TSTP Solution File: GRP682+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP682+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 11:23:02 EST 2010
% Result : Theorem 0.41s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 58 unt; 0 def)
% Number of atoms : 80 ( 76 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 19 ~; 9 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 38 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3,X4] : ld(ld(X4,X3),mult(ld(X4,X3),mult(X2,X1))) = mult(ld(X4,mult(X4,X2)),X1),
file('/tmp/tmpDWv5qv/sel_GRP682+1.p_1',f05) ).
fof(2,axiom,
! [X3,X4] : mult(rd(X4,X3),X3) = rd(mult(X4,X3),X3),
file('/tmp/tmpDWv5qv/sel_GRP682+1.p_1',f04) ).
fof(3,axiom,
! [X3,X4] : ld(X4,mult(X4,ld(X3,X3))) = rd(mult(rd(X4,X4),X3),X3),
file('/tmp/tmpDWv5qv/sel_GRP682+1.p_1',f07) ).
fof(4,axiom,
! [X1,X2,X3,X4] : rd(mult(mult(X4,X3),rd(X2,X1)),rd(X2,X1)) = mult(X4,rd(mult(X3,X1),X1)),
file('/tmp/tmpDWv5qv/sel_GRP682+1.p_1',f06) ).
fof(5,axiom,
! [X4] : ld(X4,mult(X4,X4)) = X4,
file('/tmp/tmpDWv5qv/sel_GRP682+1.p_1',f01) ).
fof(6,conjecture,
! [X5,X6,X7] :
( ld(ld(X5,X6),mult(ld(X5,X6),X7)) = ld(X5,mult(X5,X7))
& ld(rd(X5,X6),mult(rd(X5,X6),X7)) = ld(X5,mult(X5,X7)) ),
file('/tmp/tmpDWv5qv/sel_GRP682+1.p_1',goals) ).
fof(7,axiom,
! [X3,X4] : mult(X4,ld(X4,X3)) = ld(X4,mult(X4,X3)),
file('/tmp/tmpDWv5qv/sel_GRP682+1.p_1',f03) ).
fof(8,axiom,
! [X4] : rd(mult(X4,X4),X4) = X4,
file('/tmp/tmpDWv5qv/sel_GRP682+1.p_1',f02) ).
fof(9,negated_conjecture,
~ ! [X5,X6,X7] :
( ld(ld(X5,X6),mult(ld(X5,X6),X7)) = ld(X5,mult(X5,X7))
& ld(rd(X5,X6),mult(rd(X5,X6),X7)) = ld(X5,mult(X5,X7)) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(10,plain,
! [X5,X6,X7,X8] : ld(ld(X8,X7),mult(ld(X8,X7),mult(X6,X5))) = mult(ld(X8,mult(X8,X6)),X5),
inference(variable_rename,[status(thm)],[1]) ).
cnf(11,plain,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
inference(split_conjunct,[status(thm)],[10]) ).
fof(12,plain,
! [X5,X6] : mult(rd(X6,X5),X5) = rd(mult(X6,X5),X5),
inference(variable_rename,[status(thm)],[2]) ).
cnf(13,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(split_conjunct,[status(thm)],[12]) ).
fof(14,plain,
! [X5,X6] : ld(X6,mult(X6,ld(X5,X5))) = rd(mult(rd(X6,X6),X5),X5),
inference(variable_rename,[status(thm)],[3]) ).
cnf(15,plain,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(split_conjunct,[status(thm)],[14]) ).
fof(16,plain,
! [X5,X6,X7,X8] : rd(mult(mult(X8,X7),rd(X6,X5)),rd(X6,X5)) = mult(X8,rd(mult(X7,X5),X5)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(17,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,plain,
! [X5] : ld(X5,mult(X5,X5)) = X5,
inference(variable_rename,[status(thm)],[5]) ).
cnf(19,plain,
ld(X1,mult(X1,X1)) = X1,
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,negated_conjecture,
? [X5,X6,X7] :
( ld(ld(X5,X6),mult(ld(X5,X6),X7)) != ld(X5,mult(X5,X7))
| ld(rd(X5,X6),mult(rd(X5,X6),X7)) != ld(X5,mult(X5,X7)) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(21,negated_conjecture,
? [X8,X9,X10] :
( ld(ld(X8,X9),mult(ld(X8,X9),X10)) != ld(X8,mult(X8,X10))
| ld(rd(X8,X9),mult(rd(X8,X9),X10)) != ld(X8,mult(X8,X10)) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,negated_conjecture,
( ld(ld(esk1_0,esk2_0),mult(ld(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0))
| ld(rd(esk1_0,esk2_0),mult(rd(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0)) ),
inference(skolemize,[status(esa)],[21]) ).
cnf(23,negated_conjecture,
( ld(rd(esk1_0,esk2_0),mult(rd(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0))
| ld(ld(esk1_0,esk2_0),mult(ld(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X5,X6] : mult(X6,ld(X6,X5)) = ld(X6,mult(X6,X5)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(25,plain,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X5] : rd(mult(X5,X5),X5) = X5,
inference(variable_rename,[status(thm)],[8]) ).
cnf(27,plain,
rd(mult(X1,X1),X1) = X1,
inference(split_conjunct,[status(thm)],[26]) ).
cnf(28,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[19,25,theory(equality)]) ).
cnf(29,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[27,13,theory(equality)]) ).
cnf(30,plain,
mult(rd(rd(X1,X1),X2),X2) = ld(X1,mult(X1,ld(X2,X2))),
inference(rw,[status(thm)],[15,13,theory(equality)]) ).
cnf(31,plain,
mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[30,25,theory(equality)]) ).
cnf(34,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
inference(rw,[status(thm)],[11,25,theory(equality)]) ).
cnf(35,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(rw,[status(thm)],[34,25,theory(equality)]) ).
cnf(37,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(spm,[status(thm)],[35,25,theory(equality)]) ).
cnf(44,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(rw,[status(thm)],[17,13,theory(equality)]) ).
cnf(45,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[44,13,theory(equality)]) ).
cnf(48,plain,
mult(rd(mult(X1,X2),mult(rd(X3,X4),X4)),mult(rd(X3,X4),X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(spm,[status(thm)],[45,13,theory(equality)]) ).
cnf(58,negated_conjecture,
( mult(ld(esk1_0,esk2_0),ld(ld(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0))
| ld(rd(esk1_0,esk2_0),mult(rd(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0)) ),
inference(rw,[status(thm)],[23,25,theory(equality)]) ).
cnf(59,negated_conjecture,
( mult(ld(esk1_0,esk2_0),ld(ld(esk1_0,esk2_0),esk3_0)) != mult(esk1_0,ld(esk1_0,esk3_0))
| ld(rd(esk1_0,esk2_0),mult(rd(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0)) ),
inference(rw,[status(thm)],[58,25,theory(equality)]) ).
cnf(60,negated_conjecture,
( mult(ld(esk1_0,esk2_0),ld(ld(esk1_0,esk2_0),esk3_0)) != mult(esk1_0,ld(esk1_0,esk3_0))
| mult(rd(esk1_0,esk2_0),ld(rd(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0)) ),
inference(rw,[status(thm)],[59,25,theory(equality)]) ).
cnf(61,negated_conjecture,
( mult(ld(esk1_0,esk2_0),ld(ld(esk1_0,esk2_0),esk3_0)) != mult(esk1_0,ld(esk1_0,esk3_0))
| mult(rd(esk1_0,esk2_0),ld(rd(esk1_0,esk2_0),esk3_0)) != mult(esk1_0,ld(esk1_0,esk3_0)) ),
inference(rw,[status(thm)],[60,25,theory(equality)]) ).
cnf(62,plain,
ld(X1,X1) = mult(X1,ld(X1,ld(X1,X1))),
inference(spm,[status(thm)],[25,28,theory(equality)]) ).
cnf(64,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,X3)),ld(X3,X3)),
inference(spm,[status(thm)],[35,28,theory(equality)]) ).
cnf(67,plain,
rd(X1,X1) = mult(rd(rd(X1,X1),X1),X1),
inference(spm,[status(thm)],[13,29,theory(equality)]) ).
cnf(71,plain,
rd(X1,X1) = mult(X1,ld(X1,ld(X1,X1))),
inference(rw,[status(thm)],[67,31,theory(equality)]) ).
cnf(76,plain,
ld(X1,X1) = rd(X1,X1),
inference(rw,[status(thm)],[71,62,theory(equality)]) ).
cnf(78,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[29,76,theory(equality)]) ).
cnf(79,plain,
mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[31,76,theory(equality)]) ).
cnf(255,plain,
mult(X1,ld(X1,mult(X2,X3))) = mult(mult(X1,ld(X1,X2)),X3),
inference(spm,[status(thm)],[37,28,theory(equality)]) ).
cnf(337,plain,
mult(mult(X1,mult(X1,ld(X1,X2))),X3) = mult(X1,ld(X1,mult(mult(X1,X2),X3))),
inference(spm,[status(thm)],[255,25,theory(equality)]) ).
cnf(341,plain,
mult(X1,X2) = mult(X1,ld(X1,mult(X1,X2))),
inference(spm,[status(thm)],[255,28,theory(equality)]) ).
cnf(359,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[64,255,theory(equality)]),28,theory(equality)]) ).
cnf(363,plain,
mult(X1,X2) = mult(X1,mult(X1,ld(X1,X2))),
inference(rw,[status(thm)],[341,25,theory(equality)]) ).
cnf(400,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),X3)) = mult(X1,ld(X1,X3)),
inference(spm,[status(thm)],[359,25,theory(equality)]) ).
cnf(417,negated_conjecture,
( $false
| mult(rd(esk1_0,esk2_0),ld(rd(esk1_0,esk2_0),esk3_0)) != mult(esk1_0,ld(esk1_0,esk3_0)) ),
inference(rw,[status(thm)],[61,359,theory(equality)]) ).
cnf(418,negated_conjecture,
mult(rd(esk1_0,esk2_0),ld(rd(esk1_0,esk2_0),esk3_0)) != mult(esk1_0,ld(esk1_0,esk3_0)),
inference(cn,[status(thm)],[417,theory(equality)]) ).
cnf(420,plain,
mult(X1,ld(X1,mult(X2,ld(mult(X1,ld(X1,X2)),X3)))) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[400,255,theory(equality)]) ).
cnf(883,plain,
mult(mult(X1,X2),X3) = mult(X1,ld(X1,mult(mult(X1,X2),X3))),
inference(rw,[status(thm)],[337,363,theory(equality)]) ).
cnf(1502,plain,
mult(rd(mult(X1,X2),mult(ld(X3,X3),X3)),mult(ld(X3,X3),X3)) = mult(X1,mult(rd(X2,X3),X3)),
inference(spm,[status(thm)],[48,76,theory(equality)]) ).
cnf(1552,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1502,78,theory(equality)]),78,theory(equality)]) ).
cnf(1587,plain,
mult(rd(X1,X2),X2) = mult(X1,mult(rd(ld(X1,X1),X2),X2)),
inference(spm,[status(thm)],[1552,28,theory(equality)]) ).
cnf(1627,plain,
mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1587,79,theory(equality)]),363,theory(equality)]) ).
cnf(5898,plain,
mult(X1,ld(X1,mult(mult(X1,X2),ld(mult(X1,mult(X1,ld(X1,X2))),X3)))) = mult(X1,ld(X1,X3)),
inference(spm,[status(thm)],[420,25,theory(equality)]) ).
cnf(5969,plain,
mult(mult(X1,X2),ld(mult(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5898,363,theory(equality)]),883,theory(equality)]) ).
cnf(6267,plain,
mult(mult(X1,ld(X2,X2)),ld(mult(X1,ld(X2,X2)),X3)) = mult(rd(X1,X2),ld(rd(X1,X2),X3)),
inference(spm,[status(thm)],[5969,1627,theory(equality)]) ).
cnf(6350,plain,
mult(X1,ld(X1,X3)) = mult(rd(X1,X2),ld(rd(X1,X2),X3)),
inference(rw,[status(thm)],[6267,5969,theory(equality)]) ).
cnf(6916,negated_conjecture,
$false,
inference(rw,[status(thm)],[418,6350,theory(equality)]) ).
cnf(6917,negated_conjecture,
$false,
inference(cn,[status(thm)],[6916,theory(equality)]) ).
cnf(6918,negated_conjecture,
$false,
6917,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP682+1.p
% --creating new selector for []
% -running prover on /tmp/tmpDWv5qv/sel_GRP682+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP682+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP682+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP682+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
%
%------------------------------------------------------------------------------