TSTP Solution File: ALG070+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG070+1 : TPTP v5.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:46:40 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 13 unt; 0 def)
% Number of atoms : 204 ( 66 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 245 ( 96 ~; 93 |; 32 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 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 : 89 ( 0 sgn 58 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> ( op1(X1,X1) != X2
| op1(X1,X2) = X1 ) ) ),
file('/tmp/tmpXyL3l8/sel_ALG070+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/tmpXyL3l8/sel_ALG070+1.p_1',co1) ).
fof(4,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/tmp/tmpXyL3l8/sel_ALG070+1.p_1',ax1) ).
fof(5,axiom,
~ ! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> ( op2(X1,X1) != X2
| op2(X1,X2) = X1 ) ) ),
file('/tmp/tmpXyL3l8/sel_ALG070+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(11,plain,
! [X1] :
( ~ sorti1(X1)
| ! [X2] :
( ~ sorti1(X2)
| op1(X1,X1) != X2
| op1(X1,X2) = X1 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(12,plain,
! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( ~ sorti1(X4)
| op1(X3,X3) != X4
| op1(X3,X4) = X3 ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
! [X3,X4] :
( ~ sorti1(X4)
| op1(X3,X3) != X4
| op1(X3,X4) = X3
| ~ sorti1(X3) ),
inference(shift_quantors,[status(thm)],[12]) ).
cnf(14,plain,
( op1(X1,X2) = X1
| ~ sorti1(X1)
| op1(X1,X1) != X2
| ~ 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(20,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
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(24,plain,
! [X1] :
( ~ sorti1(X1)
| ! [X2] :
( ~ sorti1(X2)
| sorti1(op1(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(25,plain,
! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( ~ sorti1(X4)
| sorti1(op1(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,plain,
! [X3,X4] :
( ~ sorti1(X4)
| sorti1(op1(X3,X4))
| ~ sorti1(X3) ),
inference(shift_quantors,[status(thm)],[25]) ).
cnf(27,plain,
( sorti1(op1(X1,X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
? [X1] :
( sorti2(X1)
& ? [X2] :
( sorti2(X2)
& op2(X1,X1) = X2
& op2(X1,X2) != X1 ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(29,plain,
? [X3] :
( sorti2(X3)
& ? [X4] :
( sorti2(X4)
& op2(X3,X3) = X4
& op2(X3,X4) != X3 ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,plain,
( sorti2(esk1_0)
& sorti2(esk2_0)
& op2(esk1_0,esk1_0) = esk2_0
& op2(esk1_0,esk2_0) != esk1_0 ),
inference(skolemize,[status(esa)],[29]) ).
cnf(31,plain,
op2(esk1_0,esk2_0) != esk1_0,
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,plain,
op2(esk1_0,esk1_0) = esk2_0,
inference(split_conjunct,[status(thm)],[30]) ).
cnf(33,plain,
sorti2(esk2_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(34,plain,
sorti2(esk1_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(42,negated_conjecture,
( op2(X1,h(X2)) = h(op1(j(X1),X2))
| ~ sorti1(X2)
| ~ sorti1(j(X1))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[20,22,theory(equality)]) ).
cnf(47,negated_conjecture,
( sorti1(j(op2(X1,X2)))
| ~ sorti1(j(X2))
| ~ sorti1(j(X1))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[27,21,theory(equality)]) ).
cnf(48,negated_conjecture,
( op1(j(X1),X2) = j(X1)
| j(op2(X1,X1)) != X2
| ~ sorti1(X2)
| ~ sorti1(j(X1))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[14,21,theory(equality)]) ).
cnf(52,negated_conjecture,
( sorti1(j(op2(X1,X2)))
| ~ sorti1(j(X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[47,19]) ).
cnf(53,negated_conjecture,
( sorti1(j(op2(X1,X2)))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[52,19]) ).
cnf(54,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti2(esk1_0) ),
inference(spm,[status(thm)],[53,32,theory(equality)]) ).
cnf(56,negated_conjecture,
( sorti1(j(esk2_0))
| $false ),
inference(rw,[status(thm)],[54,34,theory(equality)]) ).
cnf(57,negated_conjecture,
sorti1(j(esk2_0)),
inference(cn,[status(thm)],[56,theory(equality)]) ).
cnf(60,negated_conjecture,
( h(op1(j(X1),X2)) = op2(X1,h(X2))
| ~ sorti1(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[42,19]) ).
cnf(190,negated_conjecture,
( op1(j(X1),X2) = j(X1)
| j(op2(X1,X1)) != X2
| ~ sorti1(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[48,19]) ).
cnf(192,negated_conjecture,
( op1(j(esk1_0),X1) = j(esk1_0)
| j(esk2_0) != X1
| ~ sorti1(X1)
| ~ sorti2(esk1_0) ),
inference(spm,[status(thm)],[190,32,theory(equality)]) ).
cnf(196,negated_conjecture,
( op1(j(esk1_0),X1) = j(esk1_0)
| j(esk2_0) != X1
| ~ sorti1(X1)
| $false ),
inference(rw,[status(thm)],[192,34,theory(equality)]) ).
cnf(197,negated_conjecture,
( op1(j(esk1_0),X1) = j(esk1_0)
| j(esk2_0) != X1
| ~ sorti1(X1) ),
inference(cn,[status(thm)],[196,theory(equality)]) ).
cnf(209,negated_conjecture,
( op1(j(esk1_0),j(esk2_0)) = j(esk1_0)
| ~ sorti1(j(esk2_0)) ),
inference(er,[status(thm)],[197,theory(equality)]) ).
cnf(210,negated_conjecture,
( op1(j(esk1_0),j(esk2_0)) = j(esk1_0)
| $false ),
inference(rw,[status(thm)],[209,57,theory(equality)]) ).
cnf(211,negated_conjecture,
op1(j(esk1_0),j(esk2_0)) = j(esk1_0),
inference(cn,[status(thm)],[210,theory(equality)]) ).
cnf(215,negated_conjecture,
( h(j(esk1_0)) = op2(esk1_0,h(j(esk2_0)))
| ~ sorti1(j(esk2_0))
| ~ sorti2(esk1_0) ),
inference(spm,[status(thm)],[60,211,theory(equality)]) ).
cnf(229,negated_conjecture,
( h(j(esk1_0)) = op2(esk1_0,h(j(esk2_0)))
| $false
| ~ sorti2(esk1_0) ),
inference(rw,[status(thm)],[215,57,theory(equality)]) ).
cnf(230,negated_conjecture,
( h(j(esk1_0)) = op2(esk1_0,h(j(esk2_0)))
| $false
| $false ),
inference(rw,[status(thm)],[229,34,theory(equality)]) ).
cnf(231,negated_conjecture,
h(j(esk1_0)) = op2(esk1_0,h(j(esk2_0))),
inference(cn,[status(thm)],[230,theory(equality)]) ).
cnf(288,negated_conjecture,
( op2(esk1_0,esk2_0) = h(j(esk1_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[231,22,theory(equality)]) ).
cnf(295,negated_conjecture,
( op2(esk1_0,esk2_0) = h(j(esk1_0))
| $false ),
inference(rw,[status(thm)],[288,33,theory(equality)]) ).
cnf(296,negated_conjecture,
op2(esk1_0,esk2_0) = h(j(esk1_0)),
inference(cn,[status(thm)],[295,theory(equality)]) ).
cnf(336,plain,
h(j(esk1_0)) != esk1_0,
inference(rw,[status(thm)],[31,296,theory(equality)]) ).
cnf(385,negated_conjecture,
~ sorti2(esk1_0),
inference(spm,[status(thm)],[336,22,theory(equality)]) ).
cnf(386,negated_conjecture,
$false,
inference(rw,[status(thm)],[385,34,theory(equality)]) ).
cnf(387,negated_conjecture,
$false,
inference(cn,[status(thm)],[386,theory(equality)]) ).
cnf(388,negated_conjecture,
$false,
387,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG070+1.p
% --creating new selector for []
% -running prover on /tmp/tmpXyL3l8/sel_ALG070+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG070+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG070+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG070+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
%
%------------------------------------------------------------------------------