TSTP Solution File: SET645+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n006.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 18:25:12 EDT 2022
% Result : Theorem 1.44s 0.56s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 87 ( 16 unt; 3 typ; 0 def)
% Number of atoms : 395 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 503 ( 192 ~; 175 |; 87 &)
% ( 10 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 4 ( 0 usr; 3 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 210 ( 172 !; 38 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_6,type,
sQ15_eqProxy: ( $int * $int ) > $o ).
tff(pred_def_7,type,
sQ16_eqProxy: ( $rat * $rat ) > $o ).
tff(pred_def_8,type,
sQ17_eqProxy: ( $real * $real ) > $o ).
fof(f404,plain,
$false,
inference(subsumption_resolution,[],[f396,f399]) ).
fof(f399,plain,
~ member(sK7,sK5),
inference(subsumption_resolution,[],[f150,f395]) ).
fof(f395,plain,
member(sK8,sK6),
inference(resolution,[],[f380,f346]) ).
fof(f346,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(subsumption_resolution,[],[f345,f158]) ).
fof(f158,plain,
! [X0] : ilf_type(X0,set_type),
inference(literal_reordering,[],[f127]) ).
fof(f127,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
fof(f345,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f344,f158]) ).
fof(f344,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type)
| member(X1,X3) ),
inference(subsumption_resolution,[],[f343,f158]) ).
fof(f343,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f175,f158]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| member(X1,X3)
| ~ ilf_type(X1,set_type) ),
inference(literal_reordering,[],[f133]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| member(X1,X3)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ! [X3] :
( ( ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) )
& ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ! [X3] :
( ( ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) )
& ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ! [X3] :
( ( ( member(X0,X2)
& member(X1,X3) )
<=> member(ordered_pair(X0,X1),cross_product(X2,X3)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( member(X0,X2)
& member(X1,X3) )
<=> member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f380,plain,
member(ordered_pair(sK7,sK8),cross_product(sK5,sK6)),
inference(resolution,[],[f320,f152]) ).
fof(f152,plain,
member(ordered_pair(sK7,sK8),sK9),
inference(literal_reordering,[],[f120]) ).
fof(f120,plain,
member(ordered_pair(sK7,sK8),sK9),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( member(ordered_pair(sK7,sK8),sK9)
& ( ~ member(sK7,sK5)
| ~ member(sK8,sK6) )
& ilf_type(sK9,relation_type(sK5,sK6))
& ilf_type(sK8,set_type)
& ilf_type(sK7,set_type)
& ilf_type(sK6,set_type)
& ilf_type(sK5,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f35,f76,f75,f74,f73,f72]) ).
fof(f72,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( member(ordered_pair(X2,X3),X4)
& ( ~ member(X2,X0)
| ~ member(X3,X1) )
& ilf_type(X4,relation_type(X0,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( member(ordered_pair(X2,X3),X4)
& ( ~ member(X2,sK5)
| ~ member(X3,X1) )
& ilf_type(X4,relation_type(sK5,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK5,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( member(ordered_pair(X2,X3),X4)
& ( ~ member(X2,sK5)
| ~ member(X3,X1) )
& ilf_type(X4,relation_type(sK5,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( member(ordered_pair(X2,X3),X4)
& ( ~ member(X2,sK5)
| ~ member(X3,sK6) )
& ilf_type(X4,relation_type(sK5,sK6)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(sK6,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( member(ordered_pair(X2,X3),X4)
& ( ~ member(X2,sK5)
| ~ member(X3,sK6) )
& ilf_type(X4,relation_type(sK5,sK6)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ? [X4] :
( member(ordered_pair(sK7,X3),X4)
& ( ~ member(sK7,sK5)
| ~ member(X3,sK6) )
& ilf_type(X4,relation_type(sK5,sK6)) )
& ilf_type(X3,set_type) )
& ilf_type(sK7,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
( ? [X3] :
( ? [X4] :
( member(ordered_pair(sK7,X3),X4)
& ( ~ member(sK7,sK5)
| ~ member(X3,sK6) )
& ilf_type(X4,relation_type(sK5,sK6)) )
& ilf_type(X3,set_type) )
=> ( ? [X4] :
( member(ordered_pair(sK7,sK8),X4)
& ( ~ member(sK7,sK5)
| ~ member(sK8,sK6) )
& ilf_type(X4,relation_type(sK5,sK6)) )
& ilf_type(sK8,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( ? [X4] :
( member(ordered_pair(sK7,sK8),X4)
& ( ~ member(sK7,sK5)
| ~ member(sK8,sK6) )
& ilf_type(X4,relation_type(sK5,sK6)) )
=> ( member(ordered_pair(sK7,sK8),sK9)
& ( ~ member(sK7,sK5)
| ~ member(sK8,sK6) )
& ilf_type(sK9,relation_type(sK5,sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( member(ordered_pair(X2,X3),X4)
& ( ~ member(X2,X0)
| ~ member(X3,X1) )
& ilf_type(X4,relation_type(X0,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X2,X0)
| ~ member(X3,X1) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(X0,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_7) ).
fof(f320,plain,
! [X0] :
( ~ member(X0,sK9)
| member(X0,cross_product(sK5,sK6)) ),
inference(resolution,[],[f318,f309]) ).
fof(f309,plain,
! [X2,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(subsumption_resolution,[],[f308,f158]) ).
fof(f308,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| member(X2,X1)
| ~ member(X0,power_set(X1))
| ~ member(X2,X0) ),
inference(subsumption_resolution,[],[f307,f158]) ).
fof(f307,plain,
! [X2,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type)
| member(X2,X1)
| ~ ilf_type(X1,set_type)
| ~ member(X2,X0) ),
inference(subsumption_resolution,[],[f171,f158]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(literal_reordering,[],[f91]) ).
fof(f91,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) )
& ( member(X0,power_set(X1))
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0)
& ilf_type(sK0(X0,X1),set_type) ) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f53,f54]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X3] :
( ~ member(X3,X1)
& member(X3,X0)
& ilf_type(X3,set_type) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0)
& ilf_type(sK0(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) )
& ( member(X0,power_set(X1))
| ? [X3] :
( ~ member(X3,X1)
& member(X3,X0)
& ilf_type(X3,set_type) ) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(rectify,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) )
& ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
<=> member(X0,power_set(X1)) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f318,plain,
member(sK9,power_set(cross_product(sK5,sK6))),
inference(subsumption_resolution,[],[f317,f242]) ).
fof(f242,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f184,f158]) ).
fof(f184,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(literal_reordering,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(f317,plain,
( empty(power_set(cross_product(sK5,sK6)))
| member(sK9,power_set(cross_product(sK5,sK6))) ),
inference(resolution,[],[f296,f265]) ).
fof(f265,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| empty(X1)
| member(X0,X1) ),
inference(subsumption_resolution,[],[f264,f158]) ).
fof(f264,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(subsumption_resolution,[],[f161,f158]) ).
fof(f161,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,member_type(X1)) ),
inference(literal_reordering,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X0,set_type)
| empty(X1)
| member(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ~ ilf_type(X1,set_type)
| ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ~ ilf_type(X1,set_type)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f296,plain,
ilf_type(sK9,member_type(power_set(cross_product(sK5,sK6)))),
inference(resolution,[],[f290,f277]) ).
fof(f277,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(subsumption_resolution,[],[f276,f158]) ).
fof(f276,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(subsumption_resolution,[],[f182,f158]) ).
fof(f182,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type) ),
inference(literal_reordering,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f290,plain,
ilf_type(sK9,subset_type(cross_product(sK5,sK6))),
inference(resolution,[],[f289,f159]) ).
fof(f159,plain,
ilf_type(sK9,relation_type(sK5,sK6)),
inference(literal_reordering,[],[f118]) ).
fof(f118,plain,
ilf_type(sK9,relation_type(sK5,sK6)),
inference(cnf_transformation,[],[f77]) ).
fof(f289,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f288,f158]) ).
fof(f288,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f143,f158]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(literal_reordering,[],[f93]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f150,plain,
( ~ member(sK8,sK6)
| ~ member(sK7,sK5) ),
inference(literal_reordering,[],[f119]) ).
fof(f119,plain,
( ~ member(sK7,sK5)
| ~ member(sK8,sK6) ),
inference(cnf_transformation,[],[f77]) ).
fof(f396,plain,
member(sK7,sK5),
inference(resolution,[],[f380,f342]) ).
fof(f342,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(subsumption_resolution,[],[f341,f158]) ).
fof(f341,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(subsumption_resolution,[],[f340,f158]) ).
fof(f340,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(subsumption_resolution,[],[f339,f158]) ).
fof(f339,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,set_type)
| member(X0,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(subsumption_resolution,[],[f145,f158]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X0,X2) ),
inference(literal_reordering,[],[f134]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:08:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (32227)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.49 % (32227)Instruction limit reached!
% 0.19/0.49 % (32227)------------------------------
% 0.19/0.49 % (32227)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (32243)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)
% 0.19/0.50 % (32229)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (32235)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)
% 0.19/0.50 % (32245)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.51 % (32230)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.31/0.52 % (32227)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.52 % (32227)Termination reason: Unknown
% 1.31/0.52 % (32227)Termination phase: Saturation
% 1.31/0.52
% 1.31/0.52 % (32227)Memory used [KB]: 5628
% 1.31/0.52 % (32227)Time elapsed: 0.099 s
% 1.31/0.52 % (32227)Instructions burned: 8 (million)
% 1.31/0.52 % (32227)------------------------------
% 1.31/0.52 % (32227)------------------------------
% 1.31/0.52 % (32221)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.31/0.52 % (32242)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.31/0.53 % (32222)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.31/0.53 % (32220)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.31/0.53 % (32247)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)
% 1.31/0.53 % (32248)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.31/0.53 % (32228)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.31/0.53 % (32234)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.31/0.53 % (32224)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.31/0.53 % (32223)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)
% 1.31/0.53 % (32228)Instruction limit reached!
% 1.31/0.53 % (32228)------------------------------
% 1.31/0.53 % (32228)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.31/0.53 % (32228)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.53 % (32228)Termination reason: Unknown
% 1.31/0.53 % (32228)Termination phase: Blocked clause elimination
% 1.31/0.53
% 1.31/0.53 % (32228)Memory used [KB]: 1023
% 1.31/0.53 % (32228)Time elapsed: 0.004 s
% 1.31/0.53 % (32228)Instructions burned: 4 (million)
% 1.31/0.53 % (32228)------------------------------
% 1.31/0.53 % (32228)------------------------------
% 1.31/0.53 % (32225)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)
% 1.31/0.53 % (32231)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)
% 1.31/0.54 % (32236)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.44/0.54 % (32226)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)
% 1.44/0.54 % (32249)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.44/0.54 % (32239)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)
% 1.44/0.54 % (32240)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.44/0.54 % (32244)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.44/0.54 % (32238)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.44/0.54 % (32241)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.44/0.55 % (32237)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.44/0.55 % (32233)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.44/0.55 % (32232)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.44/0.55 TRYING [1]
% 1.44/0.55 TRYING [2]
% 1.44/0.55 % (32246)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.44/0.56 % (32234)First to succeed.
% 1.44/0.56 % (32234)Refutation found. Thanks to Tanya!
% 1.44/0.56 % SZS status Theorem for theBenchmark
% 1.44/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.44/0.56 % (32234)------------------------------
% 1.44/0.56 % (32234)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.44/0.56 % (32234)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.56 % (32234)Termination reason: Refutation
% 1.44/0.56
% 1.44/0.56 % (32234)Memory used [KB]: 6012
% 1.44/0.56 % (32234)Time elapsed: 0.010 s
% 1.44/0.56 % (32234)Instructions burned: 11 (million)
% 1.44/0.56 % (32234)------------------------------
% 1.44/0.56 % (32234)------------------------------
% 1.44/0.56 % (32219)Success in time 0.208 s
%------------------------------------------------------------------------------