%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU619^2 : 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 : n007.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 08:30:21 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 614 ( 95 equ; 0 cnn)
% Maximal formula atoms : 6 ( 13 avg)
% Number of connectives : 1038 ( 26 ~; 25 |; 31 &; 935 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 12 con; 0-4 aty)
% ( 0 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 89 ( 18 ^; 55 !; 16 ?; 89 :)
% 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,
iskpair: $i > $o ).
thf(func_def_6,type,
setukpairIL: $o ).
thf(func_def_7,type,
setukpairIR: $o ).
thf(func_def_8,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ X0 ) ) ) ) )
= iskpair ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(f2,axiom,
( setukpairIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(f3,axiom,
( setukpairIR
= ( ! [X1: $i,X0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(f4,conjecture,
( setukpairIL
=> ( setukpairIR
=> ! [X0: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(f5,negated_conjecture,
~ ( setukpairIL
=> ( setukpairIR
=> ! [X0: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ X0 ) ) ) ) )
= iskpair ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( setukpairIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
<=> ( setukpairIL = $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( setukpairIL
=> ( setukpairIR
=> ! [X0: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ! [X1: $i,X0: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( setukpairIR
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( ( setukpairIR = $true )
<=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
!= $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
!= $true )
& ( setukpairIL = $true )
& ( setukpairIR = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( setukpairIL != $true ) )
& ( ( setukpairIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( setukpairIL != $true ) )
& ( ( setukpairIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( setukpairIL != $true ) )
& ( ( setukpairIL = $true )
| ( ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f17]) ).
thf(f19,plain,
( ( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( setukpairIL = $true )
& ( setukpairIR = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
thf(f20,plain,
( ( ( setukpairIR = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( setukpairIR != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f21,plain,
( ( ( setukpairIR = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( setukpairIR != $true ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( ( setukpairIR = $true )
| ( ( in @ sK4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( setukpairIR != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f21]) ).
thf(f24,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( setukpairIL != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
setukpairIR = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
setukpairIL = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( setukpairIR != $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true ) ),
inference(definition_unfolding,[],[f24,f26]) ).
thf(f35,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(definition_unfolding,[],[f27,f30]) ).
thf(f37,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true ) ),
inference(definition_unfolding,[],[f28,f25]) ).
thf(f38,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f39,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X1: $i] :
( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f47,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f48,plain,
( ( $false
= ( in @ sK3 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( in @ sK2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(equality_resolution,[],[f45]) ).
thf(f49,plain,
( ( $false = $true )
| ( $false
= ( in @ sK2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f48,f46]) ).
thf(f50,plain,
( $false
= ( in @ sK2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f51,plain,
$false = $true,
inference(forward_demodulation,[],[f50,f47]) ).
thf(f52,plain,
$false,
inference(trivial_inequality_removal,[],[f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU619^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.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 13:56:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.28 % (3407457)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3407471)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1262165642:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (3407471) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3407457-3407471"...
% 0.21/0.28 % (3407471)...printing done.
% 0.21/0.28 % (3407471)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3407471)------------------------------
% 0.21/0.28 % (3407471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3407471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3407471)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3407471)Termination reason: Refutation
% 0.21/0.28 % (3407471)Time elapsed: 0.003 s
% 0.21/0.28 % (3407471)Peak memory usage: 12 MB
% 0.21/0.28 % (3407471)Instructions burned: 9 (million)
% 0.21/0.28 % (3407457)Success in time 0.035 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------