%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU811^2 : 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 : 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 08:33:30 AM UTC 2026
% Result : Theorem 0.25s 0.38s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 84 ( 46 unt; 0 typ; 2 def)
% Number of atoms : 527 ( 152 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 650 ( 38 ~; 50 |; 21 &; 386 @)
% ( 2 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 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 : 27 ( 23 usr; 12 con; 0-4 aty)
% ( 41 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 154 ( 0 sgn 96 !; 4 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setadjoinIL: $o ).
thf(func_def_5,type,
setadjoinE: $o ).
thf(func_def_6,type,
in__Cong: $o ).
thf(func_def_7,type,
notinself2: $o ).
thf(func_def_8,type,
omegaS: $i > $i ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_17,type,
vIFF: $o > $o > $o ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,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(f4,axiom,
( notinself2
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself2) ).
thf(f5,axiom,
( omegaS
= ( ^ [X0: $i] : ( setadjoin @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaS) ).
thf(f6,conjecture,
( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',peanoSinj) ).
thf(f7,negated_conjecture,
~ ( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
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(f10,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,[],[f2]) ).
thf(f11,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,[],[f10]) ).
thf(f14,plain,
( notinself2
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( notinself2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f17,plain,
~ ( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f18,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setadjoinE = $true )
=> ( ( in__Cong = $true )
=> ( ( notinself2 = $true )
=> ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ omega )
= $true )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( X0 != X1 )
& ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
& ( ( in @ X1 @ omega )
= $true ) )
& ( ( in @ X0 @ omega )
= $true ) )
& ( notinself2 = $true )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( X0 != X1 )
& ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
& ( ( in @ X1 @ omega )
= $true ) )
& ( ( in @ X0 @ omega )
= $true ) )
& ( notinself2 = $true )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
( ( sK0 != sK1 )
& ( ( omegaS @ sK0 )
= ( omegaS @ sK1 ) )
& ( $true
= ( in @ sK1 @ omega ) )
& ( $true
= ( in @ sK0 @ omega ) )
& ( notinself2 = $true )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
thf(f22,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f23,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,[],[f11]) ).
thf(f25,plain,
( notinself2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f26,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
setadjoinE = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f30,plain,
notinself2 = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f33,plain,
( ( omegaS @ sK0 )
= ( omegaS @ sK1 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f34,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f21]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f22,f27]) ).
thf(f38,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,[],[f23,f28]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f25,f30]) ).
thf(f41,plain,
( ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 )
@ sK0 )
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 )
@ sK1 ) ),
inference(definition_unfolding,[],[f33,f26,f26]) ).
thf(f42,plain,
( ( setadjoin @ sK0 @ sK0 )
= ( setadjoin @ sK1 @ sK1 ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ~ ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ~ ( in @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ~ ( in @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f47]) ).
thf(f64,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,[],[f38]) ).
thf(f65,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,[],[f64]) ).
thf(f66,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,[],[f65]) ).
thf(f67,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,[],[f66]) ).
thf(f68,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,[],[f67]) ).
thf(f69,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,[],[f68]) ).
thf(f70,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,[],[f69]) ).
thf(f71,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,[],[f70]) ).
thf(f72,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,[],[f71]) ).
thf(f73,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,[],[f72]) ).
thf(f75,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,[],[f73]) ).
thf(f76,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,[],[f75]) ).
thf(f77,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,[],[f76]) ).
thf(f79,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,[],[f77]) ).
thf(f84,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f85,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f89,definition,
( spl2_1
<=> ! [X4: $o] : ( $true = X4 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f90,plain,
( ! [X4: $o] : ( $true = X4 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f89]) ).
thf(f92,definition,
( spl2_2
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( X1 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f93,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( X1 = X3 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f94,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f79,f92,f89]) ).
thf(f126,plain,
( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f87,f42]) ).
thf(f406,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( setadjoin @ sK0 @ sK0 ) ) )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( sK1 = X0 ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f93,f42]) ).
thf(f413,plain,
( ( $true = $false )
| ( $true
= ( in @ sK1 @ sK0 ) )
| ( sK0 = sK1 )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f126,f93]) ).
thf(f414,plain,
( ( $true
= ( in @ sK1 @ sK0 ) )
| ( sK0 = sK1 )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f413]) ).
thf(f421,plain,
( ( $true
= ( in @ sK1 @ sK0 ) )
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f414,f34]) ).
thf(f434,plain,
( ( $true = $false )
| ( $false
= ( in @ sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f48,f421]) ).
thf(f449,plain,
( ( $false
= ( in @ sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f434]) ).
thf(f685,plain,
( ( $true = $false )
| ( $true
= ( in @ sK0 @ sK1 ) )
| ( sK0 = sK1 )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f406,f87]) ).
thf(f698,plain,
( ( $true
= ( in @ sK0 @ sK1 ) )
| ( sK0 = sK1 )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f685]) ).
thf(f704,plain,
( ( $true
= ( in @ sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f698,f34]) ).
thf(f708,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f704,f449]) ).
thf(f709,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f708]) ).
thf(f710,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f709]) ).
thf(f716,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ X1 @ X0 )
= $false ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f48,f90]) ).
thf(f757,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
= $false )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f716]) ).
thf(f787,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f757,f90]) ).
thf(f788,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f787]) ).
thf(f789,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f788]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f94]) ).
cnf(s8,plain,
~ spl2_2,
inference(sat_conversion,[],[f710]) ).
cnf(s22,plain,
~ spl2_1,
inference(sat_conversion,[],[f789]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s1,s8,s22]) ).
thf(f790,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU811^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 % Computer : n007.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 14:31:26 UTC 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.28 Running first-order model finding
% 0.08/0.29 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
% 0.25/0.38 % (3447036)Will run a generic schedule for satisfiability detection.
% 0.25/0.38 % (3447045)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1824030382:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.38 % (3447046)dis+10_1_sil=32000:sp=arity:random_seed=659440656:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.38 % (3447043)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1604006205_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.38 % Exception at run slice level
% 0.25/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.38 % (3447047)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=994562295:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.38 % (3447047)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.38 % (3447046) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3447036-3447046"...
% 0.25/0.38 % (3447046)...printing done.
% 0.25/0.38 % (3447046)Refutation found. Thanks to Tanya!
% 0.25/0.38 % SZS status Theorem for theBenchmark
% 0.25/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.38 % (3447046)------------------------------
% 0.25/0.38 % (3447046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3447046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3447046)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3447046)Termination reason: Refutation
% 0.25/0.38 % (3447046)Time elapsed: 0.039 s
% 0.25/0.38 % (3447046)Peak memory usage: 12 MB
% 0.25/0.38 % (3447046)Instructions burned: 58 (million)
% 0.25/0.38 % (3447036)Success in time 0.082 s
% 0.25/0.38 % Vampire exiting
%------------------------------------------------------------------------------