%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU681^2 : 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 : n013.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 08:32:58 AM UTC 2026
% Result : Theorem 1.23s 0.41s
% Output : Refutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 4
% Syntax : Number of formulae : 69 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 661 ( 171 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 983 ( 40 ~; 60 |; 51 &; 713 @)
% ( 0 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 27 usr; 10 con; 0-4 aty)
% ( 30 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 216 ( 73 ^; 124 !; 19 ?; 216 :)
% 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,
subsetE: $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
cartprod: $i > $i > $i ).
thf(func_def_6,type,
cartprodmempair1: $o ).
thf(func_def_7,type,
breln: $i > $i > $i > $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
vAND: $o > $o > $o ).
thf(func_def_16,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_24,type,
sK3: $i > $o ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
sK5: $i > $i > $i > $i ).
thf(func_def_28,type,
sK6: $i > $i > $i > $i ).
thf(f1,axiom,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(f2,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/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(f3,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(f4,conjecture,
( subsetE
=> ( cartprodmempair1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(f5,negated_conjecture,
~ ( subsetE
=> ( cartprodmempair1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( X3 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,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,[],[f2]) ).
thf(f9,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,[],[f8]) ).
thf(f10,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f11,plain,
~ ( subsetE
=> ( cartprodmempair1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( X3 @ X6 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
~ ( ( subsetE = $true )
=> ( ( cartprodmempair1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( breln @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
=> ( ( X3 @ ( kpair @ X4 @ X5 ) )
= $true ) ) ) )
=> ! [X6: $i] :
( ( ( in @ X6 @ X2 )
= $true )
=> ( ( X3 @ X6 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ? [X6: $i] :
( ( ( X3 @ X6 )
!= $true )
& ( ( in @ X6 @ X2 )
= $true ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( X3 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ( ( in @ X4 @ X0 )
!= $true ) ) )
& ( ( breln @ X0 @ X1 @ X2 )
= $true ) )
& ( cartprodmempair1 = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ? [X6: $i] :
( ( ( X3 @ X6 )
!= $true )
& ( ( in @ X6 @ X2 )
= $true ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( X3 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ( ( in @ X4 @ X0 )
!= $true ) ) )
& ( ( breln @ X0 @ X1 @ X2 )
= $true ) )
& ( cartprodmempair1 = $true )
& ( subsetE = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ? [X4: $i] :
( ( ( X3 @ X4 )
!= $true )
& ( ( in @ X4 @ X2 )
= $true ) )
& ! [X5: $i] :
( ! [X6: $i] :
( ( $true
= ( X3 @ ( kpair @ X5 @ X6 ) ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ X2 ) )
| ( $true
!= ( in @ X6 @ X1 ) ) )
| ( $true
!= ( in @ X5 @ X0 ) ) ) )
& ( ( breln @ X0 @ X1 @ X2 )
= $true ) )
& ( cartprodmempair1 = $true )
& ( subsetE = $true ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( $true
!= ( sK3 @ sK4 ) )
& ( $true
= ( in @ sK4 @ sK2 ) )
& ! [X5: $i] :
( ! [X6: $i] :
( ( $true
= ( sK3 @ ( kpair @ X5 @ X6 ) ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK2 ) )
| ( $true
!= ( in @ X6 @ sK1 ) ) )
| ( $true
!= ( in @ X5 @ sK0 ) ) )
& ( $true
= ( breln @ sK0 @ sK1 @ sK2 ) )
& ( cartprodmempair1 = $true )
& ( subsetE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f15]) ).
thf(f17,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,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,[],[f9]) ).
thf(f19,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f20,plain,
subsetE = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
cartprodmempair1 = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( $true
= ( breln @ sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
! [X6: $i,X5: $i] :
( ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK2 ) )
| ( $true
= ( sK3 @ ( kpair @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X6 @ sK1 ) )
| ( $true
!= ( in @ X5 @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
( $true
= ( in @ sK4 @ sK2 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( $true
!= ( sK3 @ sK4 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f29,plain,
( ( !! @ $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 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f21]) ).
thf(f30,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK0
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[],[f22,f19]) ).
thf(f31,plain,
( $true
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,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 )
& ( ( kpair @ Y3 @ Y4 )
= Y0 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f33,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 )
& ( ( kpair @ Y2 @ Y3 )
= X1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,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 )
& ( ( kpair @ Y2 @ Y3 )
= X1 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f35,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 )
& ( ( kpair @ Y1 @ Y2 )
= X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,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 )
& ( ( kpair @ Y1 @ Y2 )
= X1 ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f37,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 )
& ( ( kpair @ Y0 @ Y1 )
= X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,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 )
& ( ( kpair @ Y0 @ Y1 )
= X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f39,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 )
& ( ( kpair @ Y0 @ Y1 )
= X1 ) ) ) )
@ ( sK5 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 )
= X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 )
= X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 )
= X1 ) )
@ ( sK6 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f41]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ ( sK6 @ X3 @ X1 @ X2 ) @ X2 )
& ( ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ ( sK6 @ X3 @ X1 @ X2 ) )
= X1 ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ ( sK6 @ X3 @ X1 @ X2 ) )
= X1 ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK6 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ ( sK6 @ X3 @ X1 @ X2 ) )
= X1 )
| ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f45]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X3 @ X2 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $true
= ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f68,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( $true
= ( in @ X0 @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f31,f55]) ).
thf(f70,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f647,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK6 @ X1 @ X0 @ X2 ) @ sK1 ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $true
!= ( in @ X0 @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ X1 @ X0 @ X2 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f23,f47]) ).
thf(f2505,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
!= ( in @ X1 @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ X0 @ X1 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ X1 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ ( cartprod @ X0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f647,f46]) ).
thf(f2515,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
!= ( in @ X1 @ sK2 ) )
| ( $true
!= ( in @ ( sK5 @ X0 @ X1 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ X1 @ ( cartprod @ X0 @ sK1 ) ) ) ),
inference(duplicate_literal_removal,[],[f2505]) ).
thf(f2516,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK5 @ X0 @ X1 @ sK1 ) @ sK0 ) )
| ( $true
!= ( in @ X1 @ sK2 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( in @ X1 @ ( cartprod @ X0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f2515]) ).
thf(f2905,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ sK2 ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( in @ X0 @ ( cartprod @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f2516,f42]) ).
thf(f2915,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ sK2 ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( in @ X0 @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(duplicate_literal_removal,[],[f2905]) ).
thf(f2916,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK2 ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( in @ X0 @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f2915]) ).
thf(f3088,plain,
( ( $true != $true )
| ( $true
= ( sK3 @ sK4 ) )
| ( $false
= ( in @ sK4 @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f2916,f24]) ).
thf(f3128,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $false
= ( in @ sK4 @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f3088]) ).
thf(f3130,plain,
( $false
= ( in @ sK4 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(forward_subsumption_resolution,[],[f3128,f25]) ).
thf(f3196,plain,
( ( $true = $false )
| ( ( in @ sK4 @ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f70,f3130]) ).
thf(f3197,plain,
( ( in @ sK4 @ sK2 )
= $false ),
inference(trivial_inequality_removal,[],[f3196]) ).
thf(f3202,plain,
$true = $false,
inference(constrained_superposition,[],[f24,f3197]) ).
thf(f3204,plain,
$false,
inference(trivial_inequality_removal,[],[f3202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU681^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:09:06 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 1.23/0.41 % (2175294)Will run a generic schedule for satisfiability detection.
% 1.23/0.41 % (2175300)% WARNING: option uhcvi not known.
% 1.23/0.41 % (2175300)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2971419357:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.23/0.41 % (2175300)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.23/0.41 % (2175300)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.23/0.41 % (2175299)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1666378408_2999 on theBenchmark for (2999ds/0Mi)
% 1.23/0.41 % (2175301)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2198713725:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.23/0.41 % (2175303)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3665193605:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.23/0.41 % (2175305)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1998612602:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.23/0.41 % (2175304)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3932382154:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.23/0.41 % (2175303)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.23/0.41 % Exception at run slice level
% 1.23/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.23/0.41 % (2175302)dis+10_1_sil=32000:sp=arity:random_seed=251388301:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.23/0.41 % (2175312)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2560733328:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.23/0.41 % Exception at run slice level
% 1.23/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.23/0.41 % (2175315)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4240334435:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.23/0.41 % (2175303)Instruction limit reached!
% 1.23/0.41 % (2175303)------------------------------
% 1.23/0.41 % (2175303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.41 % (2175303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.41 % (2175303)CaDiCaL version: 2.1.3
% 1.23/0.41 % (2175303)Termination reason: Instruction limit
% 1.23/0.41 % (2175303)Termination phase: Saturation
% 1.23/0.41 % (2175303)Time elapsed: 0.053 s
% 1.23/0.41 % (2175303)Peak memory usage: 12 MB
% 1.23/0.41 % (2175303)Instructions burned: 118 (million)
% 1.23/0.41 % (2175304)Instruction limit reached!
% 1.23/0.41 % (2175304)------------------------------
% 1.23/0.41 % (2175304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.41 % (2175304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.41 % (2175304)CaDiCaL version: 2.1.3
% 1.23/0.41 % (2175304)Termination reason: Instruction limit
% 1.23/0.41 % (2175304)Termination phase: Saturation
% 1.23/0.41 % (2175304)Time elapsed: 0.063 s
% 1.23/0.41 % (2175304)Peak memory usage: 12 MB
% 1.23/0.41 % (2175304)Instructions burned: 133 (million)
% 1.23/0.41 % (2175317)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=893014009:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.23/0.41 % (2175317)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.23/0.41 % (2175317)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.23/0.41 % (2175305)Instruction limit reached!
% 1.23/0.41 % (2175305)------------------------------
% 1.23/0.41 % (2175305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.41 % (2175305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.41 % (2175305)CaDiCaL version: 2.1.3
% 1.23/0.41 % (2175305)Termination reason: Instruction limit
% 1.23/0.41 % (2175305)Termination phase: Saturation
% 1.23/0.41 % (2175305)Time elapsed: 0.078 s
% 1.23/0.41 % (2175305)Peak memory usage: 12 MB
% 1.23/0.41 % (2175305)Instructions burned: 159 (million)
% 1.23/0.41 % (2175318)ott-21_1_sil=16000:fs=off:random_seed=1960568894:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.23/0.41 % (2175302)Instruction limit reached!
% 1.23/0.41 % (2175302)------------------------------
% 1.23/0.41 % (2175302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.41 % (2175302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.41 % (2175302)CaDiCaL version: 2.1.3
% 1.23/0.41 % (2175302)Termination reason: Instruction limit
% 1.23/0.41 % (2175302)Termination phase: Saturation
% 1.23/0.41 % (2175302)Time elapsed: 0.061 s
% 1.23/0.41 % (2175302)Peak memory usage: 12 MB
% 1.23/0.41 % (2175302)Instructions burned: 104 (million)
% 1.23/0.41 % (2175320)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3538745649:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.23/0.41 % (2175322)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2319523732:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.23/0.41 % Exception at run slice level
% 1.23/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.23/0.41 % (2175315)Instruction limit reached!
% 1.23/0.41 % (2175315)------------------------------
% 1.23/0.41 % (2175315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.41 % (2175315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.41 % (2175315)CaDiCaL version: 2.1.3
% 1.23/0.41 % (2175315)Termination reason: Instruction limit
% 1.23/0.41 % (2175315)Termination phase: Saturation
% 1.23/0.41 % (2175315)Time elapsed: 0.069 s
% 1.23/0.41 % (2175315)Peak memory usage: 12 MB
% 1.23/0.41 % (2175315)Instructions burned: 131 (million)
% 1.23/0.41 % (2175325)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3005402874:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.23/0.41 % (2175326)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3446792642:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.23/0.41 % Exception at run slice level
% 1.23/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.23/0.41 % (2175301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2175294-2175301"...
% 1.23/0.41 % (2175329)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1724521753:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.23/0.41 % (2175329)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.23/0.41 % (2175301)...printing done.
% 1.23/0.41 % (2175301)Refutation found. Thanks to Tanya!
% 1.23/0.41 % SZS status Theorem for theBenchmark
% 1.23/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 1.23/0.41 % (2175301)------------------------------
% 1.23/0.41 % (2175301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.41 % (2175301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.41 % (2175301)CaDiCaL version: 2.1.3
% 1.23/0.41 % (2175301)Termination reason: Refutation
% 1.23/0.41 % (2175301)Time elapsed: 0.157 s
% 1.23/0.41 % (2175301)Peak memory usage: 13 MB
% 1.23/0.41 % (2175301)Instructions burned: 327 (million)
% 1.23/0.41 % (2175294)Success in time 0.202 s
% 1.23/0.41 % Vampire exiting
%------------------------------------------------------------------------------