%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU677^2 : 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 : n003.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 08:30:42 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 75 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 583 ( 167 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 806 ( 58 ~; 58 |; 38 &; 606 @)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 36 usr; 12 con; 0-4 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 229 ( 91 ^; 119 !; 19 ?; 229 :)
% 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,
powerset: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
dsetconstrI: $o ).
thf(func_def_7,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
powersetI1: $o ).
thf(func_def_9,type,
kpair: $i > $i > $i ).
thf(func_def_10,type,
cartprod: $i > $i > $i ).
thf(func_def_11,type,
singleton: $i > $o ).
thf(func_def_12,type,
ex1: $i > ( $i > $o ) > $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,
funcSet: $i > $i > $i ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
db3:
!>[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_33,type,
sK5: $i > $o ).
thf(func_def_36,type,
vNOT: $o > $o ).
thf(func_def_37,type,
sK8: $i > $i ).
thf(func_def_38,type,
sK9: $i > $i > $i > $i ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X2: $i,X1: $i > $o,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(f5,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(f6,axiom,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func) ).
thf(f7,axiom,
( funcSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcSet) ).
thf(f8,conjecture,
( dsetconstrI
=> ( powersetI1
=> ! [X1: $i,X0: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset) ).
thf(f9,negated_conjecture,
~ ( dsetconstrI
=> ( powersetI1
=> ! [X1: $i,X0: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ( in @ X2 @ ( funcSet @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
~ ( dsetconstrI
=> ( powersetI1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X1 @ X0 @ X2 )
=> ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
~ ( ( dsetconstrI = $true )
=> ( ( powersetI1 = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X1 @ X0 @ X2 )
= $true )
=> ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f13,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI1 ),
inference(rectify,[],[f2]) ).
thf(f16,plain,
( ( powersetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ( X1 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f18,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X2: $i,X1: $i > $o] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( ( X1 @ X0 )
= $true )
=> ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( funcSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f20,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f25,plain,
( ( powersetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f26,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( ( X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f27,plain,
( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) )
<=> ( dsetconstrI = $true ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X1 @ X0 @ X2 )
= $true )
& ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
!= $true ) )
& ( powersetI1 = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f29,plain,
( ( powersetI1 = $true )
& ( dsetconstrI = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X1 @ X0 @ X2 )
= $true )
& ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f28]) ).
thf(f30,plain,
( ( powersetI1 = $true )
& ( dsetconstrI = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X2 @ X1 )
= $true )
& ( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
!= $true ) ) ),
inference(rectify,[],[f29]) ).
thf(f31,plain,
( ( powersetI1 = $true )
& ( dsetconstrI = $true )
& ( ( func @ sK0 @ sK2 @ sK1 )
= $true )
& ( ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f30]) ).
thf(f32,plain,
( ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X0: $i,X2: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[],[f27]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X3 )
= $true )
& ( ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
& ( ( in @ X3 @ X4 )
= $true ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ( ( ( sK5 @ sK3 )
= $true )
& ( ( in @ sK3
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
!= $true )
& ( ( in @ sK3 @ sK4 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f33]) ).
thf(f35,plain,
( ( ( powersetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI1 != $true ) ) ),
inference(nnf_transformation,[],[f25]) ).
thf(f36,plain,
( ( ( powersetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true ) )
| ( powersetI1 != $true ) ) ),
inference(rectify,[],[f35]) ).
thf(f37,plain,
( ( ( powersetI1 = $true )
| ( ( ( subset @ sK6 @ sK7 )
= $true )
& ( ( in @ sK6 @ ( powerset @ sK7 ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true ) )
| ( powersetI1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f36]) ).
thf(f38,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f39,plain,
( ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f40,plain,
( ( func @ sK0 @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f41,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f42,plain,
powersetI1 = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f46,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( dsetconstrI != $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f48,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f49,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f50,plain,
! [X2: $i,X3: $i] :
( ( powersetI1 != $true )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f57,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) ) @ ( func @ Y0 @ Y1 ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f58,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( dsetconstr @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X0 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( dsetconstrI != $true ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f61,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( ( subset @ X2 @ X3 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f50,f42]) ).
thf(f73,plain,
! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ X1 )
= ( breln @ X1 ) ),
inference(argument_congruence,[],[f38]) ).
thf(f74,plain,
! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i] : ( subset @ Y1 @ ( cartprod @ X1 @ Y0 ) ) )
= ( breln @ X1 ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( breln @ X1 @ X2 )
= ( ^ [Y0: $i,Y1: $i] : ( subset @ Y1 @ ( cartprod @ X1 @ Y0 ) )
@ X2 ) ),
inference(argument_congruence,[],[f74]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( ( breln @ X1 @ X2 )
= ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
@ X3 )
= ( breln @ X1 @ X2 @ X3 ) ),
inference(argument_congruence,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
@ X3 )
= $true )
| ( $false
= ( breln @ X1 @ X2 @ X3 ) ) ),
inference(iff_proxy_clausification,[],[f78]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $true )
| ( $false
= ( breln @ X1 @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f83,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( dsetconstr @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X0 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f58,f41]) ).
thf(f89,plain,
! [X1: $i] :
( ( funcSet @ X1 )
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) ) @ ( func @ Y0 @ Y1 ) )
@ X1 ) ),
inference(argument_congruence,[],[f57]) ).
thf(f90,plain,
! [X1: $i] :
( ( funcSet @ X1 )
= ( ^ [Y0: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ Y0 ) ) @ ( func @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ Y0 ) ) @ ( func @ X1 @ Y0 ) )
@ X2 )
= ( funcSet @ X1 @ X2 ) ),
inference(argument_congruence,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( funcSet @ X1 @ X2 )
= ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X2 ) ) @ ( func @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ ( cartprod @ X0 @ X1 ) ) )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) ),
inference(superposition,[],[f83,f92]) ).
thf(f96,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true )
| ( ( func @ X1 @ X2 @ X0 )
!= $true )
| ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true ) ),
inference(superposition,[],[f93,f61]) ).
thf(f97,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f112,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $false
= ( breln @ X1 @ X2 @ X0 ) )
| ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) ),
inference(superposition,[],[f97,f82]) ).
thf(f114,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
| ( $false
= ( breln @ X1 @ X2 @ X0 ) )
| ( ( func @ X1 @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f115,plain,
( ( ( func @ sK0 @ sK2 @ sK1 )
!= $true )
| ( $false
= ( breln @ sK0 @ sK2 @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[],[f39,f114]) ).
thf(f116,plain,
( ( $false
= ( breln @ sK0 @ sK2 @ sK1 ) )
| ( ( func @ sK0 @ sK2 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f115]) ).
thf(f117,plain,
( $false
= ( breln @ sK0 @ sK2 @ sK1 ) ),
inference(forward_subsumption_resolution,[],[f116,f40]) ).
thf(f122,plain,
! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) )
@ X1 )
= ( func @ X1 ) ),
inference(argument_congruence,[],[f49]) ).
thf(f123,plain,
! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) )
& ( breln @ X1 @ Y0 @ Y1 ) ) )
= ( func @ X1 ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) )
& ( breln @ X1 @ Y0 @ Y1 ) )
@ X2 )
= ( func @ X1 @ X2 ) ),
inference(argument_congruence,[],[f123]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( func @ X1 @ X2 )
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ex1 @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) )
& ( breln @ X1 @ X2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ex1 @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) )
& ( breln @ X1 @ X2 @ Y0 ) )
@ X3 )
= ( func @ X1 @ X2 @ X3 ) ),
inference(argument_congruence,[],[f152]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( func @ X1 @ X2 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ex1 @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) )
& ( breln @ X1 @ X2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(iff_proxy_clausification,[],[f157]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( func @ X1 @ X2 @ X3 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ex1 @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) )
& ( breln @ X1 @ X2 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln @ X1 @ X2 @ X3 )
= $true )
| ( $false
= ( func @ X1 @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f205,plain,
( ( $false = $true )
| ( $false
= ( func @ sK0 @ sK2 @ sK1 ) ) ),
inference(superposition,[],[f117,f167]) ).
thf(f210,plain,
( $false
= ( func @ sK0 @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f218,plain,
$false = $true,
inference(superposition,[],[f40,f210]) ).
thf(f219,plain,
$false,
inference(trivial_inequality_removal,[],[f218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU677^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n003.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:09:14 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.22/0.30 % (2559913)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (2559922)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2283040015:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (2559924)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (2559924)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
% 0.22/0.30 % (2559922) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2559913-2559922"...
% 0.22/0.30 % (2559919)lrs+10_16_si=on:nwc=1.5:random_seed=466263522:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (2559918)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1536540950:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (2559920)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2034313114:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (2559921)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=3396164306: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)
% 0.22/0.30 % (2559923)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=912521109:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (2559924)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=3116708551:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (2559922)...printing done.
% 0.22/0.30 % (2559922)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (2559922)------------------------------
% 0.22/0.31 % (2559922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2559922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2559922)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2559922)Termination reason: Refutation
% 0.22/0.31 % (2559922)Time elapsed: 0.008 s
% 0.22/0.31 % (2559922)Peak memory usage: 12 MB
% 0.22/0.31 % (2559922)Instructions burned: 26 (million)
% 0.22/0.31 % (2559913)Success in time 0.049 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------