TSTP Solution File: SET676+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET676+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:10:15 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 93 ( 39 ~; 40 |; 7 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 1 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
file('/tmp/tmpVuwnwk/sel_SET676+3.p_1',p1) ).
fof(6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,identity_relation_of_type(X1))
<=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
file('/tmp/tmpVuwnwk/sel_SET676+3.p_1',p4) ).
fof(8,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)) ),
file('/tmp/tmpVuwnwk/sel_SET676+3.p_1',prove_relset_1_41) ).
fof(20,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpVuwnwk/sel_SET676+3.p_1',p19) ).
fof(21,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)) ),
inference(assume_negation,[status(cth)],[8]) ).
fof(41,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(42,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ilf_type(cross_product(X3,X4),relation_type(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ilf_type(cross_product(X3,X4),relation_type(X3,X4))
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[42]) ).
cnf(44,plain,
( ilf_type(cross_product(X1,X2),relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(55,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X2,identity_relation_of_type(X1))
| ilf_type(X2,relation_type(X1,X1)) )
& ( ~ ilf_type(X2,relation_type(X1,X1))
| ilf_type(X2,identity_relation_of_type(X1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(56,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3)) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3)) ) ) ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3)) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3)) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[56]) ).
fof(58,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_type(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[57]) ).
cnf(59,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(65,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ~ ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(66,negated_conjecture,
? [X2] :
( ilf_type(X2,set_type)
& ~ ilf_type(cross_product(X2,X2),identity_relation_of_type(X2)) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,negated_conjecture,
( ilf_type(esk4_0,set_type)
& ~ ilf_type(cross_product(esk4_0,esk4_0),identity_relation_of_type(esk4_0)) ),
inference(skolemize,[status(esa)],[66]) ).
cnf(68,negated_conjecture,
~ ilf_type(cross_product(esk4_0,esk4_0),identity_relation_of_type(esk4_0)),
inference(split_conjunct,[status(thm)],[67]) ).
fof(135,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[20]) ).
cnf(136,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(165,plain,
( ilf_type(cross_product(X1,X2),relation_type(X1,X2))
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[44,136,theory(equality)]) ).
cnf(166,plain,
( ilf_type(cross_product(X1,X2),relation_type(X1,X2))
| $false
| $false ),
inference(rw,[status(thm)],[165,136,theory(equality)]) ).
cnf(167,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(cn,[status(thm)],[166,theory(equality)]) ).
cnf(188,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(rw,[status(thm)],[59,136,theory(equality)]) ).
cnf(189,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| $false
| $false
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(rw,[status(thm)],[188,136,theory(equality)]) ).
cnf(190,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(cn,[status(thm)],[189,theory(equality)]) ).
cnf(191,plain,
ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)),
inference(spm,[status(thm)],[190,167,theory(equality)]) ).
cnf(298,negated_conjecture,
$false,
inference(rw,[status(thm)],[68,191,theory(equality)]) ).
cnf(299,negated_conjecture,
$false,
inference(cn,[status(thm)],[298,theory(equality)]) ).
cnf(300,negated_conjecture,
$false,
299,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET676+3.p
% --creating new selector for []
% -running prover on /tmp/tmpVuwnwk/sel_SET676+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET676+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET676+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET676+3.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------