TSTP Solution File: SWV160+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWV160+1 : TPTP v5.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 12:25:01 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 118 ( 34 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 124 ( 31 ~; 22 |; 60 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 17 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(18,axiom,
! [X1] : ~ gt(X1,X1),
file('/tmp/tmpGWeZux/sel_SWV160+1.p_1',irreflexivity_gt) ).
fof(22,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/tmp/tmpGWeZux/sel_SWV160+1.p_1',pred_minus_1) ).
fof(25,axiom,
! [X1,X2] :
( leq(X1,pred(X2))
<=> gt(X2,X1) ),
file('/tmp/tmpGWeZux/sel_SWV160+1.p_1',leq_gt_pred) ).
fof(42,conjecture,
( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X5] :
( ( leq(n0,X5)
& leq(X5,pred(pv47)) )
=> a_select3(q,pv10,X5) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X5)),minus(a_select2(x,pv10),a_select2(mu,X5))),tptp_minus_2),times(a_select2(sigma,X5),a_select2(sigma,X5)))),a_select2(rho,X5)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X5))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [X6] :
( ( leq(n0,X6)
& leq(X6,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X6,tptp_sum_index)) = n1 ) )
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,pred(pv10)) )
=> ( pv10 = X7
=> sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,X7,tptp_sum_index))) = n1 ) ) ),
file('/tmp/tmpGWeZux/sel_SWV160+1.p_1',cl5_nebula_norm_0010) ).
fof(78,negated_conjecture,
~ ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X5] :
( ( leq(n0,X5)
& leq(X5,pred(pv47)) )
=> a_select3(q,pv10,X5) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X5)),minus(a_select2(x,pv10),a_select2(mu,X5))),tptp_minus_2),times(a_select2(sigma,X5),a_select2(sigma,X5)))),a_select2(rho,X5)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X5))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [X6] :
( ( leq(n0,X6)
& leq(X6,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X6,tptp_sum_index)) = n1 ) )
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,pred(pv10)) )
=> ( pv10 = X7
=> sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,X7,tptp_sum_index))) = n1 ) ) ),
inference(assume_negation,[status(cth)],[42]) ).
fof(79,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[18,theory(equality)]) ).
fof(120,plain,
! [X2] : ~ gt(X2,X2),
inference(variable_rename,[status(thm)],[79]) ).
cnf(121,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[120]) ).
fof(128,plain,
! [X2] : minus(X2,n1) = pred(X2),
inference(variable_rename,[status(thm)],[22]) ).
cnf(129,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[128]) ).
fof(136,plain,
! [X1,X2] :
( ( ~ leq(X1,pred(X2))
| gt(X2,X1) )
& ( ~ gt(X2,X1)
| leq(X1,pred(X2)) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(137,plain,
! [X3,X4] :
( ( ~ leq(X3,pred(X4))
| gt(X4,X3) )
& ( ~ gt(X4,X3)
| leq(X3,pred(X4)) ) ),
inference(variable_rename,[status(thm)],[136]) ).
cnf(139,plain,
( gt(X1,X2)
| ~ leq(X2,pred(X1)) ),
inference(split_conjunct,[status(thm)],[137]) ).
fof(162,negated_conjecture,
( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X5] :
( ~ leq(n0,X5)
| ~ leq(X5,pred(pv47))
| a_select3(q,pv10,X5) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X5)),minus(a_select2(x,pv10),a_select2(mu,X5))),tptp_minus_2),times(a_select2(sigma,X5),a_select2(sigma,X5)))),a_select2(rho,X5)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X5))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [X6] :
( ~ leq(n0,X6)
| ~ leq(X6,pred(pv10))
| sum(n0,n4,a_select3(q,X6,tptp_sum_index)) = n1 )
& ? [X7] :
( leq(n0,X7)
& leq(X7,pred(pv10))
& pv10 = X7
& sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,X7,tptp_sum_index))) != n1 ) ),
inference(fof_nnf,[status(thm)],[78]) ).
fof(163,negated_conjecture,
( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X8] :
( ~ leq(n0,X8)
| ~ leq(X8,pred(pv47))
| a_select3(q,pv10,X8) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X8)),minus(a_select2(x,pv10),a_select2(mu,X8))),tptp_minus_2),times(a_select2(sigma,X8),a_select2(sigma,X8)))),a_select2(rho,X8)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X8))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [X9] :
( ~ leq(n0,X9)
| ~ leq(X9,pred(pv10))
| sum(n0,n4,a_select3(q,X9,tptp_sum_index)) = n1 )
& ? [X10] :
( leq(n0,X10)
& leq(X10,pred(pv10))
& pv10 = X10
& sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,X10,tptp_sum_index))) != n1 ) ),
inference(variable_rename,[status(thm)],[162]) ).
fof(164,negated_conjecture,
( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X8] :
( ~ leq(n0,X8)
| ~ leq(X8,pred(pv47))
| a_select3(q,pv10,X8) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X8)),minus(a_select2(x,pv10),a_select2(mu,X8))),tptp_minus_2),times(a_select2(sigma,X8),a_select2(sigma,X8)))),a_select2(rho,X8)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X8))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [X9] :
( ~ leq(n0,X9)
| ~ leq(X9,pred(pv10))
| sum(n0,n4,a_select3(q,X9,tptp_sum_index)) = n1 )
& leq(n0,esk1_0)
& leq(esk1_0,pred(pv10))
& pv10 = esk1_0
& sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,esk1_0,tptp_sum_index))) != n1 ),
inference(skolemize,[status(esa)],[163]) ).
fof(165,negated_conjecture,
! [X8,X9] :
( ( ~ leq(n0,X9)
| ~ leq(X9,pred(pv10))
| sum(n0,n4,a_select3(q,X9,tptp_sum_index)) = n1 )
& ( ~ leq(n0,X8)
| ~ leq(X8,pred(pv47))
| a_select3(q,pv10,X8) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X8)),minus(a_select2(x,pv10),a_select2(mu,X8))),tptp_minus_2),times(a_select2(sigma,X8),a_select2(sigma,X8)))),a_select2(rho,X8)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X8))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& leq(n0,esk1_0)
& leq(esk1_0,pred(pv10))
& pv10 = esk1_0
& sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,esk1_0,tptp_sum_index))) != n1 ),
inference(shift_quantors,[status(thm)],[164]) ).
cnf(167,negated_conjecture,
pv10 = esk1_0,
inference(split_conjunct,[status(thm)],[165]) ).
cnf(168,negated_conjecture,
leq(esk1_0,pred(pv10)),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(250,negated_conjecture,
leq(esk1_0,minus(pv10,n1)),
inference(rw,[status(thm)],[168,129,theory(equality)]),
[unfolding] ).
cnf(251,plain,
( gt(X1,X2)
| ~ leq(X2,minus(X1,n1)) ),
inference(rw,[status(thm)],[139,129,theory(equality)]),
[unfolding] ).
cnf(256,negated_conjecture,
leq(pv10,minus(pv10,n1)),
inference(rw,[status(thm)],[250,167,theory(equality)]) ).
cnf(290,negated_conjecture,
gt(pv10,pv10),
inference(spm,[status(thm)],[251,256,theory(equality)]) ).
cnf(294,negated_conjecture,
$false,
inference(sr,[status(thm)],[290,121,theory(equality)]) ).
cnf(295,negated_conjecture,
$false,
294,
[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/SWV/SWV160+1.p
% --creating new selector for [SWV003+0.ax]
% -running prover on /tmp/tmpGWeZux/sel_SWV160+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV160+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV160+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV160+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
%
%------------------------------------------------------------------------------