%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU776^2 : 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 : n011.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 09:37:06 AM UTC 2026
% Result : Theorem 1.72s 1.46s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 591 ( 151 equ; 0 cnn)
% Maximal formula atoms : 10 ( 14 avg)
% Number of connectives : 779 ( 67 ~; 43 |; 55 &; 577 @)
% ( 3 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 173 ( 62 ^; 76 !; 35 ?; 173 :)
% 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,
breln1invset: $i > $i > $i ).
thf(func_def_18,type,
sK2: $i > $i > $o ).
thf(func_def_27,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f59,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f58,f41]) ).
thf(f41,plain,
( ( in @ sK7 @ sK6 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( in @ sK7 @ sK6 )
= $true )
& ( ( in @ ( kpair @ sK7 @ sK8 ) @ sK5 )
= $true )
& ( ( in @ ( kpair @ sK8 @ sK7 ) @ ( breln1invset @ sK6 @ sK5 ) )
!= $true )
& ( ( in @ sK8 @ sK6 )
= $true )
& ( $true
= ( breln1 @ sK6 @ sK5 ) )
& ( dpsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f18,f28,f27,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ X0 ) )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
!= $true )
& ( $true
= ( in @ X3 @ X1 ) ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK6 ) )
& ? [X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ sK5 )
= $true )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ sK6 @ sK5 ) )
!= $true )
& ( ( in @ X3 @ sK6 )
= $true ) ) )
& ( $true
= ( breln1 @ sK6 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK6 ) )
& ? [X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ sK5 )
= $true )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ sK6 @ sK5 ) )
!= $true )
& ( ( in @ X3 @ sK6 )
= $true ) ) )
=> ( ( ( in @ sK7 @ sK6 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ ( kpair @ sK7 @ X3 ) @ sK5 ) )
& ( ( in @ ( kpair @ X3 @ sK7 ) @ ( breln1invset @ sK6 @ sK5 ) )
!= $true )
& ( ( in @ X3 @ sK6 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X3: $i] :
( ( $true
= ( in @ ( kpair @ sK7 @ X3 ) @ sK5 ) )
& ( ( in @ ( kpair @ X3 @ sK7 ) @ ( breln1invset @ sK6 @ sK5 ) )
!= $true )
& ( ( in @ X3 @ sK6 )
= $true ) )
=> ( ( ( in @ ( kpair @ sK7 @ sK8 ) @ sK5 )
= $true )
& ( ( in @ ( kpair @ sK8 @ sK7 ) @ ( breln1invset @ sK6 @ sK5 ) )
!= $true )
& ( ( in @ sK8 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ X0 ) )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
!= $true )
& ( $true
= ( in @ X3 @ X1 ) ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( dpsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
!= $true )
& ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ X0 ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( dpsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ( dpsetconstrI = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ X0 ) )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( dpsetconstrI
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X0 )
=> ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dpsetconstrI
=> ! [X8: $i,X0: $i] :
( ( breln1 @ X0 @ X8 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X8 )
=> ( in @ ( kpair @ X5 @ X4 ) @ ( breln1invset @ X0 @ X8 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dpsetconstrI
=> ! [X8: $i,X0: $i] :
( ( breln1 @ X0 @ X8 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X8 )
=> ( in @ ( kpair @ X5 @ X4 ) @ ( breln1invset @ X0 @ X8 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8S12mcaO3N/DTF2THF_32208.p',breln1invI) ).
thf(f58,plain,
( ( in @ sK7 @ sK6 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f57,f40]) ).
thf(f40,plain,
( ( in @ ( kpair @ sK7 @ sK8 ) @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f57,plain,
( ( ( in @ ( kpair @ sK7 @ sK8 ) @ sK5 )
!= $true )
| ( ( in @ sK7 @ sK6 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f56,f38]) ).
thf(f38,plain,
( ( in @ sK8 @ sK6 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f56,plain,
( ( ( in @ sK8 @ sK6 )
!= $true )
| ( ( in @ ( kpair @ sK7 @ sK8 ) @ sK5 )
!= $true )
| ( ( in @ sK7 @ sK6 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( in @ sK8 @ sK6 )
!= $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK5 )
@ sK8
@ sK7 )
!= $true )
| ( ( in @ sK7 @ sK6 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $true != $true )
| ( ( in @ sK7 @ sK6 )
!= $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK5 )
@ sK8
@ sK7 )
!= $true )
| ( ( in @ sK8 @ sK6 )
!= $true ) ),
inference(superposition,[status(thm)],[f53,f52]) ).
thf(f52,plain,
! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ X0 @ X4 ) @ ( dpsetconstr @ X3 @ X1 @ X2 ) )
= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ X3 ) )
| ( $true
!= ( X2 @ X0 @ X4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true )
| ( $true
!= ( in @ X0 @ X3 ) )
| ( $true
!= ( X2 @ X0 @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X0 @ X3 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( $true != $true )
| ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true )
| ( $true
!= ( X2 @ X0 @ X4 ) ) ),
inference(definition_unfolding,[status(thm)],[f34,f36]) ).
thf(f36,plain,
dpsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f34,plain,
! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X0 @ X3 ) )
| ( $true
!= ( X2 @ X0 @ X4 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true )
| ( dpsetconstrI != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( $true
!= ( in @ X0 @ X3 ) )
| ! [X4: $i] :
( ( $true
!= ( X2 @ X0 @ X4 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true ) ) )
| ( dpsetconstrI != $true ) )
& ( ( dpsetconstrI = $true )
| ( ( $true
= ( in @ sK0 @ sK3 ) )
& ( ( sK2 @ sK0 @ sK4 )
= $true )
& ( ( in @ sK4 @ sK1 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK0 @ sK4 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f22,f24,f23]) ).
thf(f23,plain,
( ? [X5: $i,X6: $i,X7: $i > $i > $o,X8: $i] :
( ( ( in @ X5 @ X8 )
= $true )
& ? [X9: $i] :
( ( $true
= ( X7 @ X5 @ X9 ) )
& ( $true
= ( in @ X9 @ X6 ) )
& ( $true
!= ( in @ ( kpair @ X5 @ X9 )
@ ( dpsetconstr @ X8 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X7 @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( $true
= ( in @ sK0 @ sK3 ) )
& ? [X9: $i] :
( ( $true
= ( sK2 @ sK0 @ X9 ) )
& ( ( in @ X9 @ sK1 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK0 @ X9 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X9: $i] :
( ( $true
= ( sK2 @ sK0 @ X9 ) )
& ( ( in @ X9 @ sK1 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK0 @ X9 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( sK2 @ sK0 @ sK4 )
= $true )
& ( ( in @ sK4 @ sK1 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK0 @ sK4 )
@ ( dpsetconstr @ sK3 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( $true
!= ( in @ X0 @ X3 ) )
| ! [X4: $i] :
( ( $true
!= ( X2 @ X0 @ X4 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true ) ) )
| ( dpsetconstrI != $true ) )
& ( ( dpsetconstrI = $true )
| ? [X5: $i,X6: $i,X7: $i > $i > $o,X8: $i] :
( ( ( in @ X5 @ X8 )
= $true )
& ? [X9: $i] :
( ( $true
= ( X7 @ X5 @ X9 ) )
& ( $true
= ( in @ X9 @ X6 ) )
& ( $true
!= ( in @ ( kpair @ X5 @ X9 )
@ ( dpsetconstr @ X8 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X7 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( $true
!= ( in @ X0 @ X3 ) )
| ! [X4: $i] :
( ( $true
!= ( X2 @ X0 @ X4 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true ) ) )
| ( dpsetconstrI != $true ) )
& ( ( dpsetconstrI = $true )
| ? [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( $true
= ( in @ X0 @ X3 ) )
& ? [X4: $i] :
( ( $true
= ( X2 @ X0 @ X4 ) )
& ( ( in @ X4 @ X1 )
= $true )
& ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( $true
!= ( in @ X0 @ X3 ) )
| ! [X4: $i] :
( ( $true
!= ( X2 @ X0 @ X4 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true ) ) )
<=> ( dpsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true )
| ( $true
!= ( X2 @ X0 @ X4 ) )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X0 @ X3 ) ) )
<=> ( dpsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( $true
= ( in @ X0 @ X3 ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( $true
= ( X2 @ X0 @ X4 ) )
=> ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true ) ) ) )
<=> ( dpsetconstrI = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( dpsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X0 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X0 @ X4 )
=> ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( dpsetconstrI
= ( ! [X4: $i,X1: $i,X3: $i > $i > $o,X0: $i] :
( ( 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8S12mcaO3N/DTF2THF_32208.p',dpsetconstrI) ).
thf(f53,plain,
( ( in @ ( kpair @ sK8 @ sK7 )
@ ( dpsetconstr @ sK6 @ sK6
@ ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK5 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
( $true
!= ( in @ ( kpair @ sK8 @ sK7 )
@ ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) )
@ sK6
@ sK5 ) ) ),
inference(definition_unfolding,[status(thm)],[f39,f42]) ).
thf(f42,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i,X1: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ X1 ) ) )
= breln1invset ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X8: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X4: $i,X5: $i] : ( in @ ( kpair @ X5 @ X4 ) @ X8 ) ) )
= breln1invset ),
file('/export/starexec/sandbox/tmp/tmp.8S12mcaO3N/DTF2THF_32208.p',breln1invset) ).
thf(f39,plain,
( ( in @ ( kpair @ sK8 @ sK7 ) @ ( breln1invset @ sK6 @ sK5 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU776^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:33:17 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : SEU776^2 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.48 % Domain : Set Theory
% 0.32/0.48 % Problem : Binary Relations on a Set
% 0.32/0.48 % Version : Especial > Reduced > Especial.
% 0.32/0.48 % English : (! A:i.! R:i.breln1 A R -> (! x:i.in x A -> (! y:i.in y A ->
% 0.32/0.48 % in (kpair x y) R -> in (kpair y x) (breln1invset A R))))
% 0.32/0.48
% 0.32/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.48 % Source : [Bro08]
% 0.32/0.48 % Names : ZFC278l [Bro08]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.36 v7.5.0, 0.14 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, 0.14 v6.0.0, 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, 0.33 v4.0.0, 0.67 v3.7.0
% 0.32/0.48 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.32/0.48 % Number of atoms : 19 ( 4 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 6 ( 3 avg)
% 0.32/0.48 % Number of connectives : 53 ( 0 ~; 0 |; 0 &; 45 @)
% 0.32/0.48 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 14 ( 4 avg)
% 0.32/0.48 % Number of types : 2 ( 0 usr)
% 0.32/0.48 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% 0.32/0.48 % Number of variables : 20 ( 11 ^; 9 !; 0 ?; 20 :)
% 0.32/0.48 % SPC : TH0_THM_EQU_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : http://mathgate.info/detsetitem.php?id=336
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 thf(in_type,type,
% 0.32/0.48 in: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(subset_type,type,
% 0.32/0.48 subset: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(kpair_type,type,
% 0.32/0.48 kpair: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(cartprod_type,type,
% 0.32/0.48 cartprod: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(breln_type,type,
% 0.32/0.48 breln: $i > $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(breln,definition,
% 0.32/0.48 ( breln
% 0.32/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstr_type,type,
% 0.32/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrI_type,type,
% 0.32/0.48 dpsetconstrI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrI,definition,
% 0.32/0.48 ( dpsetconstrI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( Xphi @ Xx @ Xy )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(breln1_type,type,
% 0.32/0.48 breln1: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(breln1,definition,
% 0.32/0.48 ( breln1
% 0.32/0.48 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(breln1invset_type,type,
% 0.32/0.48 breln1invset: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(breln1invset,definition,
% 0.32/0.48 ( breln1invset
% 0.32/0.48 = ( ^ [A: $i,R: $i] :
% 0.32/0.48 ( dpsetconstr @ A @ A
% 0.32/0.48 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(breln1invI,conjecture,
% 0.32/0.48 ( dpsetconstrI
% 0.32/0.48 => ! [A: $i,R: $i] :
% 0.32/0.48 ( ( breln1 @ A @ R )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.48 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 1.72/1.42 ---- Embedded in THF ---
% 1.72/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.42 %%% Generated on Tue Feb 24 12:33:18 EST 2026
% 1.72/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.42 %%% Logic specification used:
% 1.72/1.42 %%% thf(spec, logic, $$dhol).
% 1.72/1.42
% 1.72/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8S12mcaO3N/DTF2DTF32208.p
% See solution above
% 1.72/1.43 ------------------------
% 1.72/1.43 ---- Cleaned THF ---
% 1.72/1.43 thf(in_type,type,
% 1.72/1.43 in: $i > $i > $o ).
% 1.72/1.43
% 1.72/1.43 thf(subset_type,type,
% 1.72/1.43 subset: $i > $i > $o ).
% 1.72/1.43
% 1.72/1.43 thf(kpair_type,type,
% 1.72/1.43 kpair: $i > $i > $i ).
% 1.72/1.43
% 1.72/1.43 thf(cartprod_type,type,
% 1.72/1.43 cartprod: $i > $i > $i ).
% 1.72/1.43
% 1.72/1.43 thf(breln_type,type,
% 1.72/1.43 breln: $i > $i > $i > $o ).
% 1.72/1.43
% 1.72/1.43 thf(breln,definition,
% 1.72/1.43 ( breln
% 1.72/1.43 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf(dpsetconstr_type,type,
% 1.72/1.43 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.72/1.43
% 1.72/1.43 thf(dpsetconstrI_type,type,
% 1.72/1.43 dpsetconstrI: $o ).
% 1.72/1.43
% 1.72/1.43 thf(dpsetconstrI,definition,
% 1.72/1.43 ( dpsetconstrI
% 1.72/1.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 1.72/1.43 ( ( in @ Xx @ A )
% 1.72/1.43 => ! [Xy: $i] :
% 1.72/1.43 ( ( in @ Xy @ B )
% 1.72/1.43 => ( ( Xphi @ Xx @ Xy )
% 1.72/1.43 => ( in @ ( kpair @ Xx @ Xy )
% 1.72/1.43 @ ( dpsetconstr @ A @ B
% 1.72/1.43 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf(breln1_type,type,
% 1.72/1.43 breln1: $i > $i > $o ).
% 1.72/1.43
% 1.72/1.43 thf(breln1,definition,
% 1.72/1.43 ( breln1
% 1.72/1.43 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf(breln1invset_type,type,
% 1.72/1.43 breln1invset: $i > $i > $i ).
% 1.72/1.43
% 1.72/1.43 thf(breln1invset,definition,
% 1.72/1.43 ( breln1invset
% 1.72/1.43 = ( ^ [A: $i,R: $i] :
% 1.72/1.43 ( dpsetconstr @ A @ A
% 1.72/1.43 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf(breln1invI,conjecture,
% 1.72/1.43 ( dpsetconstrI
% 1.72/1.43 => ! [A: $i,R: $i] :
% 1.72/1.43 ( ( breln1 @ A @ R )
% 1.72/1.43 => ! [Xx: $i] :
% 1.72/1.43 ( ( in @ Xx @ A )
% 1.72/1.43 => ! [Xy: $i] :
% 1.72/1.43 ( ( in @ Xy @ A )
% 1.72/1.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.72/1.43 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 1.72/1.43 ------------------------
% 1.72/1.45 % (32338)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32208 for (2999ds/2Mi)
% 1.72/1.45 % (32336)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_32208 for (2999ds/4Mi)
% 1.72/1.45 % (32340)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_32208 for (2999ds/275Mi)
% 1.72/1.45 % (32339)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_32208 for (2999ds/2Mi)
% 1.72/1.45 % (32335)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32208 for (2999ds/183Mi)
% 1.72/1.45 % (32337)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_32208 for (2999ds/27Mi)
% 1.72/1.45 % (32341)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32208 for (2999ds/18Mi)
% 1.72/1.46 % (32338)Instruction limit reached!
% 1.72/1.46 % (32338)------------------------------
% 1.72/1.46 % (32338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (32338)Termination reason: Unknown
% 1.72/1.46 % (32338)Termination phase: Property scanning
% 1.72/1.46
% 1.72/1.46 % (32339)Instruction limit reached!
% 1.72/1.46 % (32339)------------------------------
% 1.72/1.46 % (32339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (32338)Memory used [KB]: 1023
% 1.72/1.46 % (32338)Time elapsed: 0.003 s
% 1.72/1.46 % (32338)Instructions burned: 3 (million)
% 1.72/1.46 % (32338)------------------------------
% 1.72/1.46 % (32338)------------------------------
% 1.72/1.46 % (32339)Termination reason: Unknown
% 1.72/1.46 % (32339)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (32339)Memory used [KB]: 1023
% 1.72/1.46 % (32339)Time elapsed: 0.003 s
% 1.72/1.46 % (32339)Instructions burned: 3 (million)
% 1.72/1.46 % (32339)------------------------------
% 1.72/1.46 % (32339)------------------------------
% 1.72/1.46 % (32336)Instruction limit reached!
% 1.72/1.46 % (32336)------------------------------
% 1.72/1.46 % (32336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (32336)Termination reason: Unknown
% 1.72/1.46 % (32336)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (32336)Memory used [KB]: 5500
% 1.72/1.46 % (32336)Time elapsed: 0.004 s
% 1.72/1.46 % (32336)Instructions burned: 4 (million)
% 1.72/1.46 % (32336)------------------------------
% 1.72/1.46 % (32336)------------------------------
% 1.72/1.46 % (32340)First to succeed.
% 1.72/1.46 % (32337)Also succeeded, but the first one will report.
% 1.72/1.46 % (32340)Refutation found. Thanks to Tanya!
% 1.72/1.46 % SZS status Theorem for DTF2THF_32208
% 1.72/1.46 % SZS output start Proof for DTF2THF_32208
% 1.72/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.72/1.46 thf(func_def_1, type, subset: $i > $i > $o).
% 1.72/1.46 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.72/1.46 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.72/1.46 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.72/1.46 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.72/1.46 thf(func_def_8, type, breln1: $i > $i > $o).
% 1.72/1.46 thf(func_def_9, type, breln1invset: $i > $i > $i).
% 1.72/1.46 thf(func_def_18, type, sK2: $i > $i > $o).
% 1.72/1.46 thf(func_def_27, type, ph10: !>[X0: $tType]:(X0)).
% 1.72/1.46 thf(f59,plain,(
% 1.72/1.46 $false),
% 1.72/1.46 inference(subsumption_resolution,[status(thm)],[f58,f41])).
% 1.72/1.46 thf(f41,plain,(
% 1.72/1.46 ((in @ sK7 @ sK6) = $true)),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f29])).
% 1.72/1.46 thf(f29,plain,(
% 1.72/1.46 ((((in @ sK7 @ sK6) = $true) & (((in @ (kpair @ sK7 @ sK8) @ sK5) = $true) & ((in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK6 @ sK5)) != $true) & ((in @ sK8 @ sK6) = $true))) & ($true = (breln1 @ sK6 @ sK5))) & (dpsetconstrI = $true)),
% 1.72/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f18,f28,f27,f26])).
% 1.72/1.46 thf(f26,plain,(
% 1.72/1.46 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ? [X3 : $i] : (($true = (in @ (kpair @ X2 @ X3) @ X0)) & ((in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0)) != $true) & ($true = (in @ X3 @ X1)))) & ($true = (breln1 @ X1 @ X0))) => (? [X2 : $i] : (($true = (in @ X2 @ sK6)) & ? [X3 : $i] : (((in @ (kpair @ X2 @ X3) @ sK5) = $true) & ((in @ (kpair @ X3 @ X2) @ (breln1invset @ sK6 @ sK5)) != $true) & ((in @ X3 @ sK6) = $true))) & ($true = (breln1 @ sK6 @ sK5)))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f27,plain,(
% 1.72/1.46 ? [X2 : $i] : (($true = (in @ X2 @ sK6)) & ? [X3 : $i] : (((in @ (kpair @ X2 @ X3) @ sK5) = $true) & ((in @ (kpair @ X3 @ X2) @ (breln1invset @ sK6 @ sK5)) != $true) & ((in @ X3 @ sK6) = $true))) => (((in @ sK7 @ sK6) = $true) & ? [X3 : $i] : (($true = (in @ (kpair @ sK7 @ X3) @ sK5)) & ((in @ (kpair @ X3 @ sK7) @ (breln1invset @ sK6 @ sK5)) != $true) & ((in @ X3 @ sK6) = $true)))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f28,plain,(
% 1.72/1.46 ? [X3 : $i] : (($true = (in @ (kpair @ sK7 @ X3) @ sK5)) & ((in @ (kpair @ X3 @ sK7) @ (breln1invset @ sK6 @ sK5)) != $true) & ((in @ X3 @ sK6) = $true)) => (((in @ (kpair @ sK7 @ sK8) @ sK5) = $true) & ((in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK6 @ sK5)) != $true) & ((in @ sK8 @ sK6) = $true))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f18,plain,(
% 1.72/1.46 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ? [X3 : $i] : (($true = (in @ (kpair @ X2 @ X3) @ X0)) & ((in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0)) != $true) & ($true = (in @ X3 @ X1)))) & ($true = (breln1 @ X1 @ X0))) & (dpsetconstrI = $true)),
% 1.72/1.46 inference(flattening,[status(thm)],[f17])).
% 1.72/1.46 thf(f17,plain,(
% 1.72/1.46 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0)) != $true) & ($true = (in @ (kpair @ X2 @ X3) @ X0))) & ($true = (in @ X3 @ X1))) & ($true = (in @ X2 @ X1))) & ($true = (breln1 @ X1 @ X0))) & (dpsetconstrI = $true)),
% 1.72/1.46 inference(ennf_transformation,[status(thm)],[f16])).
% 1.72/1.46 thf(f16,plain,(
% 1.72/1.46 ~((dpsetconstrI = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X1 @ X0)) => ! [X2 : $i] : (($true = (in @ X2 @ X1)) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => (($true = (in @ (kpair @ X2 @ X3) @ X0)) => ((in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0)) = $true))))))),
% 1.72/1.46 inference(fool_elimination,[status(thm)],[f15])).
% 1.72/1.46 thf(f15,plain,(
% 1.72/1.46 ~(dpsetconstrI => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ (kpair @ X2 @ X3) @ X0) => (in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0)))))))),
% 1.72/1.46 inference(rectify,[status(thm)],[f6])).
% 1.72/1.46 thf(f6,negated_conjecture,(
% 1.72/1.46 ~(dpsetconstrI => ! [X8 : $i,X0 : $i] : ((breln1 @ X0 @ X8) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X8) => (in @ (kpair @ X5 @ X4) @ (breln1invset @ X0 @ X8)))))))),
% 1.72/1.46 inference(negated_conjecture,[status(cth)],[f5])).
% 1.72/1.46 thf(f5,conjecture,(
% 1.72/1.46 dpsetconstrI => ! [X8 : $i,X0 : $i] : ((breln1 @ X0 @ X8) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X8) => (in @ (kpair @ X5 @ X4) @ (breln1invset @ X0 @ X8))))))),
% 1.72/1.46 file('/export/starexec/sandbox/tmp/tmp.8S12mcaO3N/DTF2THF_32208.p',breln1invI)).
% 1.72/1.46 thf(f58,plain,(
% 1.72/1.46 ((in @ sK7 @ sK6) != $true)),
% 1.72/1.46 inference(subsumption_resolution,[status(thm)],[f57,f40])).
% 1.72/1.46 thf(f40,plain,(
% 1.72/1.46 ((in @ (kpair @ sK7 @ sK8) @ sK5) = $true)),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f29])).
% 1.72/1.46 thf(f57,plain,(
% 1.72/1.46 ((in @ (kpair @ sK7 @ sK8) @ sK5) != $true) | ((in @ sK7 @ sK6) != $true)),
% 1.72/1.46 inference(subsumption_resolution,[status(thm)],[f56,f38])).
% 1.72/1.46 thf(f38,plain,(
% 1.72/1.46 ((in @ sK8 @ sK6) = $true)),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f29])).
% 1.72/1.46 thf(f56,plain,(
% 1.72/1.46 ((in @ sK8 @ sK6) != $true) | ((in @ (kpair @ sK7 @ sK8) @ sK5) != $true) | ((in @ sK7 @ sK6) != $true)),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.72/1.46 thf(f55,plain,(
% 1.72/1.46 ((in @ sK8 @ sK6) != $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK5)))) @ sK8 @ sK7) != $true) | ((in @ sK7 @ sK6) != $true)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.72/1.46 thf(f54,plain,(
% 1.72/1.46 ($true != $true) | ((in @ sK7 @ sK6) != $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK5)))) @ sK8 @ sK7) != $true) | ((in @ sK8 @ sK6) != $true)),
% 1.72/1.46 inference(superposition,[status(thm)],[f53,f52])).
% 1.72/1.46 thf(f52,plain,(
% 1.72/1.46 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ X2)) = $true) | ((in @ X4 @ X1) != $true) | ($true != (in @ X0 @ X3)) | ($true != (X2 @ X0 @ X4))) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.72/1.46 thf(f51,plain,(
% 1.72/1.46 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ X1) != $true) | ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true) | ($true != (in @ X0 @ X3)) | ($true != (X2 @ X0 @ X4))) )),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.72/1.46 thf(f43,plain,(
% 1.72/1.46 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ X0 @ X3)) | ((in @ X4 @ X1) != $true) | ($true != $true) | ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true) | ($true != (X2 @ X0 @ X4))) )),
% 1.72/1.46 inference(definition_unfolding,[status(thm)],[f34,f36])).
% 1.72/1.46 thf(f36,plain,(
% 1.72/1.46 (dpsetconstrI = $true)),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f29])).
% 1.72/1.46 thf(f34,plain,(
% 1.72/1.46 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ X0 @ X3)) | ($true != (X2 @ X0 @ X4)) | ((in @ X4 @ X1) != $true) | ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true) | (dpsetconstrI != $true)) )),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f25])).
% 1.72/1.46 thf(f25,plain,(
% 1.72/1.46 (! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i] : (($true != (in @ X0 @ X3)) | ! [X4 : $i] : (($true != (X2 @ X0 @ X4)) | ((in @ X4 @ X1) != $true) | ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true))) | (dpsetconstrI != $true)) & ((dpsetconstrI = $true) | (($true = (in @ sK0 @ sK3)) & (((sK2 @ sK0 @ sK4) = $true) & ((in @ sK4 @ sK1) = $true) & ($true != (in @ (kpair @ sK0 @ sK4) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))))))))),
% 1.72/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f22,f24,f23])).
% 1.72/1.46 thf(f23,plain,(
% 1.72/1.46 ? [X5 : $i,X6 : $i,X7 : $i > $i > $o,X8 : $i] : (((in @ X5 @ X8) = $true) & ? [X9 : $i] : (($true = (X7 @ X5 @ X9)) & ($true = (in @ X9 @ X6)) & ($true != (in @ (kpair @ X5 @ X9) @ (dpsetconstr @ X8 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1))))))))) => (($true = (in @ sK0 @ sK3)) & ? [X9 : $i] : (($true = (sK2 @ sK0 @ X9)) & ((in @ X9 @ sK1) = $true) & ($true != (in @ (kpair @ sK0 @ X9) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1)))))))))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f24,plain,(
% 1.72/1.46 ? [X9 : $i] : (($true = (sK2 @ sK0 @ X9)) & ((in @ X9 @ sK1) = $true) & ($true != (in @ (kpair @ sK0 @ X9) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1)))))))) => (((sK2 @ sK0 @ sK4) = $true) & ((in @ sK4 @ sK1) = $true) & ($true != (in @ (kpair @ sK0 @ sK4) @ (dpsetconstr @ sK3 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK2 @ Y0 @ Y1))))))))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f22,plain,(
% 1.72/1.46 (! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i] : (($true != (in @ X0 @ X3)) | ! [X4 : $i] : (($true != (X2 @ X0 @ X4)) | ((in @ X4 @ X1) != $true) | ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true))) | (dpsetconstrI != $true)) & ((dpsetconstrI = $true) | ? [X5 : $i,X6 : $i,X7 : $i > $i > $o,X8 : $i] : (((in @ X5 @ X8) = $true) & ? [X9 : $i] : (($true = (X7 @ X5 @ X9)) & ($true = (in @ X9 @ X6)) & ($true != (in @ (kpair @ X5 @ X9) @ (dpsetconstr @ X8 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1))))))))))),
% 1.72/1.46 inference(rectify,[status(thm)],[f21])).
% 1.72/1.46 thf(f21,plain,(
% 1.72/1.46 (! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i] : (($true != (in @ X0 @ X3)) | ! [X4 : $i] : (($true != (X2 @ X0 @ X4)) | ((in @ X4 @ X1) != $true) | ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true))) | (dpsetconstrI != $true)) & ((dpsetconstrI = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i] : (($true = (in @ X0 @ X3)) & ? [X4 : $i] : (($true = (X2 @ X0 @ X4)) & ((in @ X4 @ X1) = $true) & ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) != $true))))),
% 1.72/1.46 inference(nnf_transformation,[status(thm)],[f20])).
% 1.72/1.46 thf(f20,plain,(
% 1.72/1.46 ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i] : (($true != (in @ X0 @ X3)) | ! [X4 : $i] : (($true != (X2 @ X0 @ X4)) | ((in @ X4 @ X1) != $true) | ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true))) <=> (dpsetconstrI = $true)),
% 1.72/1.46 inference(flattening,[status(thm)],[f19])).
% 1.72/1.46 thf(f19,plain,(
% 1.72/1.46 ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i] : (! [X4 : $i] : ((((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true) | ($true != (X2 @ X0 @ X4))) | ((in @ X4 @ X1) != $true)) | ($true != (in @ X0 @ X3))) <=> (dpsetconstrI = $true)),
% 1.72/1.46 inference(ennf_transformation,[status(thm)],[f14])).
% 1.72/1.46 thf(f14,plain,(
% 1.72/1.46 ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i] : (($true = (in @ X0 @ X3)) => ! [X4 : $i] : (((in @ X4 @ X1) = $true) => (($true = (X2 @ X0 @ X4)) => ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))) = $true)))) <=> (dpsetconstrI = $true)),
% 1.72/1.46 inference(fool_elimination,[status(thm)],[f13])).
% 1.72/1.46 thf(f13,plain,(
% 1.72/1.46 (dpsetconstrI = ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i] : ((in @ X0 @ X3) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X2 @ X0 @ X4) => (in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6))))))))),
% 1.72/1.46 inference(rectify,[status(thm)],[f2])).
% 1.72/1.46 thf(f2,axiom,(
% 1.72/1.46 (dpsetconstrI = ! [X4 : $i,X1 : $i,X3 : $i > $i > $o,X0 : $i] : ((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))))))))),
% 1.72/1.46 file('/export/starexec/sandbox/tmp/tmp.8S12mcaO3N/DTF2THF_32208.p',dpsetconstrI)).
% 1.72/1.46 thf(f53,plain,(
% 1.72/1.46 ((in @ (kpair @ sK8 @ sK7) @ (dpsetconstr @ sK6 @ sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK5)))))) != $true)),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.72/1.46 thf(f48,plain,(
% 1.72/1.46 ($true != (in @ (kpair @ sK8 @ sK7) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))) @ sK6 @ sK5)))),
% 1.72/1.46 inference(definition_unfolding,[status(thm)],[f39,f42])).
% 1.72/1.46 thf(f42,plain,(
% 1.72/1.46 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f10])).
% 1.72/1.46 thf(f10,plain,(
% 1.72/1.46 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 1.72/1.46 inference(fool_elimination,[status(thm)],[f9])).
% 1.72/1.46 thf(f9,plain,(
% 1.72/1.46 ((^[X0 : $i, X1 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : (in @ (kpair @ X3 @ X2) @ X1)))) = breln1invset)),
% 1.72/1.46 inference(rectify,[status(thm)],[f4])).
% 1.72/1.46 thf(f4,axiom,(
% 1.72/1.46 ((^[X0 : $i, X8 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (in @ (kpair @ X5 @ X4) @ X8)))) = breln1invset)),
% 1.72/1.46 file('/export/starexec/sandbox/tmp/tmp.8S12mcaO3N/DTF2THF_32208.p',breln1invset)).
% 1.72/1.46 thf(f39,plain,(
% 1.72/1.46 ((in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK6 @ sK5)) != $true)),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f29])).
% 1.72/1.46 % SZS output end Proof for DTF2THF_32208
% 1.72/1.46 % (32340)------------------------------
% 1.72/1.46 % (32340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (32340)Termination reason: Refutation
% 1.72/1.46
% 1.72/1.46 % (32340)Memory used [KB]: 5500
% 1.72/1.46 % (32340)Time elapsed: 0.007 s
% 1.72/1.46 % (32340)Instructions burned: 6 (million)
% 1.72/1.46 % (32340)------------------------------
% 1.72/1.46 % (32340)------------------------------
% 1.72/1.46 % (32334)Success in time 0.021 s
%------------------------------------------------------------------------------