TSTP Solution File: REL031+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL031+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 : Sun Dec 26 01:24:12 EST 2010
% Result : Theorem 14.81s
% Output : CNFRefutation 14.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 54 unt; 0 def)
% Number of atoms : 69 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 87 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',converse_multiplicativity) ).
fof(2,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',converse_idempotence) ).
fof(3,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',composition_distributivity) ).
fof(4,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',converse_additivity) ).
fof(5,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',maddux1_join_commutativity) ).
fof(6,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',composition_associativity) ).
fof(7,axiom,
! [X1] : composition(X1,one) = X1,
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',composition_identity) ).
fof(9,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',maddux2_join_associativity) ).
fof(11,conjecture,
! [X1,X2] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X2),X2),one) = one )
=> join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) = one ),
file('/tmp/tmpE1vNNT/sel_REL031+1.p_1',goals) ).
fof(12,negated_conjecture,
~ ! [X1,X2] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X2),X2),one) = one )
=> join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) = one ),
inference(assume_negation,[status(cth)],[11]) ).
fof(13,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(14,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[13]) ).
fof(15,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(16,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(18,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(20,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(22,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[6]) ).
cnf(24,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X2] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(26,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[25]) ).
fof(29,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[9]) ).
cnf(30,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[29]) ).
fof(33,negated_conjecture,
? [X1,X2] :
( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X2),X2),one) = one
& join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) != one ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(34,negated_conjecture,
? [X3,X4] :
( join(composition(converse(X3),X3),one) = one
& join(composition(converse(X4),X4),one) = one
& join(composition(converse(composition(X3,X4)),composition(X3,X4)),one) != one ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
( join(composition(converse(esk1_0),esk1_0),one) = one
& join(composition(converse(esk2_0),esk2_0),one) = one
& join(composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0)),one) != one ),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
join(composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0)),one) != one,
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
join(composition(converse(esk2_0),esk2_0),one) = one,
inference(split_conjunct,[status(thm)],[35]) ).
cnf(38,negated_conjecture,
join(composition(converse(esk1_0),esk1_0),one) = one,
inference(split_conjunct,[status(thm)],[35]) ).
cnf(39,negated_conjecture,
join(one,composition(converse(esk2_0),esk2_0)) = one,
inference(rw,[status(thm)],[37,22,theory(equality)]) ).
cnf(40,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) = one,
inference(rw,[status(thm)],[38,22,theory(equality)]) ).
cnf(41,negated_conjecture,
join(one,composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0))) != one,
inference(rw,[status(thm)],[36,22,theory(equality)]) ).
cnf(42,plain,
composition(X1,converse(X2)) = converse(composition(X2,converse(X1))),
inference(spm,[status(thm)],[14,16,theory(equality)]) ).
cnf(43,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[14,16,theory(equality)]) ).
cnf(44,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[20,16,theory(equality)]) ).
cnf(52,plain,
composition(converse(composition(X2,X1)),X3) = composition(converse(X1),composition(converse(X2),X3)),
inference(spm,[status(thm)],[24,14,theory(equality)]) ).
cnf(132,plain,
converse(converse(X1)) = composition(converse(one),X1),
inference(spm,[status(thm)],[43,26,theory(equality)]) ).
cnf(146,plain,
X1 = composition(converse(one),X1),
inference(rw,[status(thm)],[132,16,theory(equality)]) ).
cnf(158,negated_conjecture,
join(one,X1) = join(one,join(composition(converse(esk2_0),esk2_0),X1)),
inference(spm,[status(thm)],[30,39,theory(equality)]) ).
cnf(159,plain,
one = converse(one),
inference(spm,[status(thm)],[26,146,theory(equality)]) ).
cnf(180,plain,
join(one,converse(X1)) = converse(join(one,X1)),
inference(spm,[status(thm)],[20,159,theory(equality)]) ).
cnf(185,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[146,159,theory(equality)]) ).
cnf(193,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[18,185,theory(equality)]) ).
cnf(342,negated_conjecture,
join(one,composition(join(converse(esk2_0),X1),esk2_0)) = join(one,composition(X1,esk2_0)),
inference(spm,[status(thm)],[158,18,theory(equality)]) ).
cnf(396,plain,
converse(composition(join(one,X2),converse(X1))) = join(X1,converse(composition(X2,converse(X1)))),
inference(spm,[status(thm)],[44,193,theory(equality)]) ).
cnf(403,plain,
composition(X1,join(one,converse(X2))) = join(X1,converse(composition(X2,converse(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[396,42,theory(equality)]),180,theory(equality)]) ).
cnf(404,plain,
composition(X1,join(one,converse(X2))) = join(X1,composition(X1,converse(X2))),
inference(rw,[status(thm)],[403,42,theory(equality)]) ).
cnf(1315,plain,
join(X1,composition(X1,X2)) = composition(X1,join(one,X2)),
inference(spm,[status(thm)],[404,16,theory(equality)]) ).
cnf(4038,negated_conjecture,
join(one,composition(composition(converse(esk2_0),join(one,X1)),esk2_0)) = join(one,composition(composition(converse(esk2_0),X1),esk2_0)),
inference(spm,[status(thm)],[342,1315,theory(equality)]) ).
cnf(4063,negated_conjecture,
join(one,composition(converse(esk2_0),composition(join(one,X1),esk2_0))) = join(one,composition(composition(converse(esk2_0),X1),esk2_0)),
inference(rw,[status(thm)],[4038,24,theory(equality)]) ).
cnf(4064,negated_conjecture,
join(one,composition(converse(esk2_0),composition(join(one,X1),esk2_0))) = join(one,composition(converse(esk2_0),composition(X1,esk2_0))),
inference(rw,[status(thm)],[4063,24,theory(equality)]) ).
cnf(404249,negated_conjecture,
join(one,composition(converse(esk2_0),composition(one,esk2_0))) = join(one,composition(converse(esk2_0),composition(composition(converse(esk1_0),esk1_0),esk2_0))),
inference(spm,[status(thm)],[4064,40,theory(equality)]) ).
cnf(404788,negated_conjecture,
one = join(one,composition(converse(esk2_0),composition(composition(converse(esk1_0),esk1_0),esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[404249,185,theory(equality)]),39,theory(equality)]) ).
cnf(404789,negated_conjecture,
one = join(one,composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[404788,24,theory(equality)]),52,theory(equality)]) ).
cnf(404790,negated_conjecture,
$false,
inference(sr,[status(thm)],[404789,41,theory(equality)]) ).
cnf(404791,negated_conjecture,
$false,
404790,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL031+1.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmpE1vNNT/sel_REL031+1.p_1 with time limit 29
% -prover status Theorem
% Problem REL031+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL031+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL031+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
%
%------------------------------------------------------------------------------