TSTP Solution File: GRP777+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP777+1 : TPTP v5.0.0. Released v4.1.0.
% 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 : Sat Dec 25 11:33:53 EST 2010
% Result : Theorem 0.46s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 74 unt; 0 def)
% Number of atoms : 74 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 102 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : bigC(X3,X2,X1) = product(product(X3,X2),product(X1,X3)),
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos08) ).
fof(2,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos09) ).
fof(3,conjecture,
! [X4] : bigC(a,b,X4) = bigC(c,c,X4),
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',goals) ).
fof(4,axiom,
! [X2,X3] : product(quotient(X3,X2),X2) = X3,
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos04) ).
fof(5,axiom,
! [X5,X1,X2,X3] : product(product(X3,X2),product(X1,X5)) = product(product(X3,X1),product(X2,X5)),
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos05) ).
fof(6,axiom,
! [X3] : product(X3,X3) = X3,
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos06) ).
fof(7,axiom,
! [X2,X3] : product(product(product(X3,X2),X2),product(X2,product(X2,X3))) = X2,
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos07) ).
fof(8,axiom,
! [X2,X3] : difference(X3,product(X3,X2)) = X2,
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos01) ).
fof(9,axiom,
! [X2,X3] : product(X3,difference(X3,X2)) = X2,
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos02) ).
fof(10,axiom,
! [X2,X3] : quotient(product(X3,X2),X2) = X3,
file('/tmp/tmpMAbkPb/sel_GRP777+1.p_1',sos03) ).
fof(11,negated_conjecture,
~ ! [X4] : bigC(a,b,X4) = bigC(c,c,X4),
inference(assume_negation,[status(cth)],[3]) ).
fof(12,plain,
! [X4,X5,X6] : bigC(X6,X5,X4) = product(product(X6,X5),product(X4,X6)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(13,plain,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(14,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(split_conjunct,[status(thm)],[2]) ).
fof(15,negated_conjecture,
? [X4] : bigC(a,b,X4) != bigC(c,c,X4),
inference(fof_nnf,[status(thm)],[11]) ).
fof(16,negated_conjecture,
? [X5] : bigC(a,b,X5) != bigC(c,c,X5),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,negated_conjecture,
bigC(a,b,esk1_0) != bigC(c,c,esk1_0),
inference(skolemize,[status(esa)],[16]) ).
cnf(18,negated_conjecture,
bigC(a,b,esk1_0) != bigC(c,c,esk1_0),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X4,X5] : product(quotient(X5,X4),X4) = X5,
inference(variable_rename,[status(thm)],[4]) ).
cnf(20,plain,
product(quotient(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X6,X7,X8,X9] : product(product(X9,X8),product(X7,X6)) = product(product(X9,X7),product(X8,X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(22,plain,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X4] : product(X4,X4) = X4,
inference(variable_rename,[status(thm)],[6]) ).
cnf(24,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5] : product(product(product(X5,X4),X4),product(X4,product(X4,X5))) = X4,
inference(variable_rename,[status(thm)],[7]) ).
cnf(26,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5] : difference(X5,product(X5,X4)) = X4,
inference(variable_rename,[status(thm)],[8]) ).
cnf(28,plain,
difference(X1,product(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5] : product(X5,difference(X5,X4)) = X4,
inference(variable_rename,[status(thm)],[9]) ).
cnf(30,plain,
product(X1,difference(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X4,X5] : quotient(product(X5,X4),X4) = X5,
inference(variable_rename,[status(thm)],[10]) ).
cnf(32,plain,
quotient(product(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
cnf(33,negated_conjecture,
product(product(c,c),product(esk1_0,c)) != product(product(a,b),product(esk1_0,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[18,13,theory(equality)]),13,theory(equality)]),
[unfolding] ).
cnf(38,plain,
quotient(X2,difference(X1,X2)) = X1,
inference(spm,[status(thm)],[32,30,theory(equality)]) ).
cnf(43,plain,
product(product(product(difference(X1,X2),X1),X1),product(X1,X2)) = X1,
inference(spm,[status(thm)],[26,30,theory(equality)]) ).
cnf(45,plain,
product(product(X1,X2),product(X2,product(X2,quotient(X1,X2)))) = X2,
inference(spm,[status(thm)],[26,20,theory(equality)]) ).
cnf(56,plain,
product(X1,product(X2,X3)) = product(product(X1,X2),product(X1,X3)),
inference(spm,[status(thm)],[22,24,theory(equality)]) ).
cnf(57,plain,
product(product(X1,X2),X3) = product(product(X1,X3),product(X2,X3)),
inference(spm,[status(thm)],[22,24,theory(equality)]) ).
cnf(64,plain,
difference(product(X1,X2),product(product(X1,X3),product(X2,X4))) = product(X3,X4),
inference(spm,[status(thm)],[28,22,theory(equality)]) ).
cnf(67,plain,
product(product(X1,X2),X3) = product(product(X1,quotient(X3,X4)),product(X2,X4)),
inference(spm,[status(thm)],[22,20,theory(equality)]) ).
cnf(108,negated_conjecture,
product(c,product(esk1_0,c)) != product(product(a,b),product(esk1_0,a)),
inference(rw,[status(thm)],[33,24,theory(equality)]) ).
cnf(139,plain,
quotient(X1,product(X1,X2)) = product(product(difference(X1,X2),X1),X1),
inference(spm,[status(thm)],[32,43,theory(equality)]) ).
cnf(198,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[56,24,theory(equality)]) ).
cnf(204,plain,
product(product(a,b),product(product(a,c),X1)) = product(product(a,c),product(product(c,b),X1)),
inference(spm,[status(thm)],[56,14,theory(equality)]) ).
cnf(237,plain,
product(X2,X1) = product(X1,product(difference(X1,X2),X1)),
inference(spm,[status(thm)],[198,30,theory(equality)]) ).
cnf(238,plain,
difference(product(X1,X2),product(X1,product(X2,X1))) = X1,
inference(spm,[status(thm)],[28,198,theory(equality)]) ).
cnf(277,plain,
difference(X1,product(X2,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[28,237,theory(equality)]) ).
cnf(702,plain,
product(X2,product(X1,X2)) = product(product(X1,X2),product(product(X2,product(X2,quotient(X1,X2))),product(X1,X2))),
inference(spm,[status(thm)],[198,45,theory(equality)]) ).
cnf(738,plain,
product(X2,product(X1,X2)) = product(product(X1,X2),product(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[702,22,theory(equality)]),198,theory(equality)]),20,theory(equality)]),56,theory(equality)]),24,theory(equality)]) ).
cnf(792,plain,
product(product(a,b),product(c,product(a,c))) = product(product(a,c),product(product(c,b),product(c,a))),
inference(spm,[status(thm)],[204,738,theory(equality)]) ).
cnf(863,plain,
product(product(a,c),product(b,product(a,c))) = product(product(a,c),product(product(c,b),product(c,a))),
inference(rw,[status(thm)],[792,22,theory(equality)]) ).
cnf(864,plain,
product(product(a,c),product(b,product(a,c))) = product(product(a,c),product(c,product(b,a))),
inference(rw,[status(thm)],[863,56,theory(equality)]) ).
cnf(1792,plain,
difference(product(a,c),product(product(a,c),product(c,product(b,a)))) = product(b,product(a,c)),
inference(spm,[status(thm)],[28,864,theory(equality)]) ).
cnf(1819,plain,
product(c,product(b,a)) = product(b,product(a,c)),
inference(rw,[status(thm)],[1792,28,theory(equality)]) ).
cnf(1848,plain,
product(product(b,X1),product(c,product(b,a))) = product(b,product(X1,product(a,c))),
inference(spm,[status(thm)],[56,1819,theory(equality)]) ).
cnf(3151,plain,
product(b,product(product(b,a),product(a,c))) = product(product(b,c),product(b,a)),
inference(spm,[status(thm)],[57,1848,theory(equality)]) ).
cnf(3199,plain,
product(b,product(product(b,a),product(a,c))) = product(b,product(c,a)),
inference(rw,[status(thm)],[3151,56,theory(equality)]) ).
cnf(3742,plain,
difference(b,product(b,product(c,a))) = product(product(b,a),product(a,c)),
inference(spm,[status(thm)],[28,3199,theory(equality)]) ).
cnf(3776,plain,
product(c,a) = product(product(b,a),product(a,c)),
inference(rw,[status(thm)],[3742,28,theory(equality)]) ).
cnf(3813,plain,
product(product(c,a),product(product(a,c),product(b,a))) = product(product(a,c),product(c,a)),
inference(spm,[status(thm)],[738,3776,theory(equality)]) ).
cnf(3841,plain,
product(product(c,a),product(product(a,c),product(b,a))) = product(c,product(a,c)),
inference(rw,[status(thm)],[3813,738,theory(equality)]) ).
cnf(4348,plain,
difference(X1,quotient(X1,product(X1,X2))) = product(difference(X1,product(difference(X1,X2),X1)),X1),
inference(spm,[status(thm)],[277,139,theory(equality)]) ).
cnf(4407,plain,
difference(X1,quotient(X1,product(X1,X2))) = quotient(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4348,277,theory(equality)]),139,theory(equality)]),30,theory(equality)]) ).
cnf(4443,plain,
product(X1,quotient(X1,X2)) = quotient(X1,product(X1,X2)),
inference(spm,[status(thm)],[30,4407,theory(equality)]) ).
cnf(4691,plain,
difference(product(c,a),product(c,product(a,c))) = product(product(a,c),product(b,a)),
inference(spm,[status(thm)],[28,3841,theory(equality)]) ).
cnf(4723,plain,
c = product(product(a,c),product(b,a)),
inference(rw,[status(thm)],[4691,238,theory(equality)]) ).
cnf(5084,plain,
difference(product(a,b),c) = product(c,a),
inference(spm,[status(thm)],[64,4723,theory(equality)]) ).
cnf(5176,plain,
quotient(c,product(c,a)) = product(a,b),
inference(spm,[status(thm)],[38,5084,theory(equality)]) ).
cnf(5192,plain,
product(c,quotient(c,a)) = product(a,b),
inference(rw,[status(thm)],[5176,4443,theory(equality)]) ).
cnf(6804,plain,
product(product(a,b),product(X1,a)) = product(product(c,X1),c),
inference(spm,[status(thm)],[67,5192,theory(equality)]) ).
cnf(6892,plain,
product(product(a,b),product(X1,a)) = product(c,product(X1,c)),
inference(rw,[status(thm)],[6804,198,theory(equality)]) ).
cnf(7357,negated_conjecture,
$false,
inference(rw,[status(thm)],[108,6892,theory(equality)]) ).
cnf(7358,negated_conjecture,
$false,
inference(cn,[status(thm)],[7357,theory(equality)]) ).
cnf(7359,negated_conjecture,
$false,
7358,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP777+1.p
% --creating new selector for []
% -running prover on /tmp/tmpMAbkPb/sel_GRP777+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP777+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP777+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP777+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
%
%------------------------------------------------------------------------------