TSTP Solution File: SEU418+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU418+2 : TPTP v5.0.0. Released v3.4.0.
% 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 : Sun Dec 26 08:53:50 EST 2010
% Result : Theorem 8.78s
% Output : CNFRefutation 8.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 28 unt; 0 def)
% Number of atoms : 148 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 156 ( 69 ~; 61 |; 12 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 2 sgn 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(20,axiom,
! [X1,X2] : r1_tarski(k4_xboole_0(X1,X2),X1),
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t36_xboole_1) ).
fof(597,axiom,
! [X1,X2] :
( k4_xboole_0(X1,X2) = k1_xboole_0
<=> r1_tarski(X1,X2) ),
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t37_xboole_1) ).
fof(658,axiom,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> ( r1_tarski(X1,X2)
=> r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3)) ) ) ) ),
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t49_relat_1) ).
fof(966,axiom,
! [X1] : k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t2_boole) ).
fof(1076,axiom,
! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t3_boole) ).
fof(1123,axiom,
! [X1,X2,X3] : k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t49_xboole_1) ).
fof(1324,axiom,
! [X1,X2] : k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t48_xboole_1) ).
fof(1630,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X1,X2)
=> v1_relat_1(X1) ) ),
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t3_relat_1) ).
fof(1824,axiom,
! [X1,X2,X3] :
( ( r1_tarski(X1,X2)
& r1_tarski(X1,X3) )
=> r1_tarski(X1,k3_xboole_0(X2,X3)) ),
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t19_xboole_1) ).
fof(2028,conjecture,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
file('/tmp/tmpCmCfHu/sel_SEU418+2.p_1',t8_relset_2) ).
fof(2045,negated_conjecture,
~ ! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
inference(assume_negation,[status(cth)],[2028]) ).
fof(2259,plain,
! [X3,X4] : r1_tarski(k4_xboole_0(X3,X4),X3),
inference(variable_rename,[status(thm)],[20]) ).
cnf(2260,plain,
r1_tarski(k4_xboole_0(X1,X2),X1),
inference(split_conjunct,[status(thm)],[2259]) ).
fof(4115,plain,
! [X1,X2] :
( ( k4_xboole_0(X1,X2) != k1_xboole_0
| r1_tarski(X1,X2) )
& ( ~ r1_tarski(X1,X2)
| k4_xboole_0(X1,X2) = k1_xboole_0 ) ),
inference(fof_nnf,[status(thm)],[597]) ).
fof(4116,plain,
! [X3,X4] :
( ( k4_xboole_0(X3,X4) != k1_xboole_0
| r1_tarski(X3,X4) )
& ( ~ r1_tarski(X3,X4)
| k4_xboole_0(X3,X4) = k1_xboole_0 ) ),
inference(variable_rename,[status(thm)],[4115]) ).
cnf(4118,plain,
( r1_tarski(X1,X2)
| k4_xboole_0(X1,X2) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[4116]) ).
fof(4333,plain,
! [X1] :
( ~ v1_relat_1(X1)
| ! [X2] :
( ~ v1_relat_1(X2)
| ! [X3] :
( ~ v1_relat_1(X3)
| ~ r1_tarski(X1,X2)
| r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[658]) ).
fof(4334,plain,
! [X4] :
( ~ v1_relat_1(X4)
| ! [X5] :
( ~ v1_relat_1(X5)
| ! [X6] :
( ~ v1_relat_1(X6)
| ~ r1_tarski(X4,X5)
| r1_tarski(k5_relat_1(X4,X6),k5_relat_1(X5,X6)) ) ) ),
inference(variable_rename,[status(thm)],[4333]) ).
fof(4335,plain,
! [X4,X5,X6] :
( ~ v1_relat_1(X6)
| ~ r1_tarski(X4,X5)
| r1_tarski(k5_relat_1(X4,X6),k5_relat_1(X5,X6))
| ~ v1_relat_1(X5)
| ~ v1_relat_1(X4) ),
inference(shift_quantors,[status(thm)],[4334]) ).
cnf(4336,plain,
( r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X2)
| ~ r1_tarski(X1,X2)
| ~ v1_relat_1(X3) ),
inference(split_conjunct,[status(thm)],[4335]) ).
fof(5249,plain,
! [X2] : k3_xboole_0(X2,k1_xboole_0) = k1_xboole_0,
inference(variable_rename,[status(thm)],[966]) ).
cnf(5250,plain,
k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[5249]) ).
fof(5566,plain,
! [X2] : k4_xboole_0(X2,k1_xboole_0) = X2,
inference(variable_rename,[status(thm)],[1076]) ).
cnf(5567,plain,
k4_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[5566]) ).
fof(5679,plain,
! [X4,X5,X6] : k3_xboole_0(X4,k4_xboole_0(X5,X6)) = k4_xboole_0(k3_xboole_0(X4,X5),X6),
inference(variable_rename,[status(thm)],[1123]) ).
cnf(5680,plain,
k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
inference(split_conjunct,[status(thm)],[5679]) ).
fof(6232,plain,
! [X3,X4] : k4_xboole_0(X3,k4_xboole_0(X3,X4)) = k3_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[1324]) ).
cnf(6233,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[6232]) ).
fof(7113,plain,
! [X1,X2] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(X1,X2)
| v1_relat_1(X1) ),
inference(fof_nnf,[status(thm)],[1630]) ).
fof(7114,plain,
! [X3,X4] :
( ~ v1_relat_1(X4)
| ~ r1_tarski(X3,X4)
| v1_relat_1(X3) ),
inference(variable_rename,[status(thm)],[7113]) ).
cnf(7115,plain,
( v1_relat_1(X1)
| ~ r1_tarski(X1,X2)
| ~ v1_relat_1(X2) ),
inference(split_conjunct,[status(thm)],[7114]) ).
fof(7715,plain,
! [X1,X2,X3] :
( ~ r1_tarski(X1,X2)
| ~ r1_tarski(X1,X3)
| r1_tarski(X1,k3_xboole_0(X2,X3)) ),
inference(fof_nnf,[status(thm)],[1824]) ).
fof(7716,plain,
! [X4,X5,X6] :
( ~ r1_tarski(X4,X5)
| ~ r1_tarski(X4,X6)
| r1_tarski(X4,k3_xboole_0(X5,X6)) ),
inference(variable_rename,[status(thm)],[7715]) ).
cnf(7717,plain,
( r1_tarski(X1,k3_xboole_0(X2,X3))
| ~ r1_tarski(X1,X3)
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[7716]) ).
fof(8346,negated_conjecture,
? [X1] :
( v1_relat_1(X1)
& ? [X2] :
( v1_relat_1(X2)
& ? [X3] :
( v1_relat_1(X3)
& ~ r1_tarski(k5_relat_1(k3_xboole_0(X1,X2),X3),k3_xboole_0(k5_relat_1(X1,X3),k5_relat_1(X2,X3))) ) ) ),
inference(fof_nnf,[status(thm)],[2045]) ).
fof(8347,negated_conjecture,
? [X4] :
( v1_relat_1(X4)
& ? [X5] :
( v1_relat_1(X5)
& ? [X6] :
( v1_relat_1(X6)
& ~ r1_tarski(k5_relat_1(k3_xboole_0(X4,X5),X6),k3_xboole_0(k5_relat_1(X4,X6),k5_relat_1(X5,X6))) ) ) ),
inference(variable_rename,[status(thm)],[8346]) ).
fof(8348,negated_conjecture,
( v1_relat_1(esk322_0)
& v1_relat_1(esk323_0)
& v1_relat_1(esk324_0)
& ~ r1_tarski(k5_relat_1(k3_xboole_0(esk322_0,esk323_0),esk324_0),k3_xboole_0(k5_relat_1(esk322_0,esk324_0),k5_relat_1(esk323_0,esk324_0))) ),
inference(skolemize,[status(esa)],[8347]) ).
cnf(8349,negated_conjecture,
~ r1_tarski(k5_relat_1(k3_xboole_0(esk322_0,esk323_0),esk324_0),k3_xboole_0(k5_relat_1(esk322_0,esk324_0),k5_relat_1(esk323_0,esk324_0))),
inference(split_conjunct,[status(thm)],[8348]) ).
cnf(8350,negated_conjecture,
v1_relat_1(esk324_0),
inference(split_conjunct,[status(thm)],[8348]) ).
cnf(8351,negated_conjecture,
v1_relat_1(esk323_0),
inference(split_conjunct,[status(thm)],[8348]) ).
cnf(8352,negated_conjecture,
v1_relat_1(esk322_0),
inference(split_conjunct,[status(thm)],[8348]) ).
cnf(8667,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k1_xboole_0)) = k1_xboole_0,
inference(rw,[status(thm)],[5250,6233,theory(equality)]),
[unfolding] ).
cnf(8678,plain,
k4_xboole_0(k4_xboole_0(X1,k4_xboole_0(X1,X2)),X3) = k4_xboole_0(X1,k4_xboole_0(X1,k4_xboole_0(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5680,6233,theory(equality)]),6233,theory(equality)]),
[unfolding] ).
cnf(8754,plain,
( r1_tarski(X1,k4_xboole_0(X2,k4_xboole_0(X2,X3)))
| ~ r1_tarski(X1,X3)
| ~ r1_tarski(X1,X2) ),
inference(rw,[status(thm)],[7717,6233,theory(equality)]),
[unfolding] ).
cnf(8799,negated_conjecture,
~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k4_xboole_0(k5_relat_1(esk322_0,esk324_0),k4_xboole_0(k5_relat_1(esk322_0,esk324_0),k5_relat_1(esk323_0,esk324_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8349,6233,theory(equality)]),6233,theory(equality)]),
[unfolding] ).
cnf(9201,plain,
k4_xboole_0(X1,X1) = k1_xboole_0,
inference(rw,[status(thm)],[8667,5567,theory(equality)]) ).
cnf(12472,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk323_0,esk324_0))
| ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0)) ),
inference(spm,[status(thm)],[8799,8754,theory(equality)]) ).
cnf(14669,plain,
( r1_tarski(k5_relat_1(X1,X3),k5_relat_1(X2,X3))
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X2)
| ~ r1_tarski(X1,X2) ),
inference(csr,[status(thm)],[4336,7115]) ).
cnf(73506,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0))
| ~ v1_relat_1(esk324_0)
| ~ v1_relat_1(esk323_0)
| ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) ),
inference(spm,[status(thm)],[12472,14669,theory(equality)]) ).
cnf(73513,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0))
| $false
| ~ v1_relat_1(esk323_0)
| ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) ),
inference(rw,[status(thm)],[73506,8350,theory(equality)]) ).
cnf(73514,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0))
| $false
| $false
| ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) ),
inference(rw,[status(thm)],[73513,8351,theory(equality)]) ).
cnf(73515,negated_conjecture,
( ~ r1_tarski(k5_relat_1(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk324_0),k5_relat_1(esk322_0,esk324_0))
| ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) ),
inference(cn,[status(thm)],[73514,theory(equality)]) ).
cnf(73522,negated_conjecture,
( ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0)
| ~ v1_relat_1(esk324_0)
| ~ v1_relat_1(esk322_0)
| ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk322_0) ),
inference(spm,[status(thm)],[73515,14669,theory(equality)]) ).
cnf(73529,negated_conjecture,
( ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0)
| $false
| ~ v1_relat_1(esk322_0)
| ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk322_0) ),
inference(rw,[status(thm)],[73522,8350,theory(equality)]) ).
cnf(73530,negated_conjecture,
( ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0)
| $false
| $false
| ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk322_0) ),
inference(rw,[status(thm)],[73529,8352,theory(equality)]) ).
cnf(73531,negated_conjecture,
( ~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[73530,2260,theory(equality)]) ).
cnf(73532,negated_conjecture,
~ r1_tarski(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0),
inference(cn,[status(thm)],[73531,theory(equality)]) ).
cnf(73538,negated_conjecture,
k4_xboole_0(k4_xboole_0(esk322_0,k4_xboole_0(esk322_0,esk323_0)),esk323_0) != k1_xboole_0,
inference(spm,[status(thm)],[73532,4118,theory(equality)]) ).
cnf(73542,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[73538,8678,theory(equality)]),9201,theory(equality)]),5567,theory(equality)]),9201,theory(equality)]) ).
cnf(73543,negated_conjecture,
$false,
inference(cn,[status(thm)],[73542,theory(equality)]) ).
cnf(73544,negated_conjecture,
$false,
73543,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU418+2.p
% --creating new selector for [SET007+3.ax, SET007+0.ax, SET007+1.ax, SET007+2.ax, SET007+4.ax, SET007+6.ax, SET007+7.ax, SET007+8.ax, SET007+9.ax, SET007+10.ax, SET007+11.ax, SET007+13.ax, SET007+14.ax, SET007+16.ax, SET007+17.ax, SET007+18.ax, SET007+20.ax, SET007+22.ax, SET007+24.ax, SET007+26.ax, SET007+31.ax, SET007+35.ax, SET007+40.ax, SET007+48.ax, SET007+54.ax, SET007+55.ax, SET007+59.ax, SET007+60.ax, SET007+61.ax, SET007+64.ax, SET007+80.ax, SET007+117.ax, SET007+126.ax, SET007+188.ax, SET007+200.ax, SET007+210.ax, SET007+212.ax, SET007+213.ax, SET007+225.ax, SET007+363.ax, SET007+393.ax, SET007+441.ax]
% -running prover on /tmp/tmpCmCfHu/sel_SEU418+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU418+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU418+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU418+2.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
%
%------------------------------------------------------------------------------