TSTP Solution File: REL013+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL013+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 01:04:21 EST 2010
% Result : Theorem 184.98s
% Output : CNFRefutation 184.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 12
% Syntax : Number of formulae : 107 ( 100 unt; 0 def)
% Number of atoms : 114 ( 110 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 149 ( 13 sgn 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',converse_multiplicativity) ).
fof(2,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',converse_idempotence) ).
fof(3,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',composition_distributivity) ).
fof(4,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',converse_additivity) ).
fof(5,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',maddux1_join_commutativity) ).
fof(6,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',composition_associativity) ).
fof(7,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',def_zero) ).
fof(8,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',converse_cancellativity) ).
fof(9,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',maddux4_definiton_of_meet) ).
fof(10,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',maddux2_join_associativity) ).
fof(11,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',maddux3_a_kind_of_de_Morgan) ).
fof(12,conjecture,
! [X1] :
( composition(X1,zero) = zero
& composition(zero,X1) = zero ),
file('/tmp/tmpTihWNQ/sel_REL013+1.p_4',goals) ).
fof(13,negated_conjecture,
~ ! [X1] :
( composition(X1,zero) = zero
& composition(zero,X1) = zero ),
inference(assume_negation,[status(cth)],[12]) ).
fof(14,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(15,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[14]) ).
fof(16,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(17,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(19,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(21,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(23,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[6]) ).
cnf(25,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(27,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[8]) ).
cnf(29,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[9]) ).
cnf(31,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[10]) ).
cnf(33,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[11]) ).
cnf(35,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,negated_conjecture,
? [X1] :
( composition(X1,zero) != zero
| composition(zero,X1) != zero ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(37,negated_conjecture,
? [X2] :
( composition(X2,zero) != zero
| composition(zero,X2) != zero ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,negated_conjecture,
( composition(esk1_0,zero) != zero
| composition(zero,esk1_0) != zero ),
inference(skolemize,[status(esa)],[37]) ).
cnf(39,negated_conjecture,
( composition(zero,esk1_0) != zero
| composition(esk1_0,zero) != zero ),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(40,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(rw,[status(thm)],[27,31,theory(equality)]),
[unfolding] ).
cnf(41,plain,
complement(join(zero,complement(zero))) = zero,
inference(spm,[status(thm)],[40,40,theory(equality)]) ).
cnf(43,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[15,17,theory(equality)]) ).
cnf(45,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[21,17,theory(equality)]) ).
cnf(56,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[23,33,theory(equality)]) ).
cnf(58,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[33,23,theory(equality)]) ).
cnf(62,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[58,33,theory(equality)]) ).
cnf(73,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[29,23,theory(equality)]) ).
cnf(74,plain,
join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1),
inference(spm,[status(thm)],[73,17,theory(equality)]) ).
cnf(80,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[35,23,theory(equality)]) ).
cnf(84,plain,
join(complement(join(complement(X1),complement(X1))),zero) = X1,
inference(spm,[status(thm)],[80,40,theory(equality)]) ).
cnf(88,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[80,80,theory(equality)]) ).
cnf(89,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[80,23,theory(equality)]) ).
cnf(94,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = X1,
inference(rw,[status(thm)],[84,23,theory(equality)]) ).
cnf(95,plain,
join(complement(X1),complement(join(complement(X1),join(complement(X2),complement(join(complement(X1),X2)))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[88,23,theory(equality)]),33,theory(equality)]),23,theory(equality)]) ).
cnf(200,plain,
join(zero,complement(join(zero,zero))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[94,40,theory(equality)]) ).
cnf(201,plain,
join(X1,X2) = join(zero,join(complement(join(complement(X1),complement(X1))),X2)),
inference(spm,[status(thm)],[33,94,theory(equality)]) ).
cnf(202,plain,
join(zero,complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[94,41,theory(equality)]) ).
cnf(213,plain,
join(complement(X1),complement(complement(X1))) = join(zero,complement(zero)),
inference(rw,[status(thm)],[200,202,theory(equality)]) ).
cnf(215,plain,
join(complement(join(zero,complement(zero))),complement(join(complement(X1),complement(complement(complement(X1)))))) = X1,
inference(spm,[status(thm)],[80,213,theory(equality)]) ).
cnf(220,plain,
join(zero,complement(join(complement(X1),complement(complement(complement(X1)))))) = X1,
inference(rw,[status(thm)],[215,41,theory(equality)]) ).
cnf(299,plain,
join(X1,join(zero,complement(zero))) = join(zero,join(X1,complement(join(zero,zero)))),
inference(spm,[status(thm)],[62,202,theory(equality)]) ).
cnf(1168,plain,
join(zero,composition(X1,complement(composition(converse(X1),join(zero,complement(zero)))))) = zero,
inference(spm,[status(thm)],[74,41,theory(equality)]) ).
cnf(3533,plain,
join(X1,complement(join(zero,zero))) = join(complement(join(complement(X1),complement(X1))),join(zero,complement(zero))),
inference(spm,[status(thm)],[299,201,theory(equality)]) ).
cnf(3570,plain,
join(X1,complement(join(zero,zero))) = join(complement(zero),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3533,56,theory(equality)]),23,theory(equality)]),94,theory(equality)]) ).
cnf(3594,plain,
join(zero,complement(join(complement(zero),complement(join(zero,zero))))) = join(zero,zero),
inference(spm,[status(thm)],[94,3570,theory(equality)]) ).
cnf(3635,plain,
zero = join(zero,zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3594,3570,theory(equality)]),94,theory(equality)]) ).
cnf(3668,plain,
join(zero,X1) = join(zero,join(zero,X1)),
inference(spm,[status(thm)],[33,3635,theory(equality)]) ).
cnf(3835,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[3668,94,theory(equality)]) ).
cnf(3902,plain,
converse(converse(X1)) = join(converse(zero),X1),
inference(spm,[status(thm)],[45,3835,theory(equality)]) ).
cnf(3911,plain,
X1 = join(X1,zero),
inference(spm,[status(thm)],[23,3835,theory(equality)]) ).
cnf(3931,plain,
composition(X1,complement(composition(converse(X1),complement(zero)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1168,3835,theory(equality)]),3835,theory(equality)]) ).
cnf(3952,plain,
complement(join(complement(X1),complement(complement(complement(X1))))) = X1,
inference(rw,[status(thm)],[220,3835,theory(equality)]) ).
cnf(3955,plain,
complement(join(complement(X1),complement(X1))) = X1,
inference(rw,[status(thm)],[94,3835,theory(equality)]) ).
cnf(3956,plain,
complement(complement(zero)) = zero,
inference(rw,[status(thm)],[41,3835,theory(equality)]) ).
cnf(3958,plain,
X1 = join(converse(zero),X1),
inference(rw,[status(thm)],[3902,17,theory(equality)]) ).
cnf(4083,plain,
zero = converse(zero),
inference(spm,[status(thm)],[3911,3958,theory(equality)]) ).
cnf(4458,plain,
complement(join(X1,X1)) = join(complement(X1),complement(X1)),
inference(spm,[status(thm)],[3955,3955,theory(equality)]) ).
cnf(4508,plain,
complement(complement(join(X1,X1))) = X1,
inference(rw,[status(thm)],[3955,4458,theory(equality)]) ).
cnf(5666,plain,
complement(join(X1,complement(complement(X1)))) = complement(join(X1,X1)),
inference(spm,[status(thm)],[3952,4508,theory(equality)]) ).
cnf(6026,plain,
join(complement(join(X1,X1)),complement(join(complement(complement(X1)),complement(X1)))) = complement(X1),
inference(spm,[status(thm)],[89,5666,theory(equality)]) ).
cnf(6069,plain,
complement(join(X1,X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6026,23,theory(equality)]),213,theory(equality)]),3835,theory(equality)]),3956,theory(equality)]),3911,theory(equality)]) ).
cnf(6105,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[80,6069,theory(equality)]) ).
cnf(6150,plain,
X1 = join(X1,X1),
inference(rw,[status(thm)],[6105,80,theory(equality)]) ).
cnf(6183,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[33,6150,theory(equality)]) ).
cnf(6218,plain,
join(X1,X2) = join(X2,join(X1,X2)),
inference(spm,[status(thm)],[56,6150,theory(equality)]) ).
cnf(6435,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[6183,80,theory(equality)]) ).
cnf(6504,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[6435,23,theory(equality)]) ).
cnf(6937,plain,
zero = complement(join(complement(zero),X1)),
inference(spm,[status(thm)],[3835,6504,theory(equality)]) ).
cnf(7146,plain,
join(complement(zero),complement(join(complement(zero),join(complement(X1),zero)))) = join(complement(zero),X1),
inference(spm,[status(thm)],[95,6937,theory(equality)]) ).
cnf(7203,plain,
complement(zero) = join(complement(zero),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[7146,23,theory(equality)]),3835,theory(equality)]),6937,theory(equality)]),23,theory(equality)]),3835,theory(equality)]) ).
cnf(7230,plain,
converse(complement(zero)) = join(converse(complement(zero)),X1),
inference(spm,[status(thm)],[45,7203,theory(equality)]) ).
cnf(7253,plain,
join(X1,complement(zero)) = complement(zero),
inference(spm,[status(thm)],[6218,7203,theory(equality)]) ).
cnf(7595,plain,
converse(complement(zero)) = complement(zero),
inference(spm,[status(thm)],[7253,7230,theory(equality)]) ).
cnf(7691,plain,
composition(complement(zero),complement(composition(complement(zero),complement(zero)))) = zero,
inference(spm,[status(thm)],[3931,7595,theory(equality)]) ).
cnf(8551,plain,
join(zero,composition(X1,complement(composition(complement(zero),complement(zero))))) = composition(join(complement(zero),X1),complement(composition(complement(zero),complement(zero)))),
inference(spm,[status(thm)],[19,7691,theory(equality)]) ).
cnf(8570,plain,
composition(X1,complement(composition(complement(zero),complement(zero)))) = composition(join(complement(zero),X1),complement(composition(complement(zero),complement(zero)))),
inference(rw,[status(thm)],[8551,3835,theory(equality)]) ).
cnf(8571,plain,
composition(X1,complement(composition(complement(zero),complement(zero)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8570,7203,theory(equality)]),7691,theory(equality)]) ).
cnf(8600,plain,
zero = composition(X1,composition(X2,complement(composition(complement(zero),complement(zero))))),
inference(spm,[status(thm)],[25,8571,theory(equality)]) ).
cnf(8635,plain,
zero = composition(X1,zero),
inference(rw,[status(thm)],[8600,8571,theory(equality)]) ).
cnf(8677,plain,
converse(zero) = composition(converse(zero),X1),
inference(spm,[status(thm)],[43,8635,theory(equality)]) ).
cnf(8708,negated_conjecture,
( composition(zero,esk1_0) != zero
| $false ),
inference(rw,[status(thm)],[39,8635,theory(equality)]) ).
cnf(8709,negated_conjecture,
composition(zero,esk1_0) != zero,
inference(cn,[status(thm)],[8708,theory(equality)]) ).
cnf(8716,plain,
zero = composition(converse(zero),X1),
inference(rw,[status(thm)],[8677,4083,theory(equality)]) ).
cnf(8717,plain,
zero = composition(zero,X1),
inference(rw,[status(thm)],[8716,4083,theory(equality)]) ).
cnf(8807,negated_conjecture,
$false,
inference(rw,[status(thm)],[8709,8717,theory(equality)]) ).
cnf(8808,negated_conjecture,
$false,
inference(cn,[status(thm)],[8807,theory(equality)]) ).
cnf(8809,negated_conjecture,
$false,
8808,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL013+1.p
% --creating new selector for [REL001+0.ax]
% eprover: CPU time limit exceeded, terminating
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpTihWNQ/sel_REL013+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpTihWNQ/sel_REL013+1.p_2 with time limit 81
% -prover status ResourceOut
% --creating new selector for [REL001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpTihWNQ/sel_REL013+1.p_3 with time limit 74
% -prover status ResourceOut
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmpTihWNQ/sel_REL013+1.p_4 with time limit 55
% -prover status Theorem
% Problem REL013+1.p solved in phase 3.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL013+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL013+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
%
%------------------------------------------------------------------------------