%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG210+2 : TPTP v5.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 : Sat Dec 25 04:16:53 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 69 ( 27 unt; 0 def)
% Number of atoms : 144 ( 79 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 121 ( 46 ~; 48 |; 24 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 23 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( element(X1)
<=> ? [X2] :
( times(X1,X2) = X1
& times(X1,X1) = X2 ) ),
file('/tmp/tmp_X62H9/sel_ALG210+2.p_1',axiom_2) ).
fof(2,conjecture,
! [X3,X1,X2] :
( ( element(X3)
& element(X1)
& X2 = times(X3,X1) )
=> element(X2) ),
file('/tmp/tmp_X62H9/sel_ALG210+2.p_1',conjecture_1) ).
fof(3,axiom,
! [X3,X1,X2] : times(times(X3,X1),X2) = times(X1,times(X2,X3)),
file('/tmp/tmp_X62H9/sel_ALG210+2.p_1',axiom_1) ).
fof(4,negated_conjecture,
~ ! [X3,X1,X2] :
( ( element(X3)
& element(X1)
& X2 = times(X3,X1) )
=> element(X2) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(5,plain,
! [X1] :
( ( ~ element(X1)
| ? [X2] :
( times(X1,X2) = X1
& times(X1,X1) = X2 ) )
& ( ! [X2] :
( times(X1,X2) != X1
| times(X1,X1) != X2 )
| element(X1) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(6,plain,
! [X3] :
( ( ~ element(X3)
| ? [X4] :
( times(X3,X4) = X3
& times(X3,X3) = X4 ) )
& ( ! [X5] :
( times(X3,X5) != X3
| times(X3,X3) != X5 )
| element(X3) ) ),
inference(variable_rename,[status(thm)],[5]) ).
fof(7,plain,
! [X3] :
( ( ~ element(X3)
| ( times(X3,esk1_1(X3)) = X3
& times(X3,X3) = esk1_1(X3) ) )
& ( ! [X5] :
( times(X3,X5) != X3
| times(X3,X3) != X5 )
| element(X3) ) ),
inference(skolemize,[status(esa)],[6]) ).
fof(8,plain,
! [X3,X5] :
( ( times(X3,X5) != X3
| times(X3,X3) != X5
| element(X3) )
& ( ~ element(X3)
| ( times(X3,esk1_1(X3)) = X3
& times(X3,X3) = esk1_1(X3) ) ) ),
inference(shift_quantors,[status(thm)],[7]) ).
fof(9,plain,
! [X3,X5] :
( ( times(X3,X5) != X3
| times(X3,X3) != X5
| element(X3) )
& ( times(X3,esk1_1(X3)) = X3
| ~ element(X3) )
& ( times(X3,X3) = esk1_1(X3)
| ~ element(X3) ) ),
inference(distribute,[status(thm)],[8]) ).
cnf(10,plain,
( times(X1,X1) = esk1_1(X1)
| ~ element(X1) ),
inference(split_conjunct,[status(thm)],[9]) ).
cnf(11,plain,
( times(X1,esk1_1(X1)) = X1
| ~ element(X1) ),
inference(split_conjunct,[status(thm)],[9]) ).
cnf(12,plain,
( element(X1)
| times(X1,X1) != X2
| times(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[9]) ).
fof(13,negated_conjecture,
? [X3,X1,X2] :
( element(X3)
& element(X1)
& X2 = times(X3,X1)
& ~ element(X2) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(14,negated_conjecture,
? [X4,X5,X6] :
( element(X4)
& element(X5)
& X6 = times(X4,X5)
& ~ element(X6) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,negated_conjecture,
( element(esk2_0)
& element(esk3_0)
& esk4_0 = times(esk2_0,esk3_0)
& ~ element(esk4_0) ),
inference(skolemize,[status(esa)],[14]) ).
cnf(16,negated_conjecture,
~ element(esk4_0),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,negated_conjecture,
esk4_0 = times(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(18,negated_conjecture,
element(esk3_0),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(19,negated_conjecture,
element(esk2_0),
inference(split_conjunct,[status(thm)],[15]) ).
fof(20,plain,
! [X4,X5,X6] : times(times(X4,X5),X6) = times(X5,times(X6,X4)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(21,plain,
times(times(X1,X2),X3) = times(X2,times(X3,X1)),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
( times(X1,times(X1,X1)) = X1
| ~ element(X1) ),
inference(spm,[status(thm)],[11,10,theory(equality)]) ).
cnf(23,negated_conjecture,
times(esk4_0,X1) = times(esk3_0,times(X1,esk2_0)),
inference(spm,[status(thm)],[21,17,theory(equality)]) ).
cnf(26,plain,
( times(esk1_1(X1),X2) = times(X1,times(X2,X1))
| ~ element(X1) ),
inference(spm,[status(thm)],[21,10,theory(equality)]) ).
cnf(28,plain,
( times(X1,X2) = times(esk1_1(X1),times(X2,X1))
| ~ element(X1) ),
inference(spm,[status(thm)],[21,11,theory(equality)]) ).
cnf(31,plain,
( element(X1)
| times(X1,times(X1,X1)) != X1 ),
inference(er,[status(thm)],[12,theory(equality)]) ).
cnf(36,plain,
( times(X1,X2) = times(times(X1,X1),times(X2,X1))
| ~ element(X1) ),
inference(spm,[status(thm)],[21,22,theory(equality)]) ).
cnf(40,plain,
( times(X1,X2) = times(X1,times(X1,times(X1,X2)))
| ~ element(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[36,21,theory(equality)]),21,theory(equality)]) ).
cnf(43,plain,
( element(times(X1,X2))
| times(times(X1,X2),times(X2,times(times(X1,X2),X1))) != times(X1,X2) ),
inference(spm,[status(thm)],[31,21,theory(equality)]) ).
cnf(47,plain,
( element(times(X1,X2))
| times(X2,times(X1,times(X1,times(X2,times(X2,X1))))) != times(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[43,21,theory(equality)]),21,theory(equality)]),21,theory(equality)]),21,theory(equality)]),21,theory(equality)]),21,theory(equality)]),21,theory(equality)]),21,theory(equality)]),21,theory(equality)]) ).
cnf(53,negated_conjecture,
( times(esk1_1(esk3_0),esk4_0) = times(esk3_0,esk2_0)
| ~ element(esk3_0) ),
inference(spm,[status(thm)],[28,17,theory(equality)]) ).
cnf(63,negated_conjecture,
( times(esk1_1(esk3_0),esk4_0) = times(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[53,18,theory(equality)]) ).
cnf(64,negated_conjecture,
times(esk1_1(esk3_0),esk4_0) = times(esk3_0,esk2_0),
inference(cn,[status(thm)],[63,theory(equality)]) ).
cnf(73,negated_conjecture,
( times(times(esk3_0,esk3_0),esk4_0) = times(esk3_0,esk2_0)
| ~ element(esk3_0) ),
inference(spm,[status(thm)],[64,10,theory(equality)]) ).
cnf(76,negated_conjecture,
( times(esk3_0,times(esk4_0,esk3_0)) = times(esk3_0,esk2_0)
| ~ element(esk3_0) ),
inference(rw,[status(thm)],[73,21,theory(equality)]) ).
cnf(77,negated_conjecture,
( times(esk3_0,times(esk4_0,esk3_0)) = times(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[76,18,theory(equality)]) ).
cnf(78,negated_conjecture,
times(esk3_0,times(esk4_0,esk3_0)) = times(esk3_0,esk2_0),
inference(cn,[status(thm)],[77,theory(equality)]) ).
cnf(79,negated_conjecture,
times(times(esk3_0,esk2_0),X1) = times(times(esk4_0,esk3_0),times(X1,esk3_0)),
inference(spm,[status(thm)],[21,78,theory(equality)]) ).
cnf(81,negated_conjecture,
times(esk2_0,times(X1,esk3_0)) = times(times(esk4_0,esk3_0),times(X1,esk3_0)),
inference(rw,[status(thm)],[79,21,theory(equality)]) ).
cnf(82,negated_conjecture,
times(esk2_0,times(X1,esk3_0)) = times(esk3_0,times(esk3_0,times(esk4_0,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[81,21,theory(equality)]),21,theory(equality)]) ).
cnf(85,negated_conjecture,
times(esk3_0,times(esk4_0,esk4_0)) = times(esk2_0,times(esk2_0,esk3_0)),
inference(spm,[status(thm)],[82,23,theory(equality)]) ).
cnf(92,negated_conjecture,
times(esk3_0,times(esk4_0,esk4_0)) = times(esk2_0,esk4_0),
inference(rw,[status(thm)],[85,17,theory(equality)]) ).
cnf(97,negated_conjecture,
times(esk3_0,times(esk2_0,esk4_0)) = times(esk2_0,times(esk4_0,esk3_0)),
inference(spm,[status(thm)],[82,92,theory(equality)]) ).
cnf(257,negated_conjecture,
( times(esk2_0,times(esk2_0,esk4_0)) = esk4_0
| ~ element(esk2_0) ),
inference(spm,[status(thm)],[40,17,theory(equality)]) ).
cnf(262,negated_conjecture,
( times(esk3_0,times(esk3_0,times(esk4_0,X1))) = times(esk4_0,X1)
| ~ element(esk3_0) ),
inference(spm,[status(thm)],[40,23,theory(equality)]) ).
cnf(290,negated_conjecture,
( times(esk2_0,times(esk2_0,esk4_0)) = esk4_0
| $false ),
inference(rw,[status(thm)],[257,19,theory(equality)]) ).
cnf(291,negated_conjecture,
times(esk2_0,times(esk2_0,esk4_0)) = esk4_0,
inference(cn,[status(thm)],[290,theory(equality)]) ).
cnf(299,negated_conjecture,
( times(esk2_0,times(X1,esk3_0)) = times(esk4_0,X1)
| ~ element(esk3_0) ),
inference(rw,[status(thm)],[262,82,theory(equality)]) ).
cnf(300,negated_conjecture,
( times(esk2_0,times(X1,esk3_0)) = times(esk4_0,X1)
| $false ),
inference(rw,[status(thm)],[299,18,theory(equality)]) ).
cnf(301,negated_conjecture,
times(esk2_0,times(X1,esk3_0)) = times(esk4_0,X1),
inference(cn,[status(thm)],[300,theory(equality)]) ).
cnf(343,negated_conjecture,
times(esk2_0,esk4_0) = times(esk4_0,esk2_0),
inference(spm,[status(thm)],[301,17,theory(equality)]) ).
cnf(353,negated_conjecture,
times(esk4_0,esk4_0) = times(esk3_0,times(esk2_0,esk4_0)),
inference(rw,[status(thm)],[97,301,theory(equality)]) ).
cnf(370,negated_conjecture,
times(times(esk2_0,esk4_0),X1) = times(esk2_0,times(X1,esk4_0)),
inference(spm,[status(thm)],[21,343,theory(equality)]) ).
cnf(376,negated_conjecture,
times(esk4_0,times(X1,esk2_0)) = times(esk2_0,times(X1,esk4_0)),
inference(rw,[status(thm)],[370,21,theory(equality)]) ).
cnf(509,plain,
( times(esk1_1(X1),X1) = X1
| ~ element(X1) ),
inference(spm,[status(thm)],[22,26,theory(equality)]) ).
cnf(580,negated_conjecture,
( times(esk3_0,esk2_0) = times(esk4_0,esk1_1(esk2_0))
| ~ element(esk2_0) ),
inference(spm,[status(thm)],[23,509,theory(equality)]) ).
cnf(595,negated_conjecture,
( times(esk3_0,esk2_0) = times(esk4_0,esk1_1(esk2_0))
| $false ),
inference(rw,[status(thm)],[580,19,theory(equality)]) ).
cnf(596,negated_conjecture,
times(esk3_0,esk2_0) = times(esk4_0,esk1_1(esk2_0)),
inference(cn,[status(thm)],[595,theory(equality)]) ).
cnf(653,negated_conjecture,
( times(esk4_0,times(esk2_0,esk2_0)) = times(esk3_0,esk2_0)
| ~ element(esk2_0) ),
inference(spm,[status(thm)],[596,10,theory(equality)]) ).
cnf(659,negated_conjecture,
( esk4_0 = times(esk3_0,esk2_0)
| ~ element(esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[653,376,theory(equality)]),291,theory(equality)]) ).
cnf(660,negated_conjecture,
( esk4_0 = times(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[659,19,theory(equality)]) ).
cnf(661,negated_conjecture,
esk4_0 = times(esk3_0,esk2_0),
inference(cn,[status(thm)],[660,theory(equality)]) ).
cnf(1255,negated_conjecture,
( element(times(esk3_0,esk2_0))
| times(esk2_0,times(esk3_0,times(esk3_0,times(esk2_0,esk4_0)))) != times(esk3_0,esk2_0) ),
inference(spm,[status(thm)],[47,17,theory(equality)]) ).
cnf(1322,negated_conjecture,
( element(esk4_0)
| times(esk2_0,times(esk3_0,times(esk3_0,times(esk2_0,esk4_0)))) != times(esk3_0,esk2_0) ),
inference(rw,[status(thm)],[1255,661,theory(equality)]) ).
cnf(1323,negated_conjecture,
( element(esk4_0)
| esk4_0 != times(esk3_0,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1322,353,theory(equality)]),92,theory(equality)]),291,theory(equality)]) ).
cnf(1324,negated_conjecture,
( element(esk4_0)
| $false ),
inference(rw,[status(thm)],[1323,661,theory(equality)]) ).
cnf(1325,negated_conjecture,
element(esk4_0),
inference(cn,[status(thm)],[1324,theory(equality)]) ).
cnf(1326,negated_conjecture,
$false,
inference(sr,[status(thm)],[1325,16,theory(equality)]) ).
cnf(1327,negated_conjecture,
$false,
1326,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG210+2.p
% --creating new selector for []
% -running prover on /tmp/tmp_X62H9/sel_ALG210+2.p_1 with time limit 29
% -prover status Theorem
% Problem ALG210+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG210+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG210+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
%
%------------------------------------------------------------------------------