TSTP Solution File: SEU103+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU103+1 : TPTP v5.0.0. Released v3.2.0.
% 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 04:36:18 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 204 ( 13 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 241 ( 91 ~; 94 |; 42 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',redefinition_k2_finsub_1) ).
fof(10,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',d6_xboole_0) ).
fof(16,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',redefinition_k1_finsub_1) ).
fof(36,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',dt_k2_finsub_1) ).
fof(37,conjecture,
! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(symmetric_difference(X1,X2),X3) ) ),
file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',t14_finsub_1) ).
fof(42,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_union2(X1,X2,X3),X1) ),
file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',dt_k1_finsub_1) ).
fof(47,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(symmetric_difference(X1,X2),X3) ) ),
inference(assume_negation,[status(cth)],[37]) ).
fof(49,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(54,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).
fof(61,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[36,theory(equality)]) ).
fof(62,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(symmetric_difference(X1,X2),X3) ) ),
inference(fof_simplification,[status(thm)],[47,theory(equality)]) ).
fof(64,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_union2(X1,X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[42,theory(equality)]) ).
fof(77,plain,
! [X1,X2,X3] :
( empty(X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1)
| prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_nnf,[status(thm)],[49]) ).
fof(78,plain,
! [X4,X5,X6] :
( empty(X4)
| ~ preboolean(X4)
| ~ element(X5,X4)
| ~ element(X6,X4)
| prebool_difference(X4,X5,X6) = set_difference(X5,X6) ),
inference(variable_rename,[status(thm)],[77]) ).
cnf(79,plain,
( prebool_difference(X1,X2,X3) = set_difference(X2,X3)
| empty(X1)
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(94,plain,
! [X3,X4] : symmetric_difference(X3,X4) = set_union2(set_difference(X3,X4),set_difference(X4,X3)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(95,plain,
symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
inference(split_conjunct,[status(thm)],[94]) ).
fof(126,plain,
! [X1,X2,X3] :
( empty(X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1)
| prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
inference(fof_nnf,[status(thm)],[54]) ).
fof(127,plain,
! [X4,X5,X6] :
( empty(X4)
| ~ preboolean(X4)
| ~ element(X5,X4)
| ~ element(X6,X4)
| prebool_union2(X4,X5,X6) = set_union2(X5,X6) ),
inference(variable_rename,[status(thm)],[126]) ).
cnf(128,plain,
( prebool_union2(X1,X2,X3) = set_union2(X2,X3)
| empty(X1)
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[127]) ).
fof(184,plain,
! [X1,X2,X3] :
( empty(X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1)
| element(prebool_difference(X1,X2,X3),X1) ),
inference(fof_nnf,[status(thm)],[61]) ).
fof(185,plain,
! [X4,X5,X6] :
( empty(X4)
| ~ preboolean(X4)
| ~ element(X5,X4)
| ~ element(X6,X4)
| element(prebool_difference(X4,X5,X6),X4) ),
inference(variable_rename,[status(thm)],[184]) ).
cnf(186,plain,
( element(prebool_difference(X1,X2,X3),X1)
| empty(X1)
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[185]) ).
fof(187,negated_conjecture,
? [X1,X2,X3] :
( ~ empty(X3)
& preboolean(X3)
& element(X1,X3)
& element(X2,X3)
& ~ element(symmetric_difference(X1,X2),X3) ),
inference(fof_nnf,[status(thm)],[62]) ).
fof(188,negated_conjecture,
? [X4,X5,X6] :
( ~ empty(X6)
& preboolean(X6)
& element(X4,X6)
& element(X5,X6)
& ~ element(symmetric_difference(X4,X5),X6) ),
inference(variable_rename,[status(thm)],[187]) ).
fof(189,negated_conjecture,
( ~ empty(esk9_0)
& preboolean(esk9_0)
& element(esk7_0,esk9_0)
& element(esk8_0,esk9_0)
& ~ element(symmetric_difference(esk7_0,esk8_0),esk9_0) ),
inference(skolemize,[status(esa)],[188]) ).
cnf(190,negated_conjecture,
~ element(symmetric_difference(esk7_0,esk8_0),esk9_0),
inference(split_conjunct,[status(thm)],[189]) ).
cnf(191,negated_conjecture,
element(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[189]) ).
cnf(192,negated_conjecture,
element(esk7_0,esk9_0),
inference(split_conjunct,[status(thm)],[189]) ).
cnf(193,negated_conjecture,
preboolean(esk9_0),
inference(split_conjunct,[status(thm)],[189]) ).
cnf(194,negated_conjecture,
~ empty(esk9_0),
inference(split_conjunct,[status(thm)],[189]) ).
fof(210,plain,
! [X1,X2,X3] :
( empty(X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1)
| element(prebool_union2(X1,X2,X3),X1) ),
inference(fof_nnf,[status(thm)],[64]) ).
fof(211,plain,
! [X4,X5,X6] :
( empty(X4)
| ~ preboolean(X4)
| ~ element(X5,X4)
| ~ element(X6,X4)
| element(prebool_union2(X4,X5,X6),X4) ),
inference(variable_rename,[status(thm)],[210]) ).
cnf(212,plain,
( element(prebool_union2(X1,X2,X3),X1)
| empty(X1)
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[211]) ).
cnf(229,negated_conjecture,
~ element(set_union2(set_difference(esk7_0,esk8_0),set_difference(esk8_0,esk7_0)),esk9_0),
inference(rw,[status(thm)],[190,95,theory(equality)]),
[unfolding] ).
cnf(332,plain,
( element(set_difference(X2,X3),X1)
| empty(X1)
| ~ preboolean(X1)
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[186,79,theory(equality)]) ).
cnf(333,plain,
( element(set_union2(X2,X3),X1)
| empty(X1)
| ~ preboolean(X1)
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[212,128,theory(equality)]) ).
cnf(461,negated_conjecture,
( empty(esk9_0)
| ~ preboolean(esk9_0)
| ~ element(set_difference(esk8_0,esk7_0),esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
inference(spm,[status(thm)],[229,333,theory(equality)]) ).
cnf(468,negated_conjecture,
( empty(esk9_0)
| $false
| ~ element(set_difference(esk8_0,esk7_0),esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
inference(rw,[status(thm)],[461,193,theory(equality)]) ).
cnf(469,negated_conjecture,
( empty(esk9_0)
| ~ element(set_difference(esk8_0,esk7_0),esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
inference(cn,[status(thm)],[468,theory(equality)]) ).
cnf(470,negated_conjecture,
( ~ element(set_difference(esk8_0,esk7_0),esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
inference(sr,[status(thm)],[469,194,theory(equality)]) ).
cnf(475,negated_conjecture,
( empty(esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0)
| ~ preboolean(esk9_0)
| ~ element(esk7_0,esk9_0)
| ~ element(esk8_0,esk9_0) ),
inference(spm,[status(thm)],[470,332,theory(equality)]) ).
cnf(476,negated_conjecture,
( empty(esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0)
| $false
| ~ element(esk7_0,esk9_0)
| ~ element(esk8_0,esk9_0) ),
inference(rw,[status(thm)],[475,193,theory(equality)]) ).
cnf(477,negated_conjecture,
( empty(esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0)
| $false
| $false
| ~ element(esk8_0,esk9_0) ),
inference(rw,[status(thm)],[476,192,theory(equality)]) ).
cnf(478,negated_conjecture,
( empty(esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[477,191,theory(equality)]) ).
cnf(479,negated_conjecture,
( empty(esk9_0)
| ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
inference(cn,[status(thm)],[478,theory(equality)]) ).
cnf(480,negated_conjecture,
~ element(set_difference(esk7_0,esk8_0),esk9_0),
inference(sr,[status(thm)],[479,194,theory(equality)]) ).
cnf(481,negated_conjecture,
( empty(esk9_0)
| ~ preboolean(esk9_0)
| ~ element(esk8_0,esk9_0)
| ~ element(esk7_0,esk9_0) ),
inference(spm,[status(thm)],[480,332,theory(equality)]) ).
cnf(482,negated_conjecture,
( empty(esk9_0)
| $false
| ~ element(esk8_0,esk9_0)
| ~ element(esk7_0,esk9_0) ),
inference(rw,[status(thm)],[481,193,theory(equality)]) ).
cnf(483,negated_conjecture,
( empty(esk9_0)
| $false
| $false
| ~ element(esk7_0,esk9_0) ),
inference(rw,[status(thm)],[482,191,theory(equality)]) ).
cnf(484,negated_conjecture,
( empty(esk9_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[483,192,theory(equality)]) ).
cnf(485,negated_conjecture,
empty(esk9_0),
inference(cn,[status(thm)],[484,theory(equality)]) ).
cnf(486,negated_conjecture,
$false,
inference(sr,[status(thm)],[485,194,theory(equality)]) ).
cnf(487,negated_conjecture,
$false,
486,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU103+1.p
% --creating new selector for []
% -running prover on /tmp/tmpGRHwd2/sel_SEU103+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU103+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU103+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU103+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
%
%------------------------------------------------------------------------------