%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU632^2 : 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 : n011.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 08:32:45 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 77 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 775 ( 159 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 1675 ( 12 ~; 33 |; 76 &;1461 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 29 usr; 10 con; 0-4 aty)
% ( 23 !!; 47 ??; 0 @@+; 0 @@-)
% Number of variables : 234 ( 102 ^; 118 !; 14 ?; 234 :)
% 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,
kpair: $i > $i > $i ).
thf(func_def_7,type,
kpairp: $o ).
thf(func_def_8,type,
cartprod: $i > $i > $i ).
thf(func_def_9,type,
cartprodmempair1: $o ).
thf(func_def_10,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db2:
!>[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_17,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
vIMP: $o > $o > $o ).
thf(func_def_19,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
sK3: $i > $i > $i > $i ).
thf(func_def_28,type,
sK4: $i > $i > $i > $i ).
thf(func_def_29,type,
sK5: $i > $i > $i ).
thf(func_def_30,type,
sK6: $i > $i > $i ).
thf(f1,axiom,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ X0 ) ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(f2,axiom,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(f3,axiom,
( kpairp
= ( ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(f4,axiom,
( cartprodmempair1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( X2
= ( kpair @ X3 @ X4 ) )
& ( in @ X4 @ X1 ) )
& ( in @ X3 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(f5,conjecture,
( kpairp
=> ( cartprodmempair1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( iskpair @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(f6,negated_conjecture,
~ ( kpairp
=> ( cartprodmempair1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( iskpair @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ X0 ) ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f10,plain,
( kpairp
= ( ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( kpairp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( iskpair @ ( kpair @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( cartprodmempair1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( X2
= ( kpair @ X3 @ X4 ) )
& ( in @ X4 @ X1 ) )
& ( in @ X3 @ X0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f13,plain,
( cartprodmempair1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( cartprod @ Y2 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( kpair @ Y3 @ Y4 )
= Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
~ ( kpairp
=> ( cartprodmempair1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( iskpair @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f15,plain,
~ ( ( kpairp = $true )
=> ( ( cartprodmempair1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true )
=> ( ( iskpair @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( iskpair @ X2 )
!= $true )
& ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true ) )
& ( cartprodmempair1 = $true )
& ( kpairp = $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( iskpair @ X2 )
!= $true )
& ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true ) )
& ( cartprodmempair1 = $true )
& ( kpairp = $true ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ( $true
!= ( iskpair @ sK2 ) )
& ( $true
= ( in @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
& ( cartprodmempair1 = $true )
& ( kpairp = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
thf(f19,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,plain,
( kpairp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( iskpair @ ( kpair @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f22,plain,
( cartprodmempair1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( cartprod @ Y2 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( kpair @ Y3 @ Y4 )
= Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f23,plain,
kpairp = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f24,plain,
cartprodmempair1 = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
( $true
= ( in @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f26,plain,
( $true
!= ( iskpair @ sK2 ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f29,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ Y2 ) )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ ( setunion @ Y2 ) )
& ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y4 @ emptyset ) ) @ emptyset ) )
= Y2 ) ) ) ) )
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f21,f23,f19,f20]) ).
thf(f30,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( cartprod @ Y2 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( ^ [Y5: $i,Y6: $i] : ( setadjoin @ ( setadjoin @ Y5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y5 @ ( setadjoin @ Y6 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y4 )
= Y0 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f22,f24,f20]) ).
thf(f31,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) )
@ sK2 ) ),
inference(definition_unfolding,[],[f26,f19]) ).
thf(f32,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X1: $i] :
( $false
= ( ( in @ X1 @ ( setunion @ sK2 ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 ) )
@ X2 ) )
| ( $false
= ( in @ X1 @ ( setunion @ sK2 ) ) ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ X2 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= sK2 ) )
| ( $false
= ( in @ X1 @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= sK2 )
| ( $false
= ( in @ X1 @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ sK2 ) ) ) ),
inference(equality_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( cartprod @ Y2 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( ^ [Y5: $i,Y6: $i] : ( setadjoin @ ( setadjoin @ Y5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y5 @ ( setadjoin @ Y6 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y4 )
= Y0 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f41,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( cartprod @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( cartprod @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( cartprod @ Y0 @ X2 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( cartprod @ Y0 @ X2 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( cartprod @ X3 @ X2 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f48]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= X1 ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f49]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
& ( ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ ( setadjoin @ ( sK4 @ X3 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) )
= X1 ) ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ ( setadjoin @ ( sK4 @ X3 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) )
= X1 ) ) ),
inference(and_proxy_clausification,[],[f52]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3 @ X3 @ X1 @ X2 ) @ ( setadjoin @ ( sK4 @ X3 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) )
= X1 ) ),
inference(equality_proxy_clausification,[],[f53]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ Y2 ) )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ ( setunion @ Y2 ) )
& ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y4 @ emptyset ) ) @ emptyset ) )
= Y2 ) ) ) ) )
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
@ ( sK5 @ X1 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ ( sK5 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ ( sK5 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(and_proxy_clausification,[],[f61]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
@ ( sK6 @ X1 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f62]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ ( sK6 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ ( setadjoin @ ( sK6 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ ( setadjoin @ ( sK6 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ ( sK6 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5 @ X1 @ X2 ) @ ( setadjoin @ ( sK6 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f66]) ).
thf(f85,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK6 @ ( sK4 @ X1 @ X0 @ X2 ) @ ( sK3 @ X1 @ X0 @ X2 ) ) @ ( setunion @ X0 ) ) )
| ( $false
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f67,f55]) ).
thf(f86,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ ( sK4 @ X1 @ X0 @ X2 ) @ ( sK3 @ X1 @ X0 @ X2 ) ) @ ( setunion @ X0 ) ) )
| ( $false
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f63,f55]) ).
thf(f114,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= sK2 )
| ( $false
= ( in @ ( sK5 @ X1 @ X0 ) @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ ( sK6 @ X1 @ X0 ) @ ( setunion @ sK2 ) ) ) ),
inference(constrained_superposition,[],[f39,f68]) ).
thf(f127,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( sK2 != X0 )
| ( $false
= ( in @ ( sK5 @ ( sK4 @ X1 @ X0 @ X2 ) @ ( sK3 @ X1 @ X0 @ X2 ) ) @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ ( sK6 @ ( sK4 @ X1 @ X0 @ X2 ) @ ( sK3 @ X1 @ X0 @ X2 ) ) @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f114,f55]) ).
thf(f141,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK6 @ ( sK4 @ X0 @ sK2 @ X1 ) @ ( sK3 @ X0 @ sK2 @ X1 ) ) @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ ( sK5 @ ( sK4 @ X0 @ sK2 @ X1 ) @ ( sK3 @ X0 @ sK2 @ X1 ) ) @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(equality_resolution,[],[f127]) ).
thf(f144,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( in @ ( sK5 @ ( sK4 @ X0 @ sK2 @ X1 ) @ ( sK3 @ X0 @ sK2 @ X1 ) ) @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f85,f141]) ).
thf(f145,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( in @ ( sK5 @ ( sK4 @ X0 @ sK2 @ X1 ) @ ( sK3 @ X0 @ sK2 @ X1 ) ) @ ( setunion @ sK2 ) ) ) ),
inference(duplicate_literal_removal,[],[f144]) ).
thf(f146,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ ( sK4 @ X0 @ sK2 @ X1 ) @ ( sK3 @ X0 @ sK2 @ X1 ) ) @ ( setunion @ sK2 ) ) )
| ( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f152,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f86,f146]) ).
thf(f153,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[],[f152]) ).
thf(f154,plain,
! [X0: $i,X1: $i] :
( $false
= ( in @ sK2 @ ( cartprod @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f160,plain,
$true = $false,
inference(constrained_superposition,[],[f25,f154]) ).
thf(f161,plain,
$false,
inference(trivial_inequality_removal,[],[f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU632^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:00:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.27 % (140165)Will run a generic schedule for satisfiability detection.
% 0.21/0.27 % (140179)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=86554256:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.27 % (140174)% WARNING: option uhcvi not known.
% 0.21/0.27 % (140173)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1914651150_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.27 % (140175)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1156780698:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.27 % (140176)dis+10_1_sil=32000:sp=arity:random_seed=1714961226:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.27 % (140174)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2084831612:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.27 % (140178)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=700277718:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.27 % (140177)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4184009699:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.27 % (140174)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.27 % (140177)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.27 % Exception at run slice level
% 0.21/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.27 % (140174)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.27 % (140179) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-140165-140179"...
% 0.21/0.27 % (140179)...printing done.
% 0.21/0.27 % (140179)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (140179)------------------------------
% 0.21/0.27 % (140179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (140179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (140179)CaDiCaL version: 2.1.3
% 0.21/0.27 % (140179)Termination reason: Refutation
% 0.21/0.27 % (140179)Time elapsed: 0.012 s
% 0.21/0.27 % (140179)Peak memory usage: 13 MB
% 0.21/0.27 % (140179)Instructions burned: 41 (million)
% 0.21/0.27 % (140165)Success in time 0.038 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------