%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU709^2 : 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 : n004.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 08:33:04 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 97 ( 53 unt; 0 typ; 3 def)
% Number of atoms : 683 ( 182 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 961 ( 41 ~; 56 |; 21 &; 666 @)
% ( 3 <=>; 108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 27 usr; 16 con; 0-4 aty)
% ( 66 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 212 ( 0 sgn 126 !; 8 ?; 212 :)
% 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,
setadjoinIL: $o ).
thf(func_def_5,type,
in__Cong: $o ).
thf(func_def_6,type,
secondinupair: $o ).
thf(func_def_7,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_8,type,
iftrue: $o ).
thf(func_def_9,type,
iffalse: $o ).
thf(func_def_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
vIFF: $o > $o > $o ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_23,type,
sK1: $o ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f3,axiom,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(f4,axiom,
( iftrue
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).
thf(f5,axiom,
( iffalse
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).
thf(f6,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(f7,negated_conjecture,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f12,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( iftrue
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X2 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( iftrue
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( ( if @ Y2 @ Y1 @ Y0 @ Y3 )
= Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( iffalse
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X3 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( iffalse
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ~ Y1
=> ( ( if @ Y2 @ Y1 @ Y0 @ Y3 )
= Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( setadjoinIL = $true )
=> ( ( in__Cong = $true )
=> ( ( secondinupair = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ! [X0: $i,X1: $o,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $o,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( iffalse = $true )
& ( iftrue = $true )
& ( secondinupair = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f21,plain,
( ? [X0: $i,X1: $o,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( iffalse = $true )
& ( iftrue = $true )
& ( secondinupair = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( $true
!= ( in @ ( if @ sK0 @ sK1 @ sK2 @ sK3 ) @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( iffalse = $true )
& ( iftrue = $true )
& ( secondinupair = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f21]) ).
thf(f23,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f25,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f26,plain,
( iftrue
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( ( if @ Y2 @ Y1 @ Y0 @ Y3 )
= Y0 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
( iffalse
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ~ Y1
=> ( ( if @ Y2 @ Y1 @ Y0 @ Y3 )
= Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
secondinupair = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f31,plain,
iftrue = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
iffalse = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f35,plain,
( $true
!= ( in @ ( if @ sK0 @ sK1 @ sK2 @ sK3 ) @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f28]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f25,f30]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( ( if @ Y2 @ Y1 @ Y0 @ Y3 )
= Y0 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f26,f31]) ).
thf(f42,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ~ Y1
=> ( ( if @ Y2 @ Y1 @ Y0 @ Y3 )
= Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f27,f32]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ~ Y1
=> ( ( if @ Y2 @ Y1 @ Y0 @ Y3 )
= Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ~ Y0
=> ( ( if @ Y1 @ Y0 @ X1 @ Y2 )
= Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X2: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ~ Y0
=> ( ( if @ Y1 @ Y0 @ X1 @ Y2 )
= Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ X2
=> ( ( if @ Y0 @ X2 @ X1 @ Y1 )
= Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ X2
=> ( ( if @ Y0 @ X2 @ X1 @ Y1 )
= Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ~ X2
=> ( ( if @ X3 @ X2 @ X1 @ Y0 )
= Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ~ X2
=> ( ( if @ X3 @ X2 @ X1 @ Y0 )
= Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ~ X2
=> ( ( if @ X3 @ X2 @ X1 @ Y0 )
= Y0 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( ~ X2
=> ( ( if @ X3 @ X2 @ X1 @ X4 )
= X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ~ X2
=> ( ( if @ X3 @ X2 @ X1 @ X4 )
= X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false = ( ~ X2 ) )
| ( $true
= ( ( if @ X3 @ X2 @ X1 @ X4 )
= X4 ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true = X2 )
| ( $true
= ( ( if @ X3 @ X2 @ X1 @ X4 )
= X4 ) ) ),
inference(not_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( if @ X3 @ X2 @ X1 @ X4 )
= X4 )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true = X2 )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(equality_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( Y1
=> ( ( if @ Y2 @ Y1 @ Y0 @ Y3 )
= Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( Y0
=> ( ( if @ Y1 @ Y0 @ X1 @ Y2 )
= X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( Y0
=> ( ( if @ Y1 @ Y0 @ X1 @ Y2 )
= X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( X2
=> ( ( if @ Y0 @ X2 @ X1 @ Y1 )
= X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( X2
=> ( ( if @ Y0 @ X2 @ X1 @ Y1 )
= X1 ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( ( if @ X3 @ X2 @ X1 @ Y0 )
= X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( ( if @ X3 @ X2 @ X1 @ Y0 )
= X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X2
=> ( ( if @ X3 @ X2 @ X1 @ Y0 )
= X1 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( X2
=> ( ( if @ X3 @ X2 @ X1 @ X4 )
= X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( X2
=> ( ( if @ X3 @ X2 @ X1 @ X4 )
= X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f66,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false = X2 )
| ( $true
= ( ( if @ X3 @ X2 @ X1 @ X4 )
= X1 ) ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( if @ X3 @ X2 @ X1 @ X4 )
= X1 )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false = X2 )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(equality_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f69,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f87,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f88,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f104,plain,
( ( $true
!= ( in @ sK2 @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( sK1 = $false )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f35,f67]) ).
thf(f105,plain,
( ( $true
!= ( in @ sK3 @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $true = sK1 )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f35,f55]) ).
thf(f106,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $true = sK1 )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(forward_subsumption_resolution,[],[f105,f71]) ).
thf(f107,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( sK1 = $false )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(forward_subsumption_resolution,[],[f104,f90]) ).
thf(f108,plain,
( ( $true = $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $true = sK1 ) ),
inference(forward_demodulation,[],[f106,f33]) ).
thf(f109,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $true = sK1 ) ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f110,plain,
( ( $true = $false )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( sK1 = $false ) ),
inference(forward_demodulation,[],[f107,f33]) ).
thf(f111,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( sK1 = $false ) ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f113,definition,
( spl4_3
<=> ( $true = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f115,plain,
( ( $true = sK1 )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f117,definition,
( spl4_4
<=> ( ( in @ sK3 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f119,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f120,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f109,f117,f113]) ).
thf(f122,definition,
( spl4_5
<=> ( sK1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f124,plain,
( ( sK1 = $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f125,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f111,f117,f122]) ).
thf(f141,plain,
( ( $true = $false )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f119,f34]) ).
thf(f147,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f148,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f147]) ).
thf(f152,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_5 ),
inference(constrained_superposition,[],[f124,f115]) ).
thf(f157,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f158,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f157]) ).
cnf(s4,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f120]) ).
cnf(s5,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f125]) ).
cnf(s8,plain,
~ spl4_4,
inference(sat_conversion,[],[f148]) ).
cnf(s11,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f158]) ).
cnf(s12,plain,
spl4_5,
inference(rat,[],[s5,s8]) ).
cnf(s13,plain,
~ spl4_3,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s4,s8,s13]) ).
thf(f160,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU709^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:13:07 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.24 % (1346065)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (1346071)% WARNING: option uhcvi not known.
% 0.09/0.24 % (1346071)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=788777406:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.24 % (1346071)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.24 % (1346071)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.24 % (1346071) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1346065-1346071"...
% 0.09/0.24 % (1346071)...printing done.
% 0.09/0.24 % (1346071)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (1346071)------------------------------
% 0.09/0.24 % (1346071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (1346071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (1346071)CaDiCaL version: 2.1.3
% 0.09/0.24 % (1346071)Termination reason: Refutation
% 0.09/0.24 % (1346071)Time elapsed: 0.004 s
% 0.09/0.24 % (1346071)Peak memory usage: 13 MB
% 0.09/0.24 % (1346071)Instructions burned: 14 (million)
% 0.09/0.24 % (1346065)Success in time 0.018 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------