TPTP Problem File: SWV164+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV164+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Domain : Software Verification
% Problem : Simplified proof obligation cl5_nebula_norm_0014
% Version : [DFS04] axioms : Especial.
% English : Proof obligation emerging from the norm-safety verification for
% the cl5_nebula program. norm-safety ensures that the contents of
% certain one-dimensional arrays add up to one.
% Refs : [Fis04] Fischer (2004), Email to G. Sutcliffe
% : [DFS04] Denney et al. (2004), Using Automated Theorem Provers
% Source : [Fis04]
% Names : cl5_nebula_norm_0014 [Fis04]
% Status : Theorem
% Rating : 0.09 v9.0.0, 0.08 v8.1.0, 0.06 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.13 v5.5.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.33 v5.2.0, 0.15 v5.1.0, 0.19 v5.0.0, 0.29 v4.1.0, 0.30 v4.0.1, 0.35 v4.0.0, 0.38 v3.7.0, 0.35 v3.5.0, 0.37 v3.3.0
% Syntax : Number of formulae : 100 ( 64 unt; 0 def)
% Number of atoms : 272 ( 82 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 177 ( 5 ~; 17 |; 96 &)
% ( 5 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 11 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 42 ( 42 usr; 20 con; 0-4 aty)
% Number of variables : 170 ( 170 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v3.3.0 - Bugfix in SWV003+0
%------------------------------------------------------------------------------
%----Include NASA software certification axioms
include('Axioms/SWV003+0.ax').
%------------------------------------------------------------------------------
%----Proof obligation generated by the AutoBayes/AutoFilter system
fof(cl5_nebula_norm_0014,conjecture,
( ( leq(n0,pv10)
& leq(pv10,n135299)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv10)) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,tptp_minus_1) )
=> a_select3(q,pv10,B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),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))))) ) ) ).
%----Automatically generated axioms
fof(gt_5_4,axiom,
gt(n5,n4) ).
fof(gt_135299_4,axiom,
gt(n135299,n4) ).
fof(gt_135299_5,axiom,
gt(n135299,n5) ).
fof(gt_4_tptp_minus_1,axiom,
gt(n4,tptp_minus_1) ).
fof(gt_5_tptp_minus_1,axiom,
gt(n5,tptp_minus_1) ).
fof(gt_135299_tptp_minus_1,axiom,
gt(n135299,tptp_minus_1) ).
fof(gt_0_tptp_minus_1,axiom,
gt(n0,tptp_minus_1) ).
fof(gt_1_tptp_minus_1,axiom,
gt(n1,tptp_minus_1) ).
fof(gt_2_tptp_minus_1,axiom,
gt(n2,tptp_minus_1) ).
fof(gt_3_tptp_minus_1,axiom,
gt(n3,tptp_minus_1) ).
fof(gt_4_tptp_minus_2,axiom,
gt(n4,tptp_minus_2) ).
fof(gt_5_tptp_minus_2,axiom,
gt(n5,tptp_minus_2) ).
fof(gt_tptp_minus_1_tptp_minus_2,axiom,
gt(tptp_minus_1,tptp_minus_2) ).
fof(gt_135299_tptp_minus_2,axiom,
gt(n135299,tptp_minus_2) ).
fof(gt_0_tptp_minus_2,axiom,
gt(n0,tptp_minus_2) ).
fof(gt_1_tptp_minus_2,axiom,
gt(n1,tptp_minus_2) ).
fof(gt_2_tptp_minus_2,axiom,
gt(n2,tptp_minus_2) ).
fof(gt_3_tptp_minus_2,axiom,
gt(n3,tptp_minus_2) ).
fof(gt_4_0,axiom,
gt(n4,n0) ).
fof(gt_5_0,axiom,
gt(n5,n0) ).
fof(gt_135299_0,axiom,
gt(n135299,n0) ).
fof(gt_1_0,axiom,
gt(n1,n0) ).
fof(gt_2_0,axiom,
gt(n2,n0) ).
fof(gt_3_0,axiom,
gt(n3,n0) ).
fof(gt_4_1,axiom,
gt(n4,n1) ).
fof(gt_5_1,axiom,
gt(n5,n1) ).
fof(gt_135299_1,axiom,
gt(n135299,n1) ).
fof(gt_2_1,axiom,
gt(n2,n1) ).
fof(gt_3_1,axiom,
gt(n3,n1) ).
fof(gt_4_2,axiom,
gt(n4,n2) ).
fof(gt_5_2,axiom,
gt(n5,n2) ).
fof(gt_135299_2,axiom,
gt(n135299,n2) ).
fof(gt_3_2,axiom,
gt(n3,n2) ).
fof(gt_4_3,axiom,
gt(n4,n3) ).
fof(gt_5_3,axiom,
gt(n5,n3) ).
fof(gt_135299_3,axiom,
gt(n135299,n3) ).
fof(finite_domain_4,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n4) )
=> ( X = n0
| X = n1
| X = n2
| X = n3
| X = n4 ) ) ).
fof(finite_domain_5,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n5) )
=> ( X = n0
| X = n1
| X = n2
| X = n3
| X = n4
| X = n5 ) ) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n0) )
=> X = n0 ) ).
fof(finite_domain_1,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n1) )
=> ( X = n0
| X = n1 ) ) ).
fof(finite_domain_2,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n2) )
=> ( X = n0
| X = n1
| X = n2 ) ) ).
fof(finite_domain_3,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n3) )
=> ( X = n0
| X = n1
| X = n2
| X = n3 ) ) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4 ).
fof(successor_5,axiom,
succ(succ(succ(succ(succ(n0))))) = n5 ).
fof(successor_1,axiom,
succ(n0) = n1 ).
fof(successor_2,axiom,
succ(succ(n0)) = n2 ).
fof(successor_3,axiom,
succ(succ(succ(n0))) = n3 ).
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