TSTP Solution File: SEU420+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU420+2 : TPTP v5.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 08:57:03 EST 2010
% Result : Theorem 8.99s
% Output : CNFRefutation 8.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 35 unt; 0 def)
% Number of atoms : 131 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 122 ( 57 ~; 45 |; 9 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 2 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(20,axiom,
! [X1,X2] : r1_tarski(k4_xboole_0(X1,X2),X1),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t36_xboole_1) ).
fof(599,axiom,
! [X1,X2] :
( k4_xboole_0(X1,X2) = k1_xboole_0
<=> r1_tarski(X1,X2) ),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t37_xboole_1) ).
fof(728,axiom,
! [X1] : k6_partfun1(X1) = k6_relat_1(X1),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',redefinition_k6_partfun1) ).
fof(968,axiom,
! [X1] : k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t2_boole) ).
fof(1078,axiom,
! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t3_boole) ).
fof(1126,axiom,
! [X1,X2,X3] : k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t49_xboole_1) ).
fof(1327,axiom,
! [X1,X2] : k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t48_xboole_1) ).
fof(1622,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> ( r1_tarski(X2,X3)
=> r1_tarski(k9_relat_1(X2,X1),k9_relat_1(X3,X1)) ) ) ),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t157_relat_1) ).
fof(1633,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X1,X2)
=> v1_relat_1(X1) ) ),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t3_relat_1) ).
fof(1783,axiom,
! [X1] : k3_pua2mss1(X1) = k8_eqrel_1(X1,k6_partfun1(X1)),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',d2_pua2mss1) ).
fof(1828,axiom,
! [X1,X2,X3] :
( ( r1_tarski(X1,X2)
& r1_tarski(X1,X3) )
=> r1_tarski(X1,k3_xboole_0(X2,X3)) ),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t19_xboole_1) ).
fof(2028,conjecture,
! [X1,X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> r1_tarski(k9_relat_1(k3_xboole_0(X2,X3),k3_pua2mss1(X1)),k3_xboole_0(k9_relat_1(X2,k3_pua2mss1(X1)),k9_relat_1(X3,k3_pua2mss1(X1)))) ) ),
file('/tmp/tmpwVZDgb/sel_SEU420+2.p_1',t13_relset_2) ).
fof(2055,negated_conjecture,
~ ! [X1,X2] :
( v1_relat_1(X2)
=> ! [X3] :
( v1_relat_1(X3)
=> r1_tarski(k9_relat_1(k3_xboole_0(X2,X3),k3_pua2mss1(X1)),k3_xboole_0(k9_relat_1(X2,k3_pua2mss1(X1)),k9_relat_1(X3,k3_pua2mss1(X1)))) ) ),
inference(assume_negation,[status(cth)],[2028]) ).
fof(2270,plain,
! [X3,X4] : r1_tarski(k4_xboole_0(X3,X4),X3),
inference(variable_rename,[status(thm)],[20]) ).
cnf(2271,plain,
r1_tarski(k4_xboole_0(X1,X2),X1),
inference(split_conjunct,[status(thm)],[2270]) ).
fof(4147,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)],[599]) ).
fof(4148,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)],[4147]) ).
cnf(4150,plain,
( r1_tarski(X1,X2)
| k4_xboole_0(X1,X2) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[4148]) ).
fof(4565,plain,
! [X2] : k6_partfun1(X2) = k6_relat_1(X2),
inference(variable_rename,[status(thm)],[728]) ).
cnf(4566,plain,
k6_partfun1(X1) = k6_relat_1(X1),
inference(split_conjunct,[status(thm)],[4565]) ).
fof(5281,plain,
! [X2] : k3_xboole_0(X2,k1_xboole_0) = k1_xboole_0,
inference(variable_rename,[status(thm)],[968]) ).
cnf(5282,plain,
k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[5281]) ).
fof(5598,plain,
! [X2] : k4_xboole_0(X2,k1_xboole_0) = X2,
inference(variable_rename,[status(thm)],[1078]) ).
cnf(5599,plain,
k4_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[5598]) ).
fof(5706,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)],[1126]) ).
cnf(5707,plain,
k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
inference(split_conjunct,[status(thm)],[5706]) ).
fof(6259,plain,
! [X3,X4] : k4_xboole_0(X3,k4_xboole_0(X3,X4)) = k3_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[1327]) ).
cnf(6260,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[6259]) ).
fof(7115,plain,
! [X1,X2] :
( ~ v1_relat_1(X2)
| ! [X3] :
( ~ v1_relat_1(X3)
| ~ r1_tarski(X2,X3)
| r1_tarski(k9_relat_1(X2,X1),k9_relat_1(X3,X1)) ) ),
inference(fof_nnf,[status(thm)],[1622]) ).
fof(7116,plain,
! [X4,X5] :
( ~ v1_relat_1(X5)
| ! [X6] :
( ~ v1_relat_1(X6)
| ~ r1_tarski(X5,X6)
| r1_tarski(k9_relat_1(X5,X4),k9_relat_1(X6,X4)) ) ),
inference(variable_rename,[status(thm)],[7115]) ).
fof(7117,plain,
! [X4,X5,X6] :
( ~ v1_relat_1(X6)
| ~ r1_tarski(X5,X6)
| r1_tarski(k9_relat_1(X5,X4),k9_relat_1(X6,X4))
| ~ v1_relat_1(X5) ),
inference(shift_quantors,[status(thm)],[7116]) ).
cnf(7118,plain,
( r1_tarski(k9_relat_1(X1,X2),k9_relat_1(X3,X2))
| ~ v1_relat_1(X1)
| ~ r1_tarski(X1,X3)
| ~ v1_relat_1(X3) ),
inference(split_conjunct,[status(thm)],[7117]) ).
fof(7140,plain,
! [X1,X2] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(X1,X2)
| v1_relat_1(X1) ),
inference(fof_nnf,[status(thm)],[1633]) ).
fof(7141,plain,
! [X3,X4] :
( ~ v1_relat_1(X4)
| ~ r1_tarski(X3,X4)
| v1_relat_1(X3) ),
inference(variable_rename,[status(thm)],[7140]) ).
cnf(7142,plain,
( v1_relat_1(X1)
| ~ r1_tarski(X1,X2)
| ~ v1_relat_1(X2) ),
inference(split_conjunct,[status(thm)],[7141]) ).
fof(7594,plain,
! [X2] : k3_pua2mss1(X2) = k8_eqrel_1(X2,k6_partfun1(X2)),
inference(variable_rename,[status(thm)],[1783]) ).
cnf(7595,plain,
k3_pua2mss1(X1) = k8_eqrel_1(X1,k6_partfun1(X1)),
inference(split_conjunct,[status(thm)],[7594]) ).
fof(7745,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)],[1828]) ).
fof(7746,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)],[7745]) ).
cnf(7747,plain,
( r1_tarski(X1,k3_xboole_0(X2,X3))
| ~ r1_tarski(X1,X3)
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[7746]) ).
fof(8366,negated_conjecture,
? [X1,X2] :
( v1_relat_1(X2)
& ? [X3] :
( v1_relat_1(X3)
& ~ r1_tarski(k9_relat_1(k3_xboole_0(X2,X3),k3_pua2mss1(X1)),k3_xboole_0(k9_relat_1(X2,k3_pua2mss1(X1)),k9_relat_1(X3,k3_pua2mss1(X1)))) ) ),
inference(fof_nnf,[status(thm)],[2055]) ).
fof(8367,negated_conjecture,
? [X4,X5] :
( v1_relat_1(X5)
& ? [X6] :
( v1_relat_1(X6)
& ~ r1_tarski(k9_relat_1(k3_xboole_0(X5,X6),k3_pua2mss1(X4)),k3_xboole_0(k9_relat_1(X5,k3_pua2mss1(X4)),k9_relat_1(X6,k3_pua2mss1(X4)))) ) ),
inference(variable_rename,[status(thm)],[8366]) ).
fof(8368,negated_conjecture,
( v1_relat_1(esk324_0)
& v1_relat_1(esk325_0)
& ~ r1_tarski(k9_relat_1(k3_xboole_0(esk324_0,esk325_0),k3_pua2mss1(esk323_0)),k3_xboole_0(k9_relat_1(esk324_0,k3_pua2mss1(esk323_0)),k9_relat_1(esk325_0,k3_pua2mss1(esk323_0)))) ),
inference(skolemize,[status(esa)],[8367]) ).
cnf(8369,negated_conjecture,
~ r1_tarski(k9_relat_1(k3_xboole_0(esk324_0,esk325_0),k3_pua2mss1(esk323_0)),k3_xboole_0(k9_relat_1(esk324_0,k3_pua2mss1(esk323_0)),k9_relat_1(esk325_0,k3_pua2mss1(esk323_0)))),
inference(split_conjunct,[status(thm)],[8368]) ).
cnf(8370,negated_conjecture,
v1_relat_1(esk325_0),
inference(split_conjunct,[status(thm)],[8368]) ).
cnf(8371,negated_conjecture,
v1_relat_1(esk324_0),
inference(split_conjunct,[status(thm)],[8368]) ).
cnf(8516,plain,
k8_eqrel_1(X1,k6_relat_1(X1)) = k3_pua2mss1(X1),
inference(rw,[status(thm)],[7595,4566,theory(equality)]),
[unfolding] ).
cnf(8551,negated_conjecture,
~ r1_tarski(k9_relat_1(k3_xboole_0(esk324_0,esk325_0),k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k3_xboole_0(k9_relat_1(esk324_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k9_relat_1(esk325_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[8369,8516,theory(equality)]),8516,theory(equality)]),8516,theory(equality)]),
[unfolding] ).
cnf(8723,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k1_xboole_0)) = k1_xboole_0,
inference(rw,[status(thm)],[5282,6260,theory(equality)]),
[unfolding] ).
cnf(8734,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)],[5707,6260,theory(equality)]),6260,theory(equality)]),
[unfolding] ).
cnf(8810,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)],[7747,6260,theory(equality)]),
[unfolding] ).
cnf(8857,negated_conjecture,
~ r1_tarski(k9_relat_1(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k4_xboole_0(k9_relat_1(esk324_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k4_xboole_0(k9_relat_1(esk324_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k9_relat_1(esk325_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8551,6260,theory(equality)]),6260,theory(equality)]),
[unfolding] ).
cnf(9273,plain,
k4_xboole_0(X1,X1) = k1_xboole_0,
inference(rw,[status(thm)],[8723,5599,theory(equality)]) ).
cnf(12832,negated_conjecture,
( ~ r1_tarski(k9_relat_1(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k9_relat_1(esk325_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))))
| ~ r1_tarski(k9_relat_1(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k9_relat_1(esk324_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0)))) ),
inference(spm,[status(thm)],[8857,8810,theory(equality)]) ).
cnf(13043,plain,
( r1_tarski(k9_relat_1(X1,X2),k9_relat_1(X3,X2))
| ~ v1_relat_1(X3)
| ~ r1_tarski(X1,X3) ),
inference(csr,[status(thm)],[7118,7142]) ).
cnf(74791,negated_conjecture,
( ~ r1_tarski(k9_relat_1(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k9_relat_1(esk324_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))))
| ~ v1_relat_1(esk325_0)
| ~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk325_0) ),
inference(spm,[status(thm)],[12832,13043,theory(equality)]) ).
cnf(74800,negated_conjecture,
( ~ r1_tarski(k9_relat_1(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k9_relat_1(esk324_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))))
| $false
| ~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk325_0) ),
inference(rw,[status(thm)],[74791,8370,theory(equality)]) ).
cnf(74801,negated_conjecture,
( ~ r1_tarski(k9_relat_1(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))),k9_relat_1(esk324_0,k8_eqrel_1(esk323_0,k6_relat_1(esk323_0))))
| ~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk325_0) ),
inference(cn,[status(thm)],[74800,theory(equality)]) ).
cnf(74811,negated_conjecture,
( ~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk325_0)
| ~ v1_relat_1(esk324_0)
| ~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk324_0) ),
inference(spm,[status(thm)],[74801,13043,theory(equality)]) ).
cnf(74820,negated_conjecture,
( ~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk325_0)
| $false
| ~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk324_0) ),
inference(rw,[status(thm)],[74811,8371,theory(equality)]) ).
cnf(74821,negated_conjecture,
( ~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk325_0)
| $false
| $false ),
inference(rw,[status(thm)],[74820,2271,theory(equality)]) ).
cnf(74822,negated_conjecture,
~ r1_tarski(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk325_0),
inference(cn,[status(thm)],[74821,theory(equality)]) ).
cnf(74827,negated_conjecture,
k4_xboole_0(k4_xboole_0(esk324_0,k4_xboole_0(esk324_0,esk325_0)),esk325_0) != k1_xboole_0,
inference(spm,[status(thm)],[74822,4150,theory(equality)]) ).
cnf(74831,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[74827,8734,theory(equality)]),9273,theory(equality)]),5599,theory(equality)]),9273,theory(equality)]) ).
cnf(74832,negated_conjecture,
$false,
inference(cn,[status(thm)],[74831,theory(equality)]) ).
cnf(74833,negated_conjecture,
$false,
74832,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU420+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/tmpwVZDgb/sel_SEU420+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU420+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU420+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU420+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
%
%------------------------------------------------------------------------------