%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU660^2 : 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 08:32:52 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 35 unt; 0 typ; 1 def)
% Number of atoms : 404 ( 126 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 710 ( 15 ~; 20 |; 40 &; 537 @)
% ( 1 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 30 ( 25 usr; 11 con; 0-4 aty)
% ( 39 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 189 ( 0 sgn 106 !; 12 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
kpair: $i > $i > $i ).
thf(func_def_2,type,
cartprod: $i > $i > $i ).
thf(func_def_3,type,
cartprodmempair1: $o ).
thf(func_def_5,type,
setukpairinjR: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db4:
!>[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_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
sK4: $i > $i > $i > $i ).
thf(func_def_25,type,
sK5: $i > $i > $i > $i ).
thf(f1,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(f2,axiom,
( setukpairinjR
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(f3,conjecture,
( cartprodmempair1
=> ( setukpairinjR
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
=> ( in @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(f4,negated_conjecture,
~ ( cartprodmempair1
=> ( setukpairinjR
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
=> ( in @ X3 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,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,[],[f1]) ).
thf(f6,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,[],[f5]) ).
thf(f7,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f8,plain,
~ ( cartprodmempair1
=> ( setukpairinjR
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
=> ( in @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
~ ( ( cartprodmempair1 = $true )
=> ( ( setukpairinjR = $true )
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
= $true )
=> ( ( in @ X3 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
& ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
= $true ) )
& ( setukpairinjR = $true )
& ( cartprodmempair1 = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
& ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
= $true ) )
& ( setukpairinjR = $true )
& ( cartprodmempair1 = $true ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ( $true
!= ( in @ sK3 @ sK1 ) )
& ( $true
= ( in @ ( kpair @ sK2 @ sK3 ) @ ( cartprod @ sK0 @ sK1 ) ) )
& ( setukpairinjR = $true )
& ( cartprodmempair1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f11]) ).
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(cnf_transformation,[],[f6]) ).
thf(f14,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
cartprodmempair1 = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
setukpairinjR = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( $true
= ( in @ ( kpair @ sK2 @ sK3 ) @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
( $true
!= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f21,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,[],[f13,f15]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f23,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y3 @ Y2 )
= ( kpair @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ Y2 @ Y1 )
= ( kpair @ Y0 @ X1 ) )
=> ( Y1 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ Y2 @ Y1 )
= ( kpair @ Y0 @ X1 ) )
=> ( Y1 = X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( kpair @ Y1 @ Y0 )
= ( kpair @ X2 @ X1 ) )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( kpair @ Y1 @ Y0 )
= ( kpair @ X2 @ X1 ) )
=> ( Y0 = X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( kpair @ Y0 @ X3 )
= ( kpair @ X2 @ X1 ) )
=> ( X3 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( kpair @ Y0 @ X3 )
= ( kpair @ X2 @ X1 ) )
=> ( X3 = X1 ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( ( kpair @ X4 @ X3 )
= ( kpair @ X2 @ X1 ) )
=> ( X3 = X1 ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( kpair @ X4 @ X3 )
= ( kpair @ X2 @ X1 ) ) )
| ( $true
= ( X3 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( kpair @ X2 @ X1 )
!= ( kpair @ X4 @ X3 ) )
| ( $true
= ( X3 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( kpair @ X2 @ X1 )
!= ( kpair @ X4 @ X3 ) )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[],[f32]) ).
thf(f34,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,[],[f21]) ).
thf(f35,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,[],[f34]) ).
thf(f36,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,[],[f35]) ).
thf(f37,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,[],[f36]) ).
thf(f38,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,[],[f37]) ).
thf(f39,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,[],[f38]) ).
thf(f40,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,[],[f39]) ).
thf(f41,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 ) ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( kpair @ ( sK4 @ X3 @ X1 @ X2 ) @ Y0 )
= X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( kpair @ ( sK4 @ X3 @ X1 @ X2 ) @ Y0 )
= X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( kpair @ ( sK4 @ X3 @ X1 @ X2 ) @ Y0 )
= X1 ) )
@ ( sK5 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f43]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X2 )
& ( ( kpair @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK5 @ X3 @ X1 @ X2 ) )
= X1 ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( ( kpair @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK5 @ X3 @ X1 @ X2 ) )
= X1 ) ) ),
inference(and_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f46]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( kpair @ ( sK4 @ X3 @ X1 @ X2 ) @ ( sK5 @ X3 @ X1 @ X2 ) )
= X1 )
| ( $false
= ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f47]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( kpair @ X1 @ X2 )
!= X0 )
| ( ( sK5 @ X3 @ X0 @ X4 )
= X2 )
| ( $false
= ( in @ X0 @ ( cartprod @ X3 @ X4 ) ) ) ),
inference(constrained_superposition,[],[f33,f49]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ X1 @ X2 ) @ ( cartprod @ X0 @ X3 ) ) )
| ( ( sK5 @ X0 @ ( kpair @ X1 @ X2 ) @ X3 )
= X2 ) ),
inference(equality_resolution,[],[f63]) ).
thf(f70,plain,
( ( $true = $false )
| ( sK3
= ( sK5 @ sK0 @ ( kpair @ sK2 @ sK3 ) @ sK1 ) ) ),
inference(constrained_superposition,[],[f17,f66]) ).
thf(f71,plain,
( sK3
= ( sK5 @ sK0 @ ( kpair @ sK2 @ sK3 ) @ sK1 ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f75,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ( ( in @ ( kpair @ sK2 @ sK3 ) @ ( cartprod @ sK0 @ sK1 ) )
= $false ) ),
inference(constrained_superposition,[],[f48,f71]) ).
thf(f76,plain,
( ( in @ ( kpair @ sK2 @ sK3 ) @ ( cartprod @ sK0 @ sK1 ) )
= $false ),
inference(forward_subsumption_resolution,[],[f75,f18]) ).
thf(f165,definition,
( spl6_1
<=> ( ( in @ ( kpair @ sK2 @ sK3 ) @ ( cartprod @ sK0 @ sK1 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f167,plain,
( ( ( in @ ( kpair @ sK2 @ sK3 ) @ ( cartprod @ sK0 @ sK1 ) )
= $false )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f405,plain,
spl6_1,
inference(avatar_split_clause,[],[f76,f165]) ).
thf(f406,plain,
( ( $true = $false )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f167,f17]) ).
thf(f412,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f406]) ).
thf(f413,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f412]) ).
cnf(s11,plain,
spl6_1,
inference(sat_conversion,[],[f405]) ).
cnf(s13,plain,
~ spl6_1,
inference(sat_conversion,[],[f413]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s11,s13]) ).
thf(f414,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU660^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 14:03:43 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.13 Running first-order model finding
% 0.08/0.13 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
% 0.08/0.17 % (154375)Will run a generic schedule for satisfiability detection.
% 0.08/0.17 % (154381)% WARNING: option uhcvi not known.
% 0.08/0.17 % (154381)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3146330218:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.17 % (154380)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2870838359_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.17 % (154381)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.17 % (154381)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.17 % Exception at run slice level
% 0.08/0.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.17 % (154382)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=343655422:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.17 % (154389)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3969745892:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.08/0.17 % Exception at run slice level
% 0.08/0.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.17 % (154383)dis+10_1_sil=32000:sp=arity:random_seed=1448997135:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.17 % (154381) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-154375-154381"...
% 0.08/0.17 % (154381)...printing done.
% 0.08/0.17 % (154381)Refutation found. Thanks to Tanya!
% 0.08/0.17 % SZS status Theorem for theBenchmark
% 0.08/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.18 % (154381)------------------------------
% 0.08/0.18 % (154381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18 % (154381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18 % (154381)CaDiCaL version: 2.1.3
% 0.08/0.18 % (154381)Termination reason: Refutation
% 0.08/0.18 % (154381)Time elapsed: 0.015 s
% 0.08/0.18 % (154381)Peak memory usage: 13 MB
% 0.08/0.18 % (154381)Instructions burned: 53 (million)
% 0.08/0.18 % (154375)Success in time 0.038 s
% 0.08/0.18 % Vampire exiting
%------------------------------------------------------------------------------