%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU779^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 09:37:07 AM UTC 2026
% Result : Theorem 1.63s 1.35s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 927 ( 186 equ; 0 cnn)
% Maximal formula atoms : 16 ( 15 avg)
% Number of connectives : 1313 ( 20 ~; 42 |; 97 &;1020 @)
% ( 0 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 11 con; 0-3 aty)
% ( 41 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 221 ( 95 ^; 86 !; 40 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
cartprod: $i > $i > $i ).
thf(func_def_4,type,
breln: $i > $i > $i > $o ).
thf(func_def_6,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_8,type,
breln1: $i > $i > $o ).
thf(func_def_9,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_10,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_32,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f80,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f34,f76]) ).
thf(f76,plain,
( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true = $false )
| ( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) ) ),
inference(forward_demodulation,[status(thm)],[f74,f32]) ).
thf(f32,plain,
( $true
= ( in @ sK5 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) )
& ( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK5 @ sK1 ) )
& ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
= ( breln1 @ sK1 @ sK2 ) )
& ( ( breln1 @ sK1 @ sK0 )
= $true )
& ( dpsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f18,f23,f22,f21,f20,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
!= $true )
& ( ( in @ X5 @ X1 )
= $true ) )
& ( ( in @ X4 @ X1 )
= $true ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ sK0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ X2 ) ) )
& ( ( in @ X5 @ sK1 )
= $true ) )
& ( ( in @ X4 @ sK1 )
= $true ) ) )
& ( ( breln1 @ sK1 @ X2 )
= $true ) )
& ( ( breln1 @ sK1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ sK0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ X2 ) ) )
& ( ( in @ X5 @ sK1 )
= $true ) )
& ( ( in @ X4 @ sK1 )
= $true ) ) )
& ( ( breln1 @ sK1 @ X2 )
= $true ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ sK0 ) )
& ( ( in @ ( kpair @ X5 @ X4 ) @ sK2 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( ( in @ X5 @ sK1 )
= $true ) )
& ( ( in @ X4 @ sK1 )
= $true ) ) )
& ( $true
= ( breln1 @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ sK0 ) )
& ( ( in @ ( kpair @ X5 @ X4 ) @ sK2 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( ( in @ X5 @ sK1 )
= $true ) )
& ( ( in @ X4 @ sK1 )
= $true ) ) )
=> ( ( $true
= ( in @ sK3 @ sK1 ) )
& ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ X5 ) @ sK0 ) )
& ( ( in @ ( kpair @ X5 @ X4 ) @ sK2 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( ( in @ X5 @ sK1 )
= $true ) )
& ( ( in @ X4 @ sK1 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ X5 ) @ sK0 ) )
& ( ( in @ ( kpair @ X5 @ X4 ) @ sK2 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( ( in @ X5 @ sK1 )
= $true ) )
& ( ( in @ X4 @ sK1 )
= $true ) )
=> ( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ X5 ) @ sK0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ sK4 ) @ sK2 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( ( in @ X5 @ sK1 )
= $true ) )
& ( $true
= ( in @ sK4 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ X5 ) @ sK0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ sK4 ) @ sK2 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( ( in @ X5 @ sK1 )
= $true ) )
=> ( ( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) )
& ( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK5 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
!= $true )
& ( ( in @ X5 @ X1 )
= $true ) )
& ( ( in @ X4 @ X1 )
= $true ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( dpsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
!= $true )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
& ( ( in @ X5 @ X1 )
= $true ) )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( dpsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( dpsetconstrI = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
=> ( ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( dpsetconstrI
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X0 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dpsetconstrI
=> ! [X8: $i,X0: $i] :
( ( breln1 @ X0 @ X8 )
=> ! [X9: $i] :
( ( breln1 @ X0 @ X9 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X6 ) @ X8 )
=> ( ( in @ ( kpair @ X6 @ X5 ) @ X9 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X0 @ X8 @ X9 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dpsetconstrI
=> ! [X8: $i,X0: $i] :
( ( breln1 @ X0 @ X8 )
=> ! [X9: $i] :
( ( breln1 @ X0 @ X9 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X6 ) @ X8 )
=> ( ( in @ ( kpair @ X6 @ X5 ) @ X9 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X0 @ X8 @ X9 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HkcHQWNYrS/DTF2THF_9238.p',breln1compI) ).
thf(f74,plain,
( ( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
| ( $false
= ( in @ sK5 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true = $false )
| ( $false
= ( in @ sK5 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) ) ),
inference(superposition,[status(thm)],[f35,f70]) ).
thf(f70,plain,
! [X1: $i] :
( ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[status(thm)],[f68,f31]) ).
thf(f31,plain,
( $true
= ( in @ sK4 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f68,plain,
! [X1: $i] :
( ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i] :
( ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false )
| ( $true = $false )
| ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f66,f36]) ).
thf(f36,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f66,plain,
! [X1: $i] :
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: $i] :
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
& ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: $i] :
( ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( ( in @ ( kpair @ X1 @ sK4 ) @ sK2 )
& ( in @ ( kpair @ sK3 @ X1 ) @ sK0 )
& ( in @ X1 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ ( kpair @ Y0 @ sK4 ) @ sK2 )
& ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 )
& ( in @ Y0 @ sK1 ) )
@ X1 )
= $false )
| ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) ) ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ ( kpair @ Y0 @ sK4 ) @ sK2 )
& ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 )
& ( in @ Y0 @ sK1 ) ) ) )
| ( $false
= ( in @ sK3 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 )
& ( in @ Y2 @ sK1 ) ) )
@ sK3
@ sK4 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 )
& ( in @ Y2 @ sK1 ) ) )
@ sK3
@ sK4 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f57,f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X3 @ X2 @ X1 ) )
= $true )
| ( $false
= ( X1 @ X4 @ X5 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( ( in @ X5 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ X2 )
= $false )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ( X1 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X3 @ X2 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( $true
= ( ( in @ X5 @ X2 )
=> ( ( X1 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X3 @ X2 @ X1 ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X3 @ X2 @ X1 ) ) ) )
@ X5 )
= $true )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X3 @ X2 @ X1 ) ) ) ) )
= $true )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i] :
( $true
= ( ( in @ X4 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X3 @ X2 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X1 @ Y0 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X3 @ X2 @ X1 ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X1 @ Y0 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X3 @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( X1 @ Y1 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ Y0 @ X2 @ X1 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( X1 @ Y1 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ Y0 @ X2 @ X1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( X1 @ Y2 @ Y3 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ Y1 @ Y0 @ X1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( X1 @ Y2 @ Y3 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ Y1 @ Y0 @ X1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y0 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y0 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y0 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f25]) ).
thf(f25,plain,
( dpsetconstrI
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y0 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( dpsetconstrI
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y0 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ( in @ X0 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 @ X0 @ X4 )
=> ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X5: $i,X6: $i] : ( X3 @ X5 @ X6 ) ) ) ) ) )
= dpsetconstrI ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X4: $i,X0: $i,X1: $i,X3: $i > $i > $o] :
( ( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( X3 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X6: $i,X7: $i] : ( X3 @ X6 @ X7 ) ) ) ) ) )
= dpsetconstrI ),
file('/export/starexec/sandbox/tmp/tmp.HkcHQWNYrS/DTF2THF_9238.p',dpsetconstrI) ).
thf(f28,plain,
dpsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f57,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK1 @ sK1
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 )
& ( in @ Y2 @ sK1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 ) ) ) )
@ sK1
@ sK0
@ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f26]) ).
thf(f26,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ X5 @ X0 )
& ( in @ ( kpair @ X3 @ X5 ) @ X1 )
& ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) ) )
= breln1compset ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X8: $i,X9: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X4: $i,X5: $i] :
? [X6: $i] :
( ( in @ X6 @ X0 )
& ( in @ ( kpair @ X4 @ X6 ) @ X8 )
& ( in @ ( kpair @ X6 @ X5 ) @ X9 ) ) ) )
= breln1compset ),
file('/export/starexec/sandbox/tmp/tmp.HkcHQWNYrS/DTF2THF_9238.p',breln1compset) ).
thf(f33,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f35,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f34,plain,
( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU779^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n018.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:33:30 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.38 ---- Original DTF file ---
% 0.19/0.38 thf(spec,logic,$$dhol).
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 % File : SEU779^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.38 % Domain : Set Theory
% 0.19/0.38 % Problem : Binary Relations on a Set
% 0.19/0.38 % Version : Especial > Reduced > Especial.
% 0.19/0.38 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.19/0.38 % (! y:i.in y A -> (! z:i.in z A -> in (kpair x z) R ->
% 0.19/0.38 % in (kpair z y) S -> in (kpair x y) (breln1compset A R S))))))
% 0.19/0.38
% 0.19/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.38 % Source : [Bro08]
% 0.19/0.38 % Names : ZFC281l [Bro08]
% 0.19/0.38
% 0.19/0.38 % Status : Theorem
% 0.19/0.38 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.67 v4.0.0, 1.00 v3.7.0
% 0.19/0.38 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.19/0.38 % Number of atoms : 24 ( 4 equ; 0 cnn)
% 0.19/0.38 % Maximal formula atoms : 9 ( 4 avg)
% 0.19/0.38 % Number of connectives : 73 ( 0 ~; 0 |; 2 &; 60 @)
% 0.19/0.38 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.19/0.38 % Maximal formula depth : 19 ( 5 avg)
% 0.19/0.38 % Number of types : 2 ( 0 usr)
% 0.19/0.38 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.19/0.38 % Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% 0.19/0.38 % Number of variables : 24 ( 12 ^; 11 !; 1 ?; 24 :)
% 0.19/0.38 % SPC : TH0_THM_EQU_NAR
% 0.19/0.38
% 0.19/0.38 % Comments : http://mathgate.info/detsetitem.php?id=345
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 thf(in_type,type,
% 0.19/0.38 in: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(subset_type,type,
% 0.19/0.38 subset: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(kpair_type,type,
% 0.19/0.38 kpair: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(cartprod_type,type,
% 0.19/0.38 cartprod: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(breln_type,type,
% 0.19/0.38 breln: $i > $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(breln,definition,
% 0.19/0.38 ( breln
% 0.19/0.38 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(dpsetconstr_type,type,
% 0.19/0.38 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(dpsetconstrI_type,type,
% 0.19/0.38 dpsetconstrI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(dpsetconstrI,definition,
% 0.19/0.38 ( dpsetconstrI
% 0.19/0.38 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ! [Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ B )
% 0.19/0.38 => ( ( Xphi @ Xx @ Xy )
% 0.19/0.38 => ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.38 @ ( dpsetconstr @ A @ B
% 0.19/0.38 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(breln1_type,type,
% 0.19/0.38 breln1: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(breln1,definition,
% 0.19/0.38 ( breln1
% 0.19/0.38 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(breln1compset_type,type,
% 0.19/0.38 breln1compset: $i > $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(breln1compset,definition,
% 0.19/0.38 ( breln1compset
% 0.19/0.38 = ( ^ [A: $i,R: $i,S: $i] :
% 0.19/0.38 ( dpsetconstr @ A @ A
% 0.19/0.38 @ ^ [Xx: $i,Xy: $i] :
% 0.19/0.38 ? [Xz: $i] :
% 0.19/0.38 ( ( in @ Xz @ A )
% 0.19/0.38 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.19/0.38 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(breln1compI,conjecture,
% 0.19/0.38 ( dpsetconstrI
% 0.19/0.38 => ! [A: $i,R: $i] :
% 0.19/0.38 ( ( breln1 @ A @ R )
% 0.19/0.38 => ! [S: $i] :
% 0.19/0.38 ( ( breln1 @ A @ S )
% 0.19/0.38 => ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ! [Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ A )
% 0.19/0.38 => ! [Xz: $i] :
% 0.19/0.38 ( ( in @ Xz @ A )
% 0.19/0.38 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.19/0.38 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.19/0.38 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 ------------------------
% 1.63/1.31 ---- Embedded in THF ---
% 1.63/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.31 %%% Generated on Tue Feb 24 12:33:31 EST 2026
% 1.63/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.31 %%% Logic specification used:
% 1.63/1.31 %%% thf(spec, logic, $$dhol).
% 1.63/1.31
% 1.63/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.HkcHQWNYrS/DTF2DTF9238.p
% See solution above
% 1.63/1.31 ------------------------
% 1.63/1.32 ---- Cleaned THF ---
% 1.63/1.32 thf(in_type,type,
% 1.63/1.32 in: $i > $i > $o ).
% 1.63/1.32
% 1.63/1.32 thf(subset_type,type,
% 1.63/1.32 subset: $i > $i > $o ).
% 1.63/1.32
% 1.63/1.32 thf(kpair_type,type,
% 1.63/1.32 kpair: $i > $i > $i ).
% 1.63/1.32
% 1.63/1.32 thf(cartprod_type,type,
% 1.63/1.32 cartprod: $i > $i > $i ).
% 1.63/1.32
% 1.63/1.32 thf(breln_type,type,
% 1.63/1.32 breln: $i > $i > $i > $o ).
% 1.63/1.32
% 1.63/1.32 thf(breln,definition,
% 1.63/1.32 ( breln
% 1.63/1.32 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(dpsetconstr_type,type,
% 1.63/1.32 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.63/1.32
% 1.63/1.32 thf(dpsetconstrI_type,type,
% 1.63/1.32 dpsetconstrI: $o ).
% 1.63/1.32
% 1.63/1.32 thf(dpsetconstrI,definition,
% 1.63/1.32 ( dpsetconstrI
% 1.63/1.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 1.63/1.32 ( ( in @ Xx @ A )
% 1.63/1.32 => ! [Xy: $i] :
% 1.63/1.32 ( ( in @ Xy @ B )
% 1.63/1.32 => ( ( Xphi @ Xx @ Xy )
% 1.63/1.32 => ( in @ ( kpair @ Xx @ Xy )
% 1.63/1.32 @ ( dpsetconstr @ A @ B
% 1.63/1.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(breln1_type,type,
% 1.63/1.32 breln1: $i > $i > $o ).
% 1.63/1.32
% 1.63/1.32 thf(breln1,definition,
% 1.63/1.32 ( breln1
% 1.63/1.32 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(breln1compset_type,type,
% 1.63/1.32 breln1compset: $i > $i > $i > $i ).
% 1.63/1.32
% 1.63/1.32 thf(breln1compset,definition,
% 1.63/1.32 ( breln1compset
% 1.63/1.32 = ( ^ [A: $i,R: $i,S: $i] :
% 1.63/1.32 ( dpsetconstr @ A @ A
% 1.63/1.32 @ ^ [Xx: $i,Xy: $i] :
% 1.63/1.32 ? [Xz: $i] :
% 1.63/1.32 ( ( in @ Xz @ A )
% 1.63/1.32 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 1.63/1.32 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 1.63/1.32
% 1.63/1.32 thf(breln1compI,conjecture,
% 1.63/1.32 ( dpsetconstrI
% 1.63/1.32 => ! [A: $i,R: $i] :
% 1.63/1.32 ( ( breln1 @ A @ R )
% 1.63/1.32 => ! [S: $i] :
% 1.63/1.32 ( ( breln1 @ A @ S )
% 1.63/1.32 => ! [Xx: $i] :
% 1.63/1.32 ( ( in @ Xx @ A )
% 1.63/1.32 => ! [Xy: $i] :
% 1.63/1.32 ( ( in @ Xy @ A )
% 1.63/1.32 => ! [Xz: $i] :
% 1.63/1.32 ( ( in @ Xz @ A )
% 1.63/1.32 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 1.63/1.32 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 1.63/1.32 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ).
% 1.63/1.32 ------------------------
% 1.63/1.34 % (9339)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9238 for (2999ds/2Mi)
% 1.63/1.34 % (9338)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_9238 for (2999ds/27Mi)
% 1.63/1.34 % (9337)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_9238 for (2999ds/4Mi)
% 1.63/1.34 % (9340)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_9238 for (2999ds/2Mi)
% 1.63/1.34 % (9336)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9238 for (2999ds/183Mi)
% 1.63/1.34 % (9341)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_9238 for (2999ds/275Mi)
% 1.63/1.34 % (9342)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9238 for (2999ds/18Mi)
% 1.63/1.34 % (9339)Instruction limit reached!
% 1.63/1.34 % (9339)------------------------------
% 1.63/1.34 % (9339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (9339)Termination reason: Unknown
% 1.63/1.34 % (9339)Termination phase: Preprocessing 3
% 1.63/1.34 % (9340)Instruction limit reached!
% 1.63/1.34 % (9340)------------------------------
% 1.63/1.34 % (9340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (9340)Termination reason: Unknown
% 1.63/1.34 % (9340)Termination phase: Function definition elimination
% 1.63/1.34
% 1.63/1.34 % (9340)Memory used [KB]: 1023
% 1.63/1.34 % (9340)Time elapsed: 0.003 s
% 1.63/1.34 % (9340)Instructions burned: 3 (million)
% 1.63/1.34 % (9340)------------------------------
% 1.63/1.34 % (9340)------------------------------
% 1.63/1.34
% 1.63/1.34 % (9339)Memory used [KB]: 1023
% 1.63/1.34 % (9339)Time elapsed: 0.003 s
% 1.63/1.34 % (9339)Instructions burned: 3 (million)
% 1.63/1.34 % (9339)------------------------------
% 1.63/1.34 % (9339)------------------------------
% 1.63/1.34 % (9337)Instruction limit reached!
% 1.63/1.34 % (9337)------------------------------
% 1.63/1.34 % (9337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (9337)Termination reason: Unknown
% 1.63/1.34 % (9337)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (9337)Memory used [KB]: 5500
% 1.63/1.34 % (9337)Time elapsed: 0.004 s
% 1.63/1.34 % (9337)Instructions burned: 4 (million)
% 1.63/1.34 % (9337)------------------------------
% 1.63/1.34 % (9337)------------------------------
% 1.63/1.34 % (9341)Refutation not found, incomplete strategy
% 1.63/1.34 % (9341)------------------------------
% 1.63/1.34 % (9341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (9341)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.34
% 1.63/1.34
% 1.63/1.34 % (9341)Memory used [KB]: 5500
% 1.63/1.34 % (9341)Time elapsed: 0.005 s
% 1.63/1.34 % (9341)Instructions burned: 6 (million)
% 1.63/1.34 % (9341)------------------------------
% 1.63/1.34 % (9341)------------------------------
% 1.63/1.35 % (9338)First to succeed.
% 1.63/1.35 % (9342)Instruction limit reached!
% 1.63/1.35 % (9342)------------------------------
% 1.63/1.35 % (9342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (9336)Also succeeded, but the first one will report.
% 1.63/1.35 % (9342)Termination reason: Unknown
% 1.63/1.35 % (9342)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (9342)Memory used [KB]: 5628
% 1.63/1.35 % (9342)Time elapsed: 0.011 s
% 1.63/1.35 % (9342)Instructions burned: 18 (million)
% 1.63/1.35 % (9342)------------------------------
% 1.63/1.35 % (9342)------------------------------
% 1.63/1.35 % (9338)Refutation found. Thanks to Tanya!
% 1.63/1.35 % SZS status Theorem for DTF2THF_9238
% 1.63/1.35 % SZS output start Proof for DTF2THF_9238
% 1.63/1.35 thf(func_def_0, type, in: $i > $i > $o).
% 1.63/1.35 thf(func_def_1, type, subset: $i > $i > $o).
% 1.63/1.35 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.63/1.35 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.63/1.35 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.63/1.35 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.63/1.35 thf(func_def_8, type, breln1: $i > $i > $o).
% 1.63/1.35 thf(func_def_9, type, breln1compset: $i > $i > $i > $i).
% 1.63/1.35 thf(func_def_10, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.35 thf(func_def_32, type, ph7: !>[X0: $tType]:(X0)).
% 1.63/1.35 thf(f80,plain,(
% 1.63/1.35 $false),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.63/1.35 thf(f79,plain,(
% 1.63/1.35 ($true = $false)),
% 1.63/1.35 inference(backward_demodulation,[status(thm)],[f34,f76])).
% 1.63/1.35 thf(f76,plain,(
% 1.63/1.35 ($false = (in @ (kpair @ sK5 @ sK4) @ sK2))),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.63/1.35 thf(f75,plain,(
% 1.63/1.35 ($true = $false) | ($false = (in @ (kpair @ sK5 @ sK4) @ sK2))),
% 1.63/1.35 inference(forward_demodulation,[status(thm)],[f74,f32])).
% 1.63/1.35 thf(f32,plain,(
% 1.63/1.35 ($true = (in @ sK5 @ sK1))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.35 thf(f24,plain,(
% 1.63/1.35 (((($true = (in @ sK3 @ sK1)) & ((($true = (in @ (kpair @ sK3 @ sK5) @ sK0)) & ($true = (in @ (kpair @ sK5 @ sK4) @ sK2)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2))) & ($true = (in @ sK5 @ sK1))) & ($true = (in @ sK4 @ sK1)))) & ($true = (breln1 @ sK1 @ sK2))) & ((breln1 @ sK1 @ sK0) = $true)) & (dpsetconstrI = $true)),
% 1.63/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f18,f23,f22,f21,f20,f19])).
% 1.63/1.35 thf(f19,plain,(
% 1.63/1.35 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ X0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true) & ((in @ X5 @ X1) = $true)) & ((in @ X4 @ X1) = $true))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))) => (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ sK0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK0 @ X2))) & ((in @ X5 @ sK1) = $true)) & ((in @ X4 @ sK1) = $true))) & ((breln1 @ sK1 @ X2) = $true)) & ((breln1 @ sK1 @ sK0) = $true))),
% 1.63/1.35 introduced(definition,[],[choice_axiom])).
% 1.63/1.35 thf(f20,plain,(
% 1.63/1.35 ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ sK0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK0 @ X2))) & ((in @ X5 @ sK1) = $true)) & ((in @ X4 @ sK1) = $true))) & ((breln1 @ sK1 @ X2) = $true)) => (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ sK0)) & ((in @ (kpair @ X5 @ X4) @ sK2) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK0 @ sK2))) & ((in @ X5 @ sK1) = $true)) & ((in @ X4 @ sK1) = $true))) & ($true = (breln1 @ sK1 @ sK2)))),
% 1.63/1.35 introduced(definition,[],[choice_axiom])).
% 1.63/1.35 thf(f21,plain,(
% 1.63/1.35 ? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ sK0)) & ((in @ (kpair @ X5 @ X4) @ sK2) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK0 @ sK2))) & ((in @ X5 @ sK1) = $true)) & ((in @ X4 @ sK1) = $true))) => (($true = (in @ sK3 @ sK1)) & ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ sK3 @ X5) @ sK0)) & ((in @ (kpair @ X5 @ X4) @ sK2) = $true) & ($true != (in @ (kpair @ sK3 @ X4) @ (breln1compset @ sK1 @ sK0 @ sK2))) & ((in @ X5 @ sK1) = $true)) & ((in @ X4 @ sK1) = $true)))),
% 1.63/1.35 introduced(definition,[],[choice_axiom])).
% 1.63/1.35 thf(f22,plain,(
% 1.63/1.35 ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ sK3 @ X5) @ sK0)) & ((in @ (kpair @ X5 @ X4) @ sK2) = $true) & ($true != (in @ (kpair @ sK3 @ X4) @ (breln1compset @ sK1 @ sK0 @ sK2))) & ((in @ X5 @ sK1) = $true)) & ((in @ X4 @ sK1) = $true)) => (? [X5 : $i] : (($true = (in @ (kpair @ sK3 @ X5) @ sK0)) & ($true = (in @ (kpair @ X5 @ sK4) @ sK2)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2))) & ((in @ X5 @ sK1) = $true)) & ($true = (in @ sK4 @ sK1)))),
% 1.63/1.35 introduced(definition,[],[choice_axiom])).
% 1.63/1.35 thf(f23,plain,(
% 1.63/1.35 ? [X5 : $i] : (($true = (in @ (kpair @ sK3 @ X5) @ sK0)) & ($true = (in @ (kpair @ X5 @ sK4) @ sK2)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2))) & ((in @ X5 @ sK1) = $true)) => (($true = (in @ (kpair @ sK3 @ sK5) @ sK0)) & ($true = (in @ (kpair @ sK5 @ sK4) @ sK2)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2))) & ($true = (in @ sK5 @ sK1)))),
% 1.63/1.35 introduced(definition,[],[choice_axiom])).
% 1.63/1.35 thf(f18,plain,(
% 1.63/1.35 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ? [X4 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ X0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true) & ((in @ X5 @ X1) = $true)) & ((in @ X4 @ X1) = $true))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))) & (dpsetconstrI = $true)),
% 1.63/1.35 inference(flattening,[status(thm)],[f17])).
% 1.63/1.35 thf(f17,plain,(
% 1.63/1.35 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : (((((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true) & ($true = (in @ (kpair @ X5 @ X4) @ X2))) & ($true = (in @ (kpair @ X3 @ X5) @ X0))) & ((in @ X5 @ X1) = $true)) & ((in @ X4 @ X1) = $true)) & ((in @ X3 @ X1) = $true)) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))) & (dpsetconstrI = $true)),
% 1.63/1.35 inference(ennf_transformation,[status(thm)],[f15])).
% 1.63/1.35 thf(f15,plain,(
% 1.63/1.35 ~((dpsetconstrI = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X1 @ X0)) => ! [X2 : $i] : (($true = (breln1 @ X1 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ! [X4 : $i] : (((in @ X4 @ X1) = $true) => ! [X5 : $i] : (((in @ X5 @ X1) = $true) => (($true = (in @ (kpair @ X3 @ X5) @ X0)) => (($true = (in @ (kpair @ X5 @ X4) @ X2)) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)))))))))),
% 1.63/1.35 inference(fool_elimination,[status(thm)],[f14])).
% 1.63/1.35 thf(f14,plain,(
% 1.63/1.35 ~(dpsetconstrI => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X3 @ X5) @ X0) => ((in @ (kpair @ X5 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2))))))))))),
% 1.63/1.35 inference(rectify,[status(thm)],[f6])).
% 1.63/1.35 thf(f6,negated_conjecture,(
% 1.63/1.35 ~(dpsetconstrI => ! [X8 : $i,X0 : $i] : ((breln1 @ X0 @ X8) => ! [X9 : $i] : ((breln1 @ X0 @ X9) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X4 @ X6) @ X8) => ((in @ (kpair @ X6 @ X5) @ X9) => (in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9))))))))))),
% 1.63/1.35 inference(negated_conjecture,[status(cth)],[f5])).
% 1.63/1.35 thf(f5,conjecture,(
% 1.63/1.35 dpsetconstrI => ! [X8 : $i,X0 : $i] : ((breln1 @ X0 @ X8) => ! [X9 : $i] : ((breln1 @ X0 @ X9) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X4 @ X6) @ X8) => ((in @ (kpair @ X6 @ X5) @ X9) => (in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9)))))))))),
% 1.63/1.35 file('/export/starexec/sandbox/tmp/tmp.HkcHQWNYrS/DTF2THF_9238.p',breln1compI)).
% 1.63/1.35 thf(f74,plain,(
% 1.63/1.35 ($false = (in @ (kpair @ sK5 @ sK4) @ sK2)) | ($false = (in @ sK5 @ sK1))),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.63/1.35 thf(f72,plain,(
% 1.63/1.35 ($true = $false) | ($false = (in @ sK5 @ sK1)) | ($false = (in @ (kpair @ sK5 @ sK4) @ sK2))),
% 1.63/1.35 inference(superposition,[status(thm)],[f35,f70])).
% 1.63/1.35 thf(f70,plain,(
% 1.63/1.35 ( ! [X1 : $i] : (($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ($false = (in @ X1 @ sK1))) )),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.63/1.35 thf(f69,plain,(
% 1.63/1.35 ( ! [X1 : $i] : (($false = (in @ X1 @ sK1)) | ($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ($true = $false)) )),
% 1.63/1.35 inference(forward_demodulation,[status(thm)],[f68,f31])).
% 1.63/1.35 thf(f31,plain,(
% 1.63/1.35 ($true = (in @ sK4 @ sK1))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.35 thf(f68,plain,(
% 1.63/1.35 ( ! [X1 : $i] : (((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ($false = (in @ X1 @ sK1)) | ($false = (in @ sK4 @ sK1)) | ($false = (in @ (kpair @ sK3 @ X1) @ sK0))) )),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.63/1.35 thf(f67,plain,(
% 1.63/1.35 ( ! [X1 : $i] : (($false = (in @ sK4 @ sK1)) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ($true = $false) | ($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ($false = (in @ X1 @ sK1))) )),
% 1.63/1.35 inference(forward_demodulation,[status(thm)],[f66,f36])).
% 1.63/1.35 thf(f36,plain,(
% 1.63/1.35 ($true = (in @ sK3 @ sK1))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.35 thf(f66,plain,(
% 1.63/1.35 ( ! [X1 : $i] : (($false = (in @ sK3 @ sK1)) | ($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ($false = (in @ sK4 @ sK1)) | ($false = (in @ X1 @ sK1)) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false)) )),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.63/1.35 thf(f65,plain,(
% 1.63/1.35 ( ! [X1 : $i] : (($false = (in @ sK3 @ sK1)) | ($false = ((in @ (kpair @ X1 @ sK4) @ sK2) & (in @ (kpair @ sK3 @ X1) @ sK0))) | ($false = (in @ sK4 @ sK1)) | ($false = (in @ X1 @ sK1))) )),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.63/1.35 thf(f64,plain,(
% 1.63/1.35 ( ! [X1 : $i] : (($false = (in @ sK4 @ sK1)) | ($false = (in @ sK3 @ sK1)) | ($false = (((in @ (kpair @ X1 @ sK4) @ sK2) & (in @ (kpair @ sK3 @ X1) @ sK0)) & (in @ X1 @ sK1)))) )),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.63/1.35 thf(f63,plain,(
% 1.63/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((in @ (kpair @ Y0 @ sK4) @ sK2) & (in @ (kpair @ sK3 @ Y0) @ sK0)) & (in @ Y0 @ sK1))) @ X1) = $false) | ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK4 @ sK1))) )),
% 1.63/1.35 inference(pi_clausification,[status(thm)],[f62])).
% 1.63/1.35 thf(f62,plain,(
% 1.63/1.35 ($false = (in @ sK4 @ sK1)) | ($false = (?? @ $i @ (^[Y0 : $i]: (((in @ (kpair @ Y0 @ sK4) @ sK2) & (in @ (kpair @ sK3 @ Y0) @ sK0)) & (in @ Y0 @ sK1))))) | ($false = (in @ sK3 @ sK1))),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.63/1.35 thf(f61,plain,(
% 1.63/1.35 ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK4 @ sK1)) | (((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y2 @ Y1) @ sK2) & (in @ (kpair @ Y0 @ Y2) @ sK0)) & (in @ Y2 @ sK1))))))) @ sK3 @ sK4) = $false)),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.63/1.35 thf(f60,plain,(
% 1.63/1.35 ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK4 @ sK1)) | (((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y2 @ Y1) @ sK2) & (in @ (kpair @ Y0 @ Y2) @ sK0)) & (in @ Y2 @ sK1))))))) @ sK3 @ sK4) = $false) | ($true != $true)),
% 1.63/1.35 inference(superposition,[status(thm)],[f57,f56])).
% 1.63/1.35 thf(f56,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X3 @ X2 @ X1)) = $true) | ($false = (X1 @ X4 @ X5)) | ($false = (in @ X4 @ X3)) | ((in @ X5 @ X2) = $false)) )),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.63/1.35 thf(f55,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ X2) = $false) | ($false = (in @ X4 @ X3)) | ($true = ((X1 @ X4 @ X5) => (in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X3 @ X2 @ X1))))) )),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.63/1.35 thf(f54,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ X2) => ((X1 @ X4 @ X5) => (in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X3 @ X2 @ X1))))) | ($false = (in @ X4 @ X3))) )),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.63/1.35 thf(f53,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ X4 @ Y0) => (in @ (kpair @ X4 @ Y0) @ (dpsetconstr @ X3 @ X2 @ X1))))) @ X5) = $true) | ($false = (in @ X4 @ X3))) )),
% 1.63/1.35 inference(pi_clausification,[status(thm)],[f52])).
% 1.63/1.35 thf(f52,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ X4 @ Y0) => (in @ (kpair @ X4 @ Y0) @ (dpsetconstr @ X3 @ X2 @ X1)))))) = $true) | ($false = (in @ X4 @ X3))) )),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.63/1.35 thf(f51,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((in @ X4 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ X4 @ Y0) => (in @ (kpair @ X4 @ Y0) @ (dpsetconstr @ X3 @ X2 @ X1))))))))) )),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.63/1.35 thf(f50,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((X1 @ Y0 @ Y1) => (in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ X3 @ X2 @ X1)))))))) @ X4))) )),
% 1.63/1.35 inference(pi_clausification,[status(thm)],[f49])).
% 1.63/1.35 thf(f49,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((X1 @ Y0 @ Y1) => (in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ X3 @ X2 @ X1))))))))))) )),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.63/1.35 thf(f48,plain,(
% 1.63/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((X1 @ Y1 @ Y2) => (in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ Y0 @ X2 @ X1)))))))))) @ X3))) )),
% 1.63/1.35 inference(pi_clausification,[status(thm)],[f47])).
% 1.63/1.35 thf(f47,plain,(
% 1.63/1.35 ( ! [X2 : $i,X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((X1 @ Y1 @ Y2) => (in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ Y0 @ X2 @ X1))))))))))) = $true)) )),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.63/1.35 thf(f46,plain,(
% 1.63/1.35 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((X1 @ Y2 @ Y3) => (in @ (kpair @ Y2 @ Y3) @ (dpsetconstr @ Y1 @ Y0 @ X1)))))))))))) @ X2))) )),
% 1.63/1.35 inference(pi_clausification,[status(thm)],[f45])).
% 1.63/1.35 thf(f45,plain,(
% 1.63/1.35 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((X1 @ Y2 @ Y3) => (in @ (kpair @ Y2 @ Y3) @ (dpsetconstr @ Y1 @ Y0 @ X1))))))))))))) = $true)) )),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.63/1.35 thf(f44,plain,(
% 1.63/1.35 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y1 @ Y0)))))))))))))) @ X1))) )),
% 1.63/1.35 inference(pi_clausification,[status(thm)],[f43])).
% 1.63/1.35 thf(f43,plain,(
% 1.63/1.35 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y1 @ Y0))))))))))))))))),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.63/1.35 thf(f42,plain,(
% 1.63/1.35 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
% 1.63/1.35 inference(definition_unfolding,[status(thm)],[f28,f25])).
% 1.63/1.35 thf(f25,plain,(
% 1.63/1.35 (dpsetconstrI = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.35 thf(f13,plain,(
% 1.63/1.35 (dpsetconstrI = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
% 1.63/1.35 inference(fool_elimination,[status(thm)],[f12])).
% 1.63/1.35 thf(f12,plain,(
% 1.63/1.35 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o] : ((in @ X0 @ X1) => ! [X4 : $i] : ((in @ X4 @ X2) => ((X3 @ X0 @ X4) => (in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X1 @ X2 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6))))))) = dpsetconstrI)),
% 1.63/1.35 inference(rectify,[status(thm)],[f2])).
% 1.63/1.35 thf(f2,axiom,(
% 1.63/1.35 (! [X4 : $i,X0 : $i,X1 : $i,X3 : $i > $i > $o] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((X3 @ X4 @ X5) => (in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X0 @ X1 @ (^[X6 : $i, X7 : $i] : (X3 @ X6 @ X7))))))) = dpsetconstrI)),
% 1.63/1.35 file('/export/starexec/sandbox/tmp/tmp.HkcHQWNYrS/DTF2THF_9238.p',dpsetconstrI)).
% 1.63/1.35 thf(f28,plain,(
% 1.63/1.35 (dpsetconstrI = $true)),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.35 thf(f57,plain,(
% 1.63/1.35 ($true != (in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK1 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y2 @ Y1) @ sK2) & (in @ (kpair @ Y0 @ Y2) @ sK0)) & (in @ Y2 @ sK1))))))))))),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.63/1.35 thf(f39,plain,(
% 1.63/1.35 ($true != (in @ (kpair @ sK3 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y5 @ Y4) @ Y2) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ Y5 @ Y0))))))))))))) @ sK1 @ sK0 @ sK2)))),
% 1.63/1.35 inference(definition_unfolding,[status(thm)],[f33,f26])).
% 1.63/1.35 thf(f26,plain,(
% 1.63/1.35 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y5 @ Y4) @ Y2) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ Y5 @ Y0))))))))))))))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.35 thf(f11,plain,(
% 1.63/1.35 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y5 @ Y4) @ Y2) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ Y5 @ Y0))))))))))))))),
% 1.63/1.35 inference(fool_elimination,[status(thm)],[f10])).
% 1.63/1.35 thf(f10,plain,(
% 1.63/1.35 ((^[X0 : $i, X1 : $i, X2 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X3 : $i, X4 : $i] : (? [X5 : $i] : ((in @ X5 @ X0) & (in @ (kpair @ X3 @ X5) @ X1) & (in @ (kpair @ X5 @ X4) @ X2)))))) = breln1compset)),
% 1.63/1.35 inference(rectify,[status(thm)],[f4])).
% 1.63/1.35 thf(f4,axiom,(
% 1.63/1.35 ((^[X0 : $i, X8 : $i, X9 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (? [X6 : $i] : ((in @ X6 @ X0) & (in @ (kpair @ X4 @ X6) @ X8) & (in @ (kpair @ X6 @ X5) @ X9)))))) = breln1compset)),
% 1.63/1.35 file('/export/starexec/sandbox/tmp/tmp.HkcHQWNYrS/DTF2THF_9238.p',breln1compset)).
% 1.63/1.35 thf(f33,plain,(
% 1.63/1.35 ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2)))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.35 thf(f35,plain,(
% 1.63/1.35 ($true = (in @ (kpair @ sK3 @ sK5) @ sK0))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.35 thf(f34,plain,(
% 1.63/1.35 ($true = (in @ (kpair @ sK5 @ sK4) @ sK2))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.35 % SZS output end Proof for DTF2THF_9238
% 1.63/1.35 % (9338)------------------------------
% 1.63/1.35 % (9338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (9338)Termination reason: Refutation
% 1.63/1.35
% 1.63/1.35 % (9338)Memory used [KB]: 5628
% 1.63/1.35 % (9338)Time elapsed: 0.011 s
% 1.63/1.35 % (9338)Instructions burned: 10 (million)
% 1.63/1.35 % (9338)------------------------------
% 1.63/1.35 % (9338)------------------------------
% 1.63/1.35 % (9335)Success in time 0.024 s
%------------------------------------------------------------------------------