%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU611^2 : 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 : n015.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 08:32:40 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 107 ( 55 unt; 0 typ; 5 def)
% Number of atoms : 688 ( 146 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 887 ( 78 ~; 85 |; 18 &; 573 @)
% ( 5 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 15 con; 0-4 aty)
% ( 45 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 178 ( 0 sgn 86 !; 8 ?; 178 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrEL: $o ).
thf(func_def_4,type,
dsetconstrER: $o ).
thf(func_def_5,type,
binunion: $i > $i > $i ).
thf(func_def_6,type,
binunionE: $o ).
thf(func_def_7,type,
symdiff: $i > $i > $i ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $o > $o ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vOR: $o > $o > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_21,type,
sK3: $o ).
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,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f3,axiom,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f4,axiom,
( symdiff
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiff) ).
thf(f5,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(f6,negated_conjecture,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,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,[],[f7]) ).
thf(f9,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( symdiff
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( binunionE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
=> ! [X3: $o] :
( ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( binunionE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
=> ! [X3: $o] :
( ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true ) )
& ( binunionE = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true ) )
& ( binunionE = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ( $true != sK3 )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) )
& ( ( $true = sK3 )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
!= ( in @ sK2 @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ ( symdiff @ sK0 @ sK1 ) ) )
& ( binunionE = $true )
& ( dsetconstrER = $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)],[f19]) ).
thf(f21,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,[],[f8]) ).
thf(f22,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f24,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f25,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f26,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
binunionE = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f28,plain,
( $true
= ( in @ sK2 @ ( symdiff @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f29,plain,
( ( $true = sK3 )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
!= ( in @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f30,plain,
( ( $true = sK3 )
| ( $true
!= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f31,plain,
$true != sK3,
inference(cnf_transformation,[],[f20]) ).
thf(f34,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,[],[f21,f25]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f22,f26]) ).
thf(f36,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f27]) ).
thf(f37,plain,
( $true
= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f28,f24]) ).
thf(f38,plain,
( $true
= ( in @ sK2
@ ( dsetconstr @ ( binunion @ sK0 @ sK1 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK0 )
| ~ ( in @ Y0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
| ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
| ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binunion @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
| ( in @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binunion @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
| ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binunion @ X3 @ X2 ) )
=> ( ( in @ X1 @ X3 )
| ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ X1 @ X3 )
| ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,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,[],[f34]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,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,[],[f55]) ).
thf(f57,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f62,definition,
( spl4_1
<=> ( $true
= ( in @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f63,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f64,plain,
( ( $true
!= ( in @ sK2 @ sK0 ) )
| spl4_1 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f66,definition,
( spl4_2
<=> ( $true
= ( in @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f67,plain,
( ( $true
!= ( in @ sK2 @ sK1 ) )
| spl4_2 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f68,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f70,definition,
( spl4_3
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f73,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f29,f70,f66,f62]) ).
thf(f74,plain,
( spl4_1
| ~ spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f30,f70,f66,f62]) ).
thf(f75,plain,
~ spl4_3,
inference(avatar_split_clause,[],[f31,f70]) ).
thf(f103,plain,
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK0 )
| ~ ( in @ Y0 @ sK1 ) )
@ sK2 ) ) ),
inference(constrained_superposition,[],[f38,f53]) ).
thf(f104,plain,
( ( $true = $false )
| ( $true
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f60,f38]) ).
thf(f111,plain,
( $true
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f112,plain,
( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK0 )
| ~ ( in @ Y0 @ sK1 ) )
@ sK2 ) ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f113,plain,
( $true
= ( ~ ( in @ sK2 @ sK0 )
| ~ ( in @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
( ( $true
= ( ~ ( in @ sK2 @ sK1 ) ) )
| ( $true
= ( ~ ( in @ sK2 @ sK0 ) ) ) ),
inference(or_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( ( ( in @ sK2 @ sK1 )
= $false )
| ( $true
= ( ~ ( in @ sK2 @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f114]) ).
thf(f116,plain,
( ( ( in @ sK2 @ sK1 )
= $false )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(not_proxy_clausification,[],[f115]) ).
thf(f119,definition,
( spl4_4
<=> ( ( in @ sK2 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f121,plain,
( ( ( in @ sK2 @ sK0 )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f123,definition,
( spl4_5
<=> ( ( in @ sK2 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f125,plain,
( ( ( in @ sK2 @ sK1 )
= $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f127,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f116,f123,f119]) ).
thf(f136,plain,
( ( $true = $false )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(constrained_superposition,[],[f111,f46]) ).
thf(f139,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f141,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f139,f67]) ).
thf(f144,plain,
( $false
| spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f141,f64]) ).
thf(f145,plain,
( spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f144]) ).
thf(f146,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_demodulation,[],[f63,f121]) ).
thf(f147,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f148,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f147]) ).
thf(f149,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f68,f125]) ).
thf(f150,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f149]) ).
thf(f151,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f150]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s2,plain,
( spl4_1
| ~ spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f74]) ).
cnf(s3,plain,
~ spl4_3,
inference(sat_conversion,[],[f75]) ).
cnf(s5,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f127]) ).
cnf(s9,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f145]) ).
cnf(s10,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f148]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f151]) ).
cnf(s14,plain,
( spl4_1
| ~ spl4_2 ),
inference(rat,[],[s2,s3]) ).
cnf(s15,plain,
( ~ spl4_1
| spl4_2 ),
inference(rat,[],[s1,s3]) ).
cnf(s16,plain,
spl4_1,
inference(rat,[],[s14,s9]) ).
cnf(s17,plain,
~ spl4_4,
inference(rat,[],[s10,s16]) ).
cnf(s18,plain,
spl4_2,
inference(rat,[],[s15,s16]) ).
cnf(s19,plain,
spl4_5,
inference(rat,[],[s5,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s11,s19,s18]) ).
thf(f162,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU611^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:01:27 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.19/0.28 % (3565961)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (3565966)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1334492794_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (3565967)% WARNING: option uhcvi not known.
% 0.19/0.28 % (3565967)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1408460937:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (3565968)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2371511167:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (3565969)dis+10_1_sil=32000:sp=arity:random_seed=3922829051:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (3565970)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=700955539:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (3565972)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3441736107:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (3565971)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3742948203:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (3565967)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (3565970)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (3565967)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (3565974)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2269106527:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (3565969) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3565961-3565969"...
% 0.19/0.28 % (3565970) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3565961-3565970"...
% 0.19/0.28 % (3565967) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3565961-3565967"...
% 0.19/0.28 % (3565968) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3565961-3565968"...
% 0.19/0.28 % (3565969)...printing done.
% 0.19/0.28 % (3565970)...printing done.
% 0.19/0.28 % (3565967)...printing done.
% 0.19/0.28 % (3565969)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (3565969)------------------------------
% 0.19/0.28 % (3565969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3565969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3565969)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3565969)Termination reason: Refutation
% 0.19/0.28 % (3565969)Time elapsed: 0.008 s
% 0.19/0.28 % (3565969)Peak memory usage: 12 MB
% 0.19/0.28 % (3565969)Instructions burned: 12 (million)
% 0.19/0.28 % (3565961)Success in time 0.055 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------