%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU789^2 : 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 : n025.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 09:37:13 AM UTC 2026
% Result : Theorem 1.76s 1.45s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 7
% Syntax : Number of formulae : 145 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 1888 ( 528 equ; 0 cnn)
% Maximal formula atoms : 13 ( 13 avg)
% Number of connectives : 3720 ( 14 ~; 346 |; 20 &;2981 @)
% ( 0 <=>; 246 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 10 con; 0-3 aty)
% ( 113 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 444 ( 130 ^; 308 !; 6 ?; 444 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
breln1: $i > $i > $o ).
thf(func_def_7,type,
breln1invset: $i > $i > $i ).
thf(func_def_25,type,
sK3: $i > $i > $i > $i ).
thf(func_def_26,type,
sK4: $i > $i > $i > $i ).
thf(f345,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f344]) ).
thf(f344,plain,
$false = $true,
inference(superposition,[status(thm)],[f30,f320]) ).
thf(f320,plain,
( ( breln1 @ sK1 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f319]) ).
thf(f319,plain,
( ( sK0 != sK0 )
| ( ( breln1 @ sK1 @ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f29,f279]) ).
thf(f279,plain,
! [X0: $i,X1: $i] :
( ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( $false
= ( breln1 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f278]) ).
thf(f278,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false = $true )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f275]) ).
thf(f275,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ X1 ) )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( $false = $true )
| ( $false
= ( breln1 @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f46,f272]) ).
thf(f272,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f271]) ).
thf(f271,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ X1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f266]) ).
thf(f266,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f209,f263]) ).
thf(f263,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 )
= $true )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f262]) ).
thf(f262,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 )
= $true )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false = $true )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f259]) ).
thf(f259,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false = $true )
| ( ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 )
= $true )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f46,f257]) ).
thf(f257,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f256]) ).
thf(f256,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false = $true )
| ( $false
= ( breln1 @ X1 @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f253]) ).
thf(f253,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false = $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f59,f251]) ).
thf(f251,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X1 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f250]) ).
thf(f250,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X1 ) @ X1 ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false = $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f246]) ).
thf(f246,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X1 @ X0 ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $false = $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X1 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ) ),
inference(superposition,[status(thm)],[f241,f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( ( subset @ X1 @ X3 )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( breln1 @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X1 @ X3 )
= $true )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) @ X1 )
=> ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) @ X3 ) ) ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X1 @ X3 )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( ( subset @ X1 @ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) ) )
= $false )
| ( ( subset @ X1 @ X3 )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( breln1 @ X2 @ X3 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( ( subset @ X1 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( subset @ X1 @ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) ) )
| ( ( breln1 @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) )
=> ( subset @ X1 @ X3 ) )
= $true )
| ( ( breln1 @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( breln1 @ X2 @ X3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) )
=> ( subset @ X1 @ X3 ) ) )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) )
@ X3 )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) ) )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ X1 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ X1 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f36,f28]) ).
thf(f28,plain,
subbreln1 = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( setextsub = $true )
& ( ( breln1 @ sK1 @ sK0 )
= $true )
& ( sK0
!= ( breln1invset @ sK1 @ ( breln1invset @ sK1 @ sK0 ) ) )
& ( subbreln1 = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
!= X0 ) )
=> ( ( ( breln1 @ sK1 @ sK0 )
= $true )
& ( sK0
!= ( breln1invset @ sK1 @ ( breln1invset @ sK1 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( setextsub = $true )
& ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
!= X0 ) )
& ( subbreln1 = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
!= X0 ) )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( subbreln1 = $true )
& ( setextsub = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( ( setextsub = $true )
=> ( ( subbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
=> ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X2: $i,X0: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X2 ) )
= X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X2: $i,X0: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X2 ) )
= X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',woz2Ex) ).
thf(f36,plain,
( subbreln1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( subbreln1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) )
=> ( subset @ X1 @ X2 ) ) ) )
= subbreln1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X2: $i] :
( ( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( subset @ X2 @ X3 ) ) ) )
= subbreln1 ),
file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',subbreln1) ).
thf(f241,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f240]) ).
thf(f240,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f239]) ).
thf(f239,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( $false != $false )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X1 @ X0 ) ) ),
inference(equality_factoring,[status(thm)],[f236]) ).
thf(f236,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 )
= $false )
| ( ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 )
= $false )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 )
= $false )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( ( breln1 @ X3 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f235]) ).
thf(f235,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X3 @ X0 ) )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) )
| ( ( breln1 @ X3 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
= $false )
| ( ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 )
= $false )
| ( $false = $true )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 )
= $false )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f222]) ).
thf(f222,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X0 )
= $true )
| ( ( breln1 @ X3 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
= $false )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X0 )
= $true )
| ( ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 )
= $false )
| ( ( breln1 @ X3 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
= $false )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 )
= $false )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 )
= $false )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f64,f151]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) ) @ X3 )
= $true )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X0 )
= $true )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X2 )
= $false )
| ( ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X2 )
= $false )
| ( $false
= ( breln1 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X1 ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X4 @ X0 ) )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X1 )
= $false )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X4 @ X0 ) )
| ( $false = $true )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X0 )
= $true )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X1 )
= $false )
| ( $false
= ( breln1 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) ) )
| ( ( in @ ( kpair @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) ) @ X3 )
= $true )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X2 )
= $false )
| ( $false
= ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X1 ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X3 ) ) )
| ( ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X2 )
= $false ) ),
inference(superposition,[status(thm)],[f121,f96]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ X2 ) )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X4 @ X2 ) )
| ( ( ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ X2 ) )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ X2 ) )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
= $true )
| ( $false
= ( in @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X3 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) ) )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ X1 ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ X1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f34,f27]) ).
thf(f27,plain,
breln1invE = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f34,plain,
( breln1invE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( breln1invE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( breln1invE
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( breln1invE
= ( ! [X0: $i,X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ ( breln1invset @ X0 @ X2 ) )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',breln1invE) ).
thf(f121,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK4 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ ( sK3 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) ) @ X2 )
= $true )
| ( ( breln1 @ X3 @ ( breln1invset @ X1 @ X2 ) )
= $false )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ X1 )
= $false )
| ( ( subset @ ( breln1invset @ X1 @ X2 ) @ X0 )
= $true )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ X1 )
= $false )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( ( in @ ( kpair @ ( sK4 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ ( sK3 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) ) @ X2 )
= $true )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( ( breln1 @ X3 @ ( breln1invset @ X1 @ X2 ) )
= $false )
| ( ( in @ ( sK4 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ X1 )
= $false )
| ( ( subset @ ( breln1invset @ X1 @ X2 ) @ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f96,f65]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) @ X1 )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( ( subset @ X1 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( subset @ X1 @ X3 )
= $true )
| ( $false
= ( ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) @ X1 )
=> ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) @ X3 ) ) )
| ( ( breln1 @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK3 @ X3 @ X1 @ X2 ) @ ( sK4 @ X3 @ X1 @ X2 ) ) @ X3 )
= $false )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( subset @ X1 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( subset @ X1 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f209,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $false )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f207]) ).
thf(f207,plain,
! [X0: $i,X1: $i] :
( ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
= $false )
| ( $false = $true )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f84,f205]) ).
thf(f205,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f204]) ).
thf(f204,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false = $true )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f201]) ).
thf(f201,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f46,f199]) ).
thf(f199,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f198]) ).
thf(f198,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f195]) ).
thf(f195,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f59,f193]) ).
thf(f193,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X0 ) @ X0 ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f192]) ).
thf(f192,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false = $true )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X0 ) @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f188]) ).
thf(f188,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X0 ) @ X0 ) )
| ( $false = $true )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
inference(superposition,[status(thm)],[f185,f63]) ).
thf(f185,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 )
= $false )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false != $false )
| ( ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 )
= $false )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( $false
= ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f181]) ).
thf(f181,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 )
= $false )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= $true )
| ( $false != $false )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( $false
= ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) ) ),
inference(equality_factoring,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 )
= $false )
| ( ( breln1 @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $false )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 )
= $false )
| ( ( breln1 @ X3 @ X2 )
= $false )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( ( subset @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( ( breln1 @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $false )
| ( ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 )
= $false )
| ( ( subset @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $true )
| ( ( breln1 @ X3 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f171]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( ( subset @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $true )
| ( ( subset @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $true )
| ( ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 )
= $false )
| ( ( breln1 @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $false )
| ( ( breln1 @ X3 @ X2 )
= $false )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 )
= $false )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( ( breln1 @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $false )
| ( ( breln1 @ X3 @ X2 )
= $false ) ),
inference(superposition,[status(thm)],[f65,f140]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) ) @ X2 )
= $false )
| ( $false
= ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X1 ) )
| ( ( breln1 @ X4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $false )
| ( $false
= ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( ( subset @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $true )
| ( ( breln1 @ X4 @ X3 )
= $false )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( breln1 @ X4 @ X3 )
= $false )
| ( $false = $true )
| ( $false
= ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X1 ) )
| ( ( in @ ( kpair @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) ) @ X2 )
= $false )
| ( ( subset @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $true )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( in @ ( sK4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X1 )
= $false )
| ( ( breln1 @ X4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f77,f111]) ).
thf(f111,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ ( sK4 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ ( sK3 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) ) @ X1 ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( ( breln1 @ X3 @ X2 )
= $false )
| ( ( subset @ X2 @ ( breln1invset @ X0 @ X1 ) )
= $true )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ X0 ) )
| ( ( in @ ( sK4 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( in @ ( kpair @ ( sK4 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ ( sK3 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) ) @ X1 ) )
| ( ( in @ ( sK4 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ X0 )
= $false )
| ( $false
= ( breln1 @ X0 @ X1 ) )
| ( ( subset @ X2 @ ( breln1invset @ X0 @ X1 ) )
= $true )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X0 @ X1 ) ) )
| ( ( breln1 @ X3 @ X2 )
= $false )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f77,f64]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $false )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ X2 ) )
| ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
= $true )
| ( $false
= ( in @ X4 @ X2 ) )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) )
= $true )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ X2 ) )
| ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( ( in @ X3 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) )
@ X3 )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f35,f26]) ).
thf(f26,plain,
breln1invI = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f35,plain,
( breln1invI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( breln1invI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) )
= breln1invI ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $i,X2: $i] :
( ( ( breln1 @ X0 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X5 @ X4 ) @ ( breln1invset @ X0 @ X2 ) ) ) ) ) )
= breln1invI ),
file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',breln1invI) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
= $true )
| ( $false
= ( subset @ X2 @ X1 ) )
| ( $false
= ( subset @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f32,f31]) ).
thf(f31,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f32,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',setextsub) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) )
= $true )
| ( ( breln1 @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
=> ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f33,f25]) ).
thf(f25,plain,
breln1invprop = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f33,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( breln1invprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( breln1invprop
= ( ! [X0: $i,X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',breln1invprop) ).
thf(f29,plain,
( sK0
!= ( breln1invset @ sK1 @ ( breln1invset @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f30,plain,
( ( breln1 @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU789^2 : 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
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:34:12 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.48 thf(spec,logic,$$dhol).
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % File : SEU789^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.48 % Domain : Set Theory
% 0.27/0.48 % Problem : Binary Relations on a Set - Second Wizard of Oz Examples
% 0.27/0.48 % Version : Especial > Reduced > Especial.
% 0.27/0.48 % English : (! A:i.! R:i.breln1 A R -> R = breln1invset A (breln1invset A R))
% 0.27/0.48
% 0.27/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.48 % Source : [Bro08]
% 0.27/0.48 % Names : ZFC291l [Bro08]
% 0.27/0.48
% 0.27/0.48 % Status : Theorem
% 0.27/0.48 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.27/0.48 % Syntax : Number of formulae : 16 ( 5 unt; 10 typ; 5 def)
% 0.27/0.48 % Number of atoms : 39 ( 7 equ; 0 cnn)
% 0.27/0.48 % Maximal formula atoms : 7 ( 6 avg)
% 0.27/0.48 % Number of connectives : 89 ( 0 ~; 0 |; 0 &; 66 @)
% 0.27/0.48 % ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% 0.27/0.48 % Maximal formula depth : 11 ( 3 avg)
% 0.27/0.48 % Number of types : 2 ( 0 usr)
% 0.27/0.48 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.27/0.48 % Number of symbols : 11 ( 10 usr; 5 con; 0-2 aty)
% 0.27/0.48 % Number of variables : 19 ( 0 ^; 19 !; 0 ?; 19 :)
% 0.27/0.48 % SPC : TH0_THM_EQU_NAR
% 0.27/0.48
% 0.27/0.48 % Comments : http://mathgate.info/detsetitem.php?id=354
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 thf(in_type,type,
% 0.27/0.48 in: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(subset_type,type,
% 0.27/0.48 subset: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(setextsub_type,type,
% 0.27/0.48 setextsub: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setextsub,definition,
% 0.27/0.48 ( setextsub
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( ( subset @ B @ A )
% 0.27/0.48 => ( A = B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(kpair_type,type,
% 0.27/0.48 kpair: $i > $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(breln1_type,type,
% 0.27/0.48 breln1: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(subbreln1_type,type,
% 0.27/0.48 subbreln1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subbreln1,definition,
% 0.27/0.48 ( subbreln1
% 0.27/0.48 = ( ! [A: $i,R: $i] :
% 0.27/0.48 ( ( breln1 @ A @ R )
% 0.27/0.48 => ! [S: $i] :
% 0.27/0.48 ( ( breln1 @ A @ S )
% 0.27/0.48 => ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ! [Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ A )
% 0.27/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.27/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(breln1invset_type,type,
% 0.27/0.48 breln1invset: $i > $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(breln1invprop_type,type,
% 0.27/0.48 breln1invprop: $o ).
% 0.27/0.48
% 0.27/0.48 thf(breln1invprop,definition,
% 0.27/0.48 ( breln1invprop
% 0.27/0.48 = ( ! [A: $i,R: $i] :
% 0.27/0.48 ( ( breln1 @ A @ R )
% 0.27/0.48 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(breln1invI_type,type,
% 0.27/0.48 breln1invI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(breln1invI,definition,
% 0.27/0.48 ( breln1invI
% 0.27/0.48 = ( ! [A: $i,R: $i] :
% 0.27/0.48 ( ( breln1 @ A @ R )
% 0.27/0.48 => ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ! [Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ A )
% 0.27/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.48 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(breln1invE_type,type,
% 0.27/0.48 breln1invE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(breln1invE,definition,
% 0.27/0.48 ( breln1invE
% 0.27/0.48 = ( ! [A: $i,R: $i] :
% 0.27/0.48 ( ( breln1 @ A @ R )
% 0.27/0.48 => ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ! [Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ A )
% 0.27/0.48 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.27/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(woz2Ex,conjecture,
% 0.27/0.48 ( setextsub
% 0.27/0.48 => ( subbreln1
% 0.27/0.48 => ( breln1invprop
% 0.27/0.48 => ( breln1invI
% 0.27/0.48 => ( breln1invE
% 0.27/0.48 => ! [A: $i,R: $i] :
% 0.27/0.48 ( ( breln1 @ A @ R )
% 0.27/0.48 => ( R
% 0.27/0.48 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 ------------------------
% 1.68/1.34 ---- Embedded in THF ---
% 1.68/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.34 %%% Generated on Tue Feb 24 12:34:13 EST 2026
% 1.68/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.34 %%% Logic specification used:
% 1.68/1.34 %%% thf(spec, logic, $$dhol).
% 1.68/1.34
% 1.68/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2DTF2912.p
% See solution above
% 1.68/1.34 ------------------------
% 1.68/1.35 ---- Cleaned THF ---
% 1.68/1.35 thf(in_type,type,
% 1.68/1.35 in: $i > $i > $o ).
% 1.68/1.35
% 1.68/1.35 thf(subset_type,type,
% 1.68/1.35 subset: $i > $i > $o ).
% 1.68/1.35
% 1.68/1.35 thf(setextsub_type,type,
% 1.68/1.35 setextsub: $o ).
% 1.68/1.35
% 1.68/1.35 thf(setextsub,definition,
% 1.68/1.35 ( setextsub
% 1.68/1.35 = ( ! [A: $i,B: $i] :
% 1.68/1.35 ( ( subset @ A @ B )
% 1.68/1.35 => ( ( subset @ B @ A )
% 1.68/1.35 => ( A = B ) ) ) ) ) ).
% 1.68/1.35
% 1.68/1.35 thf(kpair_type,type,
% 1.68/1.35 kpair: $i > $i > $i ).
% 1.68/1.35
% 1.68/1.35 thf(breln1_type,type,
% 1.68/1.35 breln1: $i > $i > $o ).
% 1.68/1.35
% 1.68/1.35 thf(subbreln1_type,type,
% 1.68/1.35 subbreln1: $o ).
% 1.68/1.35
% 1.68/1.35 thf(subbreln1,definition,
% 1.68/1.35 ( subbreln1
% 1.68/1.35 = ( ! [A: $i,R: $i] :
% 1.68/1.35 ( ( breln1 @ A @ R )
% 1.68/1.35 => ! [S: $i] :
% 1.68/1.35 ( ( breln1 @ A @ S )
% 1.68/1.35 => ( ! [Xx: $i] :
% 1.68/1.35 ( ( in @ Xx @ A )
% 1.68/1.35 => ! [Xy: $i] :
% 1.68/1.35 ( ( in @ Xy @ A )
% 1.68/1.35 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.68/1.35 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 1.68/1.35 => ( subset @ R @ S ) ) ) ) ) ) ).
% 1.68/1.35
% 1.68/1.35 thf(breln1invset_type,type,
% 1.68/1.35 breln1invset: $i > $i > $i ).
% 1.68/1.35
% 1.68/1.35 thf(breln1invprop_type,type,
% 1.68/1.35 breln1invprop: $o ).
% 1.68/1.35
% 1.68/1.35 thf(breln1invprop,definition,
% 1.68/1.35 ( breln1invprop
% 1.68/1.35 = ( ! [A: $i,R: $i] :
% 1.68/1.35 ( ( breln1 @ A @ R )
% 1.68/1.35 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 1.68/1.35
% 1.68/1.35 thf(breln1invI_type,type,
% 1.68/1.35 breln1invI: $o ).
% 1.68/1.35
% 1.68/1.35 thf(breln1invI,definition,
% 1.68/1.35 ( breln1invI
% 1.68/1.35 = ( ! [A: $i,R: $i] :
% 1.68/1.35 ( ( breln1 @ A @ R )
% 1.68/1.35 => ! [Xx: $i] :
% 1.68/1.35 ( ( in @ Xx @ A )
% 1.68/1.35 => ! [Xy: $i] :
% 1.68/1.35 ( ( in @ Xy @ A )
% 1.68/1.35 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.68/1.35 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 1.68/1.35
% 1.68/1.35 thf(breln1invE_type,type,
% 1.68/1.35 breln1invE: $o ).
% 1.68/1.35
% 1.68/1.35 thf(breln1invE,definition,
% 1.68/1.35 ( breln1invE
% 1.68/1.35 = ( ! [A: $i,R: $i] :
% 1.68/1.35 ( ( breln1 @ A @ R )
% 1.68/1.35 => ! [Xx: $i] :
% 1.68/1.35 ( ( in @ Xx @ A )
% 1.68/1.35 => ! [Xy: $i] :
% 1.68/1.35 ( ( in @ Xy @ A )
% 1.68/1.35 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 1.68/1.35 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 1.68/1.35
% 1.68/1.35 thf(woz2Ex,conjecture,
% 1.68/1.35 ( setextsub
% 1.68/1.35 => ( subbreln1
% 1.68/1.35 => ( breln1invprop
% 1.68/1.35 => ( breln1invI
% 1.68/1.35 => ( breln1invE
% 1.68/1.35 => ! [A: $i,R: $i] :
% 1.68/1.35 ( ( breln1 @ A @ R )
% 1.68/1.35 => ( R
% 1.68/1.35 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ).
% 1.68/1.35 ------------------------
% 1.68/1.37 % (3059)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_2912 for (2999ds/4Mi)
% 1.68/1.37 % (3060)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_2912 for (2999ds/27Mi)
% 1.68/1.37 % (3059)Instruction limit reached!
% 1.68/1.37 % (3059)------------------------------
% 1.68/1.37 % (3059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (3059)Termination reason: Unknown
% 1.68/1.37 % (3059)Termination phase: Saturation
% 1.68/1.37
% 1.68/1.37 % (3059)Memory used [KB]: 5500
% 1.68/1.37 % (3059)Time elapsed: 0.003 s
% 1.68/1.37 % (3059)Instructions burned: 5 (million)
% 1.68/1.37 % (3059)------------------------------
% 1.68/1.37 % (3059)------------------------------
% 1.68/1.37 % (3062)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_2912 for (2999ds/2Mi)
% 1.68/1.38 % (3058)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/183Mi)
% 1.68/1.38 % (3061)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/2Mi)
% 1.68/1.38 % (3062)Instruction limit reached!
% 1.68/1.38 % (3062)------------------------------
% 1.68/1.38 % (3062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (3062)Termination reason: Unknown
% 1.68/1.38 % (3062)Termination phase: Property scanning
% 1.68/1.38
% 1.68/1.38 % (3062)Memory used [KB]: 1023
% 1.68/1.38 % (3062)Time elapsed: 0.003 s
% 1.68/1.38 % (3062)Instructions burned: 3 (million)
% 1.68/1.38 % (3062)------------------------------
% 1.68/1.38 % (3062)------------------------------
% 1.68/1.38 % (3061)Instruction limit reached!
% 1.68/1.38 % (3061)------------------------------
% 1.68/1.38 % (3061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (3061)Termination reason: Unknown
% 1.68/1.38 % (3061)Termination phase: shuffling
% 1.68/1.38
% 1.68/1.38 % (3061)Memory used [KB]: 895
% 1.68/1.38 % (3061)Time elapsed: 0.003 s
% 1.68/1.38 % (3061)Instructions burned: 2 (million)
% 1.68/1.38 % (3061)------------------------------
% 1.68/1.38 % (3061)------------------------------
% 1.68/1.38 % (3064)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/18Mi)
% 1.68/1.38 % (3060)Instruction limit reached!
% 1.68/1.38 % (3060)------------------------------
% 1.68/1.38 % (3060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (3060)Termination reason: Unknown
% 1.68/1.38 % (3060)Termination phase: Saturation
% 1.68/1.38
% 1.68/1.38 % (3060)Memory used [KB]: 5628
% 1.68/1.38 % (3060)Time elapsed: 0.011 s
% 1.68/1.38 % (3060)Instructions burned: 27 (million)
% 1.68/1.38 % (3060)------------------------------
% 1.68/1.38 % (3060)------------------------------
% 1.68/1.38 % (3065)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/3Mi)
% 1.68/1.38 % (3065)Instruction limit reached!
% 1.68/1.38 % (3065)------------------------------
% 1.68/1.38 % (3065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (3065)Termination reason: Unknown
% 1.68/1.38 % (3065)Termination phase: Property scanning
% 1.68/1.38
% 1.68/1.38 % (3065)Memory used [KB]: 1023
% 1.68/1.38 % (3065)Time elapsed: 0.002 s
% 1.68/1.38 % (3065)Instructions burned: 3 (million)
% 1.68/1.38 % (3065)------------------------------
% 1.68/1.38 % (3065)------------------------------
% 1.68/1.38 % (3064)Instruction limit reached!
% 1.68/1.38 % (3064)------------------------------
% 1.68/1.38 % (3064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (3064)Termination reason: Unknown
% 1.68/1.38 % (3064)Termination phase: Saturation
% 1.68/1.38
% 1.68/1.38 % (3064)Memory used [KB]: 5628
% 1.68/1.38 % (3064)Time elapsed: 0.007 s
% 1.68/1.38 % (3064)Instructions burned: 18 (million)
% 1.68/1.38 % (3064)------------------------------
% 1.68/1.38 % (3064)------------------------------
% 1.68/1.39 % (3063)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_2912 for (2999ds/275Mi)
% 1.68/1.39 % (3069)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/1041Mi)
% 1.68/1.39 % (3070)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/7Mi)
% 1.68/1.39 % (3068)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_2912 for (2999ds/3Mi)
% 1.68/1.39 % (3066)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_2912 for (2999ds/37Mi)
% 1.68/1.39 % (3068)Instruction limit reached!
% 1.68/1.39 % (3068)------------------------------
% 1.68/1.39 % (3068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (3068)Termination reason: Unknown
% 1.68/1.39 % (3068)Termination phase: Property scanning
% 1.68/1.39
% 1.68/1.39 % (3068)Memory used [KB]: 1023
% 1.68/1.39 % (3068)Time elapsed: 0.003 s
% 1.68/1.39 % (3068)Instructions burned: 3 (million)
% 1.68/1.39 % (3068)------------------------------
% 1.68/1.39 % (3068)------------------------------
% 1.68/1.39 % (3070)Instruction limit reached!
% 1.68/1.39 % (3070)------------------------------
% 1.68/1.39 % (3070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (3070)Termination reason: Unknown
% 1.68/1.39 % (3070)Termination phase: Saturation
% 1.68/1.39
% 1.68/1.39 % (3070)Memory used [KB]: 1023
% 1.68/1.39 % (3070)Time elapsed: 0.003 s
% 1.68/1.39 % (3070)Instructions burned: 7 (million)
% 1.68/1.39 % (3070)------------------------------
% 1.68/1.39 % (3070)------------------------------
% 1.68/1.39 % (3067)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_2912 for (2999ds/15Mi)
% 1.76/1.40 % (3067)Instruction limit reached!
% 1.76/1.40 % (3067)------------------------------
% 1.76/1.40 % (3067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.40 % (3067)Termination reason: Unknown
% 1.76/1.40 % (3067)Termination phase: Saturation
% 1.76/1.40
% 1.76/1.40 % (3067)Memory used [KB]: 5628
% 1.76/1.40 % (3067)Time elapsed: 0.011 s
% 1.76/1.40 % (3067)Instructions burned: 15 (million)
% 1.76/1.40 % (3067)------------------------------
% 1.76/1.40 % (3067)------------------------------
% 1.76/1.40 % (3072)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/3Mi)
% 1.76/1.41 % (3072)Instruction limit reached!
% 1.76/1.41 % (3072)------------------------------
% 1.76/1.41 % (3072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.41 % (3072)Termination reason: Unknown
% 1.76/1.41 % (3072)Termination phase: Property scanning
% 1.76/1.41
% 1.76/1.41 % (3072)Memory used [KB]: 1023
% 1.76/1.41 % (3072)Time elapsed: 0.003 s
% 1.76/1.41 % (3072)Instructions burned: 5 (million)
% 1.76/1.41 % (3072)------------------------------
% 1.76/1.41 % (3072)------------------------------
% 1.76/1.41 % (3071)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/16Mi)
% 1.76/1.41 % (3066)Instruction limit reached!
% 1.76/1.41 % (3066)------------------------------
% 1.76/1.41 % (3066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.41 % (3066)Termination reason: Unknown
% 1.76/1.41 % (3066)Termination phase: Saturation
% 1.76/1.41
% 1.76/1.41 % (3066)Memory used [KB]: 5756
% 1.76/1.41 % (3066)Time elapsed: 0.020 s
% 1.76/1.41 % (3066)Instructions burned: 38 (million)
% 1.76/1.41 % (3066)------------------------------
% 1.76/1.41 % (3066)------------------------------
% 1.76/1.41 % (3071)Instruction limit reached!
% 1.76/1.41 % (3071)------------------------------
% 1.76/1.41 % (3071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.41 % (3071)Termination reason: Unknown
% 1.76/1.41 % (3071)Termination phase: Saturation
% 1.76/1.41
% 1.76/1.41 % (3071)Memory used [KB]: 5756
% 1.76/1.41 % (3071)Time elapsed: 0.007 s
% 1.76/1.41 % (3071)Instructions burned: 16 (million)
% 1.76/1.41 % (3071)------------------------------
% 1.76/1.41 % (3071)------------------------------
% 1.76/1.41 % (3074)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/7Mi)
% 1.76/1.42 % (3074)Refutation not found, incomplete strategy
% 1.76/1.42 % (3074)------------------------------
% 1.76/1.42 % (3074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (3074)Termination reason: Refutation not found, incomplete strategy
% 1.76/1.42
% 1.76/1.42
% 1.76/1.42 % (3074)Memory used [KB]: 5500
% 1.76/1.42 % (3074)Time elapsed: 0.003 s
% 1.76/1.42 % (3074)Instructions burned: 6 (million)
% 1.76/1.42 % (3074)------------------------------
% 1.76/1.42 % (3074)------------------------------
% 1.76/1.42 % (3073)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/3Mi)
% 1.76/1.42 % (3075)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/3Mi)
% 1.76/1.42 % (3073)Instruction limit reached!
% 1.76/1.42 % (3073)------------------------------
% 1.76/1.42 % (3073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (3073)Termination reason: Unknown
% 1.76/1.42 % (3073)Termination phase: Preprocessing 3
% 1.76/1.42
% 1.76/1.42 % (3073)Memory used [KB]: 1023
% 1.76/1.42 % (3073)Time elapsed: 0.004 s
% 1.76/1.42 % (3073)Instructions burned: 3 (million)
% 1.76/1.42 % (3073)------------------------------
% 1.76/1.42 % (3073)------------------------------
% 1.76/1.42 % (3075)Instruction limit reached!
% 1.76/1.42 % (3075)------------------------------
% 1.76/1.42 % (3075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (3075)Termination reason: Unknown
% 1.76/1.42 % (3075)Termination phase: Function definition elimination
% 1.76/1.42
% 1.76/1.42 % (3075)Memory used [KB]: 1023
% 1.76/1.42 % (3075)Time elapsed: 0.002 s
% 1.76/1.42 % (3075)Instructions burned: 4 (million)
% 1.76/1.42 % (3075)------------------------------
% 1.76/1.42 % (3075)------------------------------
% 1.76/1.42 % (3076)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/4Mi)
% 1.76/1.42 % (3076)Instruction limit reached!
% 1.76/1.42 % (3076)------------------------------
% 1.76/1.42 % (3076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (3076)Termination reason: Unknown
% 1.76/1.42 % (3076)Termination phase: Function definition elimination
% 1.76/1.42
% 1.76/1.42 % (3076)Memory used [KB]: 1023
% 1.76/1.42 % (3076)Time elapsed: 0.002 s
% 1.76/1.42 % (3076)Instructions burned: 4 (million)
% 1.76/1.42 % (3076)------------------------------
% 1.76/1.42 % (3076)------------------------------
% 1.76/1.43 % (3077)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/18Mi)
% 1.76/1.43 % (3077)Instruction limit reached!
% 1.76/1.43 % (3077)------------------------------
% 1.76/1.43 % (3077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.43 % (3077)Termination reason: Unknown
% 1.76/1.43 % (3077)Termination phase: Saturation
% 1.76/1.43
% 1.76/1.43 % (3077)Memory used [KB]: 5628
% 1.76/1.43 % (3077)Time elapsed: 0.007 s
% 1.76/1.43 % (3077)Instructions burned: 20 (million)
% 1.76/1.43 % (3077)------------------------------
% 1.76/1.43 % (3077)------------------------------
% 1.76/1.43 % (3079)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/6Mi)
% 1.76/1.44 % (3080)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/902Mi)
% 1.76/1.44 % (3058)First to succeed.
% 1.76/1.44 % (3079)Instruction limit reached!
% 1.76/1.44 % (3079)------------------------------
% 1.76/1.44 % (3079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.44 % (3079)Termination reason: Unknown
% 1.76/1.44 % (3079)Termination phase: Saturation
% 1.76/1.44
% 1.76/1.44 % (3079)Memory used [KB]: 5500
% 1.76/1.44 % (3079)Time elapsed: 0.003 s
% 1.76/1.44 % (3079)Instructions burned: 6 (million)
% 1.76/1.44 % (3079)------------------------------
% 1.76/1.44 % (3079)------------------------------
% 1.76/1.44 % (3080)Refutation not found, incomplete strategy
% 1.76/1.44 % (3080)------------------------------
% 1.76/1.44 % (3080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.44 % (3080)Termination reason: Refutation not found, incomplete strategy
% 1.76/1.44
% 1.76/1.44
% 1.76/1.44 % (3080)Memory used [KB]: 5500
% 1.76/1.44 % (3080)Time elapsed: 0.004 s
% 1.76/1.44 % (3080)Instructions burned: 7 (million)
% 1.76/1.44 % (3080)------------------------------
% 1.76/1.44 % (3080)------------------------------
% 1.76/1.44 % (3078)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/710Mi)
% 1.76/1.44 % (3081)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_2912 for (2999ds/21Mi)
% 1.76/1.45 % (3058)Refutation found. Thanks to Tanya!
% 1.76/1.45 % SZS status Theorem for DTF2THF_2912
% 1.76/1.45 % SZS output start Proof for DTF2THF_2912
% 1.76/1.45 thf(func_def_0, type, in: $i > $i > $o).
% 1.76/1.45 thf(func_def_1, type, subset: $i > $i > $o).
% 1.76/1.45 thf(func_def_4, type, kpair: $i > $i > $i).
% 1.76/1.45 thf(func_def_5, type, breln1: $i > $i > $o).
% 1.76/1.45 thf(func_def_7, type, breln1invset: $i > $i > $i).
% 1.76/1.45 thf(func_def_25, type, sK3: $i > $i > $i > $i).
% 1.76/1.45 thf(func_def_26, type, sK4: $i > $i > $i > $i).
% 1.76/1.45 thf(f345,plain,(
% 1.76/1.45 $false),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f344])).
% 1.76/1.45 thf(f344,plain,(
% 1.76/1.45 ($false = $true)),
% 1.76/1.45 inference(superposition,[status(thm)],[f30,f320])).
% 1.76/1.45 thf(f320,plain,(
% 1.76/1.45 ((breln1 @ sK1 @ sK0) = $false)),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f319])).
% 1.76/1.45 thf(f319,plain,(
% 1.76/1.45 (sK0 != sK0) | ((breln1 @ sK1 @ sK0) = $false)),
% 1.76/1.45 inference(superposition,[status(thm)],[f29,f279])).
% 1.76/1.45 thf(f279,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1) | ($false = (breln1 @ X0 @ X1))) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f278])).
% 1.76/1.45 thf(f278,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ X1)) | ($false = $true) | ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1)) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f275])).
% 1.76/1.45 thf(f275,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ X1)) | ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1) | ($false = $true) | ($false = (breln1 @ X0 @ X1))) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f46,f272])).
% 1.76/1.45 thf(f272,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ X1)) | ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f271])).
% 1.76/1.45 thf(f271,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ X1))) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f266])).
% 1.76/1.45 thf(f266,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ X1)) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ X1)) | ($false = $true)) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f209,f263])).
% 1.76/1.45 thf(f263,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1) = $true) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ X1))) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f262])).
% 1.76/1.45 thf(f262,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1) = $true) | ($false = (breln1 @ X0 @ X1)) | ($false = $true) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1)))) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f259])).
% 1.76/1.45 thf(f259,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ X1)) | ($false = $true) | ((subset @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1) = $true) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1)))) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f46,f257])).
% 1.76/1.45 thf(f257,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X1 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ($false = (breln1 @ X1 @ X0)) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f256])).
% 1.76/1.45 thf(f256,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ($false = $true) | ($false = (breln1 @ X1 @ X0))) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f253])).
% 1.76/1.45 thf(f253,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = (breln1 @ X1 @ X0)) | ($false = (breln1 @ X1 @ X0)) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true)) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f59,f251])).
% 1.76/1.45 thf(f251,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X1) @ X1)) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true) | ($false = (breln1 @ X1 @ X0)) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0)))) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f250])).
% 1.76/1.45 thf(f250,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X1) @ X1)) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ($false = (breln1 @ X1 @ X0))) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f246])).
% 1.76/1.45 thf(f246,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X1 @ X0)) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true) | ($false = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ($false = (breln1 @ X1 @ X0)) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = (in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X1) @ X1)) | ($false = (breln1 @ X1 @ X0)) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0))))) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f241,f63])).
% 1.76/1.45 thf(f63,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ (sK4 @ X3 @ X1 @ X2) @ X2) = $true) | ((subset @ X1 @ X3) = $true) | ((breln1 @ X2 @ X1) = $false) | ((breln1 @ X2 @ X3) = $false)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.76/1.45 thf(f61,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((subset @ X1 @ X3) = $true) | ($false = ((in @ (sK4 @ X3 @ X1 @ X2) @ X2) => ((in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ (sK4 @ X3 @ X1 @ X2)) @ X1) => (in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ (sK4 @ X3 @ X1 @ X2)) @ X3)))) | ((breln1 @ X2 @ X3) = $false) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.76/1.45 thf(f60,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((subset @ X1 @ X3) = $true) | ((breln1 @ X2 @ X1) = $false) | ((breln1 @ X2 @ X3) = $false) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ Y0) @ X1) => (in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ Y0) @ X3)))) @ (sK4 @ X3 @ X1 @ X2)))) )),
% 1.76/1.45 inference(sigma_clausification,[status(thm)],[f58])).
% 1.76/1.45 thf(f58,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | ((breln1 @ X2 @ X3) = $false) | ((subset @ X1 @ X3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ Y0) @ X1) => (in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ Y0) @ X3))))))) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.76/1.45 thf(f57,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ (sK3 @ X3 @ X1 @ X2) @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ Y0) @ X1) => (in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ Y0) @ X3)))))) = $false) | ((subset @ X1 @ X3) = $true) | ((breln1 @ X2 @ X1) = $false) | ((breln1 @ X2 @ X3) = $false)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.76/1.45 thf(f56,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | ((breln1 @ X2 @ X3) = $false) | ((subset @ X1 @ X3) = $true) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X3))))))) @ (sK3 @ X3 @ X1 @ X2)))) )),
% 1.76/1.45 inference(sigma_clausification,[status(thm)],[f55])).
% 1.76/1.45 thf(f55,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | ((subset @ X1 @ X3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X3))))))))) | ((breln1 @ X2 @ X3) = $false)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.76/1.45 thf(f54,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X3)))))))) => (subset @ X1 @ X3)) = $true) | ((breln1 @ X2 @ X3) = $false)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.76/1.45 thf(f53,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((breln1 @ X2 @ X3) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X3)))))))) => (subset @ X1 @ X3))) = $true) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.76/1.45 thf(f52,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0)))) @ X3) = $true) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f51])).
% 1.76/1.45 thf(f51,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0))))) = $true) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.76/1.45 thf(f50,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((breln1 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0)))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.76/1.45 thf(f49,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ X1 @ Y1))))))) @ X2) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f48])).
% 1.76/1.45 thf(f48,plain,(
% 1.76/1.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ X1 @ Y1)))))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.76/1.45 thf(f47,plain,(
% 1.76/1.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))) @ X1) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f41])).
% 1.76/1.45 thf(f41,plain,(
% 1.76/1.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))) = $true)),
% 1.76/1.45 inference(definition_unfolding,[status(thm)],[f36,f28])).
% 1.76/1.45 thf(f28,plain,(
% 1.76/1.45 (subbreln1 = $true)),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.45 thf(f24,plain,(
% 1.76/1.45 (setextsub = $true) & (((breln1 @ sK1 @ sK0) = $true) & (sK0 != (breln1invset @ sK1 @ (breln1invset @ sK1 @ sK0)))) & (subbreln1 = $true) & (breln1invE = $true) & (breln1invI = $true) & (breln1invprop = $true)),
% 1.76/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f23])).
% 1.76/1.45 thf(f23,plain,(
% 1.76/1.45 ? [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) & ((breln1invset @ X1 @ (breln1invset @ X1 @ X0)) != X0)) => (((breln1 @ sK1 @ sK0) = $true) & (sK0 != (breln1invset @ sK1 @ (breln1invset @ sK1 @ sK0))))),
% 1.76/1.45 introduced(definition,[],[choice_axiom])).
% 1.76/1.45 thf(f22,plain,(
% 1.76/1.45 (setextsub = $true) & ? [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) & ((breln1invset @ X1 @ (breln1invset @ X1 @ X0)) != X0)) & (subbreln1 = $true) & (breln1invE = $true) & (breln1invI = $true) & (breln1invprop = $true)),
% 1.76/1.45 inference(flattening,[status(thm)],[f21])).
% 1.76/1.45 thf(f21,plain,(
% 1.76/1.45 ((((? [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) & ((breln1invset @ X1 @ (breln1invset @ X1 @ X0)) != X0)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (subbreln1 = $true)) & (setextsub = $true)),
% 1.76/1.45 inference(ennf_transformation,[status(thm)],[f20])).
% 1.76/1.45 thf(f20,plain,(
% 1.76/1.45 ~((setextsub = $true) => ((subbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ! [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) => ((breln1invset @ X1 @ (breln1invset @ X1 @ X0)) = X0)))))))),
% 1.76/1.45 inference(fool_elimination,[status(thm)],[f19])).
% 1.76/1.45 thf(f19,plain,(
% 1.76/1.45 ~(setextsub => (subbreln1 => (breln1invprop => (breln1invI => (breln1invE => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ((breln1invset @ X1 @ (breln1invset @ X1 @ X0)) = X0)))))))),
% 1.76/1.45 inference(rectify,[status(thm)],[f7])).
% 1.76/1.45 thf(f7,negated_conjecture,(
% 1.76/1.45 ~(setextsub => (subbreln1 => (breln1invprop => (breln1invI => (breln1invE => ! [X2 : $i,X0 : $i] : ((breln1 @ X0 @ X2) => ((breln1invset @ X0 @ (breln1invset @ X0 @ X2)) = X2)))))))),
% 1.76/1.45 inference(negated_conjecture,[status(cth)],[f6])).
% 1.76/1.45 thf(f6,conjecture,(
% 1.76/1.45 setextsub => (subbreln1 => (breln1invprop => (breln1invI => (breln1invE => ! [X2 : $i,X0 : $i] : ((breln1 @ X0 @ X2) => ((breln1invset @ X0 @ (breln1invset @ X0 @ X2)) = X2))))))),
% 1.76/1.45 file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',woz2Ex)).
% 1.76/1.45 thf(f36,plain,(
% 1.76/1.45 (subbreln1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f18])).
% 1.76/1.45 thf(f18,plain,(
% 1.76/1.45 (subbreln1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))),
% 1.76/1.45 inference(fool_elimination,[status(thm)],[f17])).
% 1.76/1.45 thf(f17,plain,(
% 1.76/1.45 (! [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)))) = subbreln1)),
% 1.76/1.45 inference(rectify,[status(thm)],[f2])).
% 1.76/1.45 thf(f2,axiom,(
% 1.76/1.45 (! [X0 : $i,X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((breln1 @ X0 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))) = subbreln1)),
% 1.76/1.45 file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',subbreln1)).
% 1.76/1.45 thf(f241,plain,(
% 1.76/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X2) @ X1)) | ($false = (breln1 @ X2 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = (breln1 @ X2 @ X0)) | ($false = (breln1 @ X1 @ X0)) | ($false = (in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X2) @ X1)) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f240])).
% 1.76/1.45 thf(f240,plain,(
% 1.76/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false != $false) | ($false = (breln1 @ X2 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = (breln1 @ X1 @ X0)) | ($false = (breln1 @ X2 @ X0)) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ($false = (in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X2) @ X1)) | ($false = (in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X2) @ X1))) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f239])).
% 1.76/1.45 thf(f239,plain,(
% 1.76/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ($false = (in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X2) @ X1)) | ($false = (breln1 @ X2 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)))) | ($false = (in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X2) @ X1)) | ($false = (in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X2) @ X1)) | ($false = (breln1 @ X2 @ X0)) | ($false != $false) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $true) | ($false = (breln1 @ X1 @ X0))) )),
% 1.76/1.45 inference(equality_factoring,[status(thm)],[f236])).
% 1.76/1.45 thf(f236,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X1)) | ($false = (breln1 @ X1 @ (breln1invset @ X2 @ X0))) | ($false = (breln1 @ X2 @ X0)) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X1) = $false) | ((in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X2) = $false) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X2) = $false) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X0) = $true) | ($false = (breln1 @ X3 @ X0)) | ((breln1 @ X3 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0))) = $false)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f235])).
% 1.76/1.45 thf(f235,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (breln1 @ X3 @ X0)) | ($false = (breln1 @ X2 @ X0)) | ($false = (in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X1)) | ((breln1 @ X3 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0))) = $false) | ((in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X2) = $false) | ($false = $true) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X0) = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X2 @ X0))) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X1) = $false) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X2) = $false)) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f222])).
% 1.76/1.45 thf(f222,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X0) = $true) | ((breln1 @ X3 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0))) = $false) | ($false = (breln1 @ X3 @ X0)) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X0) = $true) | ((in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X2) = $false) | ((breln1 @ X3 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0))) = $false) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X2) = $false) | ($false = (breln1 @ X3 @ X0)) | ($false = (in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X1)) | ($false = (breln1 @ X1 @ (breln1invset @ X2 @ X0))) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X0)) @ X3) @ X1) = $false) | ($false = (breln1 @ X2 @ X0)) | ($false = $true)) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f64,f151])).
% 1.76/1.45 thf(f151,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4)) @ X3) = $true) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X0) = $true) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ X2) = $false) | ((in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ X2) = $false) | ($false = (breln1 @ X4 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)))) | ($false = (in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ X1)) | ((breln1 @ X2 @ X3) = $false) | ($false = (breln1 @ X4 @ X0)) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ X1) = $false) | ($false = (breln1 @ X1 @ (breln1invset @ X2 @ X3)))) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.76/1.45 thf(f142,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($false = (breln1 @ X4 @ X0)) | ($false = $true) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X0) = $true) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ X1) = $false) | ($false = (breln1 @ X4 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)))) | ((in @ (kpair @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4)) @ X3) = $true) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ X2) = $false) | ($false = (in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ X1)) | ((breln1 @ X2 @ X3) = $false) | ($false = (breln1 @ X1 @ (breln1invset @ X2 @ X3))) | ((in @ (sK4 @ X0 @ (breln1invset @ X1 @ (breln1invset @ X2 @ X3)) @ X4) @ X2) = $false)) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f121,f96])).
% 1.76/1.45 thf(f96,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ (kpair @ X4 @ X3) @ (breln1invset @ X2 @ X1))) | ((in @ (kpair @ X3 @ X4) @ X1) = $true) | ($false = (in @ X4 @ X2)) | ($false = (in @ X3 @ X2)) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.76/1.45 thf(f95,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X3 @ X2)) | ((breln1 @ X2 @ X1) = $false) | ($false = (in @ X4 @ X2)) | (((in @ (kpair @ X4 @ X3) @ (breln1invset @ X2 @ X1)) => (in @ (kpair @ X3 @ X4) @ X1)) = $true)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.76/1.45 thf(f94,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X3 @ X2)) | ((breln1 @ X2 @ X1) = $false) | (((in @ X4 @ X2) => ((in @ (kpair @ X4 @ X3) @ (breln1invset @ X2 @ X1)) => (in @ (kpair @ X3 @ X4) @ X1))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.76/1.45 thf(f93,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X3 @ X2)) | ((breln1 @ X2 @ X1) = $false) | (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ Y0 @ X3) @ (breln1invset @ X2 @ X1)) => (in @ (kpair @ X3 @ Y0) @ X1)))) @ X4) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f92])).
% 1.76/1.45 thf(f92,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ Y0 @ X3) @ (breln1invset @ X2 @ X1)) => (in @ (kpair @ X3 @ Y0) @ X1))))) = $true) | ($false = (in @ X3 @ X2))) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.76/1.45 thf(f91,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ Y0 @ X3) @ (breln1invset @ X2 @ X1)) => (in @ (kpair @ X3 @ Y0) @ X1)))))) = $true) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f90])).
% 1.76/1.45 thf(f90,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | (((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y1 @ Y0) @ (breln1invset @ X2 @ X1)) => (in @ (kpair @ Y0 @ Y1) @ X1))))))) @ X3) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f89])).
% 1.76/1.45 thf(f89,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y1 @ Y0) @ (breln1invset @ X2 @ X1)) => (in @ (kpair @ Y0 @ Y1) @ X1)))))))) = $true)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.76/1.45 thf(f88,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((breln1 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y1 @ Y0) @ (breln1invset @ X2 @ X1)) => (in @ (kpair @ Y0 @ Y1) @ X1))))))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f87])).
% 1.76/1.45 thf(f87,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ (kpair @ Y2 @ Y1) @ (breln1invset @ Y0 @ X1)) => (in @ (kpair @ Y1 @ Y2) @ X1)))))))))) @ X2) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f86])).
% 1.76/1.45 thf(f86,plain,(
% 1.76/1.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ (kpair @ Y2 @ Y1) @ (breln1invset @ Y0 @ X1)) => (in @ (kpair @ Y1 @ Y2) @ X1))))))))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.76/1.45 thf(f85,plain,(
% 1.76/1.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y3 @ Y2) @ (breln1invset @ Y1 @ Y0)) => (in @ (kpair @ Y2 @ Y3) @ Y0)))))))))))) @ X1) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f39])).
% 1.76/1.45 thf(f39,plain,(
% 1.76/1.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y3 @ Y2) @ (breln1invset @ Y1 @ Y0)) => (in @ (kpair @ Y2 @ Y3) @ Y0))))))))))))) = $true)),
% 1.76/1.45 inference(definition_unfolding,[status(thm)],[f34,f27])).
% 1.76/1.45 thf(f27,plain,(
% 1.76/1.45 (breln1invE = $true)),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.45 thf(f34,plain,(
% 1.76/1.45 (breln1invE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y3 @ Y2) @ (breln1invset @ Y1 @ Y0)) => (in @ (kpair @ Y2 @ Y3) @ Y0))))))))))))))),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f10])).
% 1.76/1.45 thf(f10,plain,(
% 1.76/1.45 (breln1invE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y3 @ Y2) @ (breln1invset @ Y1 @ Y0)) => (in @ (kpair @ Y2 @ Y3) @ Y0))))))))))))))),
% 1.76/1.45 inference(fool_elimination,[status(thm)],[f9])).
% 1.76/1.45 thf(f9,plain,(
% 1.76/1.45 (breln1invE = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)) => (in @ (kpair @ X2 @ X3) @ X1))))))),
% 1.76/1.45 inference(rectify,[status(thm)],[f5])).
% 1.76/1.45 thf(f5,axiom,(
% 1.76/1.45 (breln1invE = ! [X0 : $i,X2 : $i] : ((breln1 @ X0 @ X2) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X5 @ X4) @ (breln1invset @ X0 @ X2)) => (in @ (kpair @ X4 @ X5) @ X2))))))),
% 1.76/1.45 file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',breln1invE)).
% 1.76/1.45 thf(f121,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK4 @ X0 @ (breln1invset @ X1 @ X2) @ X3) @ (sK3 @ X0 @ (breln1invset @ X1 @ X2) @ X3)) @ X2) = $true) | ((breln1 @ X3 @ (breln1invset @ X1 @ X2)) = $false) | ($false = (breln1 @ X1 @ X2)) | ((in @ (sK4 @ X0 @ (breln1invset @ X1 @ X2) @ X3) @ X1) = $false) | ((subset @ (breln1invset @ X1 @ X2) @ X0) = $true) | ($false = (breln1 @ X3 @ X0)) | ((in @ (sK3 @ X0 @ (breln1invset @ X1 @ X2) @ X3) @ X1) = $false)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.76/1.45 thf(f116,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ X0 @ (breln1invset @ X1 @ X2) @ X3) @ X1) = $false) | ($false = (breln1 @ X3 @ X0)) | ((in @ (kpair @ (sK4 @ X0 @ (breln1invset @ X1 @ X2) @ X3) @ (sK3 @ X0 @ (breln1invset @ X1 @ X2) @ X3)) @ X2) = $true) | ($false = (breln1 @ X1 @ X2)) | ((breln1 @ X3 @ (breln1invset @ X1 @ X2)) = $false) | ((in @ (sK4 @ X0 @ (breln1invset @ X1 @ X2) @ X3) @ X1) = $false) | ((subset @ (breln1invset @ X1 @ X2) @ X0) = $true) | ($false = $true)) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f96,f65])).
% 1.76/1.45 thf(f65,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ (sK4 @ X3 @ X1 @ X2)) @ X1) = $true) | ((breln1 @ X2 @ X1) = $false) | ((breln1 @ X2 @ X3) = $false) | ((subset @ X1 @ X3) = $true)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.76/1.45 thf(f62,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | ((subset @ X1 @ X3) = $true) | ($false = ((in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ (sK4 @ X3 @ X1 @ X2)) @ X1) => (in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ (sK4 @ X3 @ X1 @ X2)) @ X3))) | ((breln1 @ X2 @ X3) = $false)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.76/1.45 thf(f64,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ (kpair @ (sK3 @ X3 @ X1 @ X2) @ (sK4 @ X3 @ X1 @ X2)) @ X3) = $false) | ((breln1 @ X2 @ X3) = $false) | ((breln1 @ X2 @ X1) = $false) | ((subset @ X1 @ X3) = $true)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.76/1.45 thf(f59,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ (sK3 @ X3 @ X1 @ X2) @ X2) = $true) | ((breln1 @ X2 @ X3) = $false) | ((breln1 @ X2 @ X1) = $false) | ((subset @ X1 @ X3) = $true)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.76/1.45 thf(f209,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $false) | ($false = (breln1 @ X1 @ X0)) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0))) | ((breln1invset @ X1 @ (breln1invset @ X1 @ X0)) = X0)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.76/1.45 thf(f207,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (((breln1invset @ X1 @ (breln1invset @ X1 @ X0)) = X0) | ($false = (breln1 @ X1 @ X0)) | ((subset @ (breln1invset @ X1 @ (breln1invset @ X1 @ X0)) @ X0) = $false) | ($false = $true) | ($false = (breln1 @ X1 @ (breln1invset @ X1 @ X0)))) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f84,f205])).
% 1.76/1.45 thf(f205,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ X1))) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f204])).
% 1.76/1.45 thf(f204,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ X1)) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = $true) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true)) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f201])).
% 1.76/1.45 thf(f201,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X0 @ X1)) | ($false = $true)) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f46,f199])).
% 1.76/1.45 thf(f199,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X0 @ X1))) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f198])).
% 1.76/1.45 thf(f198,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X0 @ X1)) | ($false = $true)) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f195])).
% 1.76/1.45 thf(f195,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($false = (breln1 @ X0 @ X1)) | ($false = (breln1 @ X0 @ X1)) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1)))) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f59,f193])).
% 1.76/1.45 thf(f193,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X0) @ X0)) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X0 @ X1)) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))))) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f192])).
% 1.76/1.45 thf(f192,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ($false = $true) | ($false = (breln1 @ X0 @ X1)) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X0) @ X0))) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f188])).
% 1.76/1.45 thf(f188,plain,(
% 1.76/1.45 ( ! [X0 : $i,X1 : $i] : (($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X0) @ X0)) | ($false = $true) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X0 @ X1)) | ($false = (breln1 @ X0 @ X1)) | ($false = (breln1 @ X0 @ X1)) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))))) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f185,f63])).
% 1.76/1.45 thf(f185,plain,(
% 1.76/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X2) @ X0)) | ($false = (breln1 @ X0 @ X1)) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false = (breln1 @ X2 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ((in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X2) @ X0) = $false) | ((breln1 @ X2 @ X1) = $false) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1)))) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.76/1.45 thf(f184,plain,(
% 1.76/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (breln1 @ X2 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ($false != $false) | ((in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X2) @ X0) = $false) | ($false = (breln1 @ X0 @ X1)) | ((breln1 @ X2 @ X1) = $false) | ($false = (in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X2) @ X0)) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true)) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f181])).
% 1.76/1.45 thf(f181,plain,(
% 1.76/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X2) @ X0) = $false) | ($false = (breln1 @ X2 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)))) | ($false = (breln1 @ X0 @ X1)) | ((subset @ X1 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1))) = $true) | ($false != $false) | ((breln1 @ X2 @ X1) = $false) | ($false = (in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X2) @ X0)) | ($false = (breln1 @ X0 @ (breln1invset @ X0 @ X1))) | ($false = (in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X0 @ X1)) @ X1 @ X2) @ X0))) )),
% 1.76/1.45 inference(equality_factoring,[status(thm)],[f178])).
% 1.76/1.45 thf(f178,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X1)) | ((in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X0) = $false) | ((breln1 @ X3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $false) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X0)) | ($false = (breln1 @ X0 @ (breln1invset @ X1 @ X2))) | ((in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X1) = $false) | ((breln1 @ X3 @ X2) = $false) | ($false = (breln1 @ X1 @ X2)) | ((subset @ X2 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $true)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 1.76/1.45 thf(f177,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X1)) | ((breln1 @ X3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $false) | ((in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X0) = $false) | ((subset @ X2 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $true) | ((breln1 @ X3 @ X2) = $false) | ($false = $true) | ($false = (breln1 @ X1 @ X2)) | ($false = (breln1 @ X0 @ (breln1invset @ X1 @ X2))) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X0)) | ((in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X1) = $false)) )),
% 1.76/1.45 inference(duplicate_literal_removal,[status(thm)],[f171])).
% 1.76/1.45 thf(f171,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = $true) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X0)) | ((subset @ X2 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $true) | ((subset @ X2 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $true) | ((in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X0) = $false) | ((breln1 @ X3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $false) | ((breln1 @ X3 @ X2) = $false) | ($false = (breln1 @ X1 @ X2)) | ($false = (breln1 @ X0 @ (breln1invset @ X1 @ X2))) | ((in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X1) = $false) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X2 @ X3) @ X1)) | ((breln1 @ X3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $false) | ((breln1 @ X3 @ X2) = $false)) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f65,f140])).
% 1.76/1.45 thf(f140,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4)) @ X2) = $false) | ($false = (in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ X1)) | ((breln1 @ X4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $false) | ($false = (in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ X0)) | ((subset @ X3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $true) | ((breln1 @ X4 @ X3) = $false) | ($false = (breln1 @ X0 @ (breln1invset @ X1 @ X2))) | ($false = (breln1 @ X1 @ X2)) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ X0)) | ((in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ X1) = $false)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.76/1.45 thf(f138,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((breln1 @ X4 @ X3) = $false) | ($false = $true) | ($false = (in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ X1)) | ((in @ (kpair @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4)) @ X2) = $false) | ((subset @ X3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $true) | ($false = (breln1 @ X0 @ (breln1invset @ X1 @ X2))) | ($false = (in @ (sK4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ X0)) | ($false = (breln1 @ X1 @ X2)) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ X0)) | ((in @ (sK3 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2)) @ X3 @ X4) @ X1) = $false) | ((breln1 @ X4 @ (breln1invset @ X0 @ (breln1invset @ X1 @ X2))) = $false)) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f77,f111])).
% 1.76/1.45 thf(f111,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (in @ (kpair @ (sK4 @ (breln1invset @ X0 @ X1) @ X2 @ X3) @ (sK3 @ (breln1invset @ X0 @ X1) @ X2 @ X3)) @ X1)) | ($false = (breln1 @ X3 @ (breln1invset @ X0 @ X1))) | ($false = (breln1 @ X0 @ X1)) | ((breln1 @ X3 @ X2) = $false) | ((subset @ X2 @ (breln1invset @ X0 @ X1)) = $true) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ X1) @ X2 @ X3) @ X0)) | ((in @ (sK4 @ (breln1invset @ X0 @ X1) @ X2 @ X3) @ X0) = $false)) )),
% 1.76/1.45 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.76/1.45 thf(f109,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = $true) | ($false = (in @ (kpair @ (sK4 @ (breln1invset @ X0 @ X1) @ X2 @ X3) @ (sK3 @ (breln1invset @ X0 @ X1) @ X2 @ X3)) @ X1)) | ((in @ (sK4 @ (breln1invset @ X0 @ X1) @ X2 @ X3) @ X0) = $false) | ($false = (breln1 @ X0 @ X1)) | ((subset @ X2 @ (breln1invset @ X0 @ X1)) = $true) | ($false = (breln1 @ X3 @ (breln1invset @ X0 @ X1))) | ((breln1 @ X3 @ X2) = $false) | ($false = (in @ (sK3 @ (breln1invset @ X0 @ X1) @ X2 @ X3) @ X0))) )),
% 1.76/1.45 inference(superposition,[status(thm)],[f77,f64])).
% 1.76/1.45 thf(f77,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ X4 @ X3) @ (breln1invset @ X2 @ X1)) = $true) | ((breln1 @ X2 @ X1) = $false) | ((in @ (kpair @ X3 @ X4) @ X1) = $false) | ($false = (in @ X4 @ X2)) | ($false = (in @ X3 @ X2))) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.76/1.45 thf(f76,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X3 @ X2)) | (((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X4 @ X3) @ (breln1invset @ X2 @ X1))) = $true) | ($false = (in @ X4 @ X2)) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.76/1.45 thf(f75,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X4 @ X3) @ (breln1invset @ X2 @ X1)))) = $true) | ($false = (in @ X3 @ X2)) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.76/1.45 thf(f74,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X3 @ X2)) | ((breln1 @ X2 @ X1) = $false) | (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X3 @ Y0) @ X1) => (in @ (kpair @ Y0 @ X3) @ (breln1invset @ X2 @ X1))))) @ X4) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f73])).
% 1.76/1.45 thf(f73,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | ($false = (in @ X3 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X3 @ Y0) @ X1) => (in @ (kpair @ Y0 @ X3) @ (breln1invset @ X2 @ X1)))))) = $true)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.76/1.45 thf(f72,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | (((in @ X3 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X3 @ Y0) @ X1) => (in @ (kpair @ Y0 @ X3) @ (breln1invset @ X2 @ X1))))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.76/1.45 thf(f71,plain,(
% 1.76/1.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y1 @ Y0) @ (breln1invset @ X2 @ X1)))))))) @ X3) = $true) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f70])).
% 1.76/1.45 thf(f70,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : (((breln1 @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y1 @ Y0) @ (breln1invset @ X2 @ X1))))))))) = $true)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.76/1.45 thf(f69,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((breln1 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y1 @ Y0) @ (breln1invset @ X2 @ X1)))))))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.76/1.45 thf(f68,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y2 @ Y1) @ (breln1invset @ Y0 @ X1))))))))))) @ X2) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f67])).
% 1.76/1.45 thf(f67,plain,(
% 1.76/1.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y2 @ Y1) @ (breln1invset @ Y0 @ X1)))))))))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.76/1.45 thf(f66,plain,(
% 1.76/1.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y3 @ Y2) @ (breln1invset @ Y1 @ Y0))))))))))))) @ X1) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f40])).
% 1.76/1.45 thf(f40,plain,(
% 1.76/1.45 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y3 @ Y2) @ (breln1invset @ Y1 @ Y0)))))))))))))))),
% 1.76/1.45 inference(definition_unfolding,[status(thm)],[f35,f26])).
% 1.76/1.45 thf(f26,plain,(
% 1.76/1.45 (breln1invI = $true)),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.45 thf(f35,plain,(
% 1.76/1.45 (breln1invI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y3 @ Y2) @ (breln1invset @ Y1 @ Y0)))))))))))))))),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f16])).
% 1.76/1.45 thf(f16,plain,(
% 1.76/1.45 (breln1invI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y3 @ Y2) @ (breln1invset @ Y1 @ Y0)))))))))))))))),
% 1.76/1.45 inference(fool_elimination,[status(thm)],[f15])).
% 1.76/1.45 thf(f15,plain,(
% 1.76/1.45 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ (kpair @ X2 @ X3) @ X1) => (in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)))))) = breln1invI)),
% 1.76/1.45 inference(rectify,[status(thm)],[f4])).
% 1.76/1.45 thf(f4,axiom,(
% 1.76/1.45 (! [X0 : $i,X2 : $i] : ((breln1 @ X0 @ X2) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X5 @ X4) @ (breln1invset @ X0 @ X2)))))) = breln1invI)),
% 1.76/1.45 file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',breln1invI)).
% 1.76/1.45 thf(f84,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : (($false = (subset @ X2 @ X1)) | ($false = (subset @ X1 @ X2)) | (X1 = X2)) )),
% 1.76/1.45 inference(equality_proxy_clausification,[status(thm)],[f83])).
% 1.76/1.45 thf(f83,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : (((X2 = X1) = $true) | ($false = (subset @ X2 @ X1)) | ($false = (subset @ X1 @ X2))) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.76/1.45 thf(f82,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : (($false = (subset @ X2 @ X1)) | (((subset @ X1 @ X2) => (X2 = X1)) = $true)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.76/1.45 thf(f81,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((subset @ X2 @ X1) => ((subset @ X1 @ X2) => (X2 = X1))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.76/1.45 thf(f80,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ Y0 @ X1) => ((subset @ X1 @ Y0) => (Y0 = X1)))) @ X2) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f79])).
% 1.76/1.45 thf(f79,plain,(
% 1.76/1.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X1) => ((subset @ X1 @ Y0) => (Y0 = X1))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.76/1.45 thf(f78,plain,(
% 1.76/1.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0)))))) @ X1) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f37])).
% 1.76/1.45 thf(f37,plain,(
% 1.76/1.45 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.76/1.45 inference(definition_unfolding,[status(thm)],[f32,f31])).
% 1.76/1.45 thf(f31,plain,(
% 1.76/1.45 (setextsub = $true)),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.45 thf(f32,plain,(
% 1.76/1.45 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f14])).
% 1.76/1.45 thf(f14,plain,(
% 1.76/1.45 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.76/1.45 inference(fool_elimination,[status(thm)],[f13])).
% 1.76/1.45 thf(f13,plain,(
% 1.76/1.45 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)),
% 1.76/1.45 inference(rectify,[status(thm)],[f1])).
% 1.76/1.45 thf(f1,axiom,(
% 1.76/1.45 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)),
% 1.76/1.45 file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',setextsub)).
% 1.76/1.45 thf(f46,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : (((breln1 @ X2 @ (breln1invset @ X2 @ X1)) = $true) | ((breln1 @ X2 @ X1) = $false)) )),
% 1.76/1.45 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.76/1.45 thf(f45,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((breln1 @ X2 @ X1) => (breln1 @ X2 @ (breln1invset @ X2 @ X1))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.76/1.45 thf(f44,plain,(
% 1.76/1.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (breln1 @ Y0 @ (breln1invset @ Y0 @ X1)))) @ X2) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f43])).
% 1.76/1.45 thf(f43,plain,(
% 1.76/1.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (breln1 @ Y0 @ (breln1invset @ Y0 @ X1))))) = $true)) )),
% 1.76/1.45 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.76/1.45 thf(f42,plain,(
% 1.76/1.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (breln1 @ Y1 @ (breln1invset @ Y1 @ Y0)))))) @ X1) = $true)) )),
% 1.76/1.45 inference(pi_clausification,[status(thm)],[f38])).
% 1.76/1.45 thf(f38,plain,(
% 1.76/1.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (breln1 @ Y1 @ (breln1invset @ Y1 @ Y0))))))) = $true)),
% 1.76/1.45 inference(definition_unfolding,[status(thm)],[f33,f25])).
% 1.76/1.45 thf(f25,plain,(
% 1.76/1.45 (breln1invprop = $true)),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.45 thf(f33,plain,(
% 1.76/1.45 (breln1invprop = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (breln1 @ Y1 @ (breln1invset @ Y1 @ Y0))))))))),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.76/1.45 thf(f12,plain,(
% 1.76/1.45 (breln1invprop = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (breln1 @ Y1 @ (breln1invset @ Y1 @ Y0))))))))),
% 1.76/1.45 inference(fool_elimination,[status(thm)],[f11])).
% 1.76/1.45 thf(f11,plain,(
% 1.76/1.45 (breln1invprop = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => (breln1 @ X0 @ (breln1invset @ X0 @ X1))))),
% 1.76/1.45 inference(rectify,[status(thm)],[f3])).
% 1.76/1.45 thf(f3,axiom,(
% 1.76/1.45 (breln1invprop = ! [X0 : $i,X2 : $i] : ((breln1 @ X0 @ X2) => (breln1 @ X0 @ (breln1invset @ X0 @ X2))))),
% 1.76/1.45 file('/export/starexec/sandbox2/tmp/tmp.hu3nj7t2JB/DTF2THF_2912.p',breln1invprop)).
% 1.76/1.45 thf(f29,plain,(
% 1.76/1.45 (sK0 != (breln1invset @ sK1 @ (breln1invset @ sK1 @ sK0)))),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.45 thf(f30,plain,(
% 1.76/1.45 ((breln1 @ sK1 @ sK0) = $true)),
% 1.76/1.45 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.45 % SZS output end Proof for DTF2THF_2912
% 1.76/1.45 % (3058)------------------------------
% 1.76/1.45 % (3058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.45 % (3058)Termination reason: Refutation
% 1.76/1.45
% 1.76/1.45 % (3058)Memory used [KB]: 6140
% 1.76/1.45 % (3058)Time elapsed: 0.071 s
% 1.76/1.45 % (3058)Instructions burned: 119 (million)
% 1.76/1.45 % (3058)------------------------------
% 1.76/1.45 % (3058)------------------------------
% 1.76/1.45 % (3057)Success in time 0.08 s
%------------------------------------------------------------------------------