TSTP Solution File: SEU339+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU339+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n026.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 : Wed Aug 31 18:33:18 EDT 2022
% Result : Theorem 0.19s 0.61s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 25
% Syntax : Number of formulae : 142 ( 40 unt; 0 def)
% Number of atoms : 431 ( 33 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 458 ( 169 ~; 147 |; 99 &)
% ( 11 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 239 ( 216 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f485,plain,
$false,
inference(resolution,[],[f480,f272]) ).
fof(f272,plain,
in(ordered_pair(sK6,sK7),the_InternalRel(sK5)),
inference(subsumption_resolution,[],[f271,f180]) ).
fof(f180,plain,
element(sK7,sF13),
inference(definition_folding,[],[f148,f178]) ).
fof(f178,plain,
sF13 = the_carrier(sK5),
introduced(function_definition,[]) ).
fof(f148,plain,
element(sK7,the_carrier(sK5)),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
( rel_str(sK5)
& antisymmetric_relstr(sK5)
& element(sK6,the_carrier(sK5))
& related(sK5,sK7,sK6)
& sK7 != sK6
& element(sK7,the_carrier(sK5))
& related(sK5,sK6,sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f74,f107,f106,f105]) ).
fof(f105,plain,
( ? [X0] :
( rel_str(X0)
& antisymmetric_relstr(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( related(X0,X2,X1)
& X1 != X2
& element(X2,the_carrier(X0))
& related(X0,X1,X2) ) ) )
=> ( rel_str(sK5)
& antisymmetric_relstr(sK5)
& ? [X1] :
( element(X1,the_carrier(sK5))
& ? [X2] :
( related(sK5,X2,X1)
& X1 != X2
& element(X2,the_carrier(sK5))
& related(sK5,X1,X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
( ? [X1] :
( element(X1,the_carrier(sK5))
& ? [X2] :
( related(sK5,X2,X1)
& X1 != X2
& element(X2,the_carrier(sK5))
& related(sK5,X1,X2) ) )
=> ( element(sK6,the_carrier(sK5))
& ? [X2] :
( related(sK5,X2,sK6)
& sK6 != X2
& element(X2,the_carrier(sK5))
& related(sK5,sK6,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
( ? [X2] :
( related(sK5,X2,sK6)
& sK6 != X2
& element(X2,the_carrier(sK5))
& related(sK5,sK6,X2) )
=> ( related(sK5,sK7,sK6)
& sK7 != sK6
& element(sK7,the_carrier(sK5))
& related(sK5,sK6,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
? [X0] :
( rel_str(X0)
& antisymmetric_relstr(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( related(X0,X2,X1)
& X1 != X2
& element(X2,the_carrier(X0))
& related(X0,X1,X2) ) ) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& related(X0,X1,X2)
& related(X0,X2,X1)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& rel_str(X0)
& antisymmetric_relstr(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( related(X0,X1,X2)
& related(X0,X2,X1) )
=> X1 = X2 ) ) ) ),
inference(negated_conjecture,[],[f39]) ).
fof(f39,conjecture,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( related(X0,X1,X2)
& related(X0,X2,X1) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_orders_2) ).
fof(f271,plain,
( ~ element(sK7,sF13)
| in(ordered_pair(sK6,sK7),the_InternalRel(sK5)) ),
inference(subsumption_resolution,[],[f269,f179]) ).
fof(f179,plain,
element(sK6,sF13),
inference(definition_folding,[],[f151,f178]) ).
fof(f151,plain,
element(sK6,the_carrier(sK5)),
inference(cnf_transformation,[],[f108]) ).
fof(f269,plain,
( in(ordered_pair(sK6,sK7),the_InternalRel(sK5))
| ~ element(sK6,sF13)
| ~ element(sK7,sF13) ),
inference(resolution,[],[f263,f147]) ).
fof(f147,plain,
related(sK5,sK6,sK7),
inference(cnf_transformation,[],[f108]) ).
fof(f263,plain,
! [X0,X1] :
( ~ related(sK5,X0,X1)
| ~ element(X1,sF13)
| ~ element(X0,sF13)
| in(ordered_pair(X0,X1),the_InternalRel(sK5)) ),
inference(forward_demodulation,[],[f262,f178]) ).
fof(f262,plain,
! [X0,X1] :
( ~ related(sK5,X0,X1)
| ~ element(X1,sF13)
| ~ element(X0,the_carrier(sK5))
| in(ordered_pair(X0,X1),the_InternalRel(sK5)) ),
inference(forward_demodulation,[],[f260,f178]) ).
fof(f260,plain,
! [X0,X1] :
( ~ related(sK5,X0,X1)
| ~ element(X1,the_carrier(sK5))
| ~ element(X0,the_carrier(sK5))
| in(ordered_pair(X0,X1),the_InternalRel(sK5)) ),
inference(resolution,[],[f128,f153]) ).
fof(f153,plain,
rel_str(sK5),
inference(cnf_transformation,[],[f108]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ related(X0,X1,X2)
| ~ element(X1,the_carrier(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0)) )
& ( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2) ) ) ) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f480,plain,
! [X0] : ~ in(X0,the_InternalRel(sK5)),
inference(resolution,[],[f463,f209]) ).
fof(f209,plain,
! [X0,X1] :
( ~ element(X1,powerset(empty_set))
| ~ in(X0,X1) ),
inference(resolution,[],[f130,f157]) ).
fof(f157,plain,
empty(empty_set),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ in(X1,X0)
| ~ element(X0,powerset(X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X0,powerset(X2))
| ~ in(X1,X0) ),
inference(rectify,[],[f70]) ).
fof(f70,plain,
! [X1,X2,X0] :
( ~ empty(X0)
| ~ element(X1,powerset(X0))
| ~ in(X2,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
! [X2,X0,X1] :
~ ( empty(X0)
& element(X1,powerset(X0))
& in(X2,X1) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X2,X1,X0] :
~ ( element(X1,powerset(X2))
& in(X0,X1)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f463,plain,
element(the_InternalRel(sK5),powerset(empty_set)),
inference(backward_demodulation,[],[f412,f450]) ).
fof(f450,plain,
empty_set = cartesian_product2(empty_set,empty_set),
inference(resolution,[],[f445,f162]) ).
fof(f162,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f445,plain,
empty(cartesian_product2(empty_set,empty_set)),
inference(subsumption_resolution,[],[f435,f301]) ).
fof(f301,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[],[f209,f185]) ).
fof(f185,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(backward_demodulation,[],[f144,f183]) ).
fof(f183,plain,
! [X0] : empty_set = sK3(X0),
inference(resolution,[],[f162,f143]) ).
fof(f143,plain,
! [X0] : empty(sK3(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
& empty(sK3(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f33,f100]) ).
fof(f100,plain,
! [X0] :
( ? [X1] :
( element(X1,powerset(X0))
& empty(X1) )
=> ( element(sK3(X0),powerset(X0))
& empty(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f144,plain,
! [X0] : element(sK3(X0),powerset(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f435,plain,
( in(sK6,empty_set)
| empty(cartesian_product2(empty_set,empty_set)) ),
inference(resolution,[],[f406,f168]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X3),cartesian_product2(X2,X1))
| in(X0,X2) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2,X3] :
( ( ( in(X0,X2)
& in(X3,X1) )
| ~ in(ordered_pair(X0,X3),cartesian_product2(X2,X1)) )
& ( in(ordered_pair(X0,X3),cartesian_product2(X2,X1))
| ~ in(X0,X2)
| ~ in(X3,X1) ) ),
inference(rectify,[],[f117]) ).
fof(f117,plain,
! [X0,X2,X1,X3] :
( ( ( in(X0,X1)
& in(X3,X2) )
| ~ in(ordered_pair(X0,X3),cartesian_product2(X1,X2)) )
& ( in(ordered_pair(X0,X3),cartesian_product2(X1,X2))
| ~ in(X0,X1)
| ~ in(X3,X2) ) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0,X2,X1,X3] :
( ( ( in(X0,X1)
& in(X3,X2) )
| ~ in(ordered_pair(X0,X3),cartesian_product2(X1,X2)) )
& ( in(ordered_pair(X0,X3),cartesian_product2(X1,X2))
| ~ in(X0,X1)
| ~ in(X3,X2) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X2,X1,X3] :
( ( in(X0,X1)
& in(X3,X2) )
<=> in(ordered_pair(X0,X3),cartesian_product2(X1,X2)) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X0,X2,X3,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f406,plain,
( in(ordered_pair(sK6,sK7),cartesian_product2(empty_set,empty_set))
| empty(cartesian_product2(empty_set,empty_set)) ),
inference(resolution,[],[f395,f173]) ).
fof(f173,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X1,X0] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X1,X0] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f395,plain,
element(ordered_pair(sK6,sK7),cartesian_product2(empty_set,empty_set)),
inference(resolution,[],[f312,f389]) ).
fof(f389,plain,
in(the_InternalRel(sK5),powerset(cartesian_product2(empty_set,empty_set))),
inference(resolution,[],[f220,f336]) ).
fof(f336,plain,
relation_of2_as_subset(the_InternalRel(sK5),empty_set,empty_set),
inference(backward_demodulation,[],[f217,f327]) ).
fof(f327,plain,
empty_set = sF13,
inference(resolution,[],[f318,f162]) ).
fof(f318,plain,
empty(sF13),
inference(resolution,[],[f317,f202]) ).
fof(f202,plain,
( in(sK6,sF13)
| empty(sF13) ),
inference(resolution,[],[f173,f179]) ).
fof(f317,plain,
~ in(sK6,sF13),
inference(subsumption_resolution,[],[f316,f138]) ).
fof(f138,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
~ ( empty(X0)
& in(X1,X0) ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X1,X0] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f316,plain,
( empty(sF13)
| ~ in(sK6,sF13) ),
inference(subsumption_resolution,[],[f315,f215]) ).
fof(f215,plain,
is_antisymmetric_in(the_InternalRel(sK5),sF13),
inference(forward_demodulation,[],[f214,f178]) ).
fof(f214,plain,
is_antisymmetric_in(the_InternalRel(sK5),the_carrier(sK5)),
inference(subsumption_resolution,[],[f213,f153]) ).
fof(f213,plain,
( is_antisymmetric_in(the_InternalRel(sK5),the_carrier(sK5))
| ~ rel_str(sK5) ),
inference(resolution,[],[f155,f152]) ).
fof(f152,plain,
antisymmetric_relstr(sK5),
inference(cnf_transformation,[],[f108]) ).
fof(f155,plain,
! [X0] :
( ~ antisymmetric_relstr(X0)
| is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ~ rel_str(X0)
| ( ( is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0))
| ~ antisymmetric_relstr(X0) )
& ( antisymmetric_relstr(X0)
| ~ is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ~ rel_str(X0)
| ( is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0))
<=> antisymmetric_relstr(X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ( is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0))
<=> antisymmetric_relstr(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_orders_2) ).
fof(f315,plain,
( empty(sF13)
| ~ in(sK6,sF13)
| ~ is_antisymmetric_in(the_InternalRel(sK5),sF13) ),
inference(resolution,[],[f283,f203]) ).
fof(f203,plain,
( in(sK7,sF13)
| empty(sF13) ),
inference(resolution,[],[f173,f180]) ).
fof(f283,plain,
! [X0] :
( ~ in(sK7,X0)
| ~ in(sK6,X0)
| ~ is_antisymmetric_in(the_InternalRel(sK5),X0) ),
inference(subsumption_resolution,[],[f282,f240]) ).
fof(f240,plain,
relation(the_InternalRel(sK5)),
inference(resolution,[],[f218,f217]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f140,f156]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(cartesian_product2(X0,X2)))
| relation(X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(cartesian_product2(X0,X2)))
| relation(X1) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X2,X1,X0] :
( ~ element(X1,powerset(cartesian_product2(X2,X0)))
| relation(X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
! [X2,X0,X1] :
( element(X1,powerset(cartesian_product2(X2,X0)))
=> relation(X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X2,X0] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f140,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X1,X2,X0] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
! [X1,X2,X0] :
( relation_of2_as_subset(X0,X1,X2)
=> element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f282,plain,
! [X0] :
( ~ is_antisymmetric_in(the_InternalRel(sK5),X0)
| ~ in(sK7,X0)
| ~ in(sK6,X0)
| ~ relation(the_InternalRel(sK5)) ),
inference(subsumption_resolution,[],[f281,f274]) ).
fof(f274,plain,
in(ordered_pair(sK7,sK6),the_InternalRel(sK5)),
inference(subsumption_resolution,[],[f273,f180]) ).
fof(f273,plain,
( ~ element(sK7,sF13)
| in(ordered_pair(sK7,sK6),the_InternalRel(sK5)) ),
inference(subsumption_resolution,[],[f270,f179]) ).
fof(f270,plain,
( ~ element(sK6,sF13)
| in(ordered_pair(sK7,sK6),the_InternalRel(sK5))
| ~ element(sK7,sF13) ),
inference(resolution,[],[f263,f150]) ).
fof(f150,plain,
related(sK5,sK7,sK6),
inference(cnf_transformation,[],[f108]) ).
fof(f281,plain,
! [X0] :
( ~ is_antisymmetric_in(the_InternalRel(sK5),X0)
| ~ in(ordered_pair(sK7,sK6),the_InternalRel(sK5))
| ~ relation(the_InternalRel(sK5))
| ~ in(sK6,X0)
| ~ in(sK7,X0) ),
inference(subsumption_resolution,[],[f276,f149]) ).
fof(f149,plain,
sK7 != sK6,
inference(cnf_transformation,[],[f108]) ).
fof(f276,plain,
! [X0] :
( ~ is_antisymmetric_in(the_InternalRel(sK5),X0)
| sK7 = sK6
| ~ in(sK7,X0)
| ~ relation(the_InternalRel(sK5))
| ~ in(ordered_pair(sK7,sK6),the_InternalRel(sK5))
| ~ in(sK6,X0) ),
inference(resolution,[],[f272,f137]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1)
| ~ in(X3,X1)
| X2 = X3
| ~ relation(X0)
| ~ in(ordered_pair(X3,X2),X0)
| ~ is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ is_antisymmetric_in(X0,X1) )
& ( is_antisymmetric_in(X0,X1)
| ( sK1(X0,X1) != sK0(X0,X1)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
& in(sK1(X0,X1),X1)
& in(sK0(X0,X1),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f92,f93]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X4,X5] :
( X4 != X5
& in(ordered_pair(X4,X5),X0)
& in(ordered_pair(X5,X4),X0)
& in(X5,X1)
& in(X4,X1) )
=> ( sK1(X0,X1) != sK0(X0,X1)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
& in(sK1(X0,X1),X1)
& in(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ is_antisymmetric_in(X0,X1) )
& ( is_antisymmetric_in(X0,X1)
| ? [X4,X5] :
( X4 != X5
& in(ordered_pair(X4,X5),X0)
& in(ordered_pair(X5,X4),X0)
& in(X5,X1)
& in(X4,X1) ) ) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X3,X2] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1)
| ~ in(X3,X1) )
| ~ is_antisymmetric_in(X0,X1) )
& ( is_antisymmetric_in(X0,X1)
| ? [X3,X2] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X2,X1)
& in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ! [X3,X2] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1)
| ~ in(X3,X1) )
<=> is_antisymmetric_in(X0,X1) ) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X3,X2),X0)
& in(X3,X1)
& in(X2,X1)
& in(ordered_pair(X2,X3),X0) )
=> X2 = X3 ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X3,X2] :
( ( in(X3,X1)
& in(X2,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f217,plain,
relation_of2_as_subset(the_InternalRel(sK5),sF13,sF13),
inference(subsumption_resolution,[],[f216,f153]) ).
fof(f216,plain,
( relation_of2_as_subset(the_InternalRel(sK5),sF13,sF13)
| ~ rel_str(sK5) ),
inference(superposition,[],[f177,f178]) ).
fof(f177,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f220,plain,
! [X3,X4,X5] :
( ~ relation_of2_as_subset(X3,X4,X5)
| in(X3,powerset(cartesian_product2(X4,X5))) ),
inference(subsumption_resolution,[],[f219,f169]) ).
fof(f169,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f219,plain,
! [X3,X4,X5] :
( in(X3,powerset(cartesian_product2(X4,X5)))
| empty(powerset(cartesian_product2(X4,X5)))
| ~ relation_of2_as_subset(X3,X4,X5) ),
inference(resolution,[],[f140,f173]) ).
fof(f312,plain,
! [X3] :
( ~ in(the_InternalRel(sK5),powerset(X3))
| element(ordered_pair(sK6,sK7),X3) ),
inference(resolution,[],[f278,f165]) ).
fof(f165,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f278,plain,
! [X3] :
( ~ element(the_InternalRel(sK5),powerset(X3))
| element(ordered_pair(sK6,sK7),X3) ),
inference(resolution,[],[f272,f175]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ in(X2,X1)
| ~ element(X1,powerset(X0))
| element(X2,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X0))
| element(X2,X0)
| ~ in(X2,X1) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X1,X2,X0] :
( element(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,plain,
! [X1,X2,X0] :
( ( in(X2,X1)
& element(X1,powerset(X0)) )
=> element(X2,X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X2,X1,X0] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f412,plain,
element(the_InternalRel(sK5),powerset(cartesian_product2(empty_set,empty_set))),
inference(resolution,[],[f409,f131]) ).
fof(f131,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f409,plain,
! [X0] :
( ~ subset(powerset(cartesian_product2(empty_set,empty_set)),X0)
| element(the_InternalRel(sK5),X0) ),
inference(resolution,[],[f392,f161]) ).
fof(f161,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f392,plain,
! [X2] :
( ~ element(powerset(cartesian_product2(empty_set,empty_set)),powerset(X2))
| element(the_InternalRel(sK5),X2) ),
inference(resolution,[],[f389,f175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU339+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 15:28:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.56 % (14677)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.56 % (14669)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.57 % (14661)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.57 % (14681)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.58 % (14673)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.58 % (14666)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.59 % (14661)Instruction limit reached!
% 0.19/0.59 % (14661)------------------------------
% 0.19/0.59 % (14661)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59 % (14661)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59 % (14661)Termination reason: Unknown
% 0.19/0.59 % (14661)Termination phase: Saturation
% 0.19/0.59
% 0.19/0.59 % (14661)Memory used [KB]: 5500
% 0.19/0.59 % (14661)Time elapsed: 0.098 s
% 0.19/0.59 % (14661)Instructions burned: 7 (million)
% 0.19/0.59 % (14661)------------------------------
% 0.19/0.59 % (14661)------------------------------
% 0.19/0.59 % (14659)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.59 % (14660)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.59 % (14664)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.59 % (14662)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.59 % (14662)Instruction limit reached!
% 0.19/0.59 % (14662)------------------------------
% 0.19/0.59 % (14662)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59 % (14662)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59 % (14662)Termination reason: Unknown
% 0.19/0.59 % (14662)Termination phase: shuffling
% 0.19/0.59
% 0.19/0.59 % (14662)Memory used [KB]: 895
% 0.19/0.59 % (14662)Time elapsed: 0.002 s
% 0.19/0.59 % (14662)Instructions burned: 2 (million)
% 0.19/0.59 % (14662)------------------------------
% 0.19/0.59 % (14662)------------------------------
% 0.19/0.60 % (14665)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.60 % (14669)First to succeed.
% 0.19/0.60 % (14657)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.60 % (14658)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.61 % (14669)Refutation found. Thanks to Tanya!
% 0.19/0.61 % SZS status Theorem for theBenchmark
% 0.19/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.61 % (14669)------------------------------
% 0.19/0.61 % (14669)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.61 % (14669)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.61 % (14669)Termination reason: Refutation
% 0.19/0.61
% 0.19/0.61 % (14669)Memory used [KB]: 1279
% 0.19/0.61 % (14669)Time elapsed: 0.110 s
% 0.19/0.61 % (14669)Instructions burned: 17 (million)
% 0.19/0.61 % (14669)------------------------------
% 0.19/0.61 % (14669)------------------------------
% 0.19/0.61 % (14653)Success in time 0.254 s
%------------------------------------------------------------------------------