ (kpair @ X6 @ X7) @ X3)) => ($true = (in @ (kpair @ X6 @ X7) @ X1))))) => (X1 = X3))))) <=> (eqbreln = $true)),
% 1.68/1.46 inference(fool_elimination,[status(thm)],[f8])).
% 1.68/1.46 thf(f8,plain,(
% 1.68/1.46 (eqbreln = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X0 @ X1) => ! [X3 : $i] : ((breln @ X2 @ X0 @ X3) => (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X1) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X6 : $i] : ((in @ X6 @ X2) => ! [X7 : $i] : ((in @ X7 @ X0) => ((in @ (kpair @ X6 @ X7) @ X3) => (in @ (kpair @ X6 @ X7) @ X1)))) => (X1 = X3))))))),
% 1.68/1.46 inference(rectify,[status(thm)],[f2])).
% 1.68/1.46 thf(f2,axiom,(
% 1.68/1.46 (eqbreln = ! [X1 : $i,X3 : $i,X0 : $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)))) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X4) => (in @ (kpair @ X5 @ X6) @ X3)))) => (X3 = X4))))))),
% 1.68/1.46 file('/export/starexec/sandbox/tmp/tmp.4e0JryDwKR/DTF2THF_11646.p',eqbreln)).
% 1.68/1.46 thf(f138,plain,(
% 1.68/1.46 ($true != sP1)),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f137,f59])).
% 1.68/1.46 thf(f59,plain,(
% 1.68/1.46 (sK11 != sK12)),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f37])).
% 1.68/1.46 thf(f137,plain,(
% 1.68/1.46 (sK11 = sK12) | ($true != sP1)),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f136,f119])).
% 1.68/1.46 thf(f119,plain,(
% 1.68/1.46 ($true != (sP0 @ sK11 @ sK12 @ sK10 @ sK10))),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.68/1.46 thf(f118,plain,(
% 1.68/1.46 ($true != $true) | ($true != (sP0 @ sK11 @ sK12 @ sK10 @ sK10))),
% 1.68/1.46 inference(duplicate_literal_removal,[status(thm)],[f117])).
% 1.68/1.46 thf(f117,plain,(
% 1.68/1.46 ($true != $true) | ($true != (sP0 @ sK11 @ sK12 @ sK10 @ sK10)) | ($true != (sP0 @ sK11 @ sK12 @ sK10 @ sK10))),
% 1.68/1.46 inference(superposition,[status(thm)],[f116,f51])).
% 1.68/1.46 thf(f51,plain,(
% 1.68/1.46 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X0)) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f32])).
% 1.68/1.46 thf(f32,plain,(
% 1.68/1.46 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((($true = (sP0 @ X3 @ X2 @ X1 @ X0)) | ! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (($true != (in @ X5 @ X1)) | ($true != (in @ (kpair @ X4 @ X5) @ X2)) | ($true = (in @ (kpair @ X4 @ X5) @ X3))))) & ((($true = (in @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X0)) & (($true = (in @ (sK9 @ X3 @ X2 @ X1 @ X0) @ X1)) & ($true = (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X2)) & ($true != (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X3)))) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))))),
% 1.68/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f29,f31,f30])).
% 1.68/1.46 thf(f30,plain,(
% 1.68/1.46 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (? [X6 : $i] : (((in @ X6 @ X0) = $true) & ? [X7 : $i] : (($true = (in @ X7 @ X1)) & ($true = (in @ (kpair @ X6 @ X7) @ X2)) & ($true != (in @ (kpair @ X6 @ X7) @ X3)))) => (($true = (in @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X0)) & ? [X7 : $i] : (($true = (in @ X7 @ X1)) & ($true = (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X7) @ X2)) & ($true != (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X7) @ X3)))))),
% 1.68/1.46 introduced(definition,[],[choice_axiom])).
% 1.68/1.46 thf(f31,plain,(
% 1.68/1.46 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X1)) & ($true = (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X7) @ X2)) & ($true != (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X7) @ X3))) => (($true = (in @ (sK9 @ X3 @ X2 @ X1 @ X0) @ X1)) & ($true = (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X2)) & ($true != (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X3))))),
% 1.68/1.46 introduced(definition,[],[choice_axiom])).
% 1.68/1.46 thf(f29,plain,(
% 1.68/1.46 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((($true = (sP0 @ X3 @ X2 @ X1 @ X0)) | ! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (($true != (in @ X5 @ X1)) | ($true != (in @ (kpair @ X4 @ X5) @ X2)) | ($true = (in @ (kpair @ X4 @ X5) @ X3))))) & (? [X6 : $i] : (((in @ X6 @ X0) = $true) & ? [X7 : $i] : (($true = (in @ X7 @ X1)) & ($true = (in @ (kpair @ X6 @ X7) @ X2)) & ($true != (in @ (kpair @ X6 @ X7) @ X3)))) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))))),
% 1.68/1.46 inference(rectify,[status(thm)],[f28])).
% 1.68/1.46 thf(f28,plain,(
% 1.68/1.46 ! [X2 : $i,X0 : $i,X3 : $i,X1 : $i] : ((($true = (sP0 @ X1 @ X3 @ X0 @ X2)) | ! [X6 : $i] : (($true != (in @ X6 @ X2)) | ! [X7 : $i] : (((in @ X7 @ X0) != $true) | ($true != (in @ (kpair @ X6 @ X7) @ X3)) | ($true = (in @ (kpair @ X6 @ X7) @ X1))))) & (? [X6 : $i] : (($true = (in @ X6 @ X2)) & ? [X7 : $i] : (((in @ X7 @ X0) = $true) & ($true = (in @ (kpair @ X6 @ X7) @ X3)) & ($true != (in @ (kpair @ X6 @ X7) @ X1)))) | ($true != (sP0 @ X1 @ X3 @ X0 @ X2))))),
% 1.68/1.46 inference(nnf_transformation,[status(thm)],[f18])).
% 1.68/1.46 thf(f116,plain,(
% 1.68/1.46 ( ! [X0 : $i] : (($true != (in @ (sK8 @ sK11 @ sK12 @ sK10 @ X0) @ sK10)) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) != $true)) )),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.68/1.46 thf(f115,plain,(
% 1.68/1.46 ( ! [X0 : $i] : (($true != $true) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) != $true) | ($true != (in @ (sK8 @ sK11 @ sK12 @ sK10 @ X0) @ sK10))) )),
% 1.68/1.46 inference(duplicate_literal_removal,[status(thm)],[f114])).
% 1.68/1.46 thf(f114,plain,(
% 1.68/1.46 ( ! [X0 : $i] : (($true != $true) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) != $true) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) != $true) | ($true != (in @ (sK8 @ sK11 @ sK12 @ sK10 @ X0) @ sK10))) )),
% 1.68/1.46 inference(superposition,[status(thm)],[f87,f50])).
% 1.68/1.46 thf(f50,plain,(
% 1.68/1.46 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK9 @ X3 @ X2 @ X1 @ X0) @ X1)) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f32])).
% 1.68/1.46 thf(f87,plain,(
% 1.68/1.46 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK9 @ sK11 @ sK12 @ X0 @ X1) @ sK10)) | ($true != (in @ (sK8 @ sK11 @ sK12 @ X0 @ X1) @ sK10)) | ((sP0 @ sK11 @ sK12 @ X0 @ X1) != $true)) )),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.68/1.46 thf(f86,plain,(
% 1.68/1.46 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ (sK9 @ sK11 @ sK12 @ X0 @ X1) @ sK10)) | ((sP0 @ sK11 @ sK12 @ X0 @ X1) != $true) | ($true != (in @ (sK8 @ sK11 @ sK12 @ X0 @ X1) @ sK10))) )),
% 1.68/1.46 inference(duplicate_literal_removal,[status(thm)],[f84])).
% 1.68/1.46 thf(f84,plain,(
% 1.68/1.46 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((sP0 @ sK11 @ sK12 @ X0 @ X1) != $true) | ((sP0 @ sK11 @ sK12 @ X0 @ X1) != $true) | ($true != (in @ (sK9 @ sK11 @ sK12 @ X0 @ X1) @ sK10)) | ($true != (in @ (sK8 @ sK11 @ sK12 @ X0 @ X1) @ sK10))) )),
% 1.68/1.46 inference(superposition,[status(thm)],[f76,f49])).
% 1.68/1.46 thf(f49,plain,(
% 1.68/1.46 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X2)) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f32])).
% 1.68/1.46 thf(f76,plain,(
% 1.68/1.46 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ (sK8 @ sK11 @ X0 @ X1 @ X2) @ (sK9 @ sK11 @ X0 @ X1 @ X2)) @ sK12)) | ($true != (in @ (sK8 @ sK11 @ X0 @ X1 @ X2) @ sK10)) | ($true != (sP0 @ sK11 @ X0 @ X1 @ X2)) | ($true != (in @ (sK9 @ sK11 @ X0 @ X1 @ X2) @ sK10))) )),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.68/1.46 thf(f73,plain,(
% 1.68/1.46 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (sP0 @ sK11 @ X0 @ X1 @ X2)) | ($true != (in @ (kpair @ (sK8 @ sK11 @ X0 @ X1 @ X2) @ (sK9 @ sK11 @ X0 @ X1 @ X2)) @ sK12)) | ($true != $true) | ($true != (in @ (sK9 @ sK11 @ X0 @ X1 @ X2) @ sK10)) | ($true != (in @ (sK8 @ sK11 @ X0 @ X1 @ X2) @ sK10))) )),
% 1.68/1.46 inference(superposition,[status(thm)],[f48,f58])).
% 1.68/1.46 thf(f58,plain,(
% 1.68/1.46 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ sK11)) | ($true != (in @ X4 @ sK10)) | ((in @ X3 @ sK10) != $true) | ($true != (in @ (kpair @ X3 @ X4) @ sK12))) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f37])).
% 1.68/1.46 thf(f48,plain,(
% 1.68/1.46 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X3)) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f32])).
% 1.68/1.46 thf(f136,plain,(
% 1.68/1.46 ($true = (sP0 @ sK11 @ sK12 @ sK10 @ sK10)) | ($true != sP1) | (sK11 = sK12)),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f135,f67])).
% 1.68/1.46 thf(f67,plain,(
% 1.68/1.46 ($true = (breln @ sK10 @ sK10 @ sK11))),
% 1.68/1.46 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.68/1.46 thf(f64,plain,(
% 1.68/1.46 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))) @ sK10 @ sK11))),
% 1.68/1.46 inference(definition_unfolding,[status(thm)],[f55,f38])).
% 1.68/1.46 thf(f38,plain,(
% 1.68/1.46 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f13])).
% 1.68/1.46 thf(f13,plain,(
% 1.68/1.46 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.68/1.46 inference(fool_elimination,[status(thm)],[f12])).
% 1.68/1.46 thf(f12,plain,(
% 1.68/1.46 (breln1 = (^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)))),
% 1.68/1.46 inference(rectify,[status(thm)],[f3])).
% 1.68/1.46 thf(f3,axiom,(
% 1.68/1.46 (breln1 = (^[X0 : $i, X3 : $i] : (breln @ X0 @ X0 @ X3)))),
% 1.68/1.46 file('/export/starexec/sandbox/tmp/tmp.4e0JryDwKR/DTF2THF_11646.p',breln1)).
% 1.68/1.46 thf(f55,plain,(
% 1.68/1.46 ($true = (breln1 @ sK10 @ sK11))),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f37])).
% 1.68/1.46 thf(f135,plain,(
% 1.68/1.46 ($true != (breln @ sK10 @ sK10 @ sK11)) | ($true = (sP0 @ sK11 @ sK12 @ sK10 @ sK10)) | (sK11 = sK12) | ($true != sP1)),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f134,f65])).
% 1.68/1.46 thf(f65,plain,(
% 1.68/1.46 ($true = (breln @ sK10 @ sK10 @ sK12))),
% 1.68/1.46 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.68/1.46 thf(f63,plain,(
% 1.68/1.46 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))) @ sK10 @ sK12))),
% 1.68/1.46 inference(definition_unfolding,[status(thm)],[f57,f38])).
% 1.68/1.46 thf(f57,plain,(
% 1.68/1.46 ($true = (breln1 @ sK10 @ sK12))),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f37])).
% 1.68/1.46 thf(f134,plain,(
% 1.68/1.46 ($true != (breln @ sK10 @ sK10 @ sK12)) | (sK11 = sK12) | ($true = (sP0 @ sK11 @ sK12 @ sK10 @ sK10)) | ($true != sP1) | ($true != (breln @ sK10 @ sK10 @ sK11))),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.68/1.46 thf(f133,plain,(
% 1.68/1.46 (sK11 = sK12) | ($true != (breln @ sK10 @ sK10 @ sK12)) | ($true != $true) | ($true != (breln @ sK10 @ sK10 @ sK11)) | ($true = (sP0 @ sK11 @ sK12 @ sK10 @ sK10)) | ($true != sP1)),
% 1.68/1.46 inference(duplicate_literal_removal,[status(thm)],[f132])).
% 1.68/1.46 thf(f132,plain,(
% 1.68/1.46 ($true = (sP0 @ sK11 @ sK12 @ sK10 @ sK10)) | (sK11 = sK12) | ($true != sP1) | ($true != (breln @ sK10 @ sK10 @ sK11)) | ($true != (breln @ sK10 @ sK10 @ sK12)) | ($true != $true) | ($true != (breln @ sK10 @ sK10 @ sK12)) | ($true = (sP0 @ sK11 @ sK12 @ sK10 @ sK10)) | ($true != (breln @ sK10 @ sK10 @ sK11))),
% 1.68/1.46 inference(superposition,[status(thm)],[f124,f39])).
% 1.68/1.46 thf(f39,plain,(
% 1.68/1.46 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = (in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X8)) | (X7 = X9) | ((breln @ X8 @ X6 @ X9) != $true) | ($true != (breln @ X8 @ X6 @ X7)) | ($true = (sP0 @ X7 @ X9 @ X6 @ X8)) | ($true != sP1)) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f27])).
% 1.68/1.46 thf(f27,plain,(
% 1.68/1.46 (($true = sP1) | ((($true = (breln @ sK4 @ sK2 @ sK5)) & ! [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK3) != $true) | ($true != (in @ X5 @ sK2)) | ($true = (in @ (kpair @ X4 @ X5) @ sK5))) | ($true != (in @ X4 @ sK4))) & (sK5 != sK3) & ($true != (sP0 @ sK3 @ sK5 @ sK2 @ sK4))) & ((breln @ sK4 @ sK2 @ sK3) = $true))) & (! [X6 : $i,X7 : $i,X8 : $i] : (! [X9 : $i] : (((breln @ X8 @ X6 @ X9) != $true) | ((((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X7) = $true) & ((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X6) = $true) & ($true != (in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9))) & ($true = (in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X8))) | (X7 = X9) | ($true = (sP0 @ X7 @ X9 @ X6 @ X8))) | ($true != (breln @ X8 @ X6 @ X7))) | ($true != sP1))),
% 1.68/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7])],[f22,f26,f25,f24,f23])).
% 1.68/1.46 thf(f23,plain,(
% 1.68/1.46 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (breln @ X2 @ X0 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ X1)) | ((in @ X5 @ X0) != $true) | ($true = (in @ (kpair @ X4 @ X5) @ X3))) | ($true != (in @ X4 @ X2))) & (X1 != X3) & ($true != (sP0 @ X1 @ X3 @ X0 @ X2))) & ($true = (breln @ X2 @ X0 @ X1))) => (? [X3 : $i] : (($true = (breln @ sK4 @ sK2 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK3) != $true) | ($true != (in @ X5 @ sK2)) | ($true = (in @ (kpair @ X4 @ X5) @ X3))) | ($true != (in @ X4 @ sK4))) & (sK3 != X3) & ((sP0 @ sK3 @ X3 @ sK2 @ sK4) != $true)) & ((breln @ sK4 @ sK2 @ sK3) = $true))),
% 1.68/1.46 introduced(definition,[],[choice_axiom])).
% 1.68/1.46 thf(f24,plain,(
% 1.68/1.46 ? [X3 : $i] : (($true = (breln @ sK4 @ sK2 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK3) != $true) | ($true != (in @ X5 @ sK2)) | ($true = (in @ (kpair @ X4 @ X5) @ X3))) | ($true != (in @ X4 @ sK4))) & (sK3 != X3) & ((sP0 @ sK3 @ X3 @ sK2 @ sK4) != $true)) => (($true = (breln @ sK4 @ sK2 @ sK5)) & ! [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK3) != $true) | ($true != (in @ X5 @ sK2)) | ($true = (in @ (kpair @ X4 @ X5) @ sK5))) | ($true != (in @ X4 @ sK4))) & (sK5 != sK3) & ($true != (sP0 @ sK3 @ sK5 @ sK2 @ sK4)))),
% 1.68/1.46 introduced(definition,[],[choice_axiom])).
% 1.68/1.46 thf(f25,plain,(
% 1.68/1.46 ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i] : (? [X10 : $i] : (? [X11 : $i] : (($true = (in @ (kpair @ X10 @ X11) @ X7)) & ($true = (in @ X11 @ X6)) & ((in @ (kpair @ X10 @ X11) @ X9) != $true)) & ($true = (in @ X10 @ X8))) => (? [X11 : $i] : (($true = (in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X11) @ X7)) & ($true = (in @ X11 @ X6)) & ($true != (in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X11) @ X9))) & ($true = (in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X8))))),
% 1.68/1.46 introduced(definition,[],[choice_axiom])).
% 1.68/1.46 thf(f26,plain,(
% 1.68/1.46 ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i] : (? [X11 : $i] : (($true = (in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X11) @ X7)) & ($true = (in @ X11 @ X6)) & ($true != (in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X11) @ X9))) => (((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X7) = $true) & ((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X6) = $true) & ($true != (in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9))))),
% 1.68/1.46 introduced(definition,[],[choice_axiom])).
% 1.68/1.46 thf(f22,plain,(
% 1.68/1.46 (($true = sP1) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (breln @ X2 @ X0 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ X1)) | ((in @ X5 @ X0) != $true) | ($true = (in @ (kpair @ X4 @ X5) @ X3))) | ($true != (in @ X4 @ X2))) & (X1 != X3) & ($true != (sP0 @ X1 @ X3 @ X0 @ X2))) & ($true = (breln @ X2 @ X0 @ X1)))) & (! [X6 : $i,X7 : $i,X8 : $i] : (! [X9 : $i] : (((breln @ X8 @ X6 @ X9) != $true) | ? [X10 : $i] : (? [X11 : $i] : (($true = (in @ (kpair @ X10 @ X11) @ X7)) & ($true = (in @ X11 @ X6)) & ((in @ (kpair @ X10 @ X11) @ X9) != $true)) & ($true = (in @ X10 @ X8))) | (X7 = X9) | ($true = (sP0 @ X7 @ X9 @ X6 @ X8))) | ($true != (breln @ X8 @ X6 @ X7))) | ($true != sP1))),
% 1.68/1.46 inference(rectify,[status(thm)],[f21])).
% 1.68/1.46 thf(f21,plain,(
% 1.68/1.46 (($true = sP1) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (breln @ X2 @ X0 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ X1)) | ((in @ X5 @ X0) != $true) | ($true = (in @ (kpair @ X4 @ X5) @ X3))) | ($true != (in @ X4 @ X2))) & (X1 != X3) & ($true != (sP0 @ X1 @ X3 @ X0 @ X2))) & ($true = (breln @ X2 @ X0 @ X1)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true != (breln @ X2 @ X0 @ X3)) | ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X1)) & ((in @ X5 @ X0) = $true) & ($true != (in @ (kpair @ X4 @ X5) @ X3))) & ($true = (in @ X4 @ X2))) | (X1 = X3) | ($true = (sP0 @ X1 @ X3 @ X0 @ X2))) | ($true != (breln @ X2 @ X0 @ X1))) | ($true != sP1))),
% 1.68/1.46 inference(nnf_transformation,[status(thm)],[f19])).
% 1.68/1.46 thf(f124,plain,(
% 1.68/1.46 ( ! [X0 : $i] : (($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ sK10) @ sK10)) | ($true != (breln @ X0 @ sK10 @ sK11)) | ($true != (breln @ X0 @ sK10 @ sK12)) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) = $true)) )),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f123,f59])).
% 1.68/1.46 thf(f123,plain,(
% 1.68/1.46 ( ! [X0 : $i] : (($true != (breln @ X0 @ sK10 @ sK11)) | (sK11 = sK12) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ sK10) @ sK10)) | ($true != (breln @ X0 @ sK10 @ sK12)) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) = $true)) )),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f122,f66])).
% 1.68/1.46 thf(f122,plain,(
% 1.68/1.46 ( ! [X0 : $i] : (((sP0 @ sK11 @ sK12 @ sK10 @ X0) = $true) | ($true != (breln @ X0 @ sK10 @ sK11)) | ($true != sP1) | (sK11 = sK12) | ($true != (breln @ X0 @ sK10 @ sK12)) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ sK10) @ sK10))) )),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.68/1.46 thf(f121,plain,(
% 1.68/1.46 ( ! [X0 : $i] : (($true != (breln @ X0 @ sK10 @ sK11)) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ sK10) @ sK10)) | (sK11 = sK12) | ($true != (breln @ X0 @ sK10 @ sK12)) | ($true != $true) | ($true != sP1) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) = $true)) )),
% 1.68/1.46 inference(duplicate_literal_removal,[status(thm)],[f120])).
% 1.68/1.46 thf(f120,plain,(
% 1.68/1.46 ( ! [X0 : $i] : (($true != $true) | ($true != (breln @ X0 @ sK10 @ sK12)) | ($true != (breln @ X0 @ sK10 @ sK12)) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ sK10) @ sK10)) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) = $true) | (sK11 = sK12) | ((sP0 @ sK11 @ sK12 @ sK10 @ X0) = $true) | ($true != (breln @ X0 @ sK10 @ sK11)) | ($true != (breln @ X0 @ sK10 @ sK11)) | ($true != sP1)) )),
% 1.68/1.46 inference(superposition,[status(thm)],[f100,f41])).
% 1.68/1.46 thf(f41,plain,(
% 1.68/1.46 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X6) = $true) | (X7 = X9) | ((breln @ X8 @ X6 @ X9) != $true) | ($true != sP1) | ($true = (sP0 @ X7 @ X9 @ X6 @ X8)) | ($true != (breln @ X8 @ X6 @ X7))) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f27])).
% 1.68/1.46 thf(f100,plain,(
% 1.68/1.46 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK7 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | ((breln @ X0 @ X1 @ sK11) != $true) | ((sP0 @ sK11 @ sK12 @ X1 @ X0) = $true) | ($true != (breln @ X0 @ X1 @ sK12))) )),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f99,f66])).
% 1.68/1.46 thf(f99,plain,(
% 1.68/1.46 ( ! [X0 : $i,X1 : $i] : (((sP0 @ sK11 @ sK12 @ X1 @ X0) = $true) | ($true != (breln @ X0 @ X1 @ sK12)) | ($true != sP1) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | ((breln @ X0 @ X1 @ sK11) != $true) | ($true != (in @ (sK7 @ sK12 @ X0 @ sK11 @ X1) @ sK10))) )),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f96,f59])).
% 1.68/1.46 thf(f96,plain,(
% 1.68/1.46 ( ! [X0 : $i,X1 : $i] : (($true != (breln @ X0 @ X1 @ sK12)) | ($true != (in @ (sK7 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | (sK11 = sK12) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | ((breln @ X0 @ X1 @ sK11) != $true) | ((sP0 @ sK11 @ sK12 @ X1 @ X0) = $true) | ($true != sP1)) )),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.68/1.46 thf(f95,plain,(
% 1.68/1.46 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK7 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | ($true != (breln @ X0 @ X1 @ sK12)) | ((sP0 @ sK11 @ sK12 @ X1 @ X0) = $true) | ((breln @ X0 @ X1 @ sK11) != $true) | ($true != sP1) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | (sK11 = sK12) | ($true != $true)) )),
% 1.68/1.46 inference(duplicate_literal_removal,[status(thm)],[f93])).
% 1.68/1.46 thf(f93,plain,(
% 1.68/1.46 ( ! [X0 : $i,X1 : $i] : (($true != (breln @ X0 @ X1 @ sK12)) | ($true != (breln @ X0 @ X1 @ sK12)) | ((sP0 @ sK11 @ sK12 @ X1 @ X0) = $true) | ($true != (in @ (sK7 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | ((sP0 @ sK11 @ sK12 @ X1 @ X0) = $true) | ($true != $true) | (sK11 = sK12) | ($true != (in @ (sK6 @ sK12 @ X0 @ sK11 @ X1) @ sK10)) | ($true != sP1) | ((breln @ X0 @ X1 @ sK11) != $true) | ((breln @ X0 @ X1 @ sK11) != $true) | (sK11 = sK12)) )),
% 1.68/1.46 inference(superposition,[status(thm)],[f72,f42])).
% 1.68/1.46 thf(f42,plain,(
% 1.68/1.46 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X7) = $true) | ($true != (breln @ X8 @ X6 @ X7)) | ((breln @ X8 @ X6 @ X9) != $true) | ($true = (sP0 @ X7 @ X9 @ X6 @ X8)) | ($true != sP1) | (X7 = X9)) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f27])).
% 1.68/1.46 thf(f72,plain,(
% 1.68/1.46 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK6 @ sK12 @ X0 @ X1 @ X2) @ (sK7 @ sK12 @ X0 @ X1 @ X2)) @ sK11) != $true) | ((breln @ X0 @ X2 @ X1) != $true) | ($true != (breln @ X0 @ X2 @ sK12)) | (sK12 = X1) | ($true != (in @ (sK7 @ sK12 @ X0 @ X1 @ X2) @ sK10)) | ($true != (in @ (sK6 @ sK12 @ X0 @ X1 @ X2) @ sK10)) | ($true = (sP0 @ X1 @ sK12 @ X2 @ X0))) )),
% 1.68/1.46 inference(subsumption_resolution,[status(thm)],[f71,f66])).
% 1.68/1.46 thf(f71,plain,(
% 1.68/1.46 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != sP1) | ($true != (in @ (sK7 @ sK12 @ X0 @ X1 @ X2) @ sK10)) | ((in @ (kpair @ (sK6 @ sK12 @ X0 @ X1 @ X2) @ (sK7 @ sK12 @ X0 @ X1 @ X2)) @ sK11) != $true) | (sK12 = X1) | ($true = (sP0 @ X1 @ sK12 @ X2 @ X0)) | ($true != (in @ (sK6 @ sK12 @ X0 @ X1 @ X2) @ sK10)) | ($true != (breln @ X0 @ X2 @ sK12)) | ((breln @ X0 @ X2 @ X1) != $true)) )),
% 1.68/1.46 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.68/1.46 thf(f69,plain,(
% 1.68/1.46 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK6 @ sK12 @ X0 @ X1 @ X2) @ sK10)) | ((breln @ X0 @ X2 @ X1) != $true) | (sK12 = X1) | ($true != (in @ (sK7 @ sK12 @ X0 @ X1 @ X2) @ sK10)) | ($true != $true) | ((in @ (kpair @ (sK6 @ sK12 @ X0 @ X1 @ X2) @ (sK7 @ sK12 @ X0 @ X1 @ X2)) @ sK11) != $true) | ($true != sP1) | ($true != (breln @ X0 @ X2 @ sK12)) | ($true = (sP0 @ X1 @ sK12 @ X2 @ X0))) )),
% 1.68/1.46 inference(superposition,[status(thm)],[f40,f56])).
% 1.68/1.46 thf(f56,plain,(
% 1.68/1.46 ( ! [X6 : $i,X5 : $i] : (($true = (in @ (kpair @ X5 @ X6) @ sK12)) | ($true != (in @ (kpair @ X5 @ X6) @ sK11)) | ($true != (in @ X6 @ sK10)) | ((in @ X5 @ sK10) != $true)) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f37])).
% 1.68/1.46 thf(f40,plain,(
% 1.68/1.46 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9)) | ((breln @ X8 @ X6 @ X9) != $true) | ($true = (sP0 @ X7 @ X9 @ X6 @ X8)) | ($true != sP1) | (X7 = X9) | ($true != (breln @ X8 @ X6 @ X7))) )),
% 1.68/1.46 inference(cnf_transformation,[status(thm)],[f27])).
% 1.68/1.46 % SZS output end Proof for DTF2THF_11646
% 1.68/1.46 % (11748)------------------------------
% 1.68/1.46 % (11748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.46 % (11748)Termination reason: Refutation
% 1.68/1.46
% 1.68/1.46 % (11748)Memory used [KB]: 5756
% 1.68/1.46 % (11748)Time elapsed: 0.024 s
% 1.68/1.46 % (11748)Instructions burned: 34 (million)
% 1.68/1.46 % (11748)------------------------------
% 1.68/1.46 % (11748)------------------------------
% 1.68/1.46 % (11742)Success in time 0.033 s
%------------------------------------------------------------------------------