TSTP Solution File: NUM394+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:21:57 EDT 2024
% Result : Theorem 0.10s 0.36s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 38
% Syntax : Number of formulae : 203 ( 50 unt; 0 def)
% Number of atoms : 544 ( 51 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 588 ( 247 ~; 237 |; 71 &)
% ( 6 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-1 aty)
% Number of variables : 241 ( 216 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f341,plain,
$false,
inference(global_subsumption,[],[f111,f113,f106,f107,f110,f142,f143,f144,f146,f147,f148,f149,f161,f108,f109,f128,f115,f127,f120,f164,f165,f166,f139,f121,f125,f126,f171,f130,f131,f172,f132,f136,f180,f137,f138,f181,f124,f129,f192,f195,f190,f141,f198,f201,f202,f204,f210,f211,f212,f205,f218,f219,f222,f133,f230,f228,f217,f134,f199,f247,f248,f200,f251,f203,f254,f206,f262,f135,f274,f275,f140,f283,f281,f285,f286,f282,f290,f291,f292,f194,f295,f280,f299,f117,f301,f302,f303,f306,f307,f326,f312,f313,f314,f317,f318,f332,f335,f329,f336,f337,f338,f339]) ).
fof(f339,plain,
~ ordinal_subset(sK0,sK0),
inference(superposition,[],[f108,f329]) ).
fof(f338,plain,
~ in(sK0,sK0),
inference(superposition,[],[f109,f329]) ).
fof(f337,plain,
ordinal_subset(sK0,sK0),
inference(superposition,[],[f228,f329]) ).
fof(f336,plain,
~ in(sK0,sK0),
inference(superposition,[],[f299,f329]) ).
fof(f329,plain,
sK0 = sK1,
inference(subsumption_resolution,[],[f328,f106]) ).
fof(f328,plain,
( sK0 = sK1
| ~ ordinal(sK0) ),
inference(subsumption_resolution,[],[f327,f107]) ).
fof(f327,plain,
( sK0 = sK1
| ~ ordinal(sK1)
| ~ ordinal(sK0) ),
inference(subsumption_resolution,[],[f310,f299]) ).
fof(f310,plain,
( in(sK0,sK1)
| sK0 = sK1
| ~ ordinal(sK1)
| ~ ordinal(sK0) ),
inference(resolution,[],[f117,f109]) ).
fof(f335,plain,
sK0 = sK1,
inference(subsumption_resolution,[],[f334,f107]) ).
fof(f334,plain,
( sK0 = sK1
| ~ ordinal(sK1) ),
inference(subsumption_resolution,[],[f333,f106]) ).
fof(f333,plain,
( sK0 = sK1
| ~ ordinal(sK0)
| ~ ordinal(sK1) ),
inference(subsumption_resolution,[],[f321,f299]) ).
fof(f321,plain,
( in(sK0,sK1)
| sK0 = sK1
| ~ ordinal(sK0)
| ~ ordinal(sK1) ),
inference(resolution,[],[f117,f109]) ).
fof(f332,plain,
sK0 = sK1,
inference(subsumption_resolution,[],[f331,f106]) ).
fof(f331,plain,
( sK0 = sK1
| ~ ordinal(sK0) ),
inference(subsumption_resolution,[],[f330,f107]) ).
fof(f330,plain,
( sK0 = sK1
| ~ ordinal(sK1)
| ~ ordinal(sK0) ),
inference(subsumption_resolution,[],[f320,f109]) ).
fof(f320,plain,
( in(sK1,sK0)
| sK0 = sK1
| ~ ordinal(sK1)
| ~ ordinal(sK0) ),
inference(resolution,[],[f117,f299]) ).
fof(f318,plain,
! [X0,X1] :
( in(sK3(powerset(X0)),X1)
| sK3(powerset(X0)) = X1
| ~ ordinal(sK3(powerset(X0)))
| ~ ordinal(X1)
| ~ empty(X0) ),
inference(resolution,[],[f117,f198]) ).
fof(f317,plain,
! [X0,X1] :
( in(sK3(powerset(X0)),X1)
| sK3(powerset(X0)) = X1
| ~ ordinal(sK3(powerset(X0)))
| ~ ordinal(X1)
| element(X1,X0) ),
inference(resolution,[],[f117,f281]) ).
fof(f314,plain,
! [X0,X1] :
( in(powerset(X0),X1)
| powerset(X0) = X1
| ~ ordinal(powerset(X0))
| ~ ordinal(X1)
| subset(X1,X0) ),
inference(resolution,[],[f117,f181]) ).
fof(f313,plain,
! [X2,X0,X1] :
( in(powerset(X0),X1)
| powerset(X0) = X1
| ~ ordinal(powerset(X0))
| ~ ordinal(X1)
| ~ in(X2,X1)
| ~ empty(X0) ),
inference(resolution,[],[f117,f200]) ).
fof(f312,plain,
! [X0,X1] :
( in(X0,X1)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X0) ),
inference(resolution,[],[f117,f139]) ).
fof(f326,plain,
sK0 = sK1,
inference(subsumption_resolution,[],[f325,f107]) ).
fof(f325,plain,
( sK0 = sK1
| ~ ordinal(sK1) ),
inference(subsumption_resolution,[],[f324,f106]) ).
fof(f324,plain,
( sK0 = sK1
| ~ ordinal(sK0)
| ~ ordinal(sK1) ),
inference(subsumption_resolution,[],[f309,f109]) ).
fof(f309,plain,
( in(sK1,sK0)
| sK0 = sK1
| ~ ordinal(sK0)
| ~ ordinal(sK1) ),
inference(resolution,[],[f117,f299]) ).
fof(f307,plain,
! [X0,X1] :
( in(sK3(powerset(X0)),X1)
| sK3(powerset(X0)) = X1
| ~ ordinal(X1)
| ~ ordinal(sK3(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f117,f198]) ).
fof(f306,plain,
! [X0,X1] :
( in(sK3(powerset(X0)),X1)
| sK3(powerset(X0)) = X1
| ~ ordinal(X1)
| ~ ordinal(sK3(powerset(X0)))
| element(X1,X0) ),
inference(resolution,[],[f117,f281]) ).
fof(f303,plain,
! [X0,X1] :
( in(powerset(X0),X1)
| powerset(X0) = X1
| ~ ordinal(X1)
| ~ ordinal(powerset(X0))
| subset(X1,X0) ),
inference(resolution,[],[f117,f181]) ).
fof(f302,plain,
! [X2,X0,X1] :
( in(powerset(X0),X1)
| powerset(X0) = X1
| ~ ordinal(X1)
| ~ ordinal(powerset(X0))
| ~ in(X2,X1)
| ~ empty(X0) ),
inference(resolution,[],[f117,f200]) ).
fof(f301,plain,
! [X0,X1] :
( in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ empty(X0) ),
inference(resolution,[],[f117,f139]) ).
fof(f117,plain,
! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f299,plain,
~ in(sK0,sK1),
inference(subsumption_resolution,[],[f298,f106]) ).
fof(f298,plain,
( ~ ordinal(sK0)
| ~ in(sK0,sK1) ),
inference(subsumption_resolution,[],[f297,f107]) ).
fof(f297,plain,
( ~ ordinal(sK1)
| ~ ordinal(sK0)
| ~ in(sK0,sK1) ),
inference(resolution,[],[f280,f108]) ).
fof(f280,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(subsumption_resolution,[],[f277,f115]) ).
fof(f277,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X1)
| ~ epsilon_transitive(X1) ),
inference(resolution,[],[f135,f124]) ).
fof(f295,plain,
! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ),
inference(resolution,[],[f194,f130]) ).
fof(f194,plain,
! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) ),
inference(resolution,[],[f129,f137]) ).
fof(f292,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(resolution,[],[f282,f124]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(resolution,[],[f282,f134]) ).
fof(f290,plain,
! [X0,X1] :
( ~ in(X0,sK2(powerset(X1)))
| element(X0,X1)
| epsilon_transitive(powerset(X1)) ),
inference(resolution,[],[f282,f190]) ).
fof(f282,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) ),
inference(resolution,[],[f140,f137]) ).
fof(f286,plain,
! [X0] :
( element(sK3(sK3(powerset(X0))),X0)
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f281,f192]) ).
fof(f285,plain,
! [X0] :
( element(sK2(sK3(powerset(X0))),X0)
| epsilon_transitive(sK3(powerset(X0))) ),
inference(resolution,[],[f281,f125]) ).
fof(f281,plain,
! [X0,X1] :
( ~ in(X0,sK3(powerset(X1)))
| element(X0,X1) ),
inference(resolution,[],[f140,f127]) ).
fof(f283,plain,
! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ in(X2,powerset(X1)) ),
inference(resolution,[],[f140,f131]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f275,plain,
! [X0] :
( ordinal_subset(sK2(powerset(X0)),X0)
| ~ ordinal(X0)
| ~ ordinal(sK2(powerset(X0)))
| epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f135,f190]) ).
fof(f274,plain,
! [X0] :
( ordinal_subset(sK3(powerset(X0)),X0)
| ~ ordinal(X0)
| ~ ordinal(sK3(powerset(X0))) ),
inference(resolution,[],[f135,f180]) ).
fof(f135,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f262,plain,
! [X0] :
( empty_set = sK3(powerset(sK3(powerset(sK3(powerset(X0))))))
| ~ empty(X0) ),
inference(resolution,[],[f206,f202]) ).
fof(f206,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK3(powerset(sK3(powerset(X0)))) ),
inference(resolution,[],[f204,f202]) ).
fof(f254,plain,
! [X0,X1] :
( sK3(powerset(X0)) = sK3(powerset(X1))
| ~ empty(X0)
| ~ empty(X1) ),
inference(resolution,[],[f203,f202]) ).
fof(f203,plain,
! [X0,X1] :
( ~ empty(X1)
| sK3(powerset(X0)) = X1
| ~ empty(X0) ),
inference(resolution,[],[f202,f138]) ).
fof(f251,plain,
! [X0,X1] :
( ~ in(X0,sK2(powerset(X1)))
| ~ empty(X1)
| epsilon_transitive(powerset(X1)) ),
inference(resolution,[],[f200,f125]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ in(X2,powerset(X0))
| ~ in(X1,X2)
| ~ empty(X0) ),
inference(resolution,[],[f141,f131]) ).
fof(f248,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(resolution,[],[f199,f134]) ).
fof(f247,plain,
! [X0,X1] :
( ~ in(X0,sK2(powerset(X1)))
| ~ empty(X1)
| epsilon_transitive(powerset(X1)) ),
inference(resolution,[],[f199,f190]) ).
fof(f199,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) ),
inference(resolution,[],[f141,f137]) ).
fof(f134,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f217,plain,
( ~ in(powerset(empty_set),empty_set)
| empty(powerset(empty_set)) ),
inference(superposition,[],[f195,f205]) ).
fof(f228,plain,
ordinal_subset(sK1,sK0),
inference(subsumption_resolution,[],[f227,f107]) ).
fof(f227,plain,
( ordinal_subset(sK1,sK0)
| ~ ordinal(sK1) ),
inference(subsumption_resolution,[],[f223,f106]) ).
fof(f223,plain,
( ordinal_subset(sK1,sK0)
| ~ ordinal(sK0)
| ~ ordinal(sK1) ),
inference(resolution,[],[f133,f108]) ).
fof(f230,plain,
ordinal_subset(sK1,sK0),
inference(subsumption_resolution,[],[f229,f106]) ).
fof(f229,plain,
( ordinal_subset(sK1,sK0)
| ~ ordinal(sK0) ),
inference(subsumption_resolution,[],[f224,f107]) ).
fof(f224,plain,
( ordinal_subset(sK1,sK0)
| ~ ordinal(sK1)
| ~ ordinal(sK0) ),
inference(resolution,[],[f133,f108]) ).
fof(f133,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f222,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(resolution,[],[f219,f129]) ).
fof(f219,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[],[f127,f205]) ).
fof(f218,plain,
( in(empty_set,powerset(empty_set))
| empty(powerset(empty_set)) ),
inference(superposition,[],[f192,f205]) ).
fof(f205,plain,
empty_set = sK3(powerset(empty_set)),
inference(resolution,[],[f204,f110]) ).
fof(f212,plain,
empty_set = sK3(powerset(empty_set)),
inference(forward_demodulation,[],[f209,f166]) ).
fof(f209,plain,
empty_set = sK3(powerset(sK14)),
inference(resolution,[],[f204,f161]) ).
fof(f211,plain,
empty_set = sK3(powerset(empty_set)),
inference(forward_demodulation,[],[f208,f165]) ).
fof(f208,plain,
empty_set = sK3(powerset(sK8)),
inference(resolution,[],[f204,f149]) ).
fof(f210,plain,
empty_set = sK3(powerset(empty_set)),
inference(forward_demodulation,[],[f207,f164]) ).
fof(f207,plain,
empty_set = sK3(powerset(sK5)),
inference(resolution,[],[f204,f143]) ).
fof(f204,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK3(powerset(X0)) ),
inference(resolution,[],[f202,f120]) ).
fof(f202,plain,
! [X0] :
( empty(sK3(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f198,f192]) ).
fof(f201,plain,
! [X0] :
( epsilon_transitive(sK3(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f198,f125]) ).
fof(f198,plain,
! [X0,X1] :
( ~ in(X1,sK3(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f141,f127]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f190,plain,
! [X0] :
( subset(sK2(powerset(X0)),X0)
| epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f181,f125]) ).
fof(f195,plain,
! [X0] :
( ~ in(X0,sK3(X0))
| empty(X0) ),
inference(resolution,[],[f192,f130]) ).
fof(f192,plain,
! [X0] :
( in(sK3(X0),X0)
| empty(X0) ),
inference(resolution,[],[f129,f127]) ).
fof(f129,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f124,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK2(X0),X0)
& in(sK2(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f77,f78]) ).
fof(f78,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK2(X0),X0)
& in(sK2(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f181,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(resolution,[],[f136,f131]) ).
fof(f138,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f137,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f180,plain,
! [X0] : subset(sK3(powerset(X0)),X0),
inference(resolution,[],[f136,f127]) ).
fof(f136,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f132,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(f172,plain,
! [X0] :
( ~ in(X0,sK2(X0))
| epsilon_transitive(X0) ),
inference(resolution,[],[f130,f125]) ).
fof(f131,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f130,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f171,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(resolution,[],[f125,f139]) ).
fof(f126,plain,
! [X0] :
( ~ subset(sK2(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f125,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f121,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ordinal(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f139,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f166,plain,
empty_set = sK14,
inference(resolution,[],[f120,f161]) ).
fof(f165,plain,
empty_set = sK8,
inference(resolution,[],[f120,f149]) ).
fof(f164,plain,
empty_set = sK5,
inference(resolution,[],[f120,f143]) ).
fof(f120,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f127,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f9,f80]) ).
fof(f80,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f115,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f128,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f109,plain,
~ in(sK1,sK0),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( ~ in(sK1,sK0)
& ~ ordinal_subset(sK0,sK1)
& ordinal(sK1)
& ordinal(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f46,f74,f73]) ).
fof(f73,plain,
( ? [X0] :
( ? [X1] :
( ~ in(X1,X0)
& ~ ordinal_subset(X0,X1)
& ordinal(X1) )
& ordinal(X0) )
=> ( ? [X1] :
( ~ in(X1,sK0)
& ~ ordinal_subset(sK0,X1)
& ordinal(X1) )
& ordinal(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
( ? [X1] :
( ~ in(X1,sK0)
& ~ ordinal_subset(sK0,X1)
& ordinal(X1) )
=> ( ~ in(sK1,sK0)
& ~ ordinal_subset(sK0,sK1)
& ordinal(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0] :
( ? [X1] :
( ~ in(X1,X0)
& ~ ordinal_subset(X0,X1)
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
? [X0] :
( ? [X1] :
( ~ in(X1,X0)
& ~ ordinal_subset(X0,X1)
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
| ordinal_subset(X0,X1) ) ) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
| ordinal_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_ordinal1) ).
fof(f108,plain,
~ ordinal_subset(sK0,sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f161,plain,
empty(sK14),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
( function(sK14)
& empty(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f17,f104]) ).
fof(f104,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK14)
& empty(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f17,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f149,plain,
empty(sK8),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f15,f92]) ).
fof(f92,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK8)
& empty(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f148,plain,
ordinal(sK7),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f14,f90]) ).
fof(f90,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f14,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f147,plain,
epsilon_connected(sK7),
inference(cnf_transformation,[],[f91]) ).
fof(f146,plain,
epsilon_transitive(sK7),
inference(cnf_transformation,[],[f91]) ).
fof(f144,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f18,f88]) ).
fof(f88,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK6)
& ~ empty(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f143,plain,
empty(sK5),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f16,f86]) ).
fof(f86,plain,
( ? [X0] : empty(X0)
=> empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f16,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f142,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
~ empty(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f84]) ).
fof(f84,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK4) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f110,plain,
empty(empty_set),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f107,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f106,plain,
ordinal(sK0),
inference(cnf_transformation,[],[f75]) ).
fof(f113,plain,
empty(empty_set),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(pure_predicate_removal,[],[f10]) ).
fof(f10,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f111,plain,
empty(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n018.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 30 00:14:43 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (20309)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34 % (20312)WARNING: value z3 for option sas not known
% 0.10/0.34 % (20312)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.35 % (20310)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.36 % (20315)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.36 TRYING [1]
% 0.10/0.36 % (20312)First to succeed.
% 0.10/0.36 % (20316)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.10/0.36 TRYING [2]
% 0.10/0.36 % (20313)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.36 % (20312)Refutation found. Thanks to Tanya!
% 0.10/0.36 % SZS status Theorem for theBenchmark
% 0.10/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.37 % (20312)------------------------------
% 0.10/0.37 % (20312)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.37 % (20312)Termination reason: Refutation
% 0.10/0.37
% 0.10/0.37 % (20312)Memory used [KB]: 949
% 0.10/0.37 % (20312)Time elapsed: 0.015 s
% 0.10/0.37 % (20312)Instructions burned: 16 (million)
% 0.10/0.37 % (20312)------------------------------
% 0.10/0.37 % (20312)------------------------------
% 0.10/0.37 % (20309)Success in time 0.046 s
% 0.10/0.37 20310 Aborted by signal SIGHUP on /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % (20310)------------------------------
% 0.10/0.37 % (20310)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.37 % (20310)Termination reason: Unknown
% 0.10/0.37 % (20310)Termination phase: Finite model building SAT solving
% 0.10/0.37
% 0.10/0.37 20314 Aborted by signal SIGHUP on /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % (20314)------------------------------
% 0.10/0.37 % (20314)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.37 % (20310)Memory used [KB]: 979
% 0.10/0.37 % (20314)Termination reason: Unknown
% 0.10/0.37 % (20310)Time elapsed: 0.014 s
% 0.10/0.37 % (20314)Termination phase: Unknown
% 0.10/0.37
% 0.10/0.37 % (20310)Instructions burned: 17 (million)
% 0.10/0.37 % (20314)Memory used [KB]: 725
% 0.10/0.37 % (20314)Time elapsed: 0.003 s
% 0.10/0.37 % (20314)Instructions burned: 1 (million)
% 0.10/0.37 % (20314)------------------------------
% 0.10/0.37 % (20314)------------------------------
% 0.10/0.37 Version : Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.37 ???
% 0.10/0.37 ???
% 0.10/0.37 ???
% 0.10/0.37 ???
% 0.10/0.37 % (20310)------------------------------
% 0.10/0.37 % (20310)------------------------------
% 0.10/0.37 Version : Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
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