TSTP Solution File: SEU406+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU406+1 : TPTP v5.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 08:27:56 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 192 ( 22 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 248 ( 101 ~; 87 |; 58 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 64 ( 0 sgn 40 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3,X4] :
~ ( r2_hidden(X1,k2_xboole_0(X3,X4))
& r2_hidden(X2,k2_xboole_0(X3,X4))
& ~ ( r2_hidden(X1,k4_xboole_0(X3,X4))
& r2_hidden(X2,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X1,X4)
& r2_hidden(X2,X4) )
& ~ ( r2_hidden(X1,k4_xboole_0(X3,X4))
& r2_hidden(X2,X4) )
& ~ ( r2_hidden(X1,X4)
& r2_hidden(X2,k4_xboole_0(X3,X4)) ) ),
file('/tmp/tmpurSWI6/sel_SEU406+1.p_1',t1_latsum_1) ).
fof(3,axiom,
! [X1,X2] : k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
file('/tmp/tmpurSWI6/sel_SEU406+1.p_1',t39_xboole_1) ).
fof(10,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/tmp/tmpurSWI6/sel_SEU406+1.p_1',commutativity_k2_xboole_0) ).
fof(13,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
| r2_hidden(X4,X2) ) ) ),
file('/tmp/tmpurSWI6/sel_SEU406+1.p_1',d2_xboole_0) ).
fof(25,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( r2_hidden(X1,k2_xboole_0(X3,X4))
& r2_hidden(X2,k2_xboole_0(X3,X4))
& ~ ( r2_hidden(X1,k4_xboole_0(X3,X4))
& r2_hidden(X2,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X1,X4)
& r2_hidden(X2,X4) )
& ~ ( r2_hidden(X1,k4_xboole_0(X3,X4))
& r2_hidden(X2,X4) )
& ~ ( r2_hidden(X1,X4)
& r2_hidden(X2,k4_xboole_0(X3,X4)) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(30,negated_conjecture,
? [X1,X2,X3,X4] :
( r2_hidden(X1,k2_xboole_0(X3,X4))
& r2_hidden(X2,k2_xboole_0(X3,X4))
& ( ~ r2_hidden(X1,k4_xboole_0(X3,X4))
| ~ r2_hidden(X2,k4_xboole_0(X3,X4)) )
& ( ~ r2_hidden(X1,X4)
| ~ r2_hidden(X2,X4) )
& ( ~ r2_hidden(X1,k4_xboole_0(X3,X4))
| ~ r2_hidden(X2,X4) )
& ( ~ r2_hidden(X1,X4)
| ~ r2_hidden(X2,k4_xboole_0(X3,X4)) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(31,negated_conjecture,
? [X5,X6,X7,X8] :
( r2_hidden(X5,k2_xboole_0(X7,X8))
& r2_hidden(X6,k2_xboole_0(X7,X8))
& ( ~ r2_hidden(X5,k4_xboole_0(X7,X8))
| ~ r2_hidden(X6,k4_xboole_0(X7,X8)) )
& ( ~ r2_hidden(X5,X8)
| ~ r2_hidden(X6,X8) )
& ( ~ r2_hidden(X5,k4_xboole_0(X7,X8))
| ~ r2_hidden(X6,X8) )
& ( ~ r2_hidden(X5,X8)
| ~ r2_hidden(X6,k4_xboole_0(X7,X8)) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,negated_conjecture,
( r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0))
& r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0))
& ( ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)) )
& ( ~ r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,esk4_0) )
& ( ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk2_0,esk4_0) )
& ( ~ r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)) ) ),
inference(skolemize,[status(esa)],[31]) ).
cnf(33,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(35,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(36,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(37,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(38,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[32]) ).
fof(41,plain,
! [X3,X4] : k2_xboole_0(X3,k4_xboole_0(X4,X3)) = k2_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[3]) ).
cnf(42,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[41]) ).
fof(59,plain,
! [X3,X4] : k2_xboole_0(X3,X4) = k2_xboole_0(X4,X3),
inference(variable_rename,[status(thm)],[10]) ).
cnf(60,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[59]) ).
fof(65,plain,
! [X1,X2,X3] :
( ( X3 != k2_xboole_0(X1,X2)
| ! [X4] :
( ( ~ r2_hidden(X4,X3)
| r2_hidden(X4,X1)
| r2_hidden(X4,X2) )
& ( ( ~ r2_hidden(X4,X1)
& ~ r2_hidden(X4,X2) )
| r2_hidden(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ r2_hidden(X4,X3)
| ( ~ r2_hidden(X4,X1)
& ~ r2_hidden(X4,X2) ) )
& ( r2_hidden(X4,X3)
| r2_hidden(X4,X1)
| r2_hidden(X4,X2) ) )
| X3 = k2_xboole_0(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(66,plain,
! [X5,X6,X7] :
( ( X7 != k2_xboole_0(X5,X6)
| ! [X8] :
( ( ~ r2_hidden(X8,X7)
| r2_hidden(X8,X5)
| r2_hidden(X8,X6) )
& ( ( ~ r2_hidden(X8,X5)
& ~ r2_hidden(X8,X6) )
| r2_hidden(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ r2_hidden(X9,X7)
| ( ~ r2_hidden(X9,X5)
& ~ r2_hidden(X9,X6) ) )
& ( r2_hidden(X9,X7)
| r2_hidden(X9,X5)
| r2_hidden(X9,X6) ) )
| X7 = k2_xboole_0(X5,X6) ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X5,X6,X7] :
( ( X7 != k2_xboole_0(X5,X6)
| ! [X8] :
( ( ~ r2_hidden(X8,X7)
| r2_hidden(X8,X5)
| r2_hidden(X8,X6) )
& ( ( ~ r2_hidden(X8,X5)
& ~ r2_hidden(X8,X6) )
| r2_hidden(X8,X7) ) ) )
& ( ( ( ~ r2_hidden(esk6_3(X5,X6,X7),X7)
| ( ~ r2_hidden(esk6_3(X5,X6,X7),X5)
& ~ r2_hidden(esk6_3(X5,X6,X7),X6) ) )
& ( r2_hidden(esk6_3(X5,X6,X7),X7)
| r2_hidden(esk6_3(X5,X6,X7),X5)
| r2_hidden(esk6_3(X5,X6,X7),X6) ) )
| X7 = k2_xboole_0(X5,X6) ) ),
inference(skolemize,[status(esa)],[66]) ).
fof(68,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ r2_hidden(X8,X7)
| r2_hidden(X8,X5)
| r2_hidden(X8,X6) )
& ( ( ~ r2_hidden(X8,X5)
& ~ r2_hidden(X8,X6) )
| r2_hidden(X8,X7) ) )
| X7 != k2_xboole_0(X5,X6) )
& ( ( ( ~ r2_hidden(esk6_3(X5,X6,X7),X7)
| ( ~ r2_hidden(esk6_3(X5,X6,X7),X5)
& ~ r2_hidden(esk6_3(X5,X6,X7),X6) ) )
& ( r2_hidden(esk6_3(X5,X6,X7),X7)
| r2_hidden(esk6_3(X5,X6,X7),X5)
| r2_hidden(esk6_3(X5,X6,X7),X6) ) )
| X7 = k2_xboole_0(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[67]) ).
fof(69,plain,
! [X5,X6,X7,X8] :
( ( ~ r2_hidden(X8,X7)
| r2_hidden(X8,X5)
| r2_hidden(X8,X6)
| X7 != k2_xboole_0(X5,X6) )
& ( ~ r2_hidden(X8,X5)
| r2_hidden(X8,X7)
| X7 != k2_xboole_0(X5,X6) )
& ( ~ r2_hidden(X8,X6)
| r2_hidden(X8,X7)
| X7 != k2_xboole_0(X5,X6) )
& ( ~ r2_hidden(esk6_3(X5,X6,X7),X5)
| ~ r2_hidden(esk6_3(X5,X6,X7),X7)
| X7 = k2_xboole_0(X5,X6) )
& ( ~ r2_hidden(esk6_3(X5,X6,X7),X6)
| ~ r2_hidden(esk6_3(X5,X6,X7),X7)
| X7 = k2_xboole_0(X5,X6) )
& ( r2_hidden(esk6_3(X5,X6,X7),X7)
| r2_hidden(esk6_3(X5,X6,X7),X5)
| r2_hidden(esk6_3(X5,X6,X7),X6)
| X7 = k2_xboole_0(X5,X6) ) ),
inference(distribute,[status(thm)],[68]) ).
cnf(75,plain,
( r2_hidden(X4,X3)
| r2_hidden(X4,X2)
| X1 != k2_xboole_0(X2,X3)
| ~ r2_hidden(X4,X1) ),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(107,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[37,60,theory(equality)]) ).
cnf(108,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[38,60,theory(equality)]) ).
cnf(142,plain,
( r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X2,X3)) ),
inference(er,[status(thm)],[75,theory(equality)]) ).
cnf(384,plain,
( r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
inference(spm,[status(thm)],[142,42,theory(equality)]) ).
cnf(1054,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[33,384,theory(equality)]) ).
cnf(1055,negated_conjecture,
( r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[34,384,theory(equality)]) ).
cnf(1056,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[36,384,theory(equality)]) ).
cnf(1073,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[1054,107,theory(equality)]) ).
cnf(1074,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(cn,[status(thm)],[1073,theory(equality)]) ).
cnf(1075,negated_conjecture,
( r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[1055,108,theory(equality)]) ).
cnf(1076,negated_conjecture,
( r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk2_0,esk4_0) ),
inference(cn,[status(thm)],[1075,theory(equality)]) ).
cnf(1077,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0))
| $false ),
inference(rw,[status(thm)],[1056,107,theory(equality)]) ).
cnf(1078,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(cn,[status(thm)],[1077,theory(equality)]) ).
cnf(1079,negated_conjecture,
~ r2_hidden(esk1_0,esk4_0),
inference(csr,[status(thm)],[1074,35]) ).
cnf(1086,negated_conjecture,
~ r2_hidden(esk2_0,esk4_0),
inference(sr,[status(thm)],[1076,1079,theory(equality)]) ).
cnf(1092,negated_conjecture,
~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)),
inference(sr,[status(thm)],[1078,1086,theory(equality)]) ).
cnf(1097,negated_conjecture,
( r2_hidden(esk1_0,esk4_0)
| ~ r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[1092,384,theory(equality)]) ).
cnf(1102,negated_conjecture,
( r2_hidden(esk1_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[1097,108,theory(equality)]) ).
cnf(1103,negated_conjecture,
r2_hidden(esk1_0,esk4_0),
inference(cn,[status(thm)],[1102,theory(equality)]) ).
cnf(1104,negated_conjecture,
$false,
inference(sr,[status(thm)],[1103,1079,theory(equality)]) ).
cnf(1105,negated_conjecture,
$false,
1104,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU406+1.p
% --creating new selector for []
% -running prover on /tmp/tmpurSWI6/sel_SEU406+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU406+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU406+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU406+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
%
%------------------------------------------------------------------------------