TSTP Solution File: ALG210+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG210+1 : TPTP v5.0.0. Released v3.1.0.
% 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 : Sat Dec 25 04:16:46 EST 2010
% Result : Theorem 0.31s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 91 ( 38 unt; 0 def)
% Number of atoms : 176 ( 95 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 145 ( 60 ~; 63 |; 19 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 21 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( element(X1)
<=> ? [X2] :
( times(X1,X2) = X1
& times(X1,X1) = X2 ) ),
file('/tmp/tmpcveeQI/sel_ALG210+1.p_1',axiom_2) ).
fof(2,conjecture,
! [X3,X1] :
( ( element(X3)
& element(X1) )
=> element(times(X3,X1)) ),
file('/tmp/tmpcveeQI/sel_ALG210+1.p_1',conjecture_1) ).
fof(3,axiom,
! [X3,X1,X2] : times(times(X3,X1),X2) = times(X1,times(X2,X3)),
file('/tmp/tmpcveeQI/sel_ALG210+1.p_1',axiom_1) ).
fof(4,negated_conjecture,
~ ! [X3,X1] :
( ( element(X3)
& element(X1) )
=> element(times(X3,X1)) ),
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] :
( element(X3)
& element(X1)
& ~ element(times(X3,X1)) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(14,negated_conjecture,
? [X4,X5] :
( element(X4)
& element(X5)
& ~ element(times(X4,X5)) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,negated_conjecture,
( element(esk2_0)
& element(esk3_0)
& ~ element(times(esk2_0,esk3_0)) ),
inference(skolemize,[status(esa)],[14]) ).
cnf(16,negated_conjecture,
~ element(times(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,negated_conjecture,
element(esk3_0),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(18,negated_conjecture,
element(esk2_0),
inference(split_conjunct,[status(thm)],[15]) ).
fof(19,plain,
! [X4,X5,X6] : times(times(X4,X5),X6) = times(X5,times(X6,X4)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(20,plain,
times(times(X1,X2),X3) = times(X2,times(X3,X1)),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,plain,
( times(X1,times(X1,X1)) = X1
| ~ element(X1) ),
inference(spm,[status(thm)],[11,10,theory(equality)]) ).
cnf(22,plain,
times(times(X2,times(X3,X1)),X4) = times(X3,times(X4,times(X1,X2))),
inference(spm,[status(thm)],[20,20,theory(equality)]) ).
cnf(23,plain,
times(times(X1,X2),times(X3,X4)) = times(X2,times(X4,times(X1,X3))),
inference(spm,[status(thm)],[20,20,theory(equality)]) ).
cnf(28,plain,
( times(X1,X2) = times(esk1_1(X1),times(X2,X1))
| ~ element(X1) ),
inference(spm,[status(thm)],[20,11,theory(equality)]) ).
cnf(29,plain,
( element(X1)
| times(X1,times(X1,X1)) != X1 ),
inference(er,[status(thm)],[12,theory(equality)]) ).
cnf(30,plain,
( element(times(X1,X2))
| times(times(X1,X2),X3) != times(X1,X2)
| times(X2,times(times(X1,X2),X1)) != X3 ),
inference(spm,[status(thm)],[12,20,theory(equality)]) ).
cnf(31,plain,
( element(times(X1,X2))
| times(times(X1,X2),X3) != times(X1,X2)
| times(X2,times(X2,times(X1,X1))) != X3 ),
inference(rw,[status(thm)],[30,20,theory(equality)]) ).
cnf(32,negated_conjecture,
times(esk2_0,times(esk2_0,esk2_0)) = esk2_0,
inference(spm,[status(thm)],[21,18,theory(equality)]) ).
cnf(33,negated_conjecture,
times(esk3_0,times(esk3_0,esk3_0)) = esk3_0,
inference(spm,[status(thm)],[21,17,theory(equality)]) ).
cnf(34,negated_conjecture,
times(esk2_0,X1) = times(times(esk2_0,esk2_0),times(X1,esk2_0)),
inference(spm,[status(thm)],[20,32,theory(equality)]) ).
cnf(35,negated_conjecture,
times(esk3_0,X1) = times(times(esk3_0,esk3_0),times(X1,esk3_0)),
inference(spm,[status(thm)],[20,33,theory(equality)]) ).
cnf(38,plain,
( element(times(X1,X2))
| times(times(X1,X2),times(X2,times(times(X1,X2),X1))) != times(X1,X2) ),
inference(spm,[status(thm)],[29,20,theory(equality)]) ).
cnf(41,plain,
( element(times(X1,X2))
| times(times(X1,X2),times(X2,times(X2,times(X1,X1)))) != times(X1,X2) ),
inference(rw,[status(thm)],[38,20,theory(equality)]) ).
cnf(43,negated_conjecture,
( element(times(esk2_0,esk2_0))
| times(times(esk2_0,esk2_0),X1) != times(esk2_0,esk2_0)
| times(esk2_0,esk2_0) != X1 ),
inference(spm,[status(thm)],[31,32,theory(equality)]) ).
cnf(44,negated_conjecture,
( element(times(esk3_0,esk3_0))
| times(times(esk3_0,esk3_0),X1) != times(esk3_0,esk3_0)
| times(esk3_0,esk3_0) != X1 ),
inference(spm,[status(thm)],[31,33,theory(equality)]) ).
cnf(48,negated_conjecture,
( element(times(esk2_0,esk2_0))
| times(times(esk2_0,esk2_0),times(esk2_0,esk2_0)) != times(esk2_0,esk2_0) ),
inference(er,[status(thm)],[43,theory(equality)]) ).
cnf(49,negated_conjecture,
( element(times(esk2_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[48,20,theory(equality)]),20,theory(equality)]),32,theory(equality)]) ).
cnf(50,negated_conjecture,
element(times(esk2_0,esk2_0)),
inference(cn,[status(thm)],[49,theory(equality)]) ).
cnf(51,negated_conjecture,
( element(times(esk3_0,esk3_0))
| times(times(esk3_0,esk3_0),times(esk3_0,esk3_0)) != times(esk3_0,esk3_0) ),
inference(er,[status(thm)],[44,theory(equality)]) ).
cnf(52,negated_conjecture,
( element(times(esk3_0,esk3_0))
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[51,20,theory(equality)]),20,theory(equality)]),33,theory(equality)]) ).
cnf(53,negated_conjecture,
element(times(esk3_0,esk3_0)),
inference(cn,[status(thm)],[52,theory(equality)]) ).
cnf(67,plain,
( element(times(X1,X2))
| times(X2,times(times(X2,times(X2,times(X1,X1))),X1)) != times(X1,X2) ),
inference(spm,[status(thm)],[41,20,theory(equality)]) ).
cnf(84,plain,
( element(times(X1,X2))
| times(X2,times(times(X2,times(X1,X1)),times(X1,X2))) != times(X1,X2) ),
inference(rw,[status(thm)],[67,20,theory(equality)]) ).
cnf(92,plain,
( element(times(X1,X2))
| times(X2,times(times(X1,X1),times(times(X1,X2),X2))) != times(X1,X2) ),
inference(spm,[status(thm)],[84,20,theory(equality)]) ).
cnf(109,plain,
( element(times(X1,X2))
| times(X2,times(times(X1,X1),times(X2,times(X2,X1)))) != times(X1,X2) ),
inference(rw,[status(thm)],[92,20,theory(equality)]) ).
cnf(139,negated_conjecture,
times(esk2_0,X1) = times(esk2_0,times(times(X1,esk2_0),esk2_0)),
inference(spm,[status(thm)],[20,34,theory(equality)]) ).
cnf(155,negated_conjecture,
times(esk2_0,X1) = times(esk2_0,times(esk2_0,times(esk2_0,X1))),
inference(rw,[status(thm)],[139,20,theory(equality)]) ).
cnf(181,negated_conjecture,
times(esk3_0,X1) = times(esk3_0,times(times(X1,esk3_0),esk3_0)),
inference(spm,[status(thm)],[20,35,theory(equality)]) ).
cnf(197,negated_conjecture,
times(esk3_0,X1) = times(esk3_0,times(esk3_0,times(esk3_0,X1))),
inference(rw,[status(thm)],[181,20,theory(equality)]) ).
cnf(323,negated_conjecture,
times(esk2_0,X1) = times(esk2_0,times(X1,times(esk2_0,esk2_0))),
inference(spm,[status(thm)],[22,32,theory(equality)]) ).
cnf(326,negated_conjecture,
times(esk3_0,X1) = times(esk3_0,times(X1,times(esk3_0,esk3_0))),
inference(spm,[status(thm)],[22,33,theory(equality)]) ).
cnf(525,negated_conjecture,
( times(esk1_1(times(esk2_0,esk2_0)),esk2_0) = times(times(esk2_0,esk2_0),esk2_0)
| ~ element(times(esk2_0,esk2_0)) ),
inference(spm,[status(thm)],[28,32,theory(equality)]) ).
cnf(526,negated_conjecture,
( times(esk1_1(times(esk3_0,esk3_0)),esk3_0) = times(times(esk3_0,esk3_0),esk3_0)
| ~ element(times(esk3_0,esk3_0)) ),
inference(spm,[status(thm)],[28,33,theory(equality)]) ).
cnf(561,negated_conjecture,
( times(esk1_1(times(esk2_0,esk2_0)),esk2_0) = esk2_0
| ~ element(times(esk2_0,esk2_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[525,20,theory(equality)]),32,theory(equality)]) ).
cnf(562,negated_conjecture,
( times(esk1_1(times(esk2_0,esk2_0)),esk2_0) = esk2_0
| $false ),
inference(rw,[status(thm)],[561,50,theory(equality)]) ).
cnf(563,negated_conjecture,
times(esk1_1(times(esk2_0,esk2_0)),esk2_0) = esk2_0,
inference(cn,[status(thm)],[562,theory(equality)]) ).
cnf(564,negated_conjecture,
( times(esk1_1(times(esk3_0,esk3_0)),esk3_0) = esk3_0
| ~ element(times(esk3_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[526,20,theory(equality)]),33,theory(equality)]) ).
cnf(565,negated_conjecture,
( times(esk1_1(times(esk3_0,esk3_0)),esk3_0) = esk3_0
| $false ),
inference(rw,[status(thm)],[564,53,theory(equality)]) ).
cnf(566,negated_conjecture,
times(esk1_1(times(esk3_0,esk3_0)),esk3_0) = esk3_0,
inference(cn,[status(thm)],[565,theory(equality)]) ).
cnf(1217,negated_conjecture,
( times(esk1_1(esk2_0),esk2_0) = times(esk2_0,esk1_1(times(esk2_0,esk2_0)))
| ~ element(esk2_0) ),
inference(spm,[status(thm)],[28,563,theory(equality)]) ).
cnf(1235,negated_conjecture,
( times(esk1_1(esk2_0),esk2_0) = times(esk2_0,esk1_1(times(esk2_0,esk2_0)))
| $false ),
inference(rw,[status(thm)],[1217,18,theory(equality)]) ).
cnf(1236,negated_conjecture,
times(esk1_1(esk2_0),esk2_0) = times(esk2_0,esk1_1(times(esk2_0,esk2_0))),
inference(cn,[status(thm)],[1235,theory(equality)]) ).
cnf(1254,negated_conjecture,
( times(esk1_1(esk3_0),esk3_0) = times(esk3_0,esk1_1(times(esk3_0,esk3_0)))
| ~ element(esk3_0) ),
inference(spm,[status(thm)],[28,566,theory(equality)]) ).
cnf(1271,negated_conjecture,
( times(esk1_1(esk3_0),esk3_0) = times(esk3_0,esk1_1(times(esk3_0,esk3_0)))
| $false ),
inference(rw,[status(thm)],[1254,17,theory(equality)]) ).
cnf(1272,negated_conjecture,
times(esk1_1(esk3_0),esk3_0) = times(esk3_0,esk1_1(times(esk3_0,esk3_0))),
inference(cn,[status(thm)],[1271,theory(equality)]) ).
cnf(1387,plain,
( element(times(X1,X2))
| times(times(X2,X2),times(times(X2,X1),times(X1,X1))) != times(X1,X2) ),
inference(spm,[status(thm)],[109,23,theory(equality)]) ).
cnf(1449,plain,
( element(times(X1,X2))
| times(times(X2,X2),times(X1,times(X1,times(X2,X1)))) != times(X1,X2) ),
inference(rw,[status(thm)],[1387,23,theory(equality)]) ).
cnf(1609,negated_conjecture,
( times(esk2_0,times(times(esk2_0,esk2_0),times(esk2_0,esk2_0))) = times(esk1_1(esk2_0),esk2_0)
| ~ element(times(esk2_0,esk2_0)) ),
inference(spm,[status(thm)],[1236,10,theory(equality)]) ).
cnf(1621,negated_conjecture,
( esk2_0 = times(esk1_1(esk2_0),esk2_0)
| ~ element(times(esk2_0,esk2_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1609,20,theory(equality)]),20,theory(equality)]),32,theory(equality)]),32,theory(equality)]) ).
cnf(1622,negated_conjecture,
( esk2_0 = times(esk1_1(esk2_0),esk2_0)
| $false ),
inference(rw,[status(thm)],[1621,50,theory(equality)]) ).
cnf(1623,negated_conjecture,
esk2_0 = times(esk1_1(esk2_0),esk2_0),
inference(cn,[status(thm)],[1622,theory(equality)]) ).
cnf(1649,negated_conjecture,
times(times(esk2_0,X1),esk1_1(esk2_0)) = times(X1,esk2_0),
inference(spm,[status(thm)],[20,1623,theory(equality)]) ).
cnf(1788,negated_conjecture,
times(times(esk2_0,X1),esk1_1(esk2_0)) = times(times(X1,times(esk2_0,esk2_0)),esk2_0),
inference(spm,[status(thm)],[1649,323,theory(equality)]) ).
cnf(1819,negated_conjecture,
times(X1,esk2_0) = times(times(X1,times(esk2_0,esk2_0)),esk2_0),
inference(rw,[status(thm)],[1788,1649,theory(equality)]) ).
cnf(1820,negated_conjecture,
times(X1,esk2_0) = times(esk2_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1819,22,theory(equality)]),155,theory(equality)]) ).
cnf(2070,negated_conjecture,
( times(esk3_0,times(times(esk3_0,esk3_0),times(esk3_0,esk3_0))) = times(esk1_1(esk3_0),esk3_0)
| ~ element(times(esk3_0,esk3_0)) ),
inference(spm,[status(thm)],[1272,10,theory(equality)]) ).
cnf(2084,negated_conjecture,
( esk3_0 = times(esk1_1(esk3_0),esk3_0)
| ~ element(times(esk3_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2070,20,theory(equality)]),20,theory(equality)]),33,theory(equality)]),33,theory(equality)]) ).
cnf(2085,negated_conjecture,
( esk3_0 = times(esk1_1(esk3_0),esk3_0)
| $false ),
inference(rw,[status(thm)],[2084,53,theory(equality)]) ).
cnf(2086,negated_conjecture,
esk3_0 = times(esk1_1(esk3_0),esk3_0),
inference(cn,[status(thm)],[2085,theory(equality)]) ).
cnf(2111,negated_conjecture,
times(times(esk3_0,X1),esk1_1(esk3_0)) = times(X1,esk3_0),
inference(spm,[status(thm)],[20,2086,theory(equality)]) ).
cnf(2440,negated_conjecture,
( element(times(esk2_0,X1))
| times(times(X1,X1),times(esk2_0,times(esk2_0,times(esk2_0,X1)))) != times(esk2_0,X1) ),
inference(spm,[status(thm)],[1449,1820,theory(equality)]) ).
cnf(2447,negated_conjecture,
~ element(times(esk3_0,esk2_0)),
inference(rw,[status(thm)],[16,1820,theory(equality)]) ).
cnf(2485,negated_conjecture,
( element(times(esk2_0,X1))
| times(X1,times(X1,times(X1,esk2_0))) != times(esk2_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2440,155,theory(equality)]),23,theory(equality)]) ).
cnf(2586,negated_conjecture,
times(times(esk3_0,X1),esk1_1(esk3_0)) = times(times(X1,times(esk3_0,esk3_0)),esk3_0),
inference(spm,[status(thm)],[2111,326,theory(equality)]) ).
cnf(2624,negated_conjecture,
times(X1,esk3_0) = times(times(X1,times(esk3_0,esk3_0)),esk3_0),
inference(rw,[status(thm)],[2586,2111,theory(equality)]) ).
cnf(2625,negated_conjecture,
times(X1,esk3_0) = times(esk3_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2624,22,theory(equality)]),197,theory(equality)]) ).
cnf(3003,negated_conjecture,
( element(times(esk3_0,esk2_0))
| times(esk3_0,times(esk3_0,times(esk3_0,esk2_0))) != times(esk3_0,esk2_0) ),
inference(spm,[status(thm)],[2485,2625,theory(equality)]) ).
cnf(3015,negated_conjecture,
( element(times(esk3_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[3003,197,theory(equality)]) ).
cnf(3016,negated_conjecture,
element(times(esk3_0,esk2_0)),
inference(cn,[status(thm)],[3015,theory(equality)]) ).
cnf(3017,negated_conjecture,
$false,
inference(sr,[status(thm)],[3016,2447,theory(equality)]) ).
cnf(3018,negated_conjecture,
$false,
3017,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG210+1.p
% --creating new selector for []
% -running prover on /tmp/tmpcveeQI/sel_ALG210+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG210+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG210+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG210+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
%
%------------------------------------------------------------------------------