TSTP Solution File: SET685+3 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET685+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_uns --cores 0 -t %d %s
% Computer : n012.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 18:21:53 EDT 2022
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 83 ( 9 unt; 0 def)
% Number of atoms : 515 ( 4 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 664 ( 232 ~; 197 |; 180 &)
% ( 13 <=>; 40 =>; 0 <=; 2 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 202 ( 129 !; 73 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f331,plain,
$false,
inference(avatar_sat_refutation,[],[f193,f197,f202,f314,f330]) ).
fof(f330,plain,
( spl17_2
| ~ spl17_3
| ~ spl17_5 ),
inference(avatar_contradiction_clause,[],[f329]) ).
fof(f329,plain,
( $false
| spl17_2
| ~ spl17_3
| ~ spl17_5 ),
inference(subsumption_resolution,[],[f322,f315]) ).
fof(f315,plain,
( ~ member(sK4,image(sK3,sK1))
| spl17_2 ),
inference(forward_demodulation,[],[f186,f215]) ).
fof(f215,plain,
! [X0] : image(sK3,X0) = image4(sK2,sK0,sK3,X0),
inference(unit_resulting_resolution,[],[f130,f130,f130,f112,f149]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ ilf_type(X3,set_type)
| image4(X0,X1,X2,X3) = image(X2,X3) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(f112,plain,
ilf_type(sK3,relation_type(sK2,sK0)),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ilf_type(sK0,set_type)
& ~ empty(sK0)
& ilf_type(sK1,set_type)
& ~ empty(sK1)
& ilf_type(sK2,set_type)
& ilf_type(sK4,member_type(sK0))
& ( ~ member(sK4,image4(sK2,sK0,sK3,sK1))
| ! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(X5,sK4),sK3)
| ~ member(X5,sK1) ) )
& ( member(sK4,image4(sK2,sK0,sK3,sK1))
| ( ilf_type(sK5,member_type(sK2))
& member(ordered_pair(sK5,sK4),sK3)
& member(sK5,sK1) ) )
& ilf_type(sK3,relation_type(sK2,sK0))
& ~ empty(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f65,f71,f70,f69,f68,f67,f66]) ).
fof(f66,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(X0))
& ( ~ member(X4,image4(X2,X0,X3,X1))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) ) )
& ( member(X4,image4(X2,X0,X3,X1))
| ? [X6] :
( ilf_type(X6,member_type(X2))
& member(ordered_pair(X6,X4),X3)
& member(X6,X1) ) ) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2) ) ) )
=> ( ilf_type(sK0,set_type)
& ~ empty(sK0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(sK0))
& ( ~ member(X4,image4(X2,sK0,X3,X1))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) ) )
& ( member(X4,image4(X2,sK0,X3,X1))
| ? [X6] :
( ilf_type(X6,member_type(X2))
& member(ordered_pair(X6,X4),X3)
& member(X6,X1) ) ) )
& ilf_type(X3,relation_type(X2,sK0)) )
& ~ empty(X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
( ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(sK0))
& ( ~ member(X4,image4(X2,sK0,X3,X1))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) ) )
& ( member(X4,image4(X2,sK0,X3,X1))
| ? [X6] :
( ilf_type(X6,member_type(X2))
& member(ordered_pair(X6,X4),X3)
& member(X6,X1) ) ) )
& ilf_type(X3,relation_type(X2,sK0)) )
& ~ empty(X2) ) )
=> ( ilf_type(sK1,set_type)
& ~ empty(sK1)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(sK0))
& ( ~ member(X4,image4(X2,sK0,X3,sK1))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,sK1) ) )
& ( member(X4,image4(X2,sK0,X3,sK1))
| ? [X6] :
( ilf_type(X6,member_type(X2))
& member(ordered_pair(X6,X4),X3)
& member(X6,sK1) ) ) )
& ilf_type(X3,relation_type(X2,sK0)) )
& ~ empty(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(sK0))
& ( ~ member(X4,image4(X2,sK0,X3,sK1))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,sK1) ) )
& ( member(X4,image4(X2,sK0,X3,sK1))
| ? [X6] :
( ilf_type(X6,member_type(X2))
& member(ordered_pair(X6,X4),X3)
& member(X6,sK1) ) ) )
& ilf_type(X3,relation_type(X2,sK0)) )
& ~ empty(X2) )
=> ( ilf_type(sK2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(sK0))
& ( ~ member(X4,image4(sK2,sK0,X3,sK1))
| ! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,sK1) ) )
& ( member(X4,image4(sK2,sK0,X3,sK1))
| ? [X6] :
( ilf_type(X6,member_type(sK2))
& member(ordered_pair(X6,X4),X3)
& member(X6,sK1) ) ) )
& ilf_type(X3,relation_type(sK2,sK0)) )
& ~ empty(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
( ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(sK0))
& ( ~ member(X4,image4(sK2,sK0,X3,sK1))
| ! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,sK1) ) )
& ( member(X4,image4(sK2,sK0,X3,sK1))
| ? [X6] :
( ilf_type(X6,member_type(sK2))
& member(ordered_pair(X6,X4),X3)
& member(X6,sK1) ) ) )
& ilf_type(X3,relation_type(sK2,sK0)) )
=> ( ? [X4] :
( ilf_type(X4,member_type(sK0))
& ( ~ member(X4,image4(sK2,sK0,sK3,sK1))
| ! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(X5,X4),sK3)
| ~ member(X5,sK1) ) )
& ( member(X4,image4(sK2,sK0,sK3,sK1))
| ? [X6] :
( ilf_type(X6,member_type(sK2))
& member(ordered_pair(X6,X4),sK3)
& member(X6,sK1) ) ) )
& ilf_type(sK3,relation_type(sK2,sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
( ? [X4] :
( ilf_type(X4,member_type(sK0))
& ( ~ member(X4,image4(sK2,sK0,sK3,sK1))
| ! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(X5,X4),sK3)
| ~ member(X5,sK1) ) )
& ( member(X4,image4(sK2,sK0,sK3,sK1))
| ? [X6] :
( ilf_type(X6,member_type(sK2))
& member(ordered_pair(X6,X4),sK3)
& member(X6,sK1) ) ) )
=> ( ilf_type(sK4,member_type(sK0))
& ( ~ member(sK4,image4(sK2,sK0,sK3,sK1))
| ! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(X5,sK4),sK3)
| ~ member(X5,sK1) ) )
& ( member(sK4,image4(sK2,sK0,sK3,sK1))
| ? [X6] :
( ilf_type(X6,member_type(sK2))
& member(ordered_pair(X6,sK4),sK3)
& member(X6,sK1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
( ? [X6] :
( ilf_type(X6,member_type(sK2))
& member(ordered_pair(X6,sK4),sK3)
& member(X6,sK1) )
=> ( ilf_type(sK5,member_type(sK2))
& member(ordered_pair(sK5,sK4),sK3)
& member(sK5,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(X0))
& ( ~ member(X4,image4(X2,X0,X3,X1))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) ) )
& ( member(X4,image4(X2,X0,X3,X1))
| ? [X6] :
( ilf_type(X6,member_type(X2))
& member(ordered_pair(X6,X4),X3)
& member(X6,X1) ) ) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2) ) ) ),
inference(rectify,[],[f64]) ).
fof(f64,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(X0))
& ( ~ member(X4,image4(X2,X0,X3,X1))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) ) )
& ( member(X4,image4(X2,X0,X3,X1))
| ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) ) ) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2) ) ) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(X0))
& ( ~ member(X4,image4(X2,X0,X3,X1))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) ) )
& ( member(X4,image4(X2,X0,X3,X1))
| ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) ) ) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(X0))
& ( ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) )
<~> member(X4,image4(X2,X0,X3,X1)) ) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2) ) ) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ilf_type(X4,member_type(X0))
& ( ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) )
<~> member(X4,image4(X2,X0,X3,X1)) ) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) )
<=> member(X4,image4(X2,X0,X3,X1)) ) ) ) ) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) )
<=> member(X4,image4(X2,X0,X3,X1)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_52) ).
fof(f130,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f186,plain,
( ~ member(sK4,image4(sK2,sK0,sK3,sK1))
| spl17_2 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f185,plain,
( spl17_2
<=> member(sK4,image4(sK2,sK0,sK3,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f322,plain,
( member(sK4,image(sK3,sK1))
| ~ spl17_3
| ~ spl17_5 ),
inference(unit_resulting_resolution,[],[f192,f130,f130,f130,f246,f201,f160]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X1,image(X2,X0)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ( ilf_type(sK11(X0,X1,X2),set_type)
& member(ordered_pair(sK11(X0,X1,X2),X1),X2)
& member(sK11(X0,X1,X2),X0) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f94,f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X1),X2)
& member(X4,X0) )
=> ( ilf_type(sK11(X0,X1,X2),set_type)
& member(ordered_pair(sK11(X0,X1,X2),X1),X2)
& member(sK11(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X1),X2)
& member(X4,X0) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) ) ),
inference(rectify,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2)
& member(X3,X0) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ( member(X1,image(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2)
& member(X3,X0) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,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,binary_relation_type)
=> ( member(X1,image(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2)
& member(X3,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f201,plain,
( member(ordered_pair(sK5,sK4),sK3)
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f199,plain,
( spl17_5
<=> member(ordered_pair(sK5,sK4),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f246,plain,
ilf_type(sK3,binary_relation_type),
inference(unit_resulting_resolution,[],[f130,f242,f177]) ).
fof(f177,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(duplicate_literal_removal,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f242,plain,
relation_like(sK3),
inference(unit_resulting_resolution,[],[f130,f130,f214,f109]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| relation_like(X2)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) )
| ~ ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f214,plain,
ilf_type(sK3,subset_type(cross_product(sK2,sK0))),
inference(unit_resulting_resolution,[],[f130,f130,f112,f155]) ).
fof(f155,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,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,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [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))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f192,plain,
( member(sK5,sK1)
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f190,plain,
( spl17_3
<=> member(sK5,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f314,plain,
( ~ spl17_2
| ~ spl17_4 ),
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f313,plain,
( $false
| ~ spl17_2
| ~ spl17_4 ),
inference(subsumption_resolution,[],[f310,f271]) ).
fof(f271,plain,
( ~ ilf_type(sK11(sK1,sK4,sK3),member_type(sK2))
| ~ spl17_2
| ~ spl17_4 ),
inference(unit_resulting_resolution,[],[f250,f252,f196]) ).
fof(f196,plain,
( ! [X5] :
( ~ member(ordered_pair(X5,sK4),sK3)
| ~ ilf_type(X5,member_type(sK2))
| ~ member(X5,sK1) )
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f195,plain,
( spl17_4
<=> ! [X5] :
( ~ member(X5,sK1)
| ~ member(ordered_pair(X5,sK4),sK3)
| ~ ilf_type(X5,member_type(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f252,plain,
( member(ordered_pair(sK11(sK1,sK4,sK3),sK4),sK3)
| ~ spl17_2 ),
inference(unit_resulting_resolution,[],[f130,f130,f216,f246,f158]) ).
fof(f158,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK11(X0,X1,X2),X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,image(X2,X0)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f216,plain,
( member(sK4,image(sK3,sK1))
| ~ spl17_2 ),
inference(backward_demodulation,[],[f187,f215]) ).
fof(f187,plain,
( member(sK4,image4(sK2,sK0,sK3,sK1))
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f250,plain,
( member(sK11(sK1,sK4,sK3),sK1)
| ~ spl17_2 ),
inference(unit_resulting_resolution,[],[f130,f130,f216,f246,f157]) ).
fof(f157,plain,
! [X2,X0,X1] :
( member(sK11(X0,X1,X2),X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f96]) ).
fof(f310,plain,
( ilf_type(sK11(sK1,sK4,sK3),member_type(sK2))
| ~ spl17_2 ),
inference(unit_resulting_resolution,[],[f111,f130,f130,f273,f131]) ).
fof(f131,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| empty(X1)
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ( ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) )
& ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ( member(X0,X1)
<=> ilf_type(X0,member_type(X1)) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ( member(X0,X1)
<=> ilf_type(X0,member_type(X1)) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( member(X0,X1)
<=> ilf_type(X0,member_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f273,plain,
( member(sK11(sK1,sK4,sK3),sK2)
| ~ spl17_2 ),
inference(unit_resulting_resolution,[],[f130,f130,f112,f130,f130,f252,f150]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| member(X2,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ 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,[],[f2]) ).
fof(f2,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)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f111,plain,
~ empty(sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f202,plain,
( spl17_2
| spl17_5 ),
inference(avatar_split_clause,[],[f114,f199,f185]) ).
fof(f114,plain,
( member(ordered_pair(sK5,sK4),sK3)
| member(sK4,image4(sK2,sK0,sK3,sK1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f197,plain,
( spl17_4
| ~ spl17_2 ),
inference(avatar_split_clause,[],[f116,f185,f195]) ).
fof(f116,plain,
! [X5] :
( ~ member(sK4,image4(sK2,sK0,sK3,sK1))
| ~ member(X5,sK1)
| ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(X5,sK4),sK3) ),
inference(cnf_transformation,[],[f72]) ).
fof(f193,plain,
( spl17_3
| spl17_2 ),
inference(avatar_split_clause,[],[f113,f185,f190]) ).
fof(f113,plain,
( member(sK4,image4(sK2,sK0,sK3,sK1))
| member(sK5,sK1) ),
inference(cnf_transformation,[],[f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET685+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 14:13:05 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.49 % (8801)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.21/0.50 % (8793)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.50 % (8809)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.50 % (8817)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.21/0.51 % (8814)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.21/0.51 % (8809)Instruction limit reached!
% 0.21/0.51 % (8809)------------------------------
% 0.21/0.51 % (8809)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (8800)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.21/0.51 % (8809)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (8809)Termination reason: Unknown
% 0.21/0.51 % (8809)Termination phase: Property scanning
% 0.21/0.51
% 0.21/0.51 % (8809)Memory used [KB]: 1535
% 0.21/0.51 % (8809)Time elapsed: 0.004 s
% 0.21/0.51 % (8809)Instructions burned: 4 (million)
% 0.21/0.51 % (8809)------------------------------
% 0.21/0.51 % (8809)------------------------------
% 0.21/0.51 % (8801)First to succeed.
% 0.21/0.51 % (8805)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (8793)Refutation not found, incomplete strategy% (8793)------------------------------
% 0.21/0.51 % (8793)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (8793)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (8793)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51
% 0.21/0.51 % (8793)Memory used [KB]: 6140
% 0.21/0.51 % (8793)Time elapsed: 0.098 s
% 0.21/0.51 % (8793)Instructions burned: 7 (million)
% 0.21/0.51 % (8793)------------------------------
% 0.21/0.51 % (8793)------------------------------
% 0.21/0.51 % (8816)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.52 % (8798)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.52 % (8801)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52 % (8801)------------------------------
% 0.21/0.52 % (8801)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (8801)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (8801)Termination reason: Refutation
% 0.21/0.52
% 0.21/0.52 % (8801)Memory used [KB]: 6268
% 0.21/0.52 % (8801)Time elapsed: 0.109 s
% 0.21/0.52 % (8801)Instructions burned: 16 (million)
% 0.21/0.52 % (8801)------------------------------
% 0.21/0.52 % (8801)------------------------------
% 0.21/0.52 % (8791)Success in time 0.17 s
%------------------------------------------------------------------------------