%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU646^2 : 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 : n001.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 08:32:49 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 391 ( 98 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 795 ( 8 ~; 14 |; 40 &; 664 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 26 usr; 10 con; 0-4 aty)
% ( 23 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 155 ( 67 ^; 78 !; 10 ?; 155 :)
% 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,
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,
kfst: $i > $i ).
thf(func_def_8,type,
kfstpairEq: $o ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_26,type,
sK3: $i > $i > $i > $i ).
thf(func_def_27,type,
sK4: $i > $i > $i > $i ).
thf(f1,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(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/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(f3,axiom,
( kfstpairEq
= ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(f4,conjecture,
( cartprodmempair1
=> ( kfstpairEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( in @ ( kfst @ X2 ) @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(f5,negated_conjecture,
~ ( cartprodmempair1
=> ( kfstpairEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( in @ ( kfst @ X2 ) @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f7,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(f8,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,[],[f7]) ).
thf(f9,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f10,plain,
~ ( cartprodmempair1
=> ( kfstpairEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( in @ ( kfst @ X2 ) @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( cartprodmempair1 = $true )
=> ( ( kfstpairEq = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true )
=> ( ( in @ ( kfst @ X2 ) @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( kfst @ X2 ) @ X0 )
!= $true )
& ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true ) )
& ( kfstpairEq = $true )
& ( cartprodmempair1 = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( kfst @ X2 ) @ X0 )
!= $true )
& ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true ) )
& ( kfstpairEq = $true )
& ( cartprodmempair1 = $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ( $true
!= ( in @ ( kfst @ sK2 ) @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
& ( kfstpairEq = $true )
& ( cartprodmempair1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
thf(f15,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f16,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,[],[f8]) ).
thf(f17,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
cartprodmempair1 = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
kfstpairEq = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
( $true
= ( in @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( $true
!= ( in @ ( kfst @ sK2 ) @ sK0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,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,[],[f16,f18,f15]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y1 ) ) ) ),
inference(definition_unfolding,[],[f17,f19,f15]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= Y0 )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 ),
inference(equality_proxy_clausification,[],[f29]) ).
thf(f31,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,[],[f24]) ).
thf(f32,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,[],[f31]) ).
thf(f33,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,[],[f32]) ).
thf(f34,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,[],[f33]) ).
thf(f35,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,[],[f34]) ).
thf(f36,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,[],[f35]) ).
thf(f37,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,[],[f36]) ).
thf(f38,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,[],[f37]) ).
thf(f39,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,[],[f38]) ).
thf(f40,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,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f42,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,[],[f40]) ).
thf(f43,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,[],[f42]) ).
thf(f44,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,[],[f43]) ).
thf(f46,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,[],[f44]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK3 @ X1 @ X0 @ X2 )
= ( kfst @ X0 ) )
| ( $false
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f30,f46]) ).
thf(f75,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kfst @ X0 ) @ X1 ) )
| ( $false
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f41,f65]) ).
thf(f80,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kfst @ X0 ) @ X1 ) )
| ( $false
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(duplicate_literal_removal,[],[f75]) ).
thf(f93,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( in @ sK2 @ ( cartprod @ sK0 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f21,f80]) ).
thf(f98,plain,
! [X0: $i] :
( $false
= ( in @ sK2 @ ( cartprod @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f108,plain,
$true = $false,
inference(constrained_superposition,[],[f20,f98]) ).
thf(f109,plain,
$false,
inference(trivial_inequality_removal,[],[f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU646^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.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 14:07:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.26 % (1295625)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (1295640)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=489808708:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.26 % (1295635)% WARNING: option uhcvi not known.
% 0.19/0.26 % (1295640) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1295625-1295640"...
% 0.19/0.26 % (1295640)...printing done.
% 0.19/0.26 % (1295634)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2955899982_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.26 % (1295640)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (1295640)------------------------------
% 0.19/0.26 % (1295640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (1295640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (1295640)CaDiCaL version: 2.1.3
% 0.19/0.26 % (1295640)Termination reason: Refutation
% 0.19/0.26 % (1295640)Time elapsed: 0.005 s
% 0.19/0.26 % (1295640)Peak memory usage: 12 MB
% 0.19/0.26 % (1295640)Instructions burned: 16 (million)
% 0.19/0.26 % (1295625)Success in time 0.031 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------