%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n014.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 08:32:56 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 599 ( 136 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 908 ( 15 ~; 25 |; 42 &; 740 @)
% ( 0 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 36 usr; 12 con; 0-4 aty)
% ( 24 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 229 ( 151 ^; 68 !; 10 ?; 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,
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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
sK4: $i > $i ).
thf(func_def_35,type,
sK5: $i > $i > $i > $i ).
thf(func_def_36,type,
sK6: $i > $i > $i > $i ).
thf(func_def_37,type,
sK7: $i > $i > $i > $i ).
thf(f1,axiom,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f2,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f3,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(f4,axiom,
( theprop
= ( ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(f5,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(f6,axiom,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func) ).
thf(f8,conjecture,
( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X0: $i,X1: $i,X2: $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
=> ! [X0: $i,X1: $i,X2: $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(f10,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f15,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( theprop
= ( ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f17,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f19,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f23,plain,
~ ( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
@ X1 ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f24,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( theprop = $true )
=> ( ( funcImageSingleton = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X2 ) ) )
@ X1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X2 ) ) )
@ X1 ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( func @ X0 @ X1 @ X2 )
= $true ) )
& ( funcImageSingleton = $true )
& ( theprop = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X2 ) ) )
@ X1 ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( func @ X0 @ X1 @ X2 )
= $true ) )
& ( funcImageSingleton = $true )
& ( theprop = $true )
& ( dsetconstrEL = $true ) ),
inference(flattening,[],[f25]) ).
thf(f27,plain,
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( func @ sK0 @ sK1 @ sK2 ) )
& ( funcImageSingleton = $true )
& ( theprop = $true )
& ( dsetconstrEL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f26]) ).
thf(f28,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f29,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f30,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f31,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f32,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f33,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f35,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f36,plain,
theprop = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f38,plain,
( $true
= ( func @ sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f39,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f40,plain,
( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) ) )
@ sK1 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f43,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f30,f29]) ).
thf(f44,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y6 )
& ( ( setadjoin @ Y7 @ emptyset )
= Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f33,f32,f43]) ).
thf(f45,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f28,f35]) ).
thf(f46,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ( setadjoin @ Y2 @ emptyset )
= Y1 ) ) )
@ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f31,f36,f29]) ).
thf(f48,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y6 )
& ( ( setadjoin @ Y7 @ emptyset )
= Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
@ sK0
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[],[f38,f44]) ).
thf(f49,plain,
( $true
= ( ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f52,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f53,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ( in @ ( sK4 @ X1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
& ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( $true
= ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f59,plain,
! [X1: $i] :
( ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK4 @ X1 ) @ emptyset ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(equality_proxy_clausification,[],[f57]) ).
thf(f88,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ( setadjoin @ Y2 @ emptyset )
= Y1 ) ) )
@ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f89,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( setadjoin @ Y0 @ emptyset )
= X1 ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( setadjoin @ Y0 @ emptyset )
= X1 ) ) ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( setadjoin @ Y0 @ emptyset )
= X1 ) )
@ X2 ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ X2 @ X1 )
& ( ( setadjoin @ X2 @ emptyset )
= X1 ) ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ X2 @ emptyset )
= X1 ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( $false
= ( in @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( $false
= ( in @ X2 @ X1 ) )
| ( ( setadjoin @ X2 @ emptyset )
!= X1 ) ),
inference(equality_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f96,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f103,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true = $false )
| ( $true
= ( in @ ( setunion @ ( dsetconstr @ X0 @ X1 ) ) @ X0 ) )
| ( $false
= ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) ) )
| ( ( setadjoin @ X2 @ emptyset )
!= ( dsetconstr @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f101,f94]) ).
thf(f105,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( in @ ( setunion @ ( dsetconstr @ X0 @ X1 ) ) @ X0 ) )
| ( $false
= ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) ) )
| ( ( setadjoin @ X2 @ emptyset )
!= ( dsetconstr @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f139,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( in @ X0
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) ) ) )
| ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) )
!= ( setadjoin @ X0 @ emptyset ) ) ),
inference(constrained_superposition,[],[f40,f105]) ).
thf(f144,plain,
! [X0: $i] :
( ( $false
= ( in @ X0
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) ) ) )
| ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) )
!= ( setadjoin @ X0 @ emptyset ) ) ),
inference(trivial_inequality_removal,[],[f139]) ).
thf(f189,plain,
( ( $true = $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) )
!= ( setadjoin @ ( sK4 @ sK3 ) @ emptyset ) ) ),
inference(constrained_superposition,[],[f58,f144]) ).
thf(f190,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) )
!= ( setadjoin @ ( sK4 @ sK3 ) @ emptyset ) ) ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f197,plain,
( ( in @ sK3 @ sK0 )
= $false ),
inference(forward_subsumption_resolution,[],[f190,f59]) ).
thf(f203,plain,
$true = $false,
inference(constrained_superposition,[],[f39,f197]) ).
thf(f204,plain,
$false,
inference(trivial_inequality_removal,[],[f203]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.21 % Computer : n014.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 14:07:01 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 Running first-order model finding
% 0.09/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.34 % (2714815)Will run a generic schedule for satisfiability detection.
% 0.25/0.34 % (2714825)dis+10_1_sil=32000:sp=arity:random_seed=985348579:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.34 % (2714823)% WARNING: option uhcvi not known.
% 0.25/0.34 % (2714827)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1785859014:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.34 % (2714823)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1576791745:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.34 % (2714822)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=650119836_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.34 % (2714823)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.34 % (2714824)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2747657759:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.34 % (2714823)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.25/0.34 % Exception at run slice level
% 0.25/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.34 % (2714826)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2863111376:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.34 % (2714828)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3016506826:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.34 % (2714826)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.34 % (2714826) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2714815-2714826"...
% 0.25/0.34 % (2714826)...printing done.
% 0.25/0.34 % (2714826)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status Theorem for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.35 % (2714826)------------------------------
% 0.25/0.35 % (2714826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (2714826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (2714826)CaDiCaL version: 2.1.3
% 0.25/0.35 % (2714826)Termination reason: Refutation
% 0.25/0.35 % (2714826)Time elapsed: 0.024 s
% 0.25/0.35 % (2714826)Peak memory usage: 12 MB
% 0.25/0.35 % (2714826)Instructions burned: 25 (million)
% 0.25/0.35 % (2714815)Success in time 0.069 s
% 0.25/0.35 % Vampire exiting
%------------------------------------------------------------------------------