%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU631^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:30:25 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 441 ( 110 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 661 ( 41 ~; 30 |; 45 &; 513 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 27 usr; 12 con; 0-4 aty)
% ( 0 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 143 ( 67 ^; 55 !; 21 ?; 143 :)
% 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,
powerset: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
dsetconstrER: $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
cartprod: $i > $i > $i ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
sK1: $i > $o ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ? [X4: $i] :
( ( X2
= ( kpair @ X3 @ X4 ) )
& ( in @ X4 @ X1 ) )
& ( in @ X3 @ X0 ) ) ) )
= cartprod ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprod) ).
thf(f4,conjecture,
( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X2
= ( kpair @ X3 @ X4 ) ) )
& ( in @ X3 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(f5,negated_conjecture,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X2
= ( kpair @ X3 @ X4 ) ) )
& ( in @ X3 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ? [X4: $i] :
( ( X2
= ( kpair @ X3 @ X4 ) )
& ( in @ X4 @ X1 ) )
& ( in @ X3 @ X0 ) ) ) )
= cartprod ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X2
= ( kpair @ X3 @ X4 ) ) )
& ( in @ X3 @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X2 )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) )
= dsetconstrER ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
=> ( ( X2 @ X1 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f13,plain,
( ( dsetconstrER = $true )
<=> ! [X1: $i,X2: $i > $o,X0: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X2 )
| ( ( in @ X4 @ X1 )
!= $true ) ) )
& ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f15,plain,
( ( ( dsetconstrER = $true )
| ? [X1: $i,X2: $i > $o,X0: $i] :
( ( ( X2 @ X1 )
!= $true )
& ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) )
& ( ! [X1: $i,X2: $i > $o,X0: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f16,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
!= $true )
& ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ( dsetconstrER = $true )
| ( ( ( sK1 @ sK0 )
!= $true )
& ( ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
thf(f18,plain,
( ! [X3: $i] :
( ( ( in @ X3 @ sK3 )
!= $true )
| ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= sK5 )
| ( $true
!= ( in @ X4 @ sK4 ) ) ) )
& ( ( in @ sK5 @ ( cartprod @ sK3 @ sK4 ) )
= $true )
& ( dsetconstrER = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f14]) ).
thf(f19,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f23,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f24,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
( ( in @ sK5 @ ( cartprod @ sK3 @ sK4 ) )
= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f26,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X3 @ sK3 )
!= $true )
| ( ( kpair @ X3 @ X4 )
!= sK5 )
| ( $true
!= ( in @ X4 @ sK4 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f29,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( ^ [Y5: $i,Y6: $i] : ( setadjoin @ ( setadjoin @ Y5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y5 @ ( setadjoin @ Y6 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y4 )
= Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f22,f23]) ).
thf(f32,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( $true != $true )
| ( ( X4 @ X3 )
= $true ) ),
inference(definition_unfolding,[],[f19,f24]) ).
thf(f33,plain,
! [X3: $i,X4: $i] :
( ( ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X3
@ X4 )
!= sK5 )
| ( ( in @ X3 @ sK3 )
!= $true )
| ( $true
!= ( in @ X4 @ sK4 ) ) ),
inference(definition_unfolding,[],[f26,f23]) ).
thf(f34,plain,
( ( in @ sK5
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( ^ [Y5: $i,Y6: $i] : ( setadjoin @ ( setadjoin @ Y5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y5 @ ( setadjoin @ Y6 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y4 )
= Y2 ) ) ) ) ) )
@ sK3
@ sK4 ) )
= $true ),
inference(definition_unfolding,[],[f25,f29]) ).
thf(f35,plain,
( ( in @ sK5
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sK3 @ sK4 ) ) )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
! [X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
!= sK5 )
| ( $true
!= ( in @ X4 @ sK4 ) )
| ( ( in @ X3 @ sK3 )
!= $true ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f37,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f38,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X5 @ X4 ) )
!= $true )
| ( ( X4 @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) )
@ sK5 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f38,f35]) ).
thf(f40,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) )
@ sK5 )
= $true ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK5 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK5 ) ) ) )
@ sK6 )
= $true ),
inference(sigma_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( ( in @ sK6 @ sK3 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK5 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK5 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( $true
= ( in @ sK6 @ sK3 ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f46,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK5 ) )
@ sK7 )
= $true ),
inference(sigma_proxy_clausification,[],[f44]) ).
thf(f47,plain,
( ( ( in @ sK7 @ sK4 )
& ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ emptyset ) )
= sK5 ) )
= $true ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
( $true
= ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ emptyset ) )
= sK5 ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( in @ sK7 @ sK4 )
= $true ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ emptyset ) )
= sK5 ),
inference(equality_proxy_clausification,[],[f48]) ).
thf(f52,plain,
( ( ( in @ sK7 @ sK4 )
!= $true )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ( sK5 != sK5 ) ),
inference(constrained_superposition,[],[f36,f50]) ).
thf(f53,plain,
( ( ( in @ sK7 @ sK4 )
!= $true )
| ( $true
!= ( in @ sK6 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
( $true
!= ( in @ sK6 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f53,f49]) ).
thf(f68,plain,
$false,
inference(forward_subsumption_resolution,[],[f54,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU631^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n009.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 13:59:30 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 Running higher-order theorem proving
% 0.22/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.32 % (4044614)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (4044625)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (4044625)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.32 % (4044624)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3898733457:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (4044621)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=760055442:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (4044619)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2305615756:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (4044623)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2891223214:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (4044620)lrs+10_16_si=on:nwc=1.5:random_seed=1936873619:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (4044622)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3655421067:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.32 % (4044625)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1335521626:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (4044621)Refutation not found, incomplete strategy
% 0.22/0.32 % (4044621)------------------------------
% 0.22/0.32 % (4044621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (4044621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (4044621)CaDiCaL version: 2.1.3
% 0.22/0.32 % (4044621)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.32 % (4044621)Time elapsed: 0.002 s
% 0.22/0.32 % (4044621)Peak memory usage: 12 MB
% 0.22/0.32 % (4044621)Instructions burned: 3 (million)
% 0.22/0.32 % (4044619) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4044614-4044619"...
% 0.22/0.32 % (4044621)------------------------------
% 0.22/0.32 % (4044621)------------------------------
% 0.22/0.32 % (4044620) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4044614-4044620"...
% 0.22/0.32 % (4044619)...printing done.
% 0.22/0.32 % (4044620)...printing done.
% 0.22/0.32 % (4044619)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (4044619)------------------------------
% 0.22/0.32 % (4044619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (4044619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (4044619)CaDiCaL version: 2.1.3
% 0.22/0.32 % (4044619)Termination reason: Refutation
% 0.22/0.32 % (4044619)Time elapsed: 0.005 s
% 0.22/0.32 % (4044619)Peak memory usage: 12 MB
% 0.22/0.32 % (4044619)Instructions burned: 8 (million)
% 0.22/0.32 % (4044614)Success in time 0.046 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------