TSTP Solution File: SET928+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET928+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 03:48:06 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 100 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 114 ( 53 ~; 39 |; 18 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 2 sgn 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',t57_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',commutativity_k2_tarski) ).
fof(4,conjecture,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',t72_zfmisc_1) ).
fof(8,axiom,
! [X1,X2,X3] :
~ ( disjoint(unordered_pair(X1,X2),X3)
& in(X1,X3) ),
file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',t55_zfmisc_1) ).
fof(9,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',t83_xboole_1) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(12,plain,
! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(18,plain,
! [X1,X2,X3] :
( in(X1,X2)
| in(X3,X2)
| disjoint(unordered_pair(X1,X3),X2) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(19,plain,
! [X4,X5,X6] :
( in(X4,X5)
| in(X6,X5)
| disjoint(unordered_pair(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[18]) ).
cnf(20,plain,
( disjoint(unordered_pair(X1,X2),X3)
| in(X2,X3)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[3]) ).
cnf(22,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,negated_conjecture,
? [X1,X2,X3] :
( ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
| in(X1,X3)
| in(X2,X3) )
& ( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
| ( ~ in(X1,X3)
& ~ in(X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(24,negated_conjecture,
? [X4,X5,X6] :
( ( set_difference(unordered_pair(X4,X5),X6) != unordered_pair(X4,X5)
| in(X4,X6)
| in(X5,X6) )
& ( set_difference(unordered_pair(X4,X5),X6) = unordered_pair(X4,X5)
| ( ~ in(X4,X6)
& ~ in(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,negated_conjecture,
( ( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != unordered_pair(esk2_0,esk3_0)
| in(esk2_0,esk4_0)
| in(esk3_0,esk4_0) )
& ( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0)
| ( ~ in(esk2_0,esk4_0)
& ~ in(esk3_0,esk4_0) ) ) ),
inference(skolemize,[status(esa)],[24]) ).
fof(26,negated_conjecture,
( ( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != unordered_pair(esk2_0,esk3_0)
| in(esk2_0,esk4_0)
| in(esk3_0,esk4_0) )
& ( ~ in(esk2_0,esk4_0)
| set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0) )
& ( ~ in(esk3_0,esk4_0)
| set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(27,negated_conjecture,
( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0)
| ~ in(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(28,negated_conjecture,
( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0)
| ~ in(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(29,negated_conjecture,
( in(esk3_0,esk4_0)
| in(esk2_0,esk4_0)
| set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != unordered_pair(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(39,plain,
! [X1,X2,X3] :
( ~ disjoint(unordered_pair(X1,X2),X3)
| ~ in(X1,X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(40,plain,
! [X4,X5,X6] :
( ~ disjoint(unordered_pair(X4,X5),X6)
| ~ in(X4,X6) ),
inference(variable_rename,[status(thm)],[39]) ).
cnf(41,plain,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_difference(X1,X2) = X1 )
& ( set_difference(X1,X2) != X1
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(43,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X3,X4) != X3
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[42]) ).
cnf(44,plain,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,plain,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(48,negated_conjecture,
( in(esk3_0,esk4_0)
| in(esk2_0,esk4_0)
| ~ disjoint(unordered_pair(esk2_0,esk3_0),esk4_0) ),
inference(spm,[status(thm)],[29,45,theory(equality)]) ).
cnf(49,negated_conjecture,
( disjoint(unordered_pair(esk2_0,esk3_0),esk4_0)
| ~ in(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[44,28,theory(equality)]) ).
cnf(50,negated_conjecture,
( disjoint(unordered_pair(esk2_0,esk3_0),esk4_0)
| ~ in(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[44,27,theory(equality)]) ).
cnf(52,plain,
( ~ disjoint(unordered_pair(X2,X1),X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[41,22,theory(equality)]) ).
cnf(61,negated_conjecture,
~ in(esk2_0,esk4_0),
inference(csr,[status(thm)],[49,41]) ).
cnf(62,negated_conjecture,
~ in(esk3_0,esk4_0),
inference(csr,[status(thm)],[50,52]) ).
cnf(63,negated_conjecture,
( in(esk2_0,esk4_0)
| ~ disjoint(unordered_pair(esk2_0,esk3_0),esk4_0) ),
inference(sr,[status(thm)],[48,62,theory(equality)]) ).
cnf(64,negated_conjecture,
~ disjoint(unordered_pair(esk2_0,esk3_0),esk4_0),
inference(sr,[status(thm)],[63,61,theory(equality)]) ).
cnf(65,negated_conjecture,
( in(esk2_0,esk4_0)
| in(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[64,20,theory(equality)]) ).
cnf(66,negated_conjecture,
in(esk3_0,esk4_0),
inference(sr,[status(thm)],[65,61,theory(equality)]) ).
cnf(67,negated_conjecture,
$false,
inference(sr,[status(thm)],[66,62,theory(equality)]) ).
cnf(68,negated_conjecture,
$false,
67,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET928+1.p
% --creating new selector for []
% -running prover on /tmp/tmp8rE5Ti/sel_SET928+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET928+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET928+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET928+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
%
%------------------------------------------------------------------------------