%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU673^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:40 AM UTC 2026
% Result : Theorem 0.44s 0.31s
% Output : Refutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 539 ( 148 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 631 ( 62 ~; 53 |; 36 &; 442 @)
% ( 6 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 16 con; 0-4 aty)
% Number of variables : 161 ( 37 ^; 100 !; 24 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
dsetconstrEL: $o ).
thf(func_def_7,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
cartprod: $i > $i > $i ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(func_def_11,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_12,type,
theprop: $o ).
thf(func_def_13,type,
breln: $i > $i > $i > $o ).
thf(func_def_14,type,
func: $i > $i > $i > $o ).
thf(func_def_15,type,
funcImageSingleton: $o ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vAND: $o > $o > $o ).
thf(func_def_22,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f4,axiom,
! [X0: $i] :
( ( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) )
= theprop ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(f7,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) )
= funcImageSingleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(f8,conjecture,
( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X2: $i,X1: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
@ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apProp) ).
thf(f9,negated_conjecture,
~ ( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X2: $i,X1: $i,X0: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
@ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f12,plain,
~ ( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) )
@ X1 ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f13,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( theprop = $true )
=> ( ( funcImageSingleton = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X1 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
@ X1 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( singleton
@ ( dsetconstr @ X2
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) ) )
= funcImageSingleton ),
inference(rectify,[],[f7]) ).
thf(f15,plain,
( ( funcImageSingleton = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X1 @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f21,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) )
= theprop ),
inference(rectify,[],[f4]) ).
thf(f22,plain,
( ! [X0: $i] :
( ( ( singleton @ X0 )
= $true )
=> ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) )
<=> ( theprop = $true ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X0 @ X2 ) )
= dsetconstrEL ),
inference(rectify,[],[f1]) ).
thf(f24,plain,
( ( dsetconstrEL = $true )
<=> ! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( ( funcImageSingleton = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
= $true ) )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f26,plain,
( ( theprop = $true )
<=> ! [X0: $i] :
( ( ( in @ ( setunion @ X0 ) @ X0 )
= $true )
| ( ( singleton @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
@ X1 )
!= $true ) )
& ( ( func @ X2 @ X1 @ X0 )
= $true ) )
& ( funcImageSingleton = $true )
& ( theprop = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f28,plain,
( ( dsetconstrEL = $true )
& ( funcImageSingleton = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
@ X1 )
!= $true ) )
& ( ( func @ X2 @ X1 @ X0 )
= $true ) )
& ( theprop = $true ) ),
inference(flattening,[],[f27]) ).
thf(f29,plain,
( ( dsetconstrEL = $true )
<=> ! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f30,plain,
( ( ( theprop = $true )
| ? [X0: $i] :
( ( ( in @ ( setunion @ X0 ) @ X0 )
!= $true )
& ( ( singleton @ X0 )
= $true ) ) )
& ( ! [X0: $i] :
( ( ( in @ ( setunion @ X0 ) @ X0 )
= $true )
| ( ( singleton @ X0 )
!= $true ) )
| ( theprop != $true ) ) ),
inference(nnf_transformation,[],[f26]) ).
thf(f31,plain,
( ( ( theprop = $true )
| ? [X0: $i] :
( ( ( in @ ( setunion @ X0 ) @ X0 )
!= $true )
& ( ( singleton @ X0 )
= $true ) ) )
& ( ! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( ( singleton @ X1 )
!= $true ) )
| ( theprop != $true ) ) ),
inference(rectify,[],[f30]) ).
thf(f32,plain,
( ( ( theprop = $true )
| ( ( ( in @ ( setunion @ sK0 ) @ sK0 )
!= $true )
& ( ( singleton @ sK0 )
= $true ) ) )
& ( ! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( ( singleton @ X1 )
!= $true ) )
| ( theprop != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f31]) ).
thf(f33,plain,
( ( ( dsetconstrEL = $true )
| ? [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(nnf_transformation,[],[f29]) ).
thf(f34,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
& ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(rectify,[],[f33]) ).
thf(f35,plain,
( ( ( dsetconstrEL = $true )
| ( ( $true
!= ( in @ sK2 @ sK3 ) )
& ( ( in @ sK2
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f34]) ).
thf(f36,plain,
( ( dsetconstrEL = $true )
& ( funcImageSingleton = $true )
& ( ( in @ sK7 @ sK6 )
= $true )
& ( ( in
@ ( setunion
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) )
@ sK5 )
!= $true )
& ( ( func @ sK6 @ sK5 @ sK4 )
= $true )
& ( theprop = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f28]) ).
thf(f37,plain,
( ( ( funcImageSingleton = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
!= $true ) )
& ( $true
= ( func @ X1 @ X2 @ X0 ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
= $true ) )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) ) )
| ( funcImageSingleton != $true ) ) ),
inference(nnf_transformation,[],[f25]) ).
thf(f38,plain,
( ( ( funcImageSingleton = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X2 ) ) )
!= $true ) )
& ( ( func @ X0 @ X1 @ X2 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X4 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ X6 ) ) )
= $true ) )
| ( ( func @ X4 @ X5 @ X6 )
!= $true ) )
| ( funcImageSingleton != $true ) ) ),
inference(rectify,[],[f37]) ).
thf(f39,plain,
( ( ( funcImageSingleton = $true )
| ( ( $true
= ( in @ sK11 @ sK8 ) )
& ( ( singleton
@ ( dsetconstr @ sK9
@ ^ [Y0: $i] : ( in @ ( kpair @ sK11 @ Y0 ) @ sK10 ) ) )
!= $true )
& ( ( func @ sK8 @ sK9 @ sK10 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X4 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ X6 ) ) )
= $true ) )
| ( ( func @ X4 @ X5 @ X6 )
!= $true ) )
| ( funcImageSingleton != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11)],[f38]) ).
thf(f40,plain,
! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( ( singleton @ X1 )
!= $true )
| ( theprop != $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f43,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
!= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f46,plain,
theprop = $true,
inference(cnf_transformation,[],[f36]) ).
thf(f47,plain,
( ( func @ sK6 @ sK5 @ sK4 )
= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f48,plain,
( ( in
@ ( setunion
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) )
@ sK5 )
!= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f49,plain,
( ( in @ sK7 @ sK6 )
= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f50,plain,
funcImageSingleton = $true,
inference(cnf_transformation,[],[f36]) ).
thf(f51,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f36]) ).
thf(f52,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ X4 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ X6 ) ) )
= $true )
| ( ( func @ X4 @ X5 @ X6 )
!= $true )
| ( funcImageSingleton != $true ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f60,plain,
! [X1: $i] :
( ( $true != $true )
| ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( ( singleton @ X1 )
!= $true ) ),
inference(definition_unfolding,[],[f40,f46]) ).
thf(f63,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f43,f51]) ).
thf(f67,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ X6 ) ) )
= $true )
| ( ( func @ X4 @ X5 @ X6 )
!= $true ) ),
inference(definition_unfolding,[],[f52,f50]) ).
thf(f68,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ X6 ) ) )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( func @ X4 @ X5 @ X6 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f69,plain,
! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( ( singleton @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f70,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f71,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( dsetconstr @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X0: $i > $o] :
( ( in
@ ( setunion
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) )
@ ( dsetconstr @ sK5 @ X0 ) )
!= $true ),
inference(unit_resulting_resolution,[],[f71,f48]) ).
thf(f73,plain,
( $true
!= ( singleton
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) ) ),
inference(unit_resulting_resolution,[],[f69,f72]) ).
thf(f75,plain,
( $true
= ( singleton
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) ) ),
inference(unit_resulting_resolution,[],[f68,f49,f47]) ).
thf(f76,plain,
$false,
inference(forward_subsumption_resolution,[],[f75,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU673^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n013.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 14:06:36 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 Running higher-order theorem proving
% 0.10/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.44/0.31 % (2171267)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.44/0.31 % (2171273)lrs+10_16_si=on:nwc=1.5:random_seed=3012691522:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.44/0.31 % (2171278)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.44/0.31 % (2171278)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.44/0.31 % (2171273)Instruction limit reached!
% 0.44/0.31 % (2171273)------------------------------
% 0.44/0.31 % (2171273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171273)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171273)Termination reason: Instruction limit
% 0.44/0.31 % (2171273)Termination phase: Saturation
% 0.44/0.31 % (2171273)Time elapsed: 0.006 s
% 0.44/0.31 % (2171273)Peak memory usage: 12 MB
% 0.44/0.31 % (2171273)Instructions burned: 20 (million)
% 0.44/0.31 % (2171274)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=150079724:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.44/0.31 % (2171275)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1150710661:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.44/0.31 % (2171276)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1452202016:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.44/0.31 % (2171277)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4210588399:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.44/0.31 % (2171278)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3199499598:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.44/0.31 % (2171274)Instruction limit reached!
% 0.44/0.31 % (2171274)------------------------------
% 0.44/0.31 % (2171274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171274)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171274)Termination reason: Instruction limit
% 0.44/0.31 % (2171274)Termination phase: Saturation
% 0.44/0.31 % (2171274)Time elapsed: 0.002 s
% 0.44/0.31 % (2171274)Peak memory usage: 11 MB
% 0.44/0.31 % (2171274)Instructions burned: 4 (million)
% 0.44/0.31 % (2171272)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3542939387:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.44/0.31 % (2171280)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2284395591:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.44/0.31 % (2171280)Instruction limit reached!
% 0.44/0.31 % (2171280)------------------------------
% 0.44/0.31 % (2171280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171280)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171280)Termination reason: Instruction limit
% 0.44/0.31 % (2171280)Termination phase: Saturation
% 0.44/0.31 % (2171280)Time elapsed: 0.001 s
% 0.44/0.31 % (2171280)Peak memory usage: 11 MB
% 0.44/0.31 % (2171280)Instructions burned: 3 (million)
% 0.44/0.31 % (2171276)Instruction limit reached!
% 0.44/0.31 % (2171276)------------------------------
% 0.44/0.31 % (2171276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171276)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171276)Termination reason: Instruction limit
% 0.44/0.31 % (2171276)Termination phase: Saturation
% 0.44/0.31 % (2171276)Time elapsed: 0.014 s
% 0.44/0.31 % (2171276)Peak memory usage: 12 MB
% 0.44/0.31 % (2171276)Instructions burned: 25 (million)
% 0.44/0.31 % (2171289)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.44/0.31 % (2171289)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=45184155:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.44/0.31 % (2171286)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1643502516:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.44/0.31 % (2171289)Instruction limit reached!
% 0.44/0.31 % (2171289)------------------------------
% 0.44/0.31 % (2171289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171289)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171289)Termination reason: Instruction limit
% 0.44/0.31 % (2171289)Termination phase: Saturation
% 0.44/0.31 % (2171289)Time elapsed: 0.002 s
% 0.44/0.31 % (2171289)Peak memory usage: 12 MB
% 0.44/0.31 % (2171289)Instructions burned: 8 (million)
% 0.44/0.31 % (2171286)Instruction limit reached!
% 0.44/0.31 % (2171286)------------------------------
% 0.44/0.31 % (2171286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171286)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171286)Termination reason: Instruction limit
% 0.44/0.31 % (2171286)Termination phase: Saturation
% 0.44/0.31 % (2171286)Time elapsed: 0.003 s
% 0.44/0.31 % (2171286)Peak memory usage: 11 MB
% 0.44/0.31 % (2171286)Instructions burned: 5 (million)
% 0.44/0.31 % (2171293)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.44/0.31 % (2171293)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.44/0.31 % (2171293)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1053953137:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.44/0.31 % (2171290)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1958179615:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.44/0.31 % (2171277)Instruction limit reached!
% 0.44/0.31 % (2171277)------------------------------
% 0.44/0.31 % (2171277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171277)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171277)Termination reason: Instruction limit
% 0.44/0.31 % (2171277)Termination phase: Saturation
% 0.44/0.31 % (2171277)Time elapsed: 0.040 s
% 0.44/0.31 % (2171277)Peak memory usage: 12 MB
% 0.44/0.31 % (2171277)Instructions burned: 76 (million)
% 0.44/0.31 % (2171293)Instruction limit reached!
% 0.44/0.31 % (2171293)------------------------------
% 0.44/0.31 % (2171293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171293)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171293)Termination reason: Instruction limit
% 0.44/0.31 % (2171293)Termination phase: Saturation
% 0.44/0.31 % (2171293)Time elapsed: 0.008 s
% 0.44/0.31 % (2171293)Peak memory usage: 12 MB
% 0.44/0.31 % (2171293)Instructions burned: 30 (million)
% 0.44/0.31 % (2171290)Instruction limit reached!
% 0.44/0.31 % (2171290)------------------------------
% 0.44/0.31 % (2171290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171290)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171290)Termination reason: Instruction limit
% 0.44/0.31 % (2171290)Termination phase: Saturation
% 0.44/0.31 % (2171290)Time elapsed: 0.007 s
% 0.44/0.31 % (2171290)Peak memory usage: 12 MB
% 0.44/0.31 % (2171290)Instructions burned: 13 (million)
% 0.44/0.31 % (2171294)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2061960661:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.44/0.31 % (2171298)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.44/0.31 % (2171298)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1608580711:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.44/0.31 % (2171298)Instruction limit reached!
% 0.44/0.31 % (2171298)------------------------------
% 0.44/0.31 % (2171298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171298)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171298)Termination reason: Instruction limit
% 0.44/0.31 % (2171298)Termination phase: Saturation
% 0.44/0.31 % (2171298)Time elapsed: 0.001 s
% 0.44/0.31 % (2171298)Peak memory usage: 11 MB
% 0.44/0.31 % (2171298)Instructions burned: 3 (million)
% 0.44/0.31 % (2171297)lrs+10_1_si=on:cs=on:random_seed=2121254607:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.44/0.31 % (2171300)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1238744238:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.44/0.31 % (2171302)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2953232926:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.44/0.31 % (2171297)Instruction limit reached!
% 0.44/0.31 % (2171297)------------------------------
% 0.44/0.31 % (2171297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171297)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171297)Termination reason: Instruction limit
% 0.44/0.31 % (2171297)Termination phase: Saturation
% 0.44/0.31 % (2171297)Time elapsed: 0.004 s
% 0.44/0.31 % (2171297)Peak memory usage: 11 MB
% 0.44/0.31 % (2171297)Instructions burned: 9 (million)
% 0.44/0.31 % (2171300) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2171267-2171300"...
% 0.44/0.31 % (2171294)Refutation not found, incomplete strategy
% 0.44/0.31 % (2171294)------------------------------
% 0.44/0.31 % (2171294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171294)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171294)Termination reason: Refutation not found, incomplete strategy
% 0.44/0.31 % (2171294)Time elapsed: 0.023 s
% 0.44/0.31 % (2171294)Peak memory usage: 12 MB
% 0.44/0.31 % (2171294)Instructions burned: 45 (million)
% 0.44/0.31 % (2171294)------------------------------
% 0.44/0.31 % (2171294)------------------------------
% 0.44/0.31 % (2171300)...printing done.
% 0.44/0.31 % (2171300)Refutation found. Thanks to Tanya!
% 0.44/0.31 % SZS status Theorem for theBenchmark
% 0.44/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.44/0.31 % (2171300)------------------------------
% 0.44/0.31 % (2171300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.31 % (2171300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.31 % (2171300)CaDiCaL version: 2.1.3
% 0.44/0.31 % (2171300)Termination reason: Refutation
% 0.44/0.31 % (2171300)Time elapsed: 0.005 s
% 0.44/0.31 % (2171300)Peak memory usage: 12 MB
% 0.44/0.31 % (2171300)Instructions burned: 8 (million)
% 0.44/0.31 % (2171267)Success in time 0.102 s
% 0.44/0.31 % Vampire exiting
%------------------------------------------------------------------------------