%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU585^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:32:33 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 114 ( 48 unt; 0 typ; 6 def)
% Number of atoms : 798 ( 221 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1141 ( 50 ~; 122 |; 18 &; 717 @)
% ( 6 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 33 ( 29 usr; 17 con; 0-4 aty)
% ( 60 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 253 ( 0 sgn 167 !; 8 ?; 253 :)
% 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,
setadjoinE: $o ).
thf(func_def_6,type,
setunionE: $o ).
thf(func_def_7,type,
uniqinunit: $o ).
thf(func_def_8,type,
binunion: $i > $i > $i ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vIMP: $o > $o > $o ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
sK3: $o ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
sK4: $o > $i > $i > $i ).
thf(f1,axiom,
( setadjoinE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(f2,axiom,
( setunionE
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X0 )
=> X2 ) )
=> X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(f3,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(f4,axiom,
( binunion
= ( ^ [X0: $i,X1: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunion) ).
thf(f5,conjecture,
( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(f6,negated_conjecture,
~ ( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( setadjoinE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( setadjoinE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y0 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( setunionE
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X0 )
=> X2 ) )
=> X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( setunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f14,plain,
~ ( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f15,plain,
~ ( ( setadjoinE = $true )
=> ( ( setunionE = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
=> ( ( ( ( in @ X2 @ X0 )
= $true )
=> ( $true = X3 ) )
=> ( ( ( ( in @ X2 @ X1 )
= $true )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
!= $true ) )
& ( ( $true = X3 )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( setadjoinE = $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
!= $true ) )
& ( ( $true = X3 )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( setadjoinE = $true ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ( $true != sK3 )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK2 @ sK1 ) ) )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK2 @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( setadjoinE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17]) ).
thf(f19,plain,
( setadjoinE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y0 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,plain,
( setunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f21,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f22,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f23,plain,
setadjoinE = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f24,plain,
setunionE = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f26,plain,
( $true
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f27,plain,
( ( $true = sK3 )
| ( $true
!= ( in @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f28,plain,
( ( $true = sK3 )
| ( $true
!= ( in @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f29,plain,
$true != sK3,
inference(cnf_transformation,[],[f18]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y0 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f19,f23]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f20,f24]) ).
thf(f34,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f21,f25]) ).
thf(f35,plain,
( $true
= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f26,f22]) ).
thf(f36,plain,
( $true
= ( in @ sK2 @ ( setunion @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ X1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> Y1 ) ) )
=> Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ X1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> Y1 ) ) )
=> Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setunion @ X2 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
= ( ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) ) )
=> X3 ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) ) ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $true = X3 ) ),
inference(sigma_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ( in @ X1 @ ( sK4 @ X3 @ X1 @ X2 ) )
=> ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> X3 ) ) )
| ( $true = X3 ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> X3 ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( in @ X1 @ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f56,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( Y2 = Y0 )
=> Y3 )
=> ( ( ( in @ Y0 @ Y1 )
=> Y3 )
=> Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f58,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( Y1 = X1 )
=> Y2 )
=> ( ( ( in @ X1 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( Y1 = X1 )
=> Y2 )
=> ( ( ( in @ X1 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ X2 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( Y0 = X1 )
=> Y1 )
=> ( ( ( in @ X1 @ X2 )
=> Y1 )
=> Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ X2 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( Y0 = X1 )
=> Y1 )
=> ( ( ( in @ X1 @ X2 )
=> Y1 )
=> Y1 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setadjoin @ X3 @ X2 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( ( X3 = X1 )
=> Y0 )
=> ( ( ( in @ X1 @ X2 )
=> Y0 )
=> Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ( X3 = X1 )
=> Y0 )
=> ( ( ( in @ X1 @ X2 )
=> Y0 )
=> Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $o] :
( ( ( X3 = X1 )
=> Y0 )
=> ( ( ( in @ X1 @ X2 )
=> Y0 )
=> Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( ( ( X3 = X1 )
=> X4 )
=> ( ( ( in @ X1 @ X2 )
=> X4 )
=> X4 ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $false
= ( ( X3 = X1 )
=> X4 ) )
| ( $true
= ( ( ( in @ X1 @ X2 )
=> X4 )
=> X4 ) ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( X3 = X1 ) )
| ( $true
= ( ( ( in @ X1 @ X2 )
=> X4 )
=> X4 ) ) ),
inference(imp_proxy_clausification,[],[f66]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( X1 = X3 )
| ( $true
= ( ( ( in @ X1 @ X2 )
=> X4 )
=> X4 ) ) ),
inference(equality_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( X1 = X3 )
| ( $false
= ( ( in @ X1 @ X2 )
=> X4 ) )
| ( $true = X4 ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( X1 = X3 )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true = X4 ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f78,definition,
( spl5_1
<=> ( $true
= ( in @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
!= ( in @ sK2 @ sK0 ) )
| spl5_1 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f82,definition,
( spl5_2
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f83,plain,
( ( $true != sK3 )
| spl5_2 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f85,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f27,f82,f78]) ).
thf(f87,definition,
( spl5_3
<=> ( $true
= ( in @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f89,plain,
( ( $true
!= ( in @ sK2 @ sK1 ) )
| spl5_3 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f90,plain,
( ~ spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f28,f82,f87]) ).
thf(f91,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f29,f82]) ).
thf(f100,definition,
( spl5_6
<=> ! [X4: $o] : ( $true = X4 ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f101,plain,
( ! [X4: $o] : ( $true = X4 )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f103,definition,
( spl5_7
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( X1 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f104,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( X1 = X3 ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f105,plain,
( spl5_6
| spl5_7 ),
inference(avatar_split_clause,[],[f72,f103,f100]) ).
thf(f121,plain,
( ( $true != $true )
| spl5_2
| ~ spl5_6 ),
inference(constrained_superposition,[],[f83,f101]) ).
thf(f122,plain,
( $false
| spl5_2
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f123,plain,
( spl5_2
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f122]) ).
thf(f157,plain,
( ! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK4 @ X0 @ X1 @ ( setadjoin @ X2 @ X3 ) ) @ X3 ) )
| ( ( sK4 @ X0 @ X1 @ ( setadjoin @ X2 @ X3 ) )
= X2 )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X2 @ X3 ) ) ) )
| ( $true = X0 ) )
| ~ spl5_7 ),
inference(constrained_superposition,[],[f104,f56]) ).
thf(f158,plain,
( ! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X0 @ X1 @ ( setadjoin @ X2 @ X3 ) ) @ X3 ) )
| ( ( sK4 @ X0 @ X1 @ ( setadjoin @ X2 @ X3 ) )
= X2 )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X2 @ X3 ) ) ) )
| ( $true = X0 ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f183,plain,
( ! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( $true = $false )
| ( ( sK4 @ X0 @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= X3 )
| ( ( sK4 @ X0 @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= X2 )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) )
| ( $true = X0 ) )
| ~ spl5_7 ),
inference(constrained_superposition,[],[f42,f158]) ).
thf(f188,plain,
( ! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( ( sK4 @ X0 @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= X3 )
| ( ( sK4 @ X0 @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= X2 )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) )
| ( $true = X0 ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f268,plain,
( ! [X2: $o,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) ) ) )
| ( $true = X2 )
| ( ( sK4 @ X2 @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) )
= X3 )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) ) ) )
| ( $true = X2 ) )
| ~ spl5_7 ),
inference(constrained_superposition,[],[f54,f188]) ).
thf(f275,plain,
( ! [X2: $o,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) ) ) )
| ( ( sK4 @ X2 @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) )
= X3 )
| ( $true = X2 )
| ( $true
= ( in @ X1 @ X0 ) ) )
| ~ spl5_7 ),
inference(duplicate_literal_removal,[],[f268]) ).
thf(f611,plain,
( ! [X2: $o,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
| ( $true = X2 )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
| ( $true = X2 )
| ( ( in @ X1 @ X3 )
= $true ) )
| ~ spl5_7 ),
inference(constrained_superposition,[],[f54,f275]) ).
thf(f616,plain,
( ! [X2: $o,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
| ( $true = X2 )
| ( ( in @ X1 @ X3 )
= $true ) )
| ~ spl5_7 ),
inference(duplicate_literal_removal,[],[f611]) ).
thf(f631,definition,
( spl5_31
<=> ! [X0: $i,X1: $i,X3: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X3 )
= $true )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_31])],[avatar_definition]) ).
thf(f632,plain,
( ! [X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
| ( ( in @ X1 @ X3 )
= $true )
| ( $true
= ( in @ X1 @ X0 ) ) )
| ~ spl5_31 ),
inference(avatar_component_clause,[],[f631]) ).
thf(f633,plain,
( spl5_6
| spl5_31
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f616,f103,f631,f100]) ).
thf(f705,plain,
( ( $true = $false )
| ( $true
= ( in @ sK2 @ sK0 ) )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ~ spl5_31 ),
inference(constrained_superposition,[],[f632,f36]) ).
thf(f724,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ~ spl5_31 ),
inference(trivial_inequality_removal,[],[f705]) ).
thf(f727,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| spl5_1
| ~ spl5_31 ),
inference(forward_subsumption_resolution,[],[f724,f80]) ).
thf(f730,plain,
( $false
| spl5_1
| spl5_3
| ~ spl5_31 ),
inference(forward_subsumption_resolution,[],[f727,f89]) ).
thf(f731,plain,
( spl5_1
| spl5_3
| ~ spl5_31 ),
inference(avatar_contradiction_clause,[],[f730]) ).
cnf(s1,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f85]) ).
cnf(s2,plain,
( spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f90]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
( spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f105]) ).
cnf(s10,plain,
( spl5_2
| ~ spl5_6 ),
inference(sat_conversion,[],[f123]) ).
cnf(s46,plain,
( spl5_6
| ~ spl5_7
| spl5_31 ),
inference(sat_conversion,[],[f633]) ).
cnf(s51,plain,
( spl5_1
| spl5_3
| ~ spl5_31 ),
inference(sat_conversion,[],[f731]) ).
cnf(s52,plain,
~ spl5_6,
inference(rat,[],[s10,s3]) ).
cnf(s55,plain,
spl5_7,
inference(rat,[],[s5,s52]) ).
cnf(s60,plain,
spl5_31,
inference(rat,[],[s46,s52,s55]) ).
cnf(s78,plain,
~ spl5_3,
inference(rat,[],[s2,s3]) ).
cnf(s79,plain,
spl5_1,
inference(rat,[],[s51,s60,s78]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s1,s3,s79]) ).
thf(f732,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU585^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:54:56 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (112694)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (112704)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2504600063:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (112700)% WARNING: option uhcvi not known.
% 0.20/0.28 % (112700)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4276221920:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (112699)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=763554849_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (112701)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1921429789:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (112702)dis+10_1_sil=32000:sp=arity:random_seed=4110360758:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (112705)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=430595155:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (112700)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (112703)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1605855848:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (112700)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (112703)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (112704) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-112694-112704"...
% 0.20/0.28 % (112719)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3459621849:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.28 % (112704)...printing done.
% 0.20/0.28 % (112704)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (112704)------------------------------
% 0.20/0.28 % (112704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (112704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (112704)CaDiCaL version: 2.1.3
% 0.20/0.28 % (112704)Termination reason: Refutation
% 0.20/0.28 % (112704)Time elapsed: 0.028 s
% 0.20/0.28 % (112704)Peak memory usage: 13 MB
% 0.20/0.28 % (112704)Instructions burned: 96 (million)
% 0.20/0.28 % (112694)Success in time 0.062 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------