TSTP Solution File: ALG178+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG178+1 : TPTP v5.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 04:13:10 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 177 ( 46 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 221 ( 93 ~; 75 |; 29 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 58 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/tmp/tmp53N-J_/sel_ALG178+1.p_1',ax2) ).
fof(2,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> op1(X1,op1(X1,X2)) = X2 ) ),
file('/tmp/tmp53N-J_/sel_ALG178+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/tmp53N-J_/sel_ALG178+1.p_1',co1) ).
fof(5,axiom,
~ ! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> op2(X1,op2(X1,X2)) = X2 ) ),
file('/tmp/tmp53N-J_/sel_ALG178+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(X1,op1(X1,X2)) = X2 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(12,plain,
! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( ~ sorti1(X4)
| op1(X3,op1(X3,X4)) = X4 ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
! [X3,X4] :
( ~ sorti1(X4)
| op1(X3,op1(X3,X4)) = X4
| ~ sorti1(X3) ),
inference(shift_quantors,[status(thm)],[12]) ).
cnf(14,plain,
( op1(X1,op1(X1,X2)) = X2
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(15,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(16,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)],[15]) ).
fof(17,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)],[16]) ).
cnf(19,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(21,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(22,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(28,plain,
? [X1] :
( sorti2(X1)
& ? [X2] :
( sorti2(X2)
& op2(X1,op2(X1,X2)) != X2 ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(29,plain,
? [X3] :
( sorti2(X3)
& ? [X4] :
( sorti2(X4)
& op2(X3,op2(X3,X4)) != X4 ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,plain,
( sorti2(esk1_0)
& sorti2(esk2_0)
& op2(esk1_0,op2(esk1_0,esk2_0)) != esk2_0 ),
inference(skolemize,[status(esa)],[29]) ).
cnf(31,plain,
op2(esk1_0,op2(esk1_0,esk2_0)) != esk2_0,
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,plain,
sorti2(esk2_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(33,plain,
sorti2(esk1_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(38,negated_conjecture,
( h(op1(j(X1),j(X2))) = op2(X1,X2)
| ~ sorti2(op2(X1,X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[22,21,theory(equality)]) ).
cnf(62,negated_conjecture,
( op2(X1,X2) = h(op1(j(X1),j(X2)))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[38,10]) ).
cnf(64,negated_conjecture,
( h(op1(j(esk1_0),j(op2(esk1_0,esk2_0)))) != esk2_0
| ~ sorti2(op2(esk1_0,esk2_0))
| ~ sorti2(esk1_0) ),
inference(spm,[status(thm)],[31,62,theory(equality)]) ).
cnf(71,negated_conjecture,
( h(op1(j(esk1_0),j(op2(esk1_0,esk2_0)))) != esk2_0
| ~ sorti2(op2(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[64,33,theory(equality)]) ).
cnf(72,negated_conjecture,
( h(op1(j(esk1_0),j(op2(esk1_0,esk2_0)))) != esk2_0
| ~ sorti2(op2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[71,theory(equality)]) ).
cnf(76,negated_conjecture,
( h(op1(j(esk1_0),j(op2(esk1_0,esk2_0)))) != esk2_0
| ~ sorti2(esk2_0)
| ~ sorti2(esk1_0) ),
inference(spm,[status(thm)],[72,10,theory(equality)]) ).
cnf(78,negated_conjecture,
( h(op1(j(esk1_0),j(op2(esk1_0,esk2_0)))) != esk2_0
| $false
| ~ sorti2(esk1_0) ),
inference(rw,[status(thm)],[76,32,theory(equality)]) ).
cnf(79,negated_conjecture,
( h(op1(j(esk1_0),j(op2(esk1_0,esk2_0)))) != esk2_0
| $false
| $false ),
inference(rw,[status(thm)],[78,33,theory(equality)]) ).
cnf(80,negated_conjecture,
h(op1(j(esk1_0),j(op2(esk1_0,esk2_0)))) != esk2_0,
inference(cn,[status(thm)],[79,theory(equality)]) ).
cnf(84,negated_conjecture,
( h(op1(j(esk1_0),op1(j(esk1_0),j(esk2_0)))) != esk2_0
| ~ sorti2(esk2_0)
| ~ sorti2(esk1_0) ),
inference(spm,[status(thm)],[80,21,theory(equality)]) ).
cnf(86,negated_conjecture,
( h(op1(j(esk1_0),op1(j(esk1_0),j(esk2_0)))) != esk2_0
| $false
| ~ sorti2(esk1_0) ),
inference(rw,[status(thm)],[84,32,theory(equality)]) ).
cnf(87,negated_conjecture,
( h(op1(j(esk1_0),op1(j(esk1_0),j(esk2_0)))) != esk2_0
| $false
| $false ),
inference(rw,[status(thm)],[86,33,theory(equality)]) ).
cnf(88,negated_conjecture,
h(op1(j(esk1_0),op1(j(esk1_0),j(esk2_0)))) != esk2_0,
inference(cn,[status(thm)],[87,theory(equality)]) ).
cnf(92,negated_conjecture,
( h(j(esk2_0)) != esk2_0
| ~ sorti1(j(esk2_0))
| ~ sorti1(j(esk1_0)) ),
inference(spm,[status(thm)],[88,14,theory(equality)]) ).
cnf(93,negated_conjecture,
( ~ sorti1(j(esk2_0))
| ~ sorti1(j(esk1_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[92,22,theory(equality)]) ).
cnf(94,negated_conjecture,
( ~ sorti1(j(esk2_0))
| ~ sorti1(j(esk1_0))
| $false ),
inference(rw,[status(thm)],[93,32,theory(equality)]) ).
cnf(95,negated_conjecture,
( ~ sorti1(j(esk2_0))
| ~ sorti1(j(esk1_0)) ),
inference(cn,[status(thm)],[94,theory(equality)]) ).
cnf(105,negated_conjecture,
( ~ sorti1(j(esk1_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[95,19,theory(equality)]) ).
cnf(106,negated_conjecture,
( ~ sorti1(j(esk1_0))
| $false ),
inference(rw,[status(thm)],[105,32,theory(equality)]) ).
cnf(107,negated_conjecture,
~ sorti1(j(esk1_0)),
inference(cn,[status(thm)],[106,theory(equality)]) ).
cnf(108,negated_conjecture,
~ sorti2(esk1_0),
inference(spm,[status(thm)],[107,19,theory(equality)]) ).
cnf(109,negated_conjecture,
$false,
inference(rw,[status(thm)],[108,33,theory(equality)]) ).
cnf(110,negated_conjecture,
$false,
inference(cn,[status(thm)],[109,theory(equality)]) ).
cnf(111,negated_conjecture,
$false,
110,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG178+1.p
% --creating new selector for []
% -running prover on /tmp/tmp53N-J_/sel_ALG178+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG178+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG178+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG178+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
%
%------------------------------------------------------------------------------