%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU690^2 : 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 : n012.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 08:32:59 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 8
% Syntax : Number of formulae : 125 ( 37 unt; 0 typ; 4 def)
% Number of atoms : 1702 ( 357 equ; 0 cnn)
% Maximal formula atoms : 13 ( 13 avg)
% Number of connectives : 2440 ( 149 ~; 271 |; 24 &;1760 @)
% ( 4 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 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; 13 con; 0-4 aty)
% ( 64 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 303 ( 0 sgn 192 !; 12 ?; 303 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
setextsub: $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
cartprod: $i > $i > $i ).
thf(func_def_6,type,
breln: $i > $i > $i > $o ).
thf(func_def_7,type,
subbreln: $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
sK4: $i > $i > $i > $i > $i ).
thf(func_def_26,type,
sK5: $i > $i > $i > $i > $i ).
thf(f1,axiom,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(f2,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(f3,axiom,
( subbreln
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(f4,conjecture,
( setextsub
=> ( subbreln
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(f5,negated_conjecture,
~ ( setextsub
=> ( subbreln
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f9,plain,
( subbreln
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f10,plain,
( subbreln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( breln @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y0 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( setextsub
=> ( subbreln
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
~ ( ( setextsub = $true )
=> ( ( subbreln = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( breln @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( breln @ X0 @ X1 @ X3 )
= $true )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true ) ) ) )
=> ( ! [X6: $i] :
( ( ( in @ X6 @ X0 )
= $true )
=> ! [X7: $i] :
( ( ( in @ X7 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
= $true )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
!= $true )
| ( ( in @ X7 @ X1 )
!= $true ) )
| ( ( in @ X6 @ X0 )
!= $true ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( ( breln @ X0 @ X1 @ X3 )
= $true ) )
& ( ( breln @ X0 @ X1 @ X2 )
= $true ) )
& ( subbreln = $true )
& ( setextsub = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
!= $true )
| ( ( in @ X7 @ X1 )
!= $true ) )
| ( ( in @ X6 @ X0 )
!= $true ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( ( breln @ X0 @ X1 @ X3 )
= $true ) )
& ( ( breln @ X0 @ X1 @ X2 )
= $true ) )
& ( subbreln = $true )
& ( setextsub = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
= $true )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
!= $true )
| ( ( in @ X7 @ X1 )
!= $true ) )
| ( ( in @ X6 @ X0 )
!= $true ) )
& ( ( breln @ X0 @ X1 @ X3 )
= $true ) )
& ( ( breln @ X0 @ X1 @ X2 )
= $true ) )
& ( subbreln = $true )
& ( setextsub = $true ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( sK2 != sK3 )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK3 ) )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) )
& ! [X6: $i] :
( ! [X7: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK3 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ sK2 ) )
| ( $true
!= ( in @ X7 @ sK1 ) ) )
| ( $true
!= ( in @ X6 @ sK0 ) ) )
& ( $true
= ( breln @ sK0 @ sK1 @ sK3 ) )
& ( $true
= ( breln @ sK0 @ sK1 @ sK2 ) )
& ( subbreln = $true )
& ( setextsub = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
thf(f17,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f19,plain,
( subbreln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( breln @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y0 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f20,plain,
setextsub = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
subbreln = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( $true
= ( breln @ sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( $true
= ( breln @ sK0 @ sK1 @ sK3 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
! [X6: $i,X7: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK3 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ sK2 ) )
| ( $true
!= ( in @ X7 @ sK1 ) )
| ( $true
!= ( in @ X6 @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK3 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK1 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f16]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f30,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y1
@ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y0 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f19,f21,f18,f18]) ).
thf(f31,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK0
@ sK1
@ sK3 ) ),
inference(definition_unfolding,[],[f23,f18]) ).
thf(f32,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK0
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[],[f22,f18]) ).
thf(f33,plain,
( $true
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
( $true
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y1
@ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y0 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y0 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ X1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ X1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ X1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ X1 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ Y0 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ Y0 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ X1 @ Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( subset @ X4 @ ( cartprod @ X3 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) ) )
=> ( subset @ X1 @ X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) ) )
=> ( subset @ X1 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) )
@ ( sK4 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(sigma_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X4 ) ) ) ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X4 ) ) ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ X3 ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X4 ) ) )
@ ( sK5 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(sigma_proxy_clausification,[],[f48]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( ( in @ ( sK5 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
=> ( ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ ( sK5 @ X1 @ X2 @ X3 @ X4 ) ) @ X1 )
=> ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ ( sK5 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 ) ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ ( sK5 @ X1 @ X2 @ X3 @ X4 ) ) @ X1 )
=> ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ ( sK5 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK5 @ X1 @ X2 @ X3 @ X4 ) @ X2 ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ ( sK5 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ ( sK5 @ X1 @ X2 @ X3 @ X4 ) ) @ X1 ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X3 @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( subset @ X2 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $true
= ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f61]) ).
thf(f91,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
!= ( in @ ( kpair @ ( sK4 @ X0 @ X1 @ sK3 @ X2 ) @ ( sK5 @ X1 @ X2 @ X0 @ sK3 ) ) @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ X1 @ X2 @ X0 @ sK3 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ X1 @ sK3 @ X2 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f24,f54]) ).
thf(f92,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK4 @ X0 @ X1 @ sK3 @ X2 ) @ ( sK5 @ X1 @ X2 @ X0 @ sK3 ) ) @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ X1 @ X2 @ X0 @ sK3 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ X1 @ sK3 @ X2 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f99,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( kpair @ ( sK4 @ X0 @ sK3 @ X1 @ X2 ) @ ( sK5 @ sK3 @ X2 @ X0 @ X1 ) ) @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X2 @ X0 @ X1 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ X1 @ X2 ) @ sK0 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X2 ) ) )
| ( $true
= ( subset @ sK3 @ X1 ) ) ),
inference(constrained_superposition,[],[f25,f55]) ).
thf(f100,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ ( sK4 @ X0 @ sK3 @ X1 @ X2 ) @ ( sK5 @ sK3 @ X2 @ X0 @ X1 ) ) @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X2 @ X0 @ X1 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ X1 @ X2 ) @ sK0 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X2 ) ) )
| ( $true
= ( subset @ sK3 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f118,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK5 @ sK2 @ X1 @ X0 @ sK3 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) ) ),
inference(constrained_superposition,[],[f92,f55]) ).
thf(f121,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK5 @ sK2 @ X1 @ X0 @ sK3 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f118]) ).
thf(f122,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK5 @ sK2 @ X1 @ X0 @ sK3 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f124,definition,
( spl6_1
<=> ( $true
= ( subset @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f126,plain,
( ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f128,definition,
( spl6_2
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK5 @ sK2 @ X1 @ X0 @ sK3 ) @ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ X1 ) @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f129,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK5 @ sK2 @ X1 @ X0 @ sK3 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f130,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f122,f128,f124]) ).
thf(f132,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X1 @ X0 @ sK2 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ X1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) ) ),
inference(constrained_superposition,[],[f54,f100]) ).
thf(f136,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X1 @ X0 @ sK2 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ X1 ) @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f132]) ).
thf(f137,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X1 @ X0 @ sK2 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ X1 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f141,definition,
( spl6_3
<=> ( $true
= ( subset @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f142,plain,
( ( $true
!= ( subset @ sK3 @ sK2 ) )
| spl6_3 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f143,plain,
( ( $true
= ( subset @ sK3 @ sK2 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f145,definition,
( spl6_4
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ X1 ) @ sK0 ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X1 @ X0 @ sK2 ) @ sK1 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f146,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ X1 ) @ sK0 ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X1 @ X0 @ sK2 ) @ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f147,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f137,f145,f141]) ).
thf(f152,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ sK3 ) )
| ( sK2 = sK3 )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f62,f143]) ).
thf(f153,plain,
( ( $false
= ( subset @ sK2 @ sK3 ) )
| ( sK2 = sK3 )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f157,plain,
( ( $false
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f153,f26]) ).
thf(f161,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f129,f53]) ).
thf(f166,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) ) )
| ~ spl6_2 ),
inference(duplicate_literal_removal,[],[f161]) ).
thf(f167,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f168,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f167,f157]) ).
thf(f169,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK4 @ X0 @ sK2 @ sK3 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f188,plain,
( ( $true != $true )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(constrained_superposition,[],[f169,f49]) ).
thf(f191,plain,
( ( $true != $true )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(duplicate_literal_removal,[],[f188]) ).
thf(f192,plain,
( ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f193,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f192,f34]) ).
thf(f194,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f193]) ).
thf(f195,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f194,f33]) ).
thf(f196,plain,
( ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f197,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f196,f157]) ).
thf(f198,plain,
( $false
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f199,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f198]) ).
thf(f209,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) ) )
| ~ spl6_4 ),
inference(constrained_superposition,[],[f146,f53]) ).
thf(f212,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) ) )
| ~ spl6_4 ),
inference(duplicate_literal_removal,[],[f209]) ).
thf(f213,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) ) )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f212]) ).
thf(f215,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK4 @ X0 @ sK3 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK1 ) ) ) )
| spl6_3
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f213,f142]) ).
thf(f219,plain,
( ( $true != $true )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| spl6_3
| ~ spl6_4 ),
inference(constrained_superposition,[],[f215,f49]) ).
thf(f222,plain,
( ( $true != $true )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| spl6_3
| ~ spl6_4 ),
inference(duplicate_literal_removal,[],[f219]) ).
thf(f223,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| spl6_3
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f224,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl6_3
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f223,f142]) ).
thf(f225,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl6_3
| ~ spl6_4 ),
inference(forward_demodulation,[],[f224,f33]) ).
thf(f226,plain,
( ( $false
= ( subset @ sK3 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl6_3
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f227,plain,
( ( $true = $false )
| spl6_3
| ~ spl6_4 ),
inference(constrained_superposition,[],[f226,f34]) ).
thf(f233,plain,
( $false
| spl6_3
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f234,plain,
( spl6_3
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f233]) ).
thf(f243,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_3 ),
inference(constrained_superposition,[],[f157,f126]) ).
thf(f249,plain,
( $false
| ~ spl6_1
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f250,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f249]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f130]) ).
cnf(s2,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f147]) ).
cnf(s4,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f199]) ).
cnf(s7,plain,
( spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f234]) ).
cnf(s9,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f250]) ).
cnf(s10,plain,
spl6_3,
inference(rat,[],[s2,s7]) ).
cnf(s11,plain,
~ spl6_1,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
~ spl6_2,
inference(rat,[],[s4,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s12,s11]) ).
thf(f251,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU690^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:10:20 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.12 Running first-order model finding
% 0.08/0.12 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
% 0.08/0.16 % (162062)Will run a generic schedule for satisfiability detection.
% 0.08/0.16 % (162068)% WARNING: option uhcvi not known.
% 0.08/0.16 % (162068)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2406722122:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.16 % (162069)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1990820314:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.16 % (162070)dis+10_1_sil=32000:sp=arity:random_seed=3136475459:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.16 % (162067)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2831509883_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.16 % (162071)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1237730914:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.16 % (162072)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1199822448:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.16 % (162073)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2125344674:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.16 % (162071)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.16 % (162068)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.16 % (162068)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.16 % Exception at run slice level
% 0.08/0.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.16 % (162071) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-162062-162071"...
% 0.08/0.16 % (162081)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=423249668:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.08/0.16 % (162071)...printing done.
% 0.08/0.16 % (162071)Refutation found. Thanks to Tanya!
% 0.08/0.16 % SZS status Theorem for theBenchmark
% 0.08/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.16 % (162071)------------------------------
% 0.08/0.16 % (162071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (162071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (162071)CaDiCaL version: 2.1.3
% 0.08/0.16 % (162071)Termination reason: Refutation
% 0.08/0.16 % (162071)Time elapsed: 0.011 s
% 0.08/0.16 % (162071)Peak memory usage: 12 MB
% 0.08/0.16 % (162071)Instructions burned: 38 (million)
% 0.08/0.16 % (162062)Success in time 0.032 s
% 0.08/0.16 % Vampire exiting
%------------------------------------------------------------------------------