TSTP Solution File: SYN084+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SYN084+1 : TPTP v5.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 13:17:53 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 1
% Syntax : Number of formulae : 56 ( 9 unt; 0 def)
% Number of atoms : 353 ( 0 equ)
% Maximal formula atoms : 114 ( 6 avg)
% Number of connectives : 444 ( 147 ~; 216 |; 72 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
( ! [X1] :
( ( big_p(a)
& ( big_p(X1)
=> big_p(f(X1)) ) )
=> big_p(f(f(X1))) )
<=> ! [X2] :
( ( ~ big_p(a)
| big_p(X2)
| big_p(f(f(X2))) )
& ( ~ big_p(a)
| ~ big_p(f(X2))
| big_p(f(f(X2))) ) ) ),
file('/tmp/tmpRQ59uk/sel_SYN084+1.p_1',pel62) ).
fof(2,negated_conjecture,
~ ( ! [X1] :
( ( big_p(a)
& ( big_p(X1)
=> big_p(f(X1)) ) )
=> big_p(f(f(X1))) )
<=> ! [X2] :
( ( ~ big_p(a)
| big_p(X2)
| big_p(f(f(X2))) )
& ( ~ big_p(a)
| ~ big_p(f(X2))
| big_p(f(f(X2))) ) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(3,negated_conjecture,
~ ( ! [X1] :
( ( big_p(a)
& ( big_p(X1)
=> big_p(f(X1)) ) )
=> big_p(f(f(X1))) )
<=> ! [X2] :
( ( ~ big_p(a)
| big_p(X2)
| big_p(f(f(X2))) )
& ( ~ big_p(a)
| ~ big_p(f(X2))
| big_p(f(f(X2))) ) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(4,negated_conjecture,
( ( ? [X1] :
( big_p(a)
& ( ~ big_p(X1)
| big_p(f(X1)) )
& ~ big_p(f(f(X1))) )
| ? [X2] :
( ( big_p(a)
& ~ big_p(X2)
& ~ big_p(f(f(X2))) )
| ( big_p(a)
& big_p(f(X2))
& ~ big_p(f(f(X2))) ) ) )
& ( ! [X1] :
( ~ big_p(a)
| ( big_p(X1)
& ~ big_p(f(X1)) )
| big_p(f(f(X1))) )
| ! [X2] :
( ( ~ big_p(a)
| big_p(X2)
| big_p(f(f(X2))) )
& ( ~ big_p(a)
| ~ big_p(f(X2))
| big_p(f(f(X2))) ) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(5,negated_conjecture,
( ( ? [X3] :
( big_p(a)
& ( ~ big_p(X3)
| big_p(f(X3)) )
& ~ big_p(f(f(X3))) )
| ? [X4] :
( ( big_p(a)
& ~ big_p(X4)
& ~ big_p(f(f(X4))) )
| ( big_p(a)
& big_p(f(X4))
& ~ big_p(f(f(X4))) ) ) )
& ( ! [X5] :
( ~ big_p(a)
| ( big_p(X5)
& ~ big_p(f(X5)) )
| big_p(f(f(X5))) )
| ! [X6] :
( ( ~ big_p(a)
| big_p(X6)
| big_p(f(f(X6))) )
& ( ~ big_p(a)
| ~ big_p(f(X6))
| big_p(f(f(X6))) ) ) ) ),
inference(variable_rename,[status(thm)],[4]) ).
fof(6,negated_conjecture,
( ( ( big_p(a)
& ( ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ~ big_p(f(f(esk1_0))) )
| ( big_p(a)
& ~ big_p(esk2_0)
& ~ big_p(f(f(esk2_0))) )
| ( big_p(a)
& big_p(f(esk2_0))
& ~ big_p(f(f(esk2_0))) ) )
& ( ! [X5] :
( ~ big_p(a)
| ( big_p(X5)
& ~ big_p(f(X5)) )
| big_p(f(f(X5))) )
| ! [X6] :
( ( ~ big_p(a)
| big_p(X6)
| big_p(f(f(X6))) )
& ( ~ big_p(a)
| ~ big_p(f(X6))
| big_p(f(f(X6))) ) ) ) ),
inference(skolemize,[status(esa)],[5]) ).
fof(7,negated_conjecture,
! [X5,X6] :
( ( ( ( ~ big_p(a)
| big_p(X6)
| big_p(f(f(X6))) )
& ( ~ big_p(a)
| ~ big_p(f(X6))
| big_p(f(f(X6))) ) )
| ~ big_p(a)
| ( big_p(X5)
& ~ big_p(f(X5)) )
| big_p(f(f(X5))) )
& ( ( big_p(a)
& ( ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ~ big_p(f(f(esk1_0))) )
| ( big_p(a)
& ~ big_p(esk2_0)
& ~ big_p(f(f(esk2_0))) )
| ( big_p(a)
& big_p(f(esk2_0))
& ~ big_p(f(f(esk2_0))) ) ) ),
inference(shift_quantors,[status(thm)],[6]) ).
fof(8,negated_conjecture,
! [X5,X6] :
( ( big_p(X5)
| ~ big_p(a)
| big_p(f(f(X5)))
| ~ big_p(a)
| big_p(X6)
| big_p(f(f(X6))) )
& ( ~ big_p(f(X5))
| ~ big_p(a)
| big_p(f(f(X5)))
| ~ big_p(a)
| big_p(X6)
| big_p(f(f(X6))) )
& ( big_p(X5)
| ~ big_p(a)
| big_p(f(f(X5)))
| ~ big_p(a)
| ~ big_p(f(X6))
| big_p(f(f(X6))) )
& ( ~ big_p(f(X5))
| ~ big_p(a)
| big_p(f(f(X5)))
| ~ big_p(a)
| ~ big_p(f(X6))
| big_p(f(f(X6))) )
& ( big_p(a)
| big_p(a)
| big_p(a) )
& ( big_p(f(esk2_0))
| big_p(a)
| big_p(a) )
& ( ~ big_p(f(f(esk2_0)))
| big_p(a)
| big_p(a) )
& ( big_p(a)
| ~ big_p(esk2_0)
| big_p(a) )
& ( big_p(f(esk2_0))
| ~ big_p(esk2_0)
| big_p(a) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(esk2_0)
| big_p(a) )
& ( big_p(a)
| ~ big_p(f(f(esk2_0)))
| big_p(a) )
& ( big_p(f(esk2_0))
| ~ big_p(f(f(esk2_0)))
| big_p(a) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0)))
| big_p(a) )
& ( big_p(a)
| big_p(a)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(f(esk2_0))
| big_p(a)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( ~ big_p(f(f(esk2_0)))
| big_p(a)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(a)
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(f(esk2_0))
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(esk2_0)
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(a)
| ~ big_p(f(f(esk2_0)))
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(f(esk2_0))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(esk1_0)
| big_p(f(esk1_0)) )
& ( big_p(a)
| big_p(a)
| ~ big_p(f(f(esk1_0))) )
& ( big_p(f(esk2_0))
| big_p(a)
| ~ big_p(f(f(esk1_0))) )
& ( ~ big_p(f(f(esk2_0)))
| big_p(a)
| ~ big_p(f(f(esk1_0))) )
& ( big_p(a)
| ~ big_p(esk2_0)
| ~ big_p(f(f(esk1_0))) )
& ( big_p(f(esk2_0))
| ~ big_p(esk2_0)
| ~ big_p(f(f(esk1_0))) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(esk2_0)
| ~ big_p(f(f(esk1_0))) )
& ( big_p(a)
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk1_0))) )
& ( big_p(f(esk2_0))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk1_0))) )
& ( ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk1_0))) ) ),
inference(distribute,[status(thm)],[7]) ).
cnf(9,negated_conjecture,
( ~ big_p(f(f(esk1_0)))
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0))) ),
inference(split_conjunct,[status(thm)],[8]) ).
cnf(13,negated_conjecture,
( big_p(f(esk2_0))
| ~ big_p(f(f(esk1_0)))
| ~ big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[8]) ).
cnf(18,negated_conjecture,
( big_p(f(esk1_0))
| ~ big_p(esk1_0)
| ~ big_p(f(f(esk2_0)))
| ~ big_p(f(f(esk2_0))) ),
inference(split_conjunct,[status(thm)],[8]) ).
cnf(22,negated_conjecture,
( big_p(f(esk1_0))
| big_p(f(esk2_0))
| ~ big_p(esk1_0)
| ~ big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[8]) ).
cnf(35,negated_conjecture,
( big_p(a)
| big_p(a)
| big_p(a) ),
inference(split_conjunct,[status(thm)],[8]) ).
cnf(36,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(X2)))
| ~ big_p(f(X1))
| ~ big_p(a)
| ~ big_p(a)
| ~ big_p(f(X2)) ),
inference(split_conjunct,[status(thm)],[8]) ).
cnf(39,negated_conjecture,
( big_p(f(f(X1)))
| big_p(X1)
| big_p(f(f(X2)))
| big_p(X2)
| ~ big_p(a)
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[8]) ).
cnf(61,negated_conjecture,
( big_p(X2)
| big_p(X1)
| big_p(f(f(X2)))
| big_p(f(f(X1)))
| $false ),
inference(rw,[status(thm)],[39,35,theory(equality)]) ).
cnf(62,negated_conjecture,
( big_p(X2)
| big_p(X1)
| big_p(f(f(X2)))
| big_p(f(f(X1))) ),
inference(cn,[status(thm)],[61,theory(equality)]) ).
cnf(63,negated_conjecture,
( big_p(f(f(X3)))
| big_p(X3) ),
inference(ef,[status(thm)],[62,theory(equality)]) ).
cnf(74,negated_conjecture,
( big_p(f(f(X2)))
| big_p(f(f(X1)))
| $false
| ~ big_p(f(X2))
| ~ big_p(f(X1)) ),
inference(rw,[status(thm)],[36,35,theory(equality)]) ).
cnf(75,negated_conjecture,
( big_p(f(f(X2)))
| big_p(f(f(X1)))
| ~ big_p(f(X2))
| ~ big_p(f(X1)) ),
inference(cn,[status(thm)],[74,theory(equality)]) ).
cnf(78,negated_conjecture,
( big_p(esk1_0)
| ~ big_p(f(f(esk2_0))) ),
inference(spm,[status(thm)],[9,63,theory(equality)]) ).
cnf(80,negated_conjecture,
( big_p(esk1_0)
| big_p(esk2_0) ),
inference(spm,[status(thm)],[78,63,theory(equality)]) ).
cnf(81,negated_conjecture,
( big_p(f(esk2_0))
| big_p(esk1_0)
| ~ big_p(f(f(esk1_0))) ),
inference(spm,[status(thm)],[13,80,theory(equality)]) ).
cnf(82,negated_conjecture,
( big_p(f(esk2_0))
| big_p(esk1_0) ),
inference(csr,[status(thm)],[81,63]) ).
cnf(83,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(esk2_0)))
| big_p(esk1_0)
| ~ big_p(f(X1)) ),
inference(spm,[status(thm)],[75,82,theory(equality)]) ).
cnf(89,negated_conjecture,
( big_p(f(f(X1)))
| big_p(esk1_0)
| ~ big_p(f(X1)) ),
inference(csr,[status(thm)],[83,78]) ).
cnf(91,negated_conjecture,
( big_p(f(f(esk2_0)))
| big_p(esk1_0) ),
inference(spm,[status(thm)],[89,82,theory(equality)]) ).
cnf(93,negated_conjecture,
big_p(esk1_0),
inference(csr,[status(thm)],[91,78]) ).
cnf(99,negated_conjecture,
( big_p(f(esk1_0))
| ~ big_p(f(f(esk2_0)))
| $false ),
inference(rw,[status(thm)],[18,93,theory(equality)]) ).
cnf(100,negated_conjecture,
( big_p(f(esk1_0))
| ~ big_p(f(f(esk2_0))) ),
inference(cn,[status(thm)],[99,theory(equality)]) ).
cnf(101,negated_conjecture,
( big_p(f(esk2_0))
| big_p(f(esk1_0))
| $false
| ~ big_p(esk2_0) ),
inference(rw,[status(thm)],[22,93,theory(equality)]) ).
cnf(102,negated_conjecture,
( big_p(f(esk2_0))
| big_p(f(esk1_0))
| ~ big_p(esk2_0) ),
inference(cn,[status(thm)],[101,theory(equality)]) ).
cnf(103,negated_conjecture,
( big_p(f(esk1_0))
| big_p(esk2_0) ),
inference(spm,[status(thm)],[100,63,theory(equality)]) ).
cnf(104,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(esk1_0)))
| big_p(esk2_0)
| ~ big_p(f(X1)) ),
inference(spm,[status(thm)],[75,103,theory(equality)]) ).
cnf(109,negated_conjecture,
( big_p(f(f(esk1_0)))
| big_p(esk2_0) ),
inference(spm,[status(thm)],[104,103,theory(equality)]) ).
cnf(119,negated_conjecture,
( big_p(esk2_0)
| ~ big_p(f(f(esk2_0))) ),
inference(spm,[status(thm)],[9,109,theory(equality)]) ).
cnf(122,negated_conjecture,
big_p(esk2_0),
inference(csr,[status(thm)],[119,63]) ).
cnf(125,negated_conjecture,
( big_p(f(esk1_0))
| big_p(f(esk2_0))
| $false ),
inference(rw,[status(thm)],[102,122,theory(equality)]) ).
cnf(126,negated_conjecture,
( big_p(f(esk1_0))
| big_p(f(esk2_0)) ),
inference(cn,[status(thm)],[125,theory(equality)]) ).
cnf(127,negated_conjecture,
( big_p(f(esk2_0))
| ~ big_p(f(f(esk1_0)))
| $false ),
inference(rw,[status(thm)],[13,122,theory(equality)]) ).
cnf(128,negated_conjecture,
( big_p(f(esk2_0))
| ~ big_p(f(f(esk1_0))) ),
inference(cn,[status(thm)],[127,theory(equality)]) ).
cnf(129,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(esk2_0)))
| big_p(f(esk1_0))
| ~ big_p(f(X1)) ),
inference(spm,[status(thm)],[75,126,theory(equality)]) ).
cnf(134,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(esk1_0))
| ~ big_p(f(X1)) ),
inference(csr,[status(thm)],[129,100]) ).
cnf(136,negated_conjecture,
( big_p(f(f(esk2_0)))
| big_p(f(esk1_0)) ),
inference(spm,[status(thm)],[134,126,theory(equality)]) ).
cnf(138,negated_conjecture,
big_p(f(esk1_0)),
inference(csr,[status(thm)],[136,100]) ).
cnf(139,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(esk1_0)))
| ~ big_p(f(X1)) ),
inference(spm,[status(thm)],[75,138,theory(equality)]) ).
cnf(143,negated_conjecture,
big_p(f(f(esk1_0))),
inference(spm,[status(thm)],[139,138,theory(equality)]) ).
cnf(152,negated_conjecture,
( big_p(f(esk2_0))
| $false ),
inference(rw,[status(thm)],[128,143,theory(equality)]) ).
cnf(153,negated_conjecture,
big_p(f(esk2_0)),
inference(cn,[status(thm)],[152,theory(equality)]) ).
cnf(154,negated_conjecture,
( $false
| ~ big_p(f(f(esk2_0))) ),
inference(rw,[status(thm)],[9,143,theory(equality)]) ).
cnf(155,negated_conjecture,
~ big_p(f(f(esk2_0))),
inference(cn,[status(thm)],[154,theory(equality)]) ).
cnf(156,negated_conjecture,
( big_p(f(f(X1)))
| big_p(f(f(esk2_0)))
| ~ big_p(f(X1)) ),
inference(spm,[status(thm)],[75,153,theory(equality)]) ).
cnf(163,negated_conjecture,
( big_p(f(f(X1)))
| ~ big_p(f(X1)) ),
inference(sr,[status(thm)],[156,155,theory(equality)]) ).
cnf(166,negated_conjecture,
big_p(f(f(esk2_0))),
inference(spm,[status(thm)],[163,153,theory(equality)]) ).
cnf(171,negated_conjecture,
$false,
inference(sr,[status(thm)],[166,155,theory(equality)]) ).
cnf(172,negated_conjecture,
$false,
171,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SYN/SYN084+1.p
% --creating new selector for []
% -running prover on /tmp/tmpRQ59uk/sel_SYN084+1.p_1 with time limit 29
% -prover status Theorem
% Problem SYN084+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SYN/SYN084+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SYN/SYN084+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
%
%------------------------------------------------------------------------------