%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU355+2 : TPTP v5.0.0. Released v3.3.0.
% 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 07:43:02 EST 2010
% Result : Theorem 14.68s
% Output : CNFRefutation 14.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 13 unt; 0 def)
% Number of atoms : 216 ( 12 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 279 ( 114 ~; 109 |; 40 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 93 ( 2 sgn 65 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(65,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/tmp/tmp1MmFK4/sel_SEU355+2.p_1',t3_xboole_1) ).
fof(256,axiom,
! [X1] : singleton(X1) != empty_set,
file('/tmp/tmp1MmFK4/sel_SEU355+2.p_1',l1_zfmisc_1) ).
fof(342,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/tmp/tmp1MmFK4/sel_SEU355+2.p_1',l2_zfmisc_1) ).
fof(473,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/tmp1MmFK4/sel_SEU355+2.p_1',d8_lattice3) ).
fof(524,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/tmp1MmFK4/sel_SEU355+2.p_1',t6_yellow_0) ).
fof(534,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/tmp1MmFK4/sel_SEU355+2.p_1',d9_lattice3) ).
fof(606,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmp1MmFK4/sel_SEU355+2.p_1',t69_enumset1) ).
fof(672,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)],[524]) ).
fof(1164,plain,
! [X1] :
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[65]) ).
fof(1165,plain,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[1164]) ).
cnf(1166,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[1165]) ).
fof(2685,plain,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[256]) ).
cnf(2686,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[2685]) ).
fof(3192,plain,
! [X1,X2] :
( ( ~ subset(singleton(X1),X2)
| in(X1,X2) )
& ( ~ in(X1,X2)
| subset(singleton(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[342]) ).
fof(3193,plain,
! [X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(variable_rename,[status(thm)],[3192]) ).
cnf(3194,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[3193]) ).
fof(4025,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)],[473]) ).
fof(4026,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)],[4025]) ).
fof(4027,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(esk304_3(X5,X6,X7),the_carrier(X5))
& in(esk304_3(X5,X6,X7),X6)
& ~ related(X5,X7,esk304_3(X5,X6,X7)) )
| relstr_element_smaller(X5,X6,X7) ) ) ) ),
inference(skolemize,[status(esa)],[4026]) ).
fof(4028,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X7,X8)
| ~ relstr_element_smaller(X5,X6,X7) )
& ( ( element(esk304_3(X5,X6,X7),the_carrier(X5))
& in(esk304_3(X5,X6,X7),X6)
& ~ related(X5,X7,esk304_3(X5,X6,X7)) )
| relstr_element_smaller(X5,X6,X7) ) )
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ),
inference(shift_quantors,[status(thm)],[4027]) ).
fof(4029,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(esk304_3(X5,X6,X7),the_carrier(X5))
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( in(esk304_3(X5,X6,X7),X6)
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( ~ related(X5,X7,esk304_3(X5,X6,X7))
| relstr_element_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ) ),
inference(distribute,[status(thm)],[4028]) ).
cnf(4031,plain,
( relstr_element_smaller(X1,X3,X2)
| in(esk304_3(X1,X3,X2),X3)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[4029]) ).
fof(4465,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)],[672]) ).
fof(4466,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)],[4465]) ).
fof(4467,negated_conjecture,
( rel_str(esk361_0)
& element(esk362_0,the_carrier(esk361_0))
& ( ~ relstr_set_smaller(esk361_0,empty_set,esk362_0)
| ~ relstr_element_smaller(esk361_0,empty_set,esk362_0) ) ),
inference(skolemize,[status(esa)],[4466]) ).
cnf(4468,negated_conjecture,
( ~ relstr_element_smaller(esk361_0,empty_set,esk362_0)
| ~ relstr_set_smaller(esk361_0,empty_set,esk362_0) ),
inference(split_conjunct,[status(thm)],[4467]) ).
cnf(4469,negated_conjecture,
element(esk362_0,the_carrier(esk361_0)),
inference(split_conjunct,[status(thm)],[4467]) ).
cnf(4470,negated_conjecture,
rel_str(esk361_0),
inference(split_conjunct,[status(thm)],[4467]) ).
fof(4548,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)],[534]) ).
fof(4549,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)],[4548]) ).
fof(4550,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(esk378_3(X5,X6,X7),the_carrier(X5))
& in(esk378_3(X5,X6,X7),X6)
& ~ related(X5,esk378_3(X5,X6,X7),X7) )
| relstr_set_smaller(X5,X6,X7) ) ) ) ),
inference(skolemize,[status(esa)],[4549]) ).
fof(4551,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X6)
| related(X5,X8,X7)
| ~ relstr_set_smaller(X5,X6,X7) )
& ( ( element(esk378_3(X5,X6,X7),the_carrier(X5))
& in(esk378_3(X5,X6,X7),X6)
& ~ related(X5,esk378_3(X5,X6,X7),X7) )
| relstr_set_smaller(X5,X6,X7) ) )
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ),
inference(shift_quantors,[status(thm)],[4550]) ).
fof(4552,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(esk378_3(X5,X6,X7),the_carrier(X5))
| relstr_set_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( in(esk378_3(X5,X6,X7),X6)
| relstr_set_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) )
& ( ~ related(X5,esk378_3(X5,X6,X7),X7)
| relstr_set_smaller(X5,X6,X7)
| ~ element(X7,the_carrier(X5))
| ~ rel_str(X5) ) ),
inference(distribute,[status(thm)],[4551]) ).
cnf(4554,plain,
( relstr_set_smaller(X1,X3,X2)
| in(esk378_3(X1,X3,X2),X3)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[4552]) ).
fof(5076,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[606]) ).
cnf(5077,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[5076]) ).
cnf(5571,plain,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[3194,5077,theory(equality)]),
[unfolding] ).
cnf(5674,plain,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[2686,5077,theory(equality)]),
[unfolding] ).
cnf(7834,plain,
( empty_set = unordered_pair(X1,X1)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[1166,5571,theory(equality)]) ).
cnf(7838,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[7834,5674,theory(equality)]) ).
cnf(117566,plain,
( relstr_set_smaller(X1,empty_set,X2)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(spm,[status(thm)],[7838,4554,theory(equality)]) ).
cnf(117567,plain,
( relstr_element_smaller(X1,empty_set,X2)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(spm,[status(thm)],[7838,4031,theory(equality)]) ).
cnf(123845,plain,
( ~ relstr_set_smaller(esk361_0,empty_set,esk362_0)
| ~ rel_str(esk361_0)
| ~ element(esk362_0,the_carrier(esk361_0)) ),
inference(spm,[status(thm)],[4468,117567,theory(equality)]) ).
cnf(123848,plain,
( ~ relstr_set_smaller(esk361_0,empty_set,esk362_0)
| $false
| ~ element(esk362_0,the_carrier(esk361_0)) ),
inference(rw,[status(thm)],[123845,4470,theory(equality)]) ).
cnf(123849,plain,
( ~ relstr_set_smaller(esk361_0,empty_set,esk362_0)
| $false
| $false ),
inference(rw,[status(thm)],[123848,4469,theory(equality)]) ).
cnf(123850,plain,
~ relstr_set_smaller(esk361_0,empty_set,esk362_0),
inference(cn,[status(thm)],[123849,theory(equality)]) ).
cnf(123851,plain,
( ~ rel_str(esk361_0)
| ~ element(esk362_0,the_carrier(esk361_0)) ),
inference(spm,[status(thm)],[123850,117566,theory(equality)]) ).
cnf(123852,plain,
( $false
| ~ element(esk362_0,the_carrier(esk361_0)) ),
inference(rw,[status(thm)],[123851,4470,theory(equality)]) ).
cnf(123853,plain,
( $false
| $false ),
inference(rw,[status(thm)],[123852,4469,theory(equality)]) ).
cnf(123854,plain,
$false,
inference(cn,[status(thm)],[123853,theory(equality)]) ).
cnf(123855,plain,
$false,
123854,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU355+2.p
% --creating new selector for []
% -running prover on /tmp/tmp1MmFK4/sel_SEU355+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU355+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU355+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU355+2.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
%
%------------------------------------------------------------------------------