TSTP Solution File: SET351+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET351+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 02:55:20 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 147 ( 8 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 160 ( 61 ~; 64 |; 30 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 51 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpY_t1Ze/sel_SET351+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpY_t1Ze/sel_SET351+4.p_1',equal_set) ).
fof(3,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/tmp/tmpY_t1Ze/sel_SET351+4.p_1',singleton) ).
fof(4,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X4] :
( member(X4,X1)
& member(X3,X4) ) ),
file('/tmp/tmpY_t1Ze/sel_SET351+4.p_1',sum) ).
fof(5,conjecture,
! [X1] : equal_set(sum(singleton(X1)),X1),
file('/tmp/tmpY_t1Ze/sel_SET351+4.p_1',thI39) ).
fof(6,negated_conjecture,
~ ! [X1] : equal_set(sum(singleton(X1)),X1),
inference(assume_negation,[status(cth)],[5]) ).
fof(7,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(8,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[7]) ).
fof(9,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[8]) ).
fof(10,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[9]) ).
fof(11,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[10]) ).
cnf(12,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(13,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(15,plain,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X3,X1] :
( ( ~ member(X3,singleton(X1))
| X3 = X1 )
& ( X3 != X1
| member(X3,singleton(X1)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(22,plain,
! [X4,X5] :
( ( ~ member(X4,singleton(X5))
| X4 = X5 )
& ( X4 != X5
| member(X4,singleton(X5)) ) ),
inference(variable_rename,[status(thm)],[21]) ).
cnf(23,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(25,plain,
! [X3,X1] :
( ( ~ member(X3,sum(X1))
| ? [X4] :
( member(X4,X1)
& member(X3,X4) ) )
& ( ! [X4] :
( ~ member(X4,X1)
| ~ member(X3,X4) )
| member(X3,sum(X1)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(26,plain,
! [X5,X6] :
( ( ~ member(X5,sum(X6))
| ? [X7] :
( member(X7,X6)
& member(X5,X7) ) )
& ( ! [X8] :
( ~ member(X8,X6)
| ~ member(X5,X8) )
| member(X5,sum(X6)) ) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,plain,
! [X5,X6] :
( ( ~ member(X5,sum(X6))
| ( member(esk2_2(X5,X6),X6)
& member(X5,esk2_2(X5,X6)) ) )
& ( ! [X8] :
( ~ member(X8,X6)
| ~ member(X5,X8) )
| member(X5,sum(X6)) ) ),
inference(skolemize,[status(esa)],[26]) ).
fof(28,plain,
! [X5,X6,X8] :
( ( ~ member(X8,X6)
| ~ member(X5,X8)
| member(X5,sum(X6)) )
& ( ~ member(X5,sum(X6))
| ( member(esk2_2(X5,X6),X6)
& member(X5,esk2_2(X5,X6)) ) ) ),
inference(shift_quantors,[status(thm)],[27]) ).
fof(29,plain,
! [X5,X6,X8] :
( ( ~ member(X8,X6)
| ~ member(X5,X8)
| member(X5,sum(X6)) )
& ( member(esk2_2(X5,X6),X6)
| ~ member(X5,sum(X6)) )
& ( member(X5,esk2_2(X5,X6))
| ~ member(X5,sum(X6)) ) ),
inference(distribute,[status(thm)],[28]) ).
cnf(30,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(32,plain,
( member(X1,sum(X2))
| ~ member(X1,X3)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(33,negated_conjecture,
? [X1] : ~ equal_set(sum(singleton(X1)),X1),
inference(fof_nnf,[status(thm)],[6]) ).
fof(34,negated_conjecture,
? [X2] : ~ equal_set(sum(singleton(X2)),X2),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
~ equal_set(sum(singleton(esk3_0)),esk3_0),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
~ equal_set(sum(singleton(esk3_0)),esk3_0),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[23,theory(equality)]) ).
cnf(38,plain,
( member(esk1_2(sum(X1),X2),esk2_2(esk1_2(sum(X1),X2),X1))
| subset(sum(X1),X2) ),
inference(spm,[status(thm)],[30,13,theory(equality)]) ).
cnf(39,plain,
( member(esk2_2(esk1_2(sum(X1),X2),X1),X1)
| subset(sum(X1),X2) ),
inference(spm,[status(thm)],[31,13,theory(equality)]) ).
cnf(51,plain,
( member(X1,sum(singleton(X2)))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[32,37,theory(equality)]) ).
cnf(53,plain,
( member(esk1_2(X1,X2),sum(singleton(X1)))
| subset(X1,X2) ),
inference(spm,[status(thm)],[51,13,theory(equality)]) ).
cnf(87,plain,
subset(X1,sum(singleton(X1))),
inference(spm,[status(thm)],[12,53,theory(equality)]) ).
cnf(92,plain,
( equal_set(sum(singleton(X1)),X1)
| ~ subset(sum(singleton(X1)),X1) ),
inference(spm,[status(thm)],[18,87,theory(equality)]) ).
cnf(98,plain,
( esk2_2(esk1_2(sum(singleton(X1)),X2),singleton(X1)) = X1
| subset(sum(singleton(X1)),X2) ),
inference(spm,[status(thm)],[24,39,theory(equality)]) ).
cnf(665,plain,
( member(esk1_2(sum(singleton(X1)),X2),X1)
| subset(sum(singleton(X1)),X2) ),
inference(spm,[status(thm)],[38,98,theory(equality)]) ).
cnf(672,plain,
subset(sum(singleton(X1)),X1),
inference(spm,[status(thm)],[12,665,theory(equality)]) ).
cnf(697,plain,
( equal_set(sum(singleton(X1)),X1)
| $false ),
inference(rw,[status(thm)],[92,672,theory(equality)]) ).
cnf(698,plain,
equal_set(sum(singleton(X1)),X1),
inference(cn,[status(thm)],[697,theory(equality)]) ).
cnf(703,negated_conjecture,
$false,
inference(rw,[status(thm)],[36,698,theory(equality)]) ).
cnf(704,negated_conjecture,
$false,
inference(cn,[status(thm)],[703,theory(equality)]) ).
cnf(705,negated_conjecture,
$false,
704,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET351+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpY_t1Ze/sel_SET351+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET351+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET351+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET351+4.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
%
%------------------------------------------------------------------------------