TSTP Solution File: SEU355+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU355+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 07:42:55 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 283 ( 115 ~; 115 |; 39 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 1 sgn 58 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,conjecture,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
file('/tmp/tmpLvieGp/sel_SEU355+1.p_1',t6_yellow_0) ).
fof(7,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/tmp/tmpLvieGp/sel_SEU355+1.p_1',t7_boole) ).
fof(10,axiom,
empty(empty_set),
file('/tmp/tmpLvieGp/sel_SEU355+1.p_1',fc1_xboole_0) ).
fof(16,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X4,X3) ) ) ) ) ),
file('/tmp/tmpLvieGp/sel_SEU355+1.p_1',d9_lattice3) ).
fof(19,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X3,X4) ) ) ) ) ),
file('/tmp/tmpLvieGp/sel_SEU355+1.p_1',d8_lattice3) ).
fof(23,negated_conjecture,
~ ! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(35,negated_conjecture,
? [X1] :
( rel_str(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& ( ~ relstr_set_smaller(X1,empty_set,X2)
| ~ relstr_element_smaller(X1,empty_set,X2) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(36,negated_conjecture,
? [X3] :
( rel_str(X3)
& ? [X4] :
( element(X4,the_carrier(X3))
& ( ~ relstr_set_smaller(X3,empty_set,X4)
| ~ relstr_element_smaller(X3,empty_set,X4) ) ) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,negated_conjecture,
( rel_str(esk2_0)
& element(esk3_0,the_carrier(esk2_0))
& ( ~ relstr_set_smaller(esk2_0,empty_set,esk3_0)
| ~ relstr_element_smaller(esk2_0,empty_set,esk3_0) ) ),
inference(skolemize,[status(esa)],[36]) ).
cnf(38,negated_conjecture,
( ~ relstr_element_smaller(esk2_0,empty_set,esk3_0)
| ~ relstr_set_smaller(esk2_0,empty_set,esk3_0) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(39,negated_conjecture,
element(esk3_0,the_carrier(esk2_0)),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(40,negated_conjecture,
rel_str(esk2_0),
inference(split_conjunct,[status(thm)],[37]) ).
fof(44,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(45,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[44]) ).
cnf(46,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(54,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[10]) ).
fof(68,plain,
! [X1] :
( ~ rel_str(X1)
| ! [X2,X3] :
( ~ element(X3,the_carrier(X1))
| ( ( ~ relstr_set_smaller(X1,X2,X3)
| ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ in(X4,X2)
| related(X1,X4,X3) ) )
& ( ? [X4] :
( element(X4,the_carrier(X1))
& in(X4,X2)
& ~ related(X1,X4,X3) )
| relstr_set_smaller(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(69,plain,
! [X5] :
( ~ rel_str(X5)
| ! [X6,X7] :
( ~ element(X7,the_carrier(X5))
| ( ( ~ relstr_set_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X8,X7) ) )
& ( ? [X9] :
( element(X9,the_carrier(X5))
& in(X9,X6)
& ~ related(X5,X9,X7) )
| relstr_set_smaller(X5,X6,X7) ) ) ) ),
inference(variable_rename,[status(thm)],[68]) ).
fof(70,plain,
! [X5] :
( ~ rel_str(X5)
| ! [X6,X7] :
( ~ element(X7,the_carrier(X5))
| ( ( ~ relstr_set_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X8,X7) ) )
& ( ( element(esk7_3(X5,X6,X7),the_carrier(X5))
& in(esk7_3(X5,X6,X7),X6)
& ~ related(X5,esk7_3(X5,X6,X7),X7) )
| relstr_set_smaller(X5,X6,X7) ) ) ) ),
inference(skolemize,[status(esa)],[69]) ).
fof(71,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X8,X7)
| ~ relstr_set_smaller(X5,X6,X7) )
& ( ( element(esk7_3(X5,X6,X7),the_carrier(X5))
& in(esk7_3(X5,X6,X7),X6)
& ~ related(X5,esk7_3(X5,X6,X7),X7) )
| relstr_set_smaller(X5,X6,X7) ) )
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ),
inference(shift_quantors,[status(thm)],[70]) ).
fof(72,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X8,X7)
| ~ relstr_set_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( element(esk7_3(X5,X6,X7),the_carrier(X5))
| relstr_set_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( in(esk7_3(X5,X6,X7),X6)
| relstr_set_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( ~ related(X5,esk7_3(X5,X6,X7),X7)
| relstr_set_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ) ),
inference(distribute,[status(thm)],[71]) ).
cnf(74,plain,
( relstr_set_smaller(X1,X3,X2)
| in(esk7_3(X1,X3,X2),X3)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(81,plain,
! [X1] :
( ~ rel_str(X1)
| ! [X2,X3] :
( ~ element(X3,the_carrier(X1))
| ( ( ~ relstr_element_smaller(X1,X2,X3)
| ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ in(X4,X2)
| related(X1,X3,X4) ) )
& ( ? [X4] :
( element(X4,the_carrier(X1))
& in(X4,X2)
& ~ related(X1,X3,X4) )
| relstr_element_smaller(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(82,plain,
! [X5] :
( ~ rel_str(X5)
| ! [X6,X7] :
( ~ element(X7,the_carrier(X5))
| ( ( ~ relstr_element_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8) ) )
& ( ? [X9] :
( element(X9,the_carrier(X5))
& in(X9,X6)
& ~ related(X5,X7,X9) )
| relstr_element_smaller(X5,X6,X7) ) ) ) ),
inference(variable_rename,[status(thm)],[81]) ).
fof(83,plain,
! [X5] :
( ~ rel_str(X5)
| ! [X6,X7] :
( ~ element(X7,the_carrier(X5))
| ( ( ~ relstr_element_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8) ) )
& ( ( element(esk9_3(X5,X6,X7),the_carrier(X5))
& in(esk9_3(X5,X6,X7),X6)
& ~ related(X5,X7,esk9_3(X5,X6,X7)) )
| relstr_element_smaller(X5,X6,X7) ) ) ) ),
inference(skolemize,[status(esa)],[82]) ).
fof(84,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8)
| ~ relstr_element_smaller(X5,X6,X7) )
& ( ( element(esk9_3(X5,X6,X7),the_carrier(X5))
& in(esk9_3(X5,X6,X7),X6)
& ~ related(X5,X7,esk9_3(X5,X6,X7)) )
| relstr_element_smaller(X5,X6,X7) ) )
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ),
inference(shift_quantors,[status(thm)],[83]) ).
fof(85,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8)
| ~ relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( element(esk9_3(X5,X6,X7),the_carrier(X5))
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( in(esk9_3(X5,X6,X7),X6)
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( ~ related(X5,X7,esk9_3(X5,X6,X7))
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ) ),
inference(distribute,[status(thm)],[84]) ).
cnf(87,plain,
( relstr_element_smaller(X1,X3,X2)
| in(esk9_3(X1,X3,X2),X3)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(106,plain,
( relstr_set_smaller(X1,X2,X3)
| ~ empty(X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[46,74,theory(equality)]) ).
cnf(109,plain,
( relstr_element_smaller(X1,X2,X3)
| ~ empty(X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[46,87,theory(equality)]) ).
cnf(115,negated_conjecture,
( ~ relstr_set_smaller(esk2_0,empty_set,esk3_0)
| ~ element(esk3_0,the_carrier(esk2_0))
| ~ rel_str(esk2_0)
| ~ empty(empty_set) ),
inference(spm,[status(thm)],[38,109,theory(equality)]) ).
cnf(117,negated_conjecture,
( ~ relstr_set_smaller(esk2_0,empty_set,esk3_0)
| $false
| ~ rel_str(esk2_0)
| ~ empty(empty_set) ),
inference(rw,[status(thm)],[115,39,theory(equality)]) ).
cnf(118,negated_conjecture,
( ~ relstr_set_smaller(esk2_0,empty_set,esk3_0)
| $false
| $false
| ~ empty(empty_set) ),
inference(rw,[status(thm)],[117,40,theory(equality)]) ).
cnf(119,negated_conjecture,
( ~ relstr_set_smaller(esk2_0,empty_set,esk3_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[118,54,theory(equality)]) ).
cnf(120,negated_conjecture,
~ relstr_set_smaller(esk2_0,empty_set,esk3_0),
inference(cn,[status(thm)],[119,theory(equality)]) ).
cnf(121,negated_conjecture,
( ~ element(esk3_0,the_carrier(esk2_0))
| ~ rel_str(esk2_0)
| ~ empty(empty_set) ),
inference(spm,[status(thm)],[120,106,theory(equality)]) ).
cnf(122,negated_conjecture,
( $false
| ~ rel_str(esk2_0)
| ~ empty(empty_set) ),
inference(rw,[status(thm)],[121,39,theory(equality)]) ).
cnf(123,negated_conjecture,
( $false
| $false
| ~ empty(empty_set) ),
inference(rw,[status(thm)],[122,40,theory(equality)]) ).
cnf(124,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[123,54,theory(equality)]) ).
cnf(125,negated_conjecture,
$false,
inference(cn,[status(thm)],[124,theory(equality)]) ).
cnf(126,negated_conjecture,
$false,
125,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU355+1.p
% --creating new selector for []
% -running prover on /tmp/tmpLvieGp/sel_SEU355+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU355+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU355+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU355+1.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
%
%------------------------------------------------------------------------------