TSTP Solution File: SET666+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET666+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 : n008.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 18:25:16 EDT 2022
% Result : Theorem 0.19s 0.55s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 6 unt; 0 def)
% Number of atoms : 358 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 519 ( 233 ~; 205 |; 39 &)
% ( 13 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 101 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f381,plain,
$false,
inference(resolution,[],[f379,f139]) ).
fof(f139,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f379,plain,
~ ilf_type(sK0,set_type),
inference(resolution,[],[f377,f139]) ).
fof(f377,plain,
( ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(sK0,set_type) ),
inference(resolution,[],[f374,f139]) ).
fof(f374,plain,
( ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type) ),
inference(resolution,[],[f371,f139]) ).
fof(f371,plain,
( ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(sK0,set_type) ),
inference(duplicate_literal_removal,[],[f367]) ).
fof(f367,plain,
( ~ ilf_type(sK0,set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type) ),
inference(resolution,[],[f333,f115]) ).
fof(f115,plain,
! [X0] :
( subset(identity_relation_of(X0),cross_product(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(identity_relation_of(X0),cross_product(X0,X0)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f333,plain,
( ~ subset(identity_relation_of(sK0),cross_product(sK0,sK0))
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type) ),
inference(resolution,[],[f330,f139]) ).
fof(f330,plain,
( ~ ilf_type(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(sK0,set_type)
| ~ subset(identity_relation_of(sK0),cross_product(sK0,sK0))
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type) ),
inference(duplicate_literal_removal,[],[f326]) ).
fof(f326,plain,
( ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ subset(identity_relation_of(sK0),cross_product(sK0,sK0))
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(sK0,set_type) ),
inference(resolution,[],[f324,f182]) ).
fof(f182,plain,
( ~ member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0)))
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type) ),
inference(resolution,[],[f179,f146]) ).
fof(f146,plain,
! [X0] : ~ empty(power_set(X0)),
inference(resolution,[],[f124,f139]) ).
fof(f124,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,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',p17) ).
fof(f179,plain,
( empty(power_set(cross_product(sK0,sK0)))
| ~ member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0)))
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type) ),
inference(duplicate_literal_removal,[],[f177]) ).
fof(f177,plain,
( ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(sK0,set_type)
| empty(power_set(cross_product(sK0,sK0)))
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0))) ),
inference(resolution,[],[f175,f135]) ).
fof(f135,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(f175,plain,
( ~ ilf_type(identity_relation_of(sK0),member_type(power_set(cross_product(sK0,sK0))))
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type) ),
inference(duplicate_literal_removal,[],[f174]) ).
fof(f174,plain,
( ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(identity_relation_of(sK0),member_type(power_set(cross_product(sK0,sK0)))) ),
inference(resolution,[],[f173,f137]) ).
fof(f137,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) )
& ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ilf_type(X1,member_type(power_set(X0)))
<=> ilf_type(X1,subset_type(X0)) )
| ~ ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,member_type(power_set(X0)))
<=> ilf_type(X1,subset_type(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f173,plain,
( ~ ilf_type(identity_relation_of(sK0),subset_type(cross_product(sK0,sK0)))
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type) ),
inference(duplicate_literal_removal,[],[f172]) ).
fof(f172,plain,
( ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),subset_type(cross_product(sK0,sK0)))
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(sK0,set_type) ),
inference(resolution,[],[f101,f164]) ).
fof(f164,plain,
( ~ ilf_type(identity_relation_of(sK0),relation_type(sK0,sK0))
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type) ),
inference(resolution,[],[f105,f94]) ).
fof(f94,plain,
~ ilf_type(identity_relation_of(sK0),identity_relation_of_type(sK0)),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
( ilf_type(sK0,set_type)
& ~ ilf_type(identity_relation_of(sK0),identity_relation_of_type(sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f55,f57]) ).
fof(f57,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ~ ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) )
=> ( ilf_type(sK0,set_type)
& ~ ilf_type(identity_relation_of(sK0),identity_relation_of_type(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
inference(negated_conjecture,[],[f25]) ).
fof(f25,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_29) ).
fof(f105,plain,
! [X0,X1] :
( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0)) )
& ( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,relation_type(X0,X0))
<=> ilf_type(X1,identity_relation_of_type(X0)) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,relation_type(X0,X0))
<=> ilf_type(X1,identity_relation_of_type(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f101,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( ! [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(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,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,[],[f1]) ).
fof(f1,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',p1) ).
fof(f324,plain,
( member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0)))
| ~ ilf_type(sK0,set_type)
| ~ subset(identity_relation_of(sK0),cross_product(sK0,sK0))
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type) ),
inference(duplicate_literal_removal,[],[f312]) ).
fof(f312,plain,
( ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),set_type)
| ~ subset(identity_relation_of(sK0),cross_product(sK0,sK0))
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0)))
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type) ),
inference(resolution,[],[f218,f96]) ).
fof(f96,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ! [X2] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) )
| ~ member(X0,power_set(X1)) )
& ( member(X0,power_set(X1))
| ( ~ member(sK1(X0,X1),X1)
& ilf_type(sK1(X0,X1),set_type)
& member(sK1(X0,X1),X0) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f60,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X3] :
( ~ member(X3,X1)
& ilf_type(X3,set_type)
& member(X3,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& ilf_type(sK1(X0,X1),set_type)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ! [X2] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) )
| ~ member(X0,power_set(X1)) )
& ( member(X0,power_set(X1))
| ? [X3] :
( ~ member(X3,X1)
& ilf_type(X3,set_type)
& member(X3,X0) ) ) ) ) ),
inference(rectify,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ! [X2] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) )
| ~ member(X0,power_set(X1)) )
& ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& ilf_type(X2,set_type)
& member(X2,X0) ) ) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X2] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) )
<=> member(X0,power_set(X1)) ) ) ),
inference(flattening,[],[f45]) ).
fof(f45,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,[],[f16]) ).
fof(f16,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',p16) ).
fof(f218,plain,
! [X7] :
( ~ member(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),X7)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),set_type)
| ~ subset(X7,cross_product(sK0,sK0))
| ~ ilf_type(X7,set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type) ),
inference(duplicate_literal_removal,[],[f214]) ).
fof(f214,plain,
! [X7] :
( ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ member(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),X7)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),set_type)
| ~ subset(X7,cross_product(sK0,sK0))
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(X7,set_type) ),
inference(resolution,[],[f123,f186]) ).
fof(f186,plain,
( ~ member(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),cross_product(sK0,sK0))
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(sK0,set_type) ),
inference(duplicate_literal_removal,[],[f183]) ).
fof(f183,plain,
( ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ ilf_type(sK0,set_type)
| ~ member(sK1(identity_relation_of(sK0),cross_product(sK0,sK0)),cross_product(sK0,sK0))
| ~ ilf_type(identity_relation_of(sK0),set_type)
| ~ ilf_type(cross_product(sK0,sK0),set_type) ),
inference(resolution,[],[f182,f98]) ).
fof(f98,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f123,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ilf_type(sK8(X0,X1),set_type)
& member(sK8(X0,X1),X0)
& ~ member(sK8(X0,X1),X1) ) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f79,f80]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X0)
& ~ member(X3,X1) )
=> ( ilf_type(sK8(X0,X1),set_type)
& member(sK8(X0,X1),X0)
& ~ member(sK8(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X0)
& ~ member(X3,X1) ) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) ) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) )
<=> subset(X0,X1) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,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,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 14:14:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.48 % (23222)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.48 % (23221)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 % (23238)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)
% 0.19/0.51 % (23214)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)
% 0.19/0.51 % (23237)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 % (23230)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51 % (23229)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.52 % (23234)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)
% 0.19/0.52 % (23220)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.52 % (23220)Instruction limit reached!
% 0.19/0.52 % (23220)------------------------------
% 0.19/0.52 % (23220)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (23220)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (23220)Termination reason: Unknown
% 0.19/0.52 % (23220)Termination phase: Clausification
% 0.19/0.52
% 0.19/0.52 % (23220)Memory used [KB]: 895
% 0.19/0.52 % (23220)Time elapsed: 0.002 s
% 0.19/0.52 % (23220)Instructions burned: 2 (million)
% 0.19/0.52 % (23220)------------------------------
% 0.19/0.52 % (23220)------------------------------
% 0.19/0.52 % (23212)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)
% 0.19/0.52 % (23223)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)
% 0.19/0.52 % (23219)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52 % (23224)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.52 % (23241)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)
% 0.19/0.53 % (23219)Instruction limit reached!
% 0.19/0.53 % (23219)------------------------------
% 0.19/0.53 % (23219)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (23219)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (23219)Termination reason: Unknown
% 0.19/0.53 % (23219)Termination phase: Saturation
% 0.19/0.53
% 0.19/0.53 % (23219)Memory used [KB]: 5500
% 0.19/0.53 % (23219)Time elapsed: 0.133 s
% 0.19/0.53 % (23219)Instructions burned: 7 (million)
% 0.19/0.53 % (23219)------------------------------
% 0.19/0.53 % (23219)------------------------------
% 0.19/0.53 % (23236)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.53 % (23233)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.53 % (23213)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)
% 0.19/0.53 TRYING [1]
% 0.19/0.53 % (23239)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)
% 0.19/0.53 % (23226)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)
% 0.19/0.53 TRYING [2]
% 0.19/0.53 % (23215)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)
% 0.19/0.53 % (23240)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.54 % (23216)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.54 % (23218)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)
% 0.19/0.54 % (23225)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.54 % (23221)First to succeed.
% 0.19/0.54 % (23213)Refutation not found, incomplete strategy% (23213)------------------------------
% 0.19/0.54 % (23213)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (23213)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (23213)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.54
% 0.19/0.54 % (23213)Memory used [KB]: 5500
% 0.19/0.54 % (23213)Time elapsed: 0.142 s
% 0.19/0.54 % (23213)Instructions burned: 5 (million)
% 0.19/0.54 % (23213)------------------------------
% 0.19/0.54 % (23213)------------------------------
% 0.19/0.54 TRYING [1]
% 0.19/0.54 % (23228)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)
% 0.19/0.54 TRYING [2]
% 0.19/0.54 TRYING [3]
% 0.19/0.54 % (23235)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)
% 0.19/0.54 % (23231)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)
% 0.19/0.54 % (23227)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)
% 0.19/0.55 % (23232)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)
% 0.19/0.55 % (23221)Refutation found. Thanks to Tanya!
% 0.19/0.55 % SZS status Theorem for theBenchmark
% 0.19/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.55 % (23221)------------------------------
% 0.19/0.55 % (23221)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55 % (23221)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55 % (23221)Termination reason: Refutation
% 0.19/0.55
% 0.19/0.55 % (23221)Memory used [KB]: 1279
% 0.19/0.55 % (23221)Time elapsed: 0.130 s
% 0.19/0.55 % (23221)Instructions burned: 24 (million)
% 0.19/0.55 % (23221)------------------------------
% 0.19/0.55 % (23221)------------------------------
% 0.19/0.55 % (23211)Success in time 0.205 s
%------------------------------------------------------------------------------