TSTP Solution File: ALG040+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG040+1 : TPTP v5.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 03:40:58 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 177 ( 41 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 222 ( 92 ~; 75 |; 33 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 92 ( 1 sgn 58 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/tmp/tmp4zz-u2/sel_ALG040+1.p_1',ax2) ).
fof(2,axiom,
? [X1] :
( sorti1(X1)
& ! [X2] :
( sorti1(X2)
=> op1(X2,X2) = X1 ) ),
file('/tmp/tmp4zz-u2/sel_ALG040+1.p_1',ax3) ).
fof(3,conjecture,
( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
file('/tmp/tmp4zz-u2/sel_ALG040+1.p_1',co1) ).
fof(5,axiom,
~ ? [X1] :
( sorti2(X1)
& ! [X2] :
( sorti2(X2)
=> op2(X2,X2) = X1 ) ),
file('/tmp/tmp4zz-u2/sel_ALG040+1.p_1',ax4) ).
fof(6,negated_conjecture,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(7,plain,
! [X1] :
( ~ sorti2(X1)
| ! [X2] :
( ~ sorti2(X2)
| sorti2(op2(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(8,plain,
! [X3] :
( ~ sorti2(X3)
| ! [X4] :
( ~ sorti2(X4)
| sorti2(op2(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[7]) ).
fof(9,plain,
! [X3,X4] :
( ~ sorti2(X4)
| sorti2(op2(X3,X4))
| ~ sorti2(X3) ),
inference(shift_quantors,[status(thm)],[8]) ).
cnf(10,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[9]) ).
fof(11,plain,
? [X1] :
( sorti1(X1)
& ! [X2] :
( ~ sorti1(X2)
| op1(X2,X2) = X1 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(12,plain,
? [X3] :
( sorti1(X3)
& ! [X4] :
( ~ sorti1(X4)
| op1(X4,X4) = X3 ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
( sorti1(esk1_0)
& ! [X4] :
( ~ sorti1(X4)
| op1(X4,X4) = esk1_0 ) ),
inference(skolemize,[status(esa)],[12]) ).
fof(14,plain,
! [X4] :
( ( ~ sorti1(X4)
| op1(X4,X4) = esk1_0 )
& sorti1(esk1_0) ),
inference(shift_quantors,[status(thm)],[13]) ).
cnf(15,plain,
sorti1(esk1_0),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
( op1(X1,X1) = esk1_0
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(17,negated_conjecture,
( ! [X1] :
( ~ sorti1(X1)
| sorti2(h(X1)) )
& ! [X2] :
( ~ sorti2(X2)
| sorti1(j(X2)) )
& ! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( ~ sorti1(X4)
| h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( ~ sorti2(X5)
| ! [X6] :
( ~ sorti2(X6)
| j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( ~ sorti2(X7)
| h(j(X7)) = X7 )
& ! [X8] :
( ~ sorti1(X8)
| j(h(X8)) = X8 ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(18,negated_conjecture,
( ! [X9] :
( ~ sorti1(X9)
| sorti2(h(X9)) )
& ! [X10] :
( ~ sorti2(X10)
| sorti1(j(X10)) )
& ! [X11] :
( ~ sorti1(X11)
| ! [X12] :
( ~ sorti1(X12)
| h(op1(X11,X12)) = op2(h(X11),h(X12)) ) )
& ! [X13] :
( ~ sorti2(X13)
| ! [X14] :
( ~ sorti2(X14)
| j(op2(X13,X14)) = op1(j(X13),j(X14)) ) )
& ! [X15] :
( ~ sorti2(X15)
| h(j(X15)) = X15 )
& ! [X16] :
( ~ sorti1(X16)
| j(h(X16)) = X16 ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,negated_conjecture,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( ~ sorti1(X16)
| j(h(X16)) = X16 )
& ( ~ sorti2(X15)
| h(j(X15)) = X15 )
& ( ~ sorti2(X14)
| j(op2(X13,X14)) = op1(j(X13),j(X14))
| ~ sorti2(X13) )
& ( ~ sorti1(X12)
| h(op1(X11,X12)) = op2(h(X11),h(X12))
| ~ sorti1(X11) )
& ( ~ sorti2(X10)
| sorti1(j(X10)) )
& ( ~ sorti1(X9)
| sorti2(h(X9)) ) ),
inference(shift_quantors,[status(thm)],[18]) ).
cnf(20,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(22,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(24,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(30,plain,
! [X1] :
( ~ sorti2(X1)
| ? [X2] :
( sorti2(X2)
& op2(X2,X2) != X1 ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(31,plain,
! [X3] :
( ~ sorti2(X3)
| ? [X4] :
( sorti2(X4)
& op2(X4,X4) != X3 ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X3] :
( ~ sorti2(X3)
| ( sorti2(esk2_1(X3))
& op2(esk2_1(X3),esk2_1(X3)) != X3 ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X3] :
( ( sorti2(esk2_1(X3))
| ~ sorti2(X3) )
& ( op2(esk2_1(X3),esk2_1(X3)) != X3
| ~ sorti2(X3) ) ),
inference(distribute,[status(thm)],[32]) ).
cnf(34,plain,
( ~ sorti2(X1)
| op2(esk2_1(X1),esk2_1(X1)) != X1 ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,plain,
( sorti2(esk2_1(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(42,negated_conjecture,
( op2(X1,h(X2)) = h(op1(j(X1),X2))
| ~ sorti1(X2)
| ~ sorti1(j(X1))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[22,24,theory(equality)]) ).
cnf(44,negated_conjecture,
( sorti2(h(op1(X1,X2)))
| ~ sorti2(h(X2))
| ~ sorti2(h(X1))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[10,22,theory(equality)]) ).
cnf(46,negated_conjecture,
( sorti2(h(op1(X1,X2)))
| ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti2(h(X2)) ),
inference(csr,[status(thm)],[44,20]) ).
cnf(47,negated_conjecture,
( sorti2(h(op1(X1,X2)))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[46,20]) ).
cnf(48,negated_conjecture,
( sorti2(h(esk1_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[47,16,theory(equality)]) ).
cnf(61,negated_conjecture,
( op2(X1,h(X2)) = h(op1(j(X1),X2))
| ~ sorti1(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[42,21]) ).
cnf(62,negated_conjecture,
( op2(X1,X2) = h(op1(j(X1),j(X2)))
| ~ sorti1(j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(spm,[status(thm)],[61,24,theory(equality)]) ).
cnf(105,negated_conjecture,
( op2(X1,X2) = h(op1(j(X1),j(X2)))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[62,21]) ).
cnf(106,negated_conjecture,
( h(op1(j(esk2_1(X1)),j(esk2_1(X1)))) != X1
| ~ sorti2(X1)
| ~ sorti2(esk2_1(X1)) ),
inference(spm,[status(thm)],[34,105,theory(equality)]) ).
cnf(211,negated_conjecture,
( h(op1(j(esk2_1(X1)),j(esk2_1(X1)))) != X1
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[106,35]) ).
cnf(212,negated_conjecture,
( h(esk1_0) != X1
| ~ sorti2(X1)
| ~ sorti1(j(esk2_1(X1))) ),
inference(spm,[status(thm)],[211,16,theory(equality)]) ).
cnf(213,negated_conjecture,
( ~ sorti1(j(esk2_1(h(esk1_0))))
| ~ sorti2(h(esk1_0)) ),
inference(er,[status(thm)],[212,theory(equality)]) ).
cnf(214,negated_conjecture,
~ sorti1(j(esk2_1(h(esk1_0)))),
inference(csr,[status(thm)],[213,48]) ).
cnf(215,negated_conjecture,
~ sorti2(esk2_1(h(esk1_0))),
inference(spm,[status(thm)],[214,21,theory(equality)]) ).
cnf(216,negated_conjecture,
~ sorti2(h(esk1_0)),
inference(spm,[status(thm)],[215,35,theory(equality)]) ).
cnf(217,negated_conjecture,
~ sorti1(esk1_0),
inference(spm,[status(thm)],[216,20,theory(equality)]) ).
cnf(220,negated_conjecture,
$false,
inference(rw,[status(thm)],[217,15,theory(equality)]) ).
cnf(221,negated_conjecture,
$false,
inference(cn,[status(thm)],[220,theory(equality)]) ).
cnf(222,negated_conjecture,
$false,
221,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG040+1.p
% --creating new selector for []
% -running prover on /tmp/tmp4zz-u2/sel_ALG040+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG040+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG040+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG040+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
%
%------------------------------------------------------------------------------