TSTP Solution File: SET096+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET096+1 : TPTP v5.3.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : manassas.cs.miami.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Core(TM)2 CPU 6600 @ 2.40GHz @ 2400MHz
% Memory : 1003MB
% OS : Linux 2.6.32.26-175.fc12.x86_64
% CPULimit : 300s
% DateTime : Fri Jun 15 08:06:28 EDT 2012
% Result : Theorem 0.13s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 19 unt; 0 def)
% Number of atoms : 158 ( 17 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 171 ( 67 ~; 65 |; 33 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 3 sgn 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( equal(X1,X2)
<=> ( subclass(X1,X2)
& subclass(X2,X1) ) ),
file('/tmp/tmpRNzRP5/sel_SET096+1.p_4',extensionality) ).
fof(2,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpRNzRP5/sel_SET096+1.p_4',subclass_defn) ).
fof(4,axiom,
! [X1] : ~ member(X1,null_class),
file('/tmp/tmpRNzRP5/sel_SET096+1.p_4',null_class_defn) ).
fof(7,axiom,
! [X1] : equal(singleton(X1),unordered_pair(X1,X1)),
file('/tmp/tmpRNzRP5/sel_SET096+1.p_4',singleton_set_defn) ).
fof(8,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( equal(X3,X1)
| equal(X3,X2) ) ) ),
file('/tmp/tmpRNzRP5/sel_SET096+1.p_4',unordered_pair_defn) ).
fof(10,conjecture,
! [X1,X2] :
( subclass(X1,singleton(X2))
=> ( equal(X1,null_class)
| equal(singleton(X2),X1) ) ),
file('/tmp/tmpRNzRP5/sel_SET096+1.p_4',two_subsets_of_singleton) ).
fof(11,negated_conjecture,
~ ! [X1,X2] :
( subclass(X1,singleton(X2))
=> ( equal(X1,null_class)
| equal(singleton(X2),X1) ) ),
inference(assume_negation,[status(cth)],[10]) ).
fof(12,plain,
! [X1] : ~ member(X1,null_class),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(13,plain,
! [X1,X2] :
( ( ~ equal(X1,X2)
| ( subclass(X1,X2)
& subclass(X2,X1) ) )
& ( ~ subclass(X1,X2)
| ~ subclass(X2,X1)
| equal(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(14,plain,
! [X3,X4] :
( ( ~ equal(X3,X4)
| ( subclass(X3,X4)
& subclass(X4,X3) ) )
& ( ~ subclass(X3,X4)
| ~ subclass(X4,X3)
| equal(X3,X4) ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,plain,
! [X3,X4] :
( ( subclass(X3,X4)
| ~ equal(X3,X4) )
& ( subclass(X4,X3)
| ~ equal(X3,X4) )
& ( ~ subclass(X3,X4)
| ~ subclass(X4,X3)
| equal(X3,X4) ) ),
inference(distribute,[status(thm)],[14]) ).
cnf(16,plain,
( X1 = X2
| ~ subclass(X2,X1)
| ~ subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(19,plain,
! [X1,X2] :
( ( ~ subclass(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subclass(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(20,plain,
! [X4,X5] :
( ( ~ subclass(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subclass(X4,X5) ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,plain,
! [X4,X5] :
( ( ~ subclass(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subclass(X4,X5) ) ),
inference(skolemize,[status(esa)],[20]) ).
fof(22,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subclass(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subclass(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[21]) ).
fof(23,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subclass(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subclass(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subclass(X4,X5) ) ),
inference(distribute,[status(thm)],[22]) ).
cnf(24,plain,
( subclass(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( subclass(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(26,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(29,plain,
! [X2] : ~ member(X2,null_class),
inference(variable_rename,[status(thm)],[12]) ).
cnf(30,plain,
~ member(X1,null_class),
inference(split_conjunct,[status(thm)],[29]) ).
fof(39,plain,
! [X2] : equal(singleton(X2),unordered_pair(X2,X2)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(40,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X3,X1,X2] :
( ( ~ member(X3,unordered_pair(X1,X2))
| ( member(X3,universal_class)
& ( equal(X3,X1)
| equal(X3,X2) ) ) )
& ( ~ member(X3,universal_class)
| ( ~ equal(X3,X1)
& ~ equal(X3,X2) )
| member(X3,unordered_pair(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(42,plain,
! [X4,X5,X6] :
( ( ~ member(X4,unordered_pair(X5,X6))
| ( member(X4,universal_class)
& ( equal(X4,X5)
| equal(X4,X6) ) ) )
& ( ~ member(X4,universal_class)
| ( ~ equal(X4,X5)
& ~ equal(X4,X6) )
| member(X4,unordered_pair(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X4,X5,X6] :
( ( member(X4,universal_class)
| ~ member(X4,unordered_pair(X5,X6)) )
& ( equal(X4,X5)
| equal(X4,X6)
| ~ member(X4,unordered_pair(X5,X6)) )
& ( ~ equal(X4,X5)
| ~ member(X4,universal_class)
| member(X4,unordered_pair(X5,X6)) )
& ( ~ equal(X4,X6)
| ~ member(X4,universal_class)
| member(X4,unordered_pair(X5,X6)) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(46,plain,
( X1 = X3
| X1 = X2
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(50,negated_conjecture,
? [X1,X2] :
( subclass(X1,singleton(X2))
& ~ equal(X1,null_class)
& ~ equal(singleton(X2),X1) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(51,negated_conjecture,
? [X3,X4] :
( subclass(X3,singleton(X4))
& ~ equal(X3,null_class)
& ~ equal(singleton(X4),X3) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,negated_conjecture,
( subclass(esk2_0,singleton(esk3_0))
& ~ equal(esk2_0,null_class)
& ~ equal(singleton(esk3_0),esk2_0) ),
inference(skolemize,[status(esa)],[51]) ).
cnf(53,negated_conjecture,
singleton(esk3_0) != esk2_0,
inference(split_conjunct,[status(thm)],[52]) ).
cnf(54,negated_conjecture,
esk2_0 != null_class,
inference(split_conjunct,[status(thm)],[52]) ).
cnf(55,negated_conjecture,
subclass(esk2_0,singleton(esk3_0)),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(56,negated_conjecture,
subclass(esk2_0,unordered_pair(esk3_0,esk3_0)),
inference(rw,[status(thm)],[55,40,theory(equality)]),
[unfolding] ).
cnf(58,negated_conjecture,
unordered_pair(esk3_0,esk3_0) != esk2_0,
inference(rw,[status(thm)],[53,40,theory(equality)]),
[unfolding] ).
cnf(65,negated_conjecture,
( unordered_pair(esk3_0,esk3_0) = esk2_0
| ~ subclass(unordered_pair(esk3_0,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[16,56,theory(equality)]) ).
cnf(66,negated_conjecture,
~ subclass(unordered_pair(esk3_0,esk3_0),esk2_0),
inference(sr,[status(thm)],[65,58,theory(equality)]) ).
cnf(67,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[30,25,theory(equality)]) ).
cnf(70,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X1
| esk1_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[46,25,theory(equality)]) ).
cnf(72,negated_conjecture,
( member(X1,unordered_pair(esk3_0,esk3_0))
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[26,56,theory(equality)]) ).
cnf(77,plain,
( X1 = null_class
| ~ subclass(X1,null_class) ),
inference(spm,[status(thm)],[16,67,theory(equality)]) ).
cnf(86,negated_conjecture,
( X1 = esk3_0
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[46,72,theory(equality)]) ).
cnf(87,negated_conjecture,
( esk1_2(esk2_0,X1) = esk3_0
| subclass(esk2_0,X1) ),
inference(spm,[status(thm)],[86,25,theory(equality)]) ).
cnf(88,negated_conjecture,
( member(esk3_0,esk2_0)
| subclass(esk2_0,X1) ),
inference(spm,[status(thm)],[25,87,theory(equality)]) ).
cnf(92,negated_conjecture,
( esk2_0 = null_class
| member(esk3_0,esk2_0) ),
inference(spm,[status(thm)],[77,88,theory(equality)]) ).
cnf(93,negated_conjecture,
member(esk3_0,esk2_0),
inference(sr,[status(thm)],[92,54,theory(equality)]) ).
cnf(107,plain,
( esk1_2(unordered_pair(X4,X5),X6) = X4
| subclass(unordered_pair(X4,X5),X6)
| X5 != X4 ),
inference(ef,[status(thm)],[70,theory(equality)]) ).
cnf(115,plain,
( esk1_2(unordered_pair(X1,X1),X2) = X1
| subclass(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[107,theory(equality)]) ).
cnf(139,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[24,115,theory(equality)]) ).
cnf(195,negated_conjecture,
~ member(esk3_0,esk2_0),
inference(spm,[status(thm)],[66,139,theory(equality)]) ).
cnf(201,negated_conjecture,
$false,
inference(rw,[status(thm)],[195,93,theory(equality)]) ).
cnf(202,negated_conjecture,
$false,
inference(cn,[status(thm)],[201,theory(equality)]) ).
cnf(203,negated_conjecture,
$false,
202,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET096+1.p
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpRNzRP5/sel_SET096+1.p_1 with time limit 29
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/tmp/tmpRNzRP5/sel_SET096+1.p_1']
% -prover status CounterSatisfiable
% -running prover on /tmp/tmpRNzRP5/sel_SET096+1.p_2 with time limit 89
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=89', '/tmp/tmpRNzRP5/sel_SET096+1.p_2']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpRNzRP5/sel_SET096+1.p_3 with time limit 119
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=119', '/tmp/tmpRNzRP5/sel_SET096+1.p_3']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpRNzRP5/sel_SET096+1.p_4 with time limit 149
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=149', '/tmp/tmpRNzRP5/sel_SET096+1.p_4']
% -prover status Theorem
% Problem SET096+1.p solved in phase 3.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET096+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET096+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
%
%------------------------------------------------------------------------------