TSTP Solution File: SEU361+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU361+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 07:45:31 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 13 unt; 0 def)
% Number of atoms : 312 ( 21 equ)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 413 ( 159 ~; 161 |; 73 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 74 ( 1 sgn 55 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [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/tmpOuJtMv/sel_SEU361+1.p_1',t6_yellow_0) ).
fof(8,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
file('/tmp/tmpOuJtMv/sel_SEU361+1.p_1',t44_yellow_0) ).
fof(9,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
file('/tmp/tmpOuJtMv/sel_SEU361+1.p_1',t42_yellow_0) ).
fof(10,axiom,
! [X1] :
( rel_str(X1)
=> bottom_of_relstr(X1) = join_on_relstr(X1,empty_set) ),
file('/tmp/tmpOuJtMv/sel_SEU361+1.p_1',d11_yellow_0) ).
fof(17,axiom,
! [X1,X2] :
( rel_str(X1)
=> element(join_on_relstr(X1,X2),the_carrier(X1)) ),
file('/tmp/tmpOuJtMv/sel_SEU361+1.p_1',dt_k1_yellow_0) ).
fof(25,axiom,
! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( ( ( X2 = join_on_relstr(X1,X3)
& ex_sup_of_relstr_set(X1,X3) )
=> ( relstr_set_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X3,X4)
=> related(X1,X2,X4) ) ) ) )
& ( ( relstr_set_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X3,X4)
=> related(X1,X2,X4) ) ) )
=> ( X2 = join_on_relstr(X1,X3)
& ex_sup_of_relstr_set(X1,X3) ) ) ) ) ),
file('/tmp/tmpOuJtMv/sel_SEU361+1.p_1',t30_yellow_0) ).
fof(29,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
inference(assume_negation,[status(cth)],[8]) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[29,theory(equality)]) ).
fof(32,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(45,plain,
! [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)],[5]) ).
fof(46,plain,
! [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)],[45]) ).
fof(47,plain,
! [X3,X4] :
( ~ element(X4,the_carrier(X3))
| ( relstr_set_smaller(X3,empty_set,X4)
& relstr_element_smaller(X3,empty_set,X4) )
| ~ rel_str(X3) ),
inference(shift_quantors,[status(thm)],[46]) ).
fof(48,plain,
! [X3,X4] :
( ( relstr_set_smaller(X3,empty_set,X4)
| ~ element(X4,the_carrier(X3))
| ~ rel_str(X3) )
& ( relstr_element_smaller(X3,empty_set,X4)
| ~ element(X4,the_carrier(X3))
| ~ rel_str(X3) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(50,plain,
( relstr_set_smaller(X1,empty_set,X2)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(57,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& ~ related(X1,bottom_of_relstr(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(58,negated_conjecture,
? [X3] :
( ~ empty_carrier(X3)
& antisymmetric_relstr(X3)
& lower_bounded_relstr(X3)
& rel_str(X3)
& ? [X4] :
( element(X4,the_carrier(X3))
& ~ related(X3,bottom_of_relstr(X3),X4) ) ),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,negated_conjecture,
( ~ empty_carrier(esk2_0)
& antisymmetric_relstr(esk2_0)
& lower_bounded_relstr(esk2_0)
& rel_str(esk2_0)
& element(esk3_0,the_carrier(esk2_0))
& ~ related(esk2_0,bottom_of_relstr(esk2_0),esk3_0) ),
inference(skolemize,[status(esa)],[58]) ).
cnf(60,negated_conjecture,
~ related(esk2_0,bottom_of_relstr(esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(61,negated_conjecture,
element(esk3_0,the_carrier(esk2_0)),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(62,negated_conjecture,
rel_str(esk2_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(63,negated_conjecture,
lower_bounded_relstr(esk2_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(64,negated_conjecture,
antisymmetric_relstr(esk2_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(65,negated_conjecture,
~ empty_carrier(esk2_0),
inference(split_conjunct,[status(thm)],[59]) ).
fof(66,plain,
! [X1] :
( empty_carrier(X1)
| ~ antisymmetric_relstr(X1)
| ~ lower_bounded_relstr(X1)
| ~ rel_str(X1)
| ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(67,plain,
! [X2] :
( empty_carrier(X2)
| ~ antisymmetric_relstr(X2)
| ~ lower_bounded_relstr(X2)
| ~ rel_str(X2)
| ( ex_sup_of_relstr_set(X2,empty_set)
& ex_inf_of_relstr_set(X2,the_carrier(X2)) ) ),
inference(variable_rename,[status(thm)],[66]) ).
fof(68,plain,
! [X2] :
( ( ex_sup_of_relstr_set(X2,empty_set)
| empty_carrier(X2)
| ~ antisymmetric_relstr(X2)
| ~ lower_bounded_relstr(X2)
| ~ rel_str(X2) )
& ( ex_inf_of_relstr_set(X2,the_carrier(X2))
| empty_carrier(X2)
| ~ antisymmetric_relstr(X2)
| ~ lower_bounded_relstr(X2)
| ~ rel_str(X2) ) ),
inference(distribute,[status(thm)],[67]) ).
cnf(70,plain,
( empty_carrier(X1)
| ex_sup_of_relstr_set(X1,empty_set)
| ~ rel_str(X1)
| ~ lower_bounded_relstr(X1)
| ~ antisymmetric_relstr(X1) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(71,plain,
! [X1] :
( ~ rel_str(X1)
| bottom_of_relstr(X1) = join_on_relstr(X1,empty_set) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(72,plain,
! [X2] :
( ~ rel_str(X2)
| bottom_of_relstr(X2) = join_on_relstr(X2,empty_set) ),
inference(variable_rename,[status(thm)],[71]) ).
cnf(73,plain,
( bottom_of_relstr(X1) = join_on_relstr(X1,empty_set)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(91,plain,
! [X1,X2] :
( ~ rel_str(X1)
| element(join_on_relstr(X1,X2),the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(92,plain,
! [X3,X4] :
( ~ rel_str(X3)
| element(join_on_relstr(X3,X4),the_carrier(X3)) ),
inference(variable_rename,[status(thm)],[91]) ).
cnf(93,plain,
( element(join_on_relstr(X1,X2),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[92]) ).
fof(112,plain,
! [X1] :
( ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ( X2 != join_on_relstr(X1,X3)
| ~ ex_sup_of_relstr_set(X1,X3)
| ( relstr_set_smaller(X1,X3,X2)
& ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ relstr_set_smaller(X1,X3,X4)
| related(X1,X2,X4) ) ) )
& ( ~ relstr_set_smaller(X1,X3,X2)
| ? [X4] :
( element(X4,the_carrier(X1))
& relstr_set_smaller(X1,X3,X4)
& ~ related(X1,X2,X4) )
| ( X2 = join_on_relstr(X1,X3)
& ex_sup_of_relstr_set(X1,X3) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(113,plain,
! [X5] :
( ~ antisymmetric_relstr(X5)
| ~ rel_str(X5)
| ! [X6] :
( ~ element(X6,the_carrier(X5))
| ! [X7] :
( ( X6 != join_on_relstr(X5,X7)
| ~ ex_sup_of_relstr_set(X5,X7)
| ( relstr_set_smaller(X5,X7,X6)
& ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ relstr_set_smaller(X5,X7,X8)
| related(X5,X6,X8) ) ) )
& ( ~ relstr_set_smaller(X5,X7,X6)
| ? [X9] :
( element(X9,the_carrier(X5))
& relstr_set_smaller(X5,X7,X9)
& ~ related(X5,X6,X9) )
| ( X6 = join_on_relstr(X5,X7)
& ex_sup_of_relstr_set(X5,X7) ) ) ) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X5] :
( ~ antisymmetric_relstr(X5)
| ~ rel_str(X5)
| ! [X6] :
( ~ element(X6,the_carrier(X5))
| ! [X7] :
( ( X6 != join_on_relstr(X5,X7)
| ~ ex_sup_of_relstr_set(X5,X7)
| ( relstr_set_smaller(X5,X7,X6)
& ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ relstr_set_smaller(X5,X7,X8)
| related(X5,X6,X8) ) ) )
& ( ~ relstr_set_smaller(X5,X7,X6)
| ( element(esk9_3(X5,X6,X7),the_carrier(X5))
& relstr_set_smaller(X5,X7,esk9_3(X5,X6,X7))
& ~ related(X5,X6,esk9_3(X5,X6,X7)) )
| ( X6 = join_on_relstr(X5,X7)
& ex_sup_of_relstr_set(X5,X7) ) ) ) ) ),
inference(skolemize,[status(esa)],[113]) ).
fof(115,plain,
! [X5,X6,X7,X8] :
( ( ( ( ( ~ element(X8,the_carrier(X5))
| ~ relstr_set_smaller(X5,X7,X8)
| related(X5,X6,X8) )
& relstr_set_smaller(X5,X7,X6) )
| X6 != join_on_relstr(X5,X7)
| ~ ex_sup_of_relstr_set(X5,X7) )
& ( ~ relstr_set_smaller(X5,X7,X6)
| ( element(esk9_3(X5,X6,X7),the_carrier(X5))
& relstr_set_smaller(X5,X7,esk9_3(X5,X6,X7))
& ~ related(X5,X6,esk9_3(X5,X6,X7)) )
| ( X6 = join_on_relstr(X5,X7)
& ex_sup_of_relstr_set(X5,X7) ) ) )
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) ),
inference(shift_quantors,[status(thm)],[114]) ).
fof(116,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,the_carrier(X5))
| ~ relstr_set_smaller(X5,X7,X8)
| related(X5,X6,X8)
| X6 != join_on_relstr(X5,X7)
| ~ ex_sup_of_relstr_set(X5,X7)
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( relstr_set_smaller(X5,X7,X6)
| X6 != join_on_relstr(X5,X7)
| ~ ex_sup_of_relstr_set(X5,X7)
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( X6 = join_on_relstr(X5,X7)
| element(esk9_3(X5,X6,X7),the_carrier(X5))
| ~ relstr_set_smaller(X5,X7,X6)
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( ex_sup_of_relstr_set(X5,X7)
| element(esk9_3(X5,X6,X7),the_carrier(X5))
| ~ relstr_set_smaller(X5,X7,X6)
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( X6 = join_on_relstr(X5,X7)
| relstr_set_smaller(X5,X7,esk9_3(X5,X6,X7))
| ~ relstr_set_smaller(X5,X7,X6)
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( ex_sup_of_relstr_set(X5,X7)
| relstr_set_smaller(X5,X7,esk9_3(X5,X6,X7))
| ~ relstr_set_smaller(X5,X7,X6)
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( X6 = join_on_relstr(X5,X7)
| ~ related(X5,X6,esk9_3(X5,X6,X7))
| ~ relstr_set_smaller(X5,X7,X6)
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) )
& ( ex_sup_of_relstr_set(X5,X7)
| ~ related(X5,X6,esk9_3(X5,X6,X7))
| ~ relstr_set_smaller(X5,X7,X6)
| ~ element(X6,the_carrier(X5))
| ~ antisymmetric_relstr(X5)
| ~ rel_str(X5) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(124,plain,
( related(X1,X2,X4)
| ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ ex_sup_of_relstr_set(X1,X3)
| X2 != join_on_relstr(X1,X3)
| ~ relstr_set_smaller(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(135,negated_conjecture,
( ~ related(esk2_0,join_on_relstr(esk2_0,empty_set),esk3_0)
| ~ rel_str(esk2_0) ),
inference(spm,[status(thm)],[60,73,theory(equality)]) ).
cnf(137,negated_conjecture,
( ~ related(esk2_0,join_on_relstr(esk2_0,empty_set),esk3_0)
| $false ),
inference(rw,[status(thm)],[135,62,theory(equality)]) ).
cnf(138,negated_conjecture,
~ related(esk2_0,join_on_relstr(esk2_0,empty_set),esk3_0),
inference(cn,[status(thm)],[137,theory(equality)]) ).
cnf(148,negated_conjecture,
( ex_sup_of_relstr_set(esk2_0,empty_set)
| empty_carrier(esk2_0)
| ~ antisymmetric_relstr(esk2_0)
| ~ rel_str(esk2_0) ),
inference(spm,[status(thm)],[70,63,theory(equality)]) ).
cnf(149,negated_conjecture,
( ex_sup_of_relstr_set(esk2_0,empty_set)
| empty_carrier(esk2_0)
| $false
| ~ rel_str(esk2_0) ),
inference(rw,[status(thm)],[148,64,theory(equality)]) ).
cnf(150,negated_conjecture,
( ex_sup_of_relstr_set(esk2_0,empty_set)
| empty_carrier(esk2_0)
| $false
| $false ),
inference(rw,[status(thm)],[149,62,theory(equality)]) ).
cnf(151,negated_conjecture,
( ex_sup_of_relstr_set(esk2_0,empty_set)
| empty_carrier(esk2_0) ),
inference(cn,[status(thm)],[150,theory(equality)]) ).
cnf(152,negated_conjecture,
ex_sup_of_relstr_set(esk2_0,empty_set),
inference(sr,[status(thm)],[151,65,theory(equality)]) ).
cnf(154,plain,
( related(X1,X2,X3)
| join_on_relstr(X1,empty_set) != X2
| ~ ex_sup_of_relstr_set(X1,empty_set)
| ~ antisymmetric_relstr(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[124,50,theory(equality)]) ).
cnf(177,negated_conjecture,
( ~ ex_sup_of_relstr_set(esk2_0,empty_set)
| ~ antisymmetric_relstr(esk2_0)
| ~ element(esk3_0,the_carrier(esk2_0))
| ~ element(join_on_relstr(esk2_0,empty_set),the_carrier(esk2_0))
| ~ rel_str(esk2_0) ),
inference(spm,[status(thm)],[138,154,theory(equality)]) ).
cnf(185,negated_conjecture,
( $false
| ~ antisymmetric_relstr(esk2_0)
| ~ element(esk3_0,the_carrier(esk2_0))
| ~ element(join_on_relstr(esk2_0,empty_set),the_carrier(esk2_0))
| ~ rel_str(esk2_0) ),
inference(rw,[status(thm)],[177,152,theory(equality)]) ).
cnf(186,negated_conjecture,
( $false
| $false
| ~ element(esk3_0,the_carrier(esk2_0))
| ~ element(join_on_relstr(esk2_0,empty_set),the_carrier(esk2_0))
| ~ rel_str(esk2_0) ),
inference(rw,[status(thm)],[185,64,theory(equality)]) ).
cnf(187,negated_conjecture,
( $false
| $false
| $false
| ~ element(join_on_relstr(esk2_0,empty_set),the_carrier(esk2_0))
| ~ rel_str(esk2_0) ),
inference(rw,[status(thm)],[186,61,theory(equality)]) ).
cnf(188,negated_conjecture,
( $false
| $false
| $false
| ~ element(join_on_relstr(esk2_0,empty_set),the_carrier(esk2_0))
| $false ),
inference(rw,[status(thm)],[187,62,theory(equality)]) ).
cnf(189,negated_conjecture,
~ element(join_on_relstr(esk2_0,empty_set),the_carrier(esk2_0)),
inference(cn,[status(thm)],[188,theory(equality)]) ).
cnf(190,negated_conjecture,
~ rel_str(esk2_0),
inference(spm,[status(thm)],[189,93,theory(equality)]) ).
cnf(191,negated_conjecture,
$false,
inference(rw,[status(thm)],[190,62,theory(equality)]) ).
cnf(192,negated_conjecture,
$false,
inference(cn,[status(thm)],[191,theory(equality)]) ).
cnf(193,negated_conjecture,
$false,
192,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU361+1.p
% --creating new selector for []
% -running prover on /tmp/tmpOuJtMv/sel_SEU361+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU361+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU361+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU361+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
%
%------------------------------------------------------------------------------