%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU780^2 : 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 : n017.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 09:37:08 AM UTC 2026
% Result : Theorem 1.77s 1.46s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 683 ( 155 equ; 0 cnn)
% Maximal formula atoms : 16 ( 15 avg)
% Number of connectives : 964 ( 64 ~; 44 |; 85 &; 730 @)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 14 con; 0-3 aty)
% ( 0 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 204 ( 69 ^; 87 !; 48 ?; 204 :)
% 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_21,type,
sK0: $i > $i > $o ).
thf(func_def_33,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f66,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f65,f61]) ).
thf(f61,plain,
( $true
= ( in @ sK12 @ sK6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( $true
= ( ( in @ ( kpair @ sK8 @ sK12 ) @ sK5 )
& ( in @ sK12 @ sK6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( $true
= ( ( in @ ( kpair @ sK8 @ sK12 ) @ sK5 )
& ( in @ sK12 @ sK6 )
& ( in @ ( kpair @ sK12 @ sK9 ) @ sK7 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ^ [Y0: $i] :
( ( in @ ( kpair @ sK8 @ Y0 ) @ sK5 )
& ( in @ Y0 @ sK6 )
& ( in @ ( kpair @ Y0 @ sK9 ) @ sK7 ) )
@ sK12 )
= $true ),
inference(sigma_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ ( kpair @ sK8 @ Y0 ) @ sK5 )
& ( in @ Y0 @ sK6 )
& ( in @ ( kpair @ Y0 @ sK9 ) @ sK7 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y0 @ Y2 ) @ sK5 )
& ( in @ Y2 @ sK6 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK7 ) ) )
@ sK8
@ sK9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $true
= ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y0 @ Y2 ) @ sK5 )
& ( in @ Y2 @ sK6 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK7 ) ) )
@ sK8
@ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f51,f52]) ).
thf(f52,plain,
( ( in @ ( kpair @ sK8 @ sK9 )
@ ( dpsetconstr @ sK6 @ sK6
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y0 @ Y2 ) @ sK5 )
& ( in @ Y2 @ sK6 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK7 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
( ( in @ ( kpair @ sK8 @ sK9 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) )
@ sK6
@ sK5
@ sK7 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f37,f30]) ).
thf(f30,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ X5 @ X0 )
& ( in @ ( kpair @ X3 @ X5 ) @ X1 ) ) ) )
= 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 @ ( kpair @ X6 @ X5 ) @ X9 )
& ( in @ X6 @ X0 )
& ( in @ ( kpair @ X4 @ X6 ) @ X8 ) ) ) )
= breln1compset ),
file('/export/starexec/sandbox/tmp/tmp.YFdbAJDISU/DTF2THF_32096.p',breln1compset) ).
thf(f37,plain,
( ( in @ ( kpair @ sK8 @ sK9 ) @ ( breln1compset @ sK6 @ sK5 @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( dpsetconstrER = $true )
& ( ( breln1 @ sK6 @ sK5 )
= $true )
& ( ( breln1 @ sK6 @ sK7 )
= $true )
& ( ( in @ ( kpair @ sK8 @ sK9 ) @ ( breln1compset @ sK6 @ sK5 @ sK7 ) )
= $true )
& ( ( in @ sK9 @ sK6 )
= $true )
& ! [X5: $i] :
( ( ( in @ ( kpair @ sK8 @ X5 ) @ sK5 )
!= $true )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ sK9 ) @ sK7 ) ) )
& ( ( in @ sK8 @ sK6 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f18,f27,f26,f25,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true )
& ( ( in @ X4 @ X1 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
| ( $true
!= ( in @ X5 @ X1 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ) )
=> ( ( ( breln1 @ sK6 @ sK5 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ sK6 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK6 @ sK5 @ X2 ) ) )
& ( ( in @ X4 @ sK6 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ sK5 ) )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) ) )
& ( ( in @ X3 @ sK6 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ? [X2: $i] :
( ( ( breln1 @ sK6 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK6 @ sK5 @ X2 ) ) )
& ( ( in @ X4 @ sK6 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ sK5 ) )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) ) )
& ( ( in @ X3 @ sK6 )
= $true ) ) )
=> ( ( ( breln1 @ sK6 @ sK7 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK6 @ sK5 @ sK7 ) ) )
& ( ( in @ X4 @ sK6 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ sK5 ) )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ sK7 )
!= $true ) ) )
& ( ( in @ X3 @ sK6 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK6 @ sK5 @ sK7 ) ) )
& ( ( in @ X4 @ sK6 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ sK5 ) )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ sK7 )
!= $true ) ) )
& ( ( in @ X3 @ sK6 )
= $true ) )
=> ( ? [X4: $i] :
( ( ( in @ ( kpair @ sK8 @ X4 ) @ ( breln1compset @ sK6 @ sK5 @ sK7 ) )
= $true )
& ( ( in @ X4 @ sK6 )
= $true )
& ! [X5: $i] :
( ( ( in @ ( kpair @ sK8 @ X5 ) @ sK5 )
!= $true )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ sK7 )
!= $true ) ) )
& ( ( in @ sK8 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X4: $i] :
( ( ( in @ ( kpair @ sK8 @ X4 ) @ ( breln1compset @ sK6 @ sK5 @ sK7 ) )
= $true )
& ( ( in @ X4 @ sK6 )
= $true )
& ! [X5: $i] :
( ( ( in @ ( kpair @ sK8 @ X5 ) @ sK5 )
!= $true )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ sK7 )
!= $true ) ) )
=> ( ( ( in @ ( kpair @ sK8 @ sK9 ) @ ( breln1compset @ sK6 @ sK5 @ sK7 ) )
= $true )
& ( ( in @ sK9 @ sK6 )
= $true )
& ! [X5: $i] :
( ( ( in @ ( kpair @ sK8 @ X5 ) @ sK5 )
!= $true )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ sK9 ) @ sK7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( dpsetconstrER = $true )
& ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true )
& ( ( in @ X4 @ X1 )
= $true )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
| ( $true
!= ( in @ X5 @ X1 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
| ( $true
!= ( in @ X5 @ X1 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( dpsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ( dpsetconstrER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true )
=> ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
& ( $true
= ( in @ X5 @ X1 ) )
& ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( dpsetconstrER
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
=> ? [X5: $i] :
( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ X5 @ X1 )
& ( in @ ( kpair @ X3 @ X5 ) @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dpsetconstrER
=> ! [X8: $i,X0: $i] :
( ( breln1 @ X0 @ X8 )
=> ! [X9: $i] :
( ( breln1 @ X0 @ X9 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X0 @ X8 @ X9 ) )
=> ? [X6: $i] :
( ( in @ ( kpair @ X6 @ X5 ) @ X9 )
& ( in @ X6 @ X0 )
& ( in @ ( kpair @ X4 @ X6 ) @ X8 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dpsetconstrER
=> ! [X8: $i,X0: $i] :
( ( breln1 @ X0 @ X8 )
=> ! [X9: $i] :
( ( breln1 @ X0 @ X9 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( breln1compset @ X0 @ X8 @ X9 ) )
=> ? [X6: $i] :
( ( in @ ( kpair @ X6 @ X5 ) @ X9 )
& ( in @ X6 @ X0 )
& ( in @ ( kpair @ X4 @ X6 ) @ X8 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YFdbAJDISU/DTF2THF_32096.p',breln1compE) ).
thf(f51,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( $true
!= ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ X1 @ X4 @ X0 ) ) )
| ( $true
= ( X0 @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
!= $true )
| ( $true
= ( X0 @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
!= $true )
| ( $true != $true )
| ( $true
= ( X0 @ X2 @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f40]) ).
thf(f40,plain,
dpsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( $true
= ( X0 @ X2 @ X3 ) )
| ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
!= $true )
| ( dpsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( $true
= ( X0 @ X2 @ X3 ) )
| ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ( ( ( sK0 @ sK2 @ sK3 )
!= $true )
& ( $true
= ( in @ ( kpair @ sK2 @ sK3 )
@ ( dpsetconstr @ sK1 @ sK4
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f22]) ).
thf(f22,plain,
( ? [X5: $i > $i > $o,X6: $i,X7: $i,X8: $i,X9: $i] :
( ( ( X5 @ X7 @ X8 )
!= $true )
& ( $true
= ( in @ ( kpair @ X7 @ X8 )
@ ( dpsetconstr @ X6 @ X9
@ ^ [Y0: $i,Y1: $i] : ( X5 @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( sK0 @ sK2 @ sK3 )
!= $true )
& ( $true
= ( in @ ( kpair @ sK2 @ sK3 )
@ ( dpsetconstr @ sK1 @ sK4
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( $true
= ( X0 @ X2 @ X3 ) )
| ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ? [X5: $i > $i > $o,X6: $i,X7: $i,X8: $i,X9: $i] :
( ( ( X5 @ X7 @ X8 )
!= $true )
& ( $true
= ( in @ ( kpair @ X7 @ X8 )
@ ( dpsetconstr @ X6 @ X9
@ ^ [Y0: $i,Y1: $i] : ( X5 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( $true
= ( X0 @ X2 @ X3 ) )
| ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( $true
!= ( X0 @ X2 @ X3 ) )
& ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( $true
= ( X0 @ X2 @ X3 ) )
| ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
!= $true ) )
<=> ( dpsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) )
= $true )
=> ( $true
= ( X0 @ X2 @ X3 ) ) )
<=> ( dpsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( dpsetconstrER
= ( ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [X5: $i,X6: $i] : ( X0 @ X5 @ X6 ) ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( dpsetconstrER
= ( ! [X3: $i > $i > $o,X0: $i,X4: $i,X5: $i,X1: $i] :
( ( in @ ( kpair @ X4 @ X5 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X6: $i,X7: $i] : ( X3 @ X6 @ X7 ) ) )
=> ( X3 @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YFdbAJDISU/DTF2THF_32096.p',dpsetconstrER) ).
thf(f65,plain,
( $true
!= ( in @ sK12 @ sK6 ) ),
inference(subsumption_resolution,[status(thm)],[f64,f62]) ).
thf(f62,plain,
( $true
= ( in @ ( kpair @ sK8 @ sK12 ) @ sK5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f64,plain,
( ( $true
!= ( in @ ( kpair @ sK8 @ sK12 ) @ sK5 ) )
| ( $true
!= ( in @ sK12 @ sK6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK12 @ sK6 ) )
| ( $true
!= ( in @ ( kpair @ sK8 @ sK12 ) @ sK5 ) ) ),
inference(superposition,[status(thm)],[f35,f59]) ).
thf(f59,plain,
( $true
= ( in @ ( kpair @ sK12 @ sK9 ) @ sK7 ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f35,plain,
! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X5 @ sK9 ) @ sK7 ) )
| ( $true
!= ( in @ X5 @ sK6 ) )
| ( ( in @ ( kpair @ sK8 @ X5 ) @ sK5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU780^2 : 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
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:32:11 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEU780^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : Binary Relations on a Set
% 0.19/0.45 % Version : Especial > Reduced > Especial.
% 0.19/0.45 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.19/0.45 % (! y:i.in y A -> in (kpair x y) (breln1compset A R S) ->
% 0.19/0.45 % (? z:i.in z A & (in (kpair x z) R & in (kpair z y) S))))))
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.45 % Source : [Bro08]
% 0.19/0.45 % Names : ZFC282l [Bro08]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 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 v4.0.1, 0.67 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.19/0.45 % Number of atoms : 22 ( 4 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 9 ( 4 avg)
% 0.19/0.45 % Number of connectives : 67 ( 0 ~; 0 |; 4 &; 56 @)
% 0.19/0.45 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 19 ( 5 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% 0.19/0.45 % Number of variables : 24 ( 12 ^; 10 !; 2 ?; 24 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : http://mathgate.info/detsetitem.php?id=346
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(in_type,type,
% 0.19/0.45 in: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(subset_type,type,
% 0.19/0.45 subset: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(kpair_type,type,
% 0.19/0.45 kpair: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(cartprod_type,type,
% 0.19/0.45 cartprod: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(breln_type,type,
% 0.19/0.45 breln: $i > $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(breln,definition,
% 0.19/0.45 ( breln
% 0.19/0.45 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(dpsetconstr_type,type,
% 0.19/0.45 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.19/0.45
% 0.19/0.45 thf(dpsetconstrER_type,type,
% 0.19/0.45 dpsetconstrER: $o ).
% 0.19/0.45
% 0.19/0.45 thf(dpsetconstrER,definition,
% 0.19/0.45 ( dpsetconstrER
% 0.19/0.45 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.19/0.45 ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.45 @ ( dpsetconstr @ A @ B
% 0.19/0.45 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.45 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(breln1_type,type,
% 0.19/0.45 breln1: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(breln1,definition,
% 0.19/0.45 ( breln1
% 0.19/0.45 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(breln1compset_type,type,
% 0.19/0.45 breln1compset: $i > $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(breln1compset,definition,
% 0.19/0.45 ( breln1compset
% 0.19/0.45 = ( ^ [A: $i,R: $i,S: $i] :
% 0.19/0.45 ( dpsetconstr @ A @ A
% 0.19/0.45 @ ^ [Xx: $i,Xy: $i] :
% 0.19/0.45 ? [Xz: $i] :
% 0.19/0.45 ( ( in @ Xz @ A )
% 0.19/0.45 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.19/0.45 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(breln1compE,conjecture,
% 0.19/0.45 ( dpsetconstrER
% 0.19/0.45 => ! [A: $i,R: $i] :
% 0.19/0.45 ( ( breln1 @ A @ R )
% 0.19/0.45 => ! [S: $i] :
% 0.19/0.45 ( ( breln1 @ A @ S )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.19/0.45 => ? [Xz: $i] :
% 0.19/0.45 ( ( in @ Xz @ A )
% 0.19/0.45 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.19/0.45 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.77/1.43 ---- Embedded in THF ---
% 1.77/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.77/1.43 %%% Generated on Tue Feb 24 12:32:12 EST 2026
% 1.77/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.77/1.43 %%% Logic specification used:
% 1.77/1.43 %%% thf(spec, logic, $$dhol).
% 1.77/1.43
% 1.77/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YFdbAJDISU/DTF2DTF32096.p
% See solution above
% 1.77/1.43 ------------------------
% 1.77/1.44 ---- Cleaned THF ---
% 1.77/1.44 thf(in_type,type,
% 1.77/1.44 in: $i > $i > $o ).
% 1.77/1.44
% 1.77/1.44 thf(subset_type,type,
% 1.77/1.44 subset: $i > $i > $o ).
% 1.77/1.44
% 1.77/1.44 thf(kpair_type,type,
% 1.77/1.44 kpair: $i > $i > $i ).
% 1.77/1.44
% 1.77/1.44 thf(cartprod_type,type,
% 1.77/1.44 cartprod: $i > $i > $i ).
% 1.77/1.44
% 1.77/1.44 thf(breln_type,type,
% 1.77/1.44 breln: $i > $i > $i > $o ).
% 1.77/1.44
% 1.77/1.44 thf(breln,definition,
% 1.77/1.44 ( breln
% 1.77/1.44 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.77/1.44
% 1.77/1.44 thf(dpsetconstr_type,type,
% 1.77/1.44 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.77/1.44
% 1.77/1.44 thf(dpsetconstrER_type,type,
% 1.77/1.44 dpsetconstrER: $o ).
% 1.77/1.44
% 1.77/1.44 thf(dpsetconstrER,definition,
% 1.77/1.44 ( dpsetconstrER
% 1.77/1.44 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 1.77/1.44 ( ( in @ ( kpair @ Xx @ Xy )
% 1.77/1.44 @ ( dpsetconstr @ A @ B
% 1.77/1.44 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 1.77/1.44 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 1.77/1.44
% 1.77/1.44 thf(breln1_type,type,
% 1.77/1.44 breln1: $i > $i > $o ).
% 1.77/1.44
% 1.77/1.44 thf(breln1,definition,
% 1.77/1.44 ( breln1
% 1.77/1.44 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.77/1.44
% 1.77/1.44 thf(breln1compset_type,type,
% 1.77/1.44 breln1compset: $i > $i > $i > $i ).
% 1.77/1.44
% 1.77/1.44 thf(breln1compset,definition,
% 1.77/1.44 ( breln1compset
% 1.77/1.44 = ( ^ [A: $i,R: $i,S: $i] :
% 1.77/1.44 ( dpsetconstr @ A @ A
% 1.77/1.44 @ ^ [Xx: $i,Xy: $i] :
% 1.77/1.44 ? [Xz: $i] :
% 1.77/1.44 ( ( in @ Xz @ A )
% 1.77/1.44 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 1.77/1.44 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 1.77/1.44
% 1.77/1.44 thf(breln1compE,conjecture,
% 1.77/1.44 ( dpsetconstrER
% 1.77/1.44 => ! [A: $i,R: $i] :
% 1.77/1.44 ( ( breln1 @ A @ R )
% 1.77/1.44 => ! [S: $i] :
% 1.77/1.44 ( ( breln1 @ A @ S )
% 1.77/1.44 => ! [Xx: $i] :
% 1.77/1.44 ( ( in @ Xx @ A )
% 1.77/1.44 => ! [Xy: $i] :
% 1.77/1.44 ( ( in @ Xy @ A )
% 1.77/1.44 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 1.77/1.44 => ? [Xz: $i] :
% 1.77/1.44 ( ( in @ Xz @ A )
% 1.77/1.44 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 1.77/1.44 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ).
% 1.77/1.44 ------------------------
% 1.77/1.46 % (32197)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32096 for (2999ds/2Mi)
% 1.77/1.46 % (32200)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32096 for (2999ds/18Mi)
% 1.77/1.46 % (32198)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_32096 for (2999ds/2Mi)
% 1.77/1.46 % (32194)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32096 for (2999ds/183Mi)
% 1.77/1.46 % (32196)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_32096 for (2999ds/27Mi)
% 1.77/1.46 % (32195)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_32096 for (2999ds/4Mi)
% 1.77/1.46 % (32199)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_32096 for (2999ds/275Mi)
% 1.77/1.46 % (32197)Instruction limit reached!
% 1.77/1.46 % (32197)------------------------------
% 1.77/1.46 % (32197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.46 % (32197)Termination reason: Unknown
% 1.77/1.46 % (32197)Termination phase: Preprocessing 3
% 1.77/1.46 % (32198)Instruction limit reached!
% 1.77/1.46 % (32198)------------------------------
% 1.77/1.46 % (32198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.46
% 1.77/1.46 % (32197)Memory used [KB]: 1023
% 1.77/1.46 % (32197)Time elapsed: 0.003 s
% 1.77/1.46 % (32197)Instructions burned: 3 (million)
% 1.77/1.46 % (32197)------------------------------
% 1.77/1.46 % (32197)------------------------------
% 1.77/1.46 % (32198)Termination reason: Unknown
% 1.77/1.46 % (32198)Termination phase: Property scanning
% 1.77/1.46
% 1.77/1.46 % (32198)Memory used [KB]: 1023
% 1.77/1.46 % (32198)Time elapsed: 0.003 s
% 1.77/1.46 % (32198)Instructions burned: 3 (million)
% 1.77/1.46 % (32198)------------------------------
% 1.77/1.46 % (32198)------------------------------
% 1.77/1.46 % (32195)Instruction limit reached!
% 1.77/1.46 % (32195)------------------------------
% 1.77/1.46 % (32195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.46 % (32195)Termination reason: Unknown
% 1.77/1.46 % (32195)Termination phase: Saturation
% 1.77/1.46
% 1.77/1.46 % (32195)Memory used [KB]: 5500
% 1.77/1.46 % (32195)Time elapsed: 0.004 s
% 1.77/1.46 % (32195)Instructions burned: 4 (million)
% 1.77/1.46 % (32195)------------------------------
% 1.77/1.46 % (32195)------------------------------
% 1.77/1.46 % (32199)Refutation not found, incomplete strategy
% 1.77/1.46 % (32199)------------------------------
% 1.77/1.46 % (32199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.46 % (32199)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.46
% 1.77/1.46
% 1.77/1.46 % (32199)Memory used [KB]: 5500
% 1.77/1.46 % (32199)Time elapsed: 0.005 s
% 1.77/1.46 % (32199)Instructions burned: 4 (million)
% 1.77/1.46 % (32199)------------------------------
% 1.77/1.46 % (32199)------------------------------
% 1.77/1.46 % (32200)First to succeed.
% 1.77/1.46 % (32194)Also succeeded, but the first one will report.
% 1.77/1.46 % (32200)Refutation found. Thanks to Tanya!
% 1.77/1.46 % SZS status Theorem for DTF2THF_32096
% 1.77/1.46 % SZS output start Proof for DTF2THF_32096
% 1.77/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.77/1.46 thf(func_def_1, type, subset: $i > $i > $o).
% 1.77/1.46 thf(func_def_2, type, kpair: $i > $i > $i).
% 1.77/1.46 thf(func_def_3, type, cartprod: $i > $i > $i).
% 1.77/1.46 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 1.77/1.46 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.77/1.46 thf(func_def_8, type, breln1: $i > $i > $o).
% 1.77/1.46 thf(func_def_9, type, breln1compset: $i > $i > $i > $i).
% 1.77/1.46 thf(func_def_21, type, sK0: $i > $i > $o).
% 1.77/1.46 thf(func_def_33, type, ph11: !>[X0: $tType]:(X0)).
% 1.77/1.46 thf(f66,plain,(
% 1.77/1.46 $false),
% 1.77/1.46 inference(subsumption_resolution,[status(thm)],[f65,f61])).
% 1.77/1.46 thf(f61,plain,(
% 1.77/1.46 ($true = (in @ sK12 @ sK6))),
% 1.77/1.46 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.77/1.46 thf(f60,plain,(
% 1.77/1.46 ($true = ((in @ (kpair @ sK8 @ sK12) @ sK5) & (in @ sK12 @ sK6)))),
% 1.77/1.46 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.77/1.46 thf(f58,plain,(
% 1.77/1.46 ($true = (((in @ (kpair @ sK8 @ sK12) @ sK5) & (in @ sK12 @ sK6)) & (in @ (kpair @ sK12 @ sK9) @ sK7)))),
% 1.77/1.46 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.77/1.46 thf(f57,plain,(
% 1.77/1.46 (((^[Y0 : $i]: (((in @ (kpair @ sK8 @ Y0) @ sK5) & (in @ Y0 @ sK6)) & (in @ (kpair @ Y0 @ sK9) @ sK7))) @ sK12) = $true)),
% 1.77/1.46 inference(sigma_clausification,[status(thm)],[f56])).
% 1.77/1.46 thf(f56,plain,(
% 1.77/1.46 ((?? @ $i @ (^[Y0 : $i]: (((in @ (kpair @ sK8 @ Y0) @ sK5) & (in @ Y0 @ sK6)) & (in @ (kpair @ Y0 @ sK9) @ sK7)))) = $true)),
% 1.77/1.46 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.77/1.46 thf(f55,plain,(
% 1.77/1.46 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y0 @ Y2) @ sK5) & (in @ Y2 @ sK6)) & (in @ (kpair @ Y2 @ Y1) @ sK7))))))) @ sK8 @ sK9))),
% 1.77/1.46 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.77/1.46 thf(f54,plain,(
% 1.77/1.46 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y0 @ Y2) @ sK5) & (in @ Y2 @ sK6)) & (in @ (kpair @ Y2 @ Y1) @ sK7))))))) @ sK8 @ sK9)) | ($true != $true)),
% 1.77/1.46 inference(superposition,[status(thm)],[f51,f52])).
% 1.77/1.46 thf(f52,plain,(
% 1.77/1.46 ((in @ (kpair @ sK8 @ sK9) @ (dpsetconstr @ sK6 @ sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y0 @ Y2) @ sK5) & (in @ Y2 @ sK6)) & (in @ (kpair @ Y2 @ Y1) @ sK7))))))))) = $true)),
% 1.77/1.46 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.77/1.46 thf(f48,plain,(
% 1.77/1.46 ((in @ (kpair @ sK8 @ sK9) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ Y5 @ Y0)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))) @ sK6 @ sK5 @ sK7)) = $true)),
% 1.77/1.46 inference(definition_unfolding,[status(thm)],[f37,f30])).
% 1.77/1.46 thf(f30,plain,(
% 1.77/1.46 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ Y5 @ Y0)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))))),
% 1.77/1.46 inference(cnf_transformation,[status(thm)],[f13])).
% 1.77/1.46 thf(f13,plain,(
% 1.77/1.46 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ Y5 @ Y0)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))))),
% 1.77/1.46 inference(fool_elimination,[status(thm)],[f12])).
% 1.77/1.46 thf(f12,plain,(
% 1.77/1.46 ((^[X0 : $i, X1 : $i, X2 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X3 : $i, X4 : $i] : (? [X5 : $i] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ X5 @ X0) & (in @ (kpair @ X3 @ X5) @ X1)))))) = breln1compset)),
% 1.77/1.46 inference(rectify,[status(thm)],[f4])).
% 1.77/1.46 thf(f4,axiom,(
% 1.77/1.46 ((^[X0 : $i, X8 : $i, X9 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (? [X6 : $i] : ((in @ (kpair @ X6 @ X5) @ X9) & (in @ X6 @ X0) & (in @ (kpair @ X4 @ X6) @ X8)))))) = breln1compset)),
% 1.77/1.46 file('/export/starexec/sandbox/tmp/tmp.YFdbAJDISU/DTF2THF_32096.p',breln1compset)).
% 1.77/1.46 thf(f37,plain,(
% 1.77/1.46 ((in @ (kpair @ sK8 @ sK9) @ (breln1compset @ sK6 @ sK5 @ sK7)) = $true)),
% 1.77/1.46 inference(cnf_transformation,[status(thm)],[f28])).
% 1.77/1.46 thf(f28,plain,(
% 1.77/1.46 (dpsetconstrER = $true) & (((breln1 @ sK6 @ sK5) = $true) & (((breln1 @ sK6 @ sK7) = $true) & ((((in @ (kpair @ sK8 @ sK9) @ (breln1compset @ sK6 @ sK5 @ sK7)) = $true) & ((in @ sK9 @ sK6) = $true) & ! [X5 : $i] : (((in @ (kpair @ sK8 @ X5) @ sK5) != $true) | ($true != (in @ X5 @ sK6)) | ($true != (in @ (kpair @ X5 @ sK9) @ sK7)))) & ((in @ sK8 @ sK6) = $true))))),
% 1.77/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f18,f27,f26,f25,f24])).
% 1.77/1.46 thf(f24,plain,(
% 1.77/1.46 ? [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) & ? [X2 : $i] : (((breln1 @ X1 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) & ((in @ X4 @ X1) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ X0)) | ($true != (in @ X5 @ X1)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true))) & ((in @ X3 @ X1) = $true)))) => (((breln1 @ sK6 @ sK5) = $true) & ? [X2 : $i] : (((breln1 @ sK6 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK6 @ sK5 @ X2))) & ((in @ X4 @ sK6) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ sK5)) | ($true != (in @ X5 @ sK6)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true))) & ((in @ X3 @ sK6) = $true))))),
% 1.77/1.46 introduced(definition,[],[choice_axiom])).
% 1.77/1.46 thf(f25,plain,(
% 1.77/1.46 ? [X2 : $i] : (((breln1 @ sK6 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK6 @ sK5 @ X2))) & ((in @ X4 @ sK6) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ sK5)) | ($true != (in @ X5 @ sK6)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true))) & ((in @ X3 @ sK6) = $true))) => (((breln1 @ sK6 @ sK7) = $true) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK6 @ sK5 @ sK7))) & ((in @ X4 @ sK6) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ sK5)) | ($true != (in @ X5 @ sK6)) | ((in @ (kpair @ X5 @ X4) @ sK7) != $true))) & ((in @ X3 @ sK6) = $true)))),
% 1.77/1.46 introduced(definition,[],[choice_axiom])).
% 1.77/1.46 thf(f26,plain,(
% 1.77/1.46 ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK6 @ sK5 @ sK7))) & ((in @ X4 @ sK6) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ sK5)) | ($true != (in @ X5 @ sK6)) | ((in @ (kpair @ X5 @ X4) @ sK7) != $true))) & ((in @ X3 @ sK6) = $true)) => (? [X4 : $i] : (((in @ (kpair @ sK8 @ X4) @ (breln1compset @ sK6 @ sK5 @ sK7)) = $true) & ((in @ X4 @ sK6) = $true) & ! [X5 : $i] : (((in @ (kpair @ sK8 @ X5) @ sK5) != $true) | ($true != (in @ X5 @ sK6)) | ((in @ (kpair @ X5 @ X4) @ sK7) != $true))) & ((in @ sK8 @ sK6) = $true))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f27,plain,(
% 1.77/1.47 ? [X4 : $i] : (((in @ (kpair @ sK8 @ X4) @ (breln1compset @ sK6 @ sK5 @ sK7)) = $true) & ((in @ X4 @ sK6) = $true) & ! [X5 : $i] : (((in @ (kpair @ sK8 @ X5) @ sK5) != $true) | ($true != (in @ X5 @ sK6)) | ((in @ (kpair @ X5 @ X4) @ sK7) != $true))) => (((in @ (kpair @ sK8 @ sK9) @ (breln1compset @ sK6 @ sK5 @ sK7)) = $true) & ((in @ sK9 @ sK6) = $true) & ! [X5 : $i] : (((in @ (kpair @ sK8 @ X5) @ sK5) != $true) | ($true != (in @ X5 @ sK6)) | ($true != (in @ (kpair @ X5 @ sK9) @ sK7))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f18,plain,(
% 1.77/1.47 (dpsetconstrER = $true) & ? [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) & ? [X2 : $i] : (((breln1 @ X1 @ X2) = $true) & ? [X3 : $i] : (? [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) & ((in @ X4 @ X1) = $true) & ! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ X0)) | ($true != (in @ X5 @ X1)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true))) & ((in @ X3 @ X1) = $true))))),
% 1.77/1.47 inference(flattening,[status(thm)],[f17])).
% 1.77/1.47 thf(f17,plain,(
% 1.77/1.47 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((! [X5 : $i] : (($true != (in @ (kpair @ X3 @ X5) @ X0)) | ($true != (in @ X5 @ X1)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)) & ((in @ X4 @ X1) = $true)) & ((in @ X3 @ X1) = $true)) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true)) & (dpsetconstrER = $true)),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f16])).
% 1.77/1.47 thf(f16,plain,(
% 1.77/1.47 ~((dpsetconstrER = $true) => ! [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) => ! [X2 : $i] : (((breln1 @ X1 @ X2) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ! [X4 : $i] : (((in @ X4 @ X1) = $true) => (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) => ? [X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ X0)) & ($true = (in @ X5 @ X1)) & ((in @ (kpair @ X5 @ X4) @ X2) = $true))))))))),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f15])).
% 1.77/1.47 thf(f15,plain,(
% 1.77/1.47 ~(dpsetconstrER => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) => ? [X5 : $i] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ X5 @ X1) & (in @ (kpair @ X3 @ X5) @ X0))))))))),
% 1.77/1.47 inference(rectify,[status(thm)],[f6])).
% 1.77/1.47 thf(f6,negated_conjecture,(
% 1.77/1.47 ~(dpsetconstrER => ! [X8 : $i,X0 : $i] : ((breln1 @ X0 @ X8) => ! [X9 : $i] : ((breln1 @ X0 @ X9) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9)) => ? [X6 : $i] : ((in @ (kpair @ X6 @ X5) @ X9) & (in @ X6 @ X0) & (in @ (kpair @ X4 @ X6) @ X8))))))))),
% 1.77/1.47 inference(negated_conjecture,[status(cth)],[f5])).
% 1.77/1.47 thf(f5,conjecture,(
% 1.77/1.47 dpsetconstrER => ! [X8 : $i,X0 : $i] : ((breln1 @ X0 @ X8) => ! [X9 : $i] : ((breln1 @ X0 @ X9) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9)) => ? [X6 : $i] : ((in @ (kpair @ X6 @ X5) @ X9) & (in @ X6 @ X0) & (in @ (kpair @ X4 @ X6) @ X8)))))))),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.YFdbAJDISU/DTF2THF_32096.p',breln1compE)).
% 1.77/1.47 thf(f51,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i,X4 : $i] : (($true != (in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ X0))) | ($true = (X0 @ X2 @ X3))) )),
% 1.77/1.47 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.77/1.47 thf(f50,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i,X4 : $i] : (((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true) | ($true = (X0 @ X2 @ X3))) )),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.77/1.47 thf(f43,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i,X4 : $i] : (((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true) | ($true != $true) | ($true = (X0 @ X2 @ X3))) )),
% 1.77/1.47 inference(definition_unfolding,[status(thm)],[f33,f40])).
% 1.77/1.47 thf(f40,plain,(
% 1.77/1.47 (dpsetconstrER = $true)),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f28])).
% 1.77/1.47 thf(f33,plain,(
% 1.77/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i,X4 : $i] : (($true = (X0 @ X2 @ X3)) | ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true) | (dpsetconstrER != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f23])).
% 1.77/1.47 thf(f23,plain,(
% 1.77/1.47 (! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (($true = (X0 @ X2 @ X3)) | ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | (((sK0 @ sK2 @ sK3) != $true) & ($true = (in @ (kpair @ sK2 @ sK3) @ (dpsetconstr @ sK1 @ sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))))))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f22])).
% 1.77/1.47 thf(f22,plain,(
% 1.77/1.47 ? [X5 : $i > $i > $o,X6 : $i,X7 : $i,X8 : $i,X9 : $i] : (((X5 @ X7 @ X8) != $true) & ($true = (in @ (kpair @ X7 @ X8) @ (dpsetconstr @ X6 @ X9 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X5 @ Y0 @ Y1)))))))) => (((sK0 @ sK2 @ sK3) != $true) & ($true = (in @ (kpair @ sK2 @ sK3) @ (dpsetconstr @ sK1 @ sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1))))))))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f21,plain,(
% 1.77/1.47 (! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (($true = (X0 @ X2 @ X3)) | ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | ? [X5 : $i > $i > $o,X6 : $i,X7 : $i,X8 : $i,X9 : $i] : (((X5 @ X7 @ X8) != $true) & ($true = (in @ (kpair @ X7 @ X8) @ (dpsetconstr @ X6 @ X9 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X5 @ Y0 @ Y1)))))))))),
% 1.77/1.47 inference(rectify,[status(thm)],[f20])).
% 1.77/1.47 thf(f20,plain,(
% 1.77/1.47 (! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (($true = (X0 @ X2 @ X3)) | ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | ? [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (($true != (X0 @ X2 @ X3)) & ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) = $true)))),
% 1.77/1.47 inference(nnf_transformation,[status(thm)],[f19])).
% 1.77/1.47 thf(f19,plain,(
% 1.77/1.47 ! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (($true = (X0 @ X2 @ X3)) | ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true)) <=> (dpsetconstrER = $true)),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f11])).
% 1.77/1.47 thf(f11,plain,(
% 1.77/1.47 ! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) = $true) => ($true = (X0 @ X2 @ X3))) <=> (dpsetconstrER = $true)),
% 1.77/1.47 inference(fool_elimination,[status(thm)],[f10])).
% 1.77/1.47 thf(f10,plain,(
% 1.77/1.47 (dpsetconstrER = ! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X1 @ X4 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6)))) => (X0 @ X2 @ X3)))),
% 1.77/1.47 inference(rectify,[status(thm)],[f2])).
% 1.77/1.47 thf(f2,axiom,(
% 1.77/1.47 (dpsetconstrER = ! [X3 : $i > $i > $o,X0 : $i,X4 : $i,X5 : $i,X1 : $i] : ((in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X0 @ X1 @ (^[X6 : $i, X7 : $i] : (X3 @ X6 @ X7)))) => (X3 @ X4 @ X5)))),
% 1.77/1.47 file('/export/starexec/sandbox/tmp/tmp.YFdbAJDISU/DTF2THF_32096.p',dpsetconstrER)).
% 1.77/1.47 thf(f65,plain,(
% 1.77/1.47 ($true != (in @ sK12 @ sK6))),
% 1.77/1.47 inference(subsumption_resolution,[status(thm)],[f64,f62])).
% 1.77/1.47 thf(f62,plain,(
% 1.77/1.47 ($true = (in @ (kpair @ sK8 @ sK12) @ sK5))),
% 1.77/1.47 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.77/1.47 thf(f64,plain,(
% 1.77/1.47 ($true != (in @ (kpair @ sK8 @ sK12) @ sK5)) | ($true != (in @ sK12 @ sK6))),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.77/1.47 thf(f63,plain,(
% 1.77/1.47 ($true != $true) | ($true != (in @ sK12 @ sK6)) | ($true != (in @ (kpair @ sK8 @ sK12) @ sK5))),
% 1.77/1.47 inference(superposition,[status(thm)],[f35,f59])).
% 1.77/1.47 thf(f59,plain,(
% 1.77/1.47 ($true = (in @ (kpair @ sK12 @ sK9) @ sK7))),
% 1.77/1.47 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.77/1.47 thf(f35,plain,(
% 1.77/1.47 ( ! [X5 : $i] : (($true != (in @ (kpair @ X5 @ sK9) @ sK7)) | ($true != (in @ X5 @ sK6)) | ((in @ (kpair @ sK8 @ X5) @ sK5) != $true)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f28])).
% 1.77/1.47 % SZS output end Proof for DTF2THF_32096
% 1.77/1.47 % (32200)------------------------------
% 1.77/1.47 % (32200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.47 % (32200)Termination reason: Refutation
% 1.77/1.47
% 1.77/1.47 % (32200)Memory used [KB]: 5628
% 1.77/1.47 % (32200)Time elapsed: 0.008 s
% 1.77/1.47 % (32200)Instructions burned: 8 (million)
% 1.77/1.47 % (32200)------------------------------
% 1.77/1.47 % (32200)------------------------------
% 1.77/1.47 % (32193)Success in time 0.023 s
%------------------------------------------------------------------------------