TPTP Problem File: SWV037+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWV037+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Domain : Software Verification
% Problem : Unsimplified proof obligation gauss_init_0061
% Version : [DFS04] axioms : Especial.
% English : Proof obligation emerging from the init-safety verification for
% the gauss program. init-safety ensures that each variable or
% individual array element has been assigned a defined value before
% it is used.
% Refs : [Fis04] Fischer (2004), Email to G. Sutcliffe
% : [DFS04] Denney et al. (2004), Using Automated Theorem Provers
% Source : [Fis04]
% Names : gauss_init_0061 [Fis04]
% Status : Theorem
% Rating : 0.78 v8.1.0, 0.75 v7.5.0, 0.81 v7.4.0, 0.70 v7.3.0, 0.69 v7.2.0, 0.66 v7.1.0, 0.74 v7.0.0, 0.73 v6.3.0, 0.79 v6.2.0, 0.88 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.3.0, 0.96 v5.2.0, 0.90 v5.0.0, 0.88 v4.1.0, 0.83 v4.0.1, 0.91 v4.0.0, 0.92 v3.7.0, 0.85 v3.5.0, 0.84 v3.3.0
% Syntax : Number of formulae : 100 ( 64 unt; 0 def)
% Number of atoms : 465 ( 163 equ)
% Maximal formula atoms : 201 ( 4 avg)
% Number of connectives : 376 ( 11 ~; 17 |; 247 &)
% ( 5 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 4 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 55 ( 55 usr; 34 con; 0-4 aty)
% Number of variables : 194 ( 194 !; 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(gauss_init_0061,conjecture,
( ( s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& ! [A] :
( ( leq(n0,A)
& leq(A,n2) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,n3) )
=> a_select3(simplex7_init,B,A) = init ) )
& ! [C] :
( ( leq(n0,C)
& leq(C,n3) )
=> a_select2(s_values7_init,C) = init )
& ! [D] :
( ( leq(n0,D)
& leq(D,n2) )
=> a_select2(s_center7_init,D) = init )
& ! [E] :
( ( leq(n0,E)
& leq(E,minus(n3,n1)) )
=> a_select2(s_try7_init,E) = init )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init ) ) )
=> ( init = init
& s_worst7_init = init
& a_select2(s_values7_init,s_worst7) = init
& ( ~ gt(plus(log(n2),divide(minus(minus(minus(plus(log(n330),log(n410)),log(pv1410)),n1),log(n4)),n2)),a_select2(s_values7,s_worst7))
=> ( init = init
& s_best7_init = init
& a_select2(s_values7_init,s_best7) = init
& ( ~ geq(plus(log(n2),divide(minus(minus(minus(plus(log(n330),log(n410)),log(pv1410)),n1),log(n4)),n2)),a_select2(s_values7,s_best7))
=> ( init = init
& s_sworst7_init = init
& a_select2(s_values7_init,s_sworst7) = init
& ( ~ leq(plus(log(n2),divide(minus(minus(minus(plus(log(n330),log(n410)),log(pv1410)),n1),log(n4)),n2)),a_select2(s_values7,s_sworst7))
=> ( init = init
& ( ~ gt(loopcounter,n1)
=> ( ! [F] :
( ( leq(n0,F)
& leq(F,n2) )
=> ! [G] :
( ( leq(n0,G)
& leq(G,n3) )
=> a_select3(simplex7_init,G,F) = init ) )
& ! [H] :
( ( leq(n0,H)
& leq(H,n3) )
=> a_select2(s_values7_init,H) = init )
& ( ~ geq(pv1403,tptp_float_0_001)
=> ( s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3) ) )
& ( gt(loopcounter,n0)
=> ( s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3) ) )
& ( gt(loopcounter,n0)
=> ( a_select2(s_values7_init,s_best7) = init
& a_select2(s_values7_init,s_sworst7) = init
& a_select2(s_values7_init,s_worst7) = init ) ) ) )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init
& s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& a_select2(s_values7_init,s_best7) = init
& a_select2(s_values7_init,s_sworst7) = init
& a_select2(s_values7_init,s_worst7) = init
& ! [I] :
( ( leq(n0,I)
& leq(I,n2) )
=> ! [J] :
( ( leq(n0,J)
& leq(J,n3) )
=> a_select3(simplex7_init,J,I) = init ) )
& ! [K] :
( ( leq(n0,K)
& leq(K,n3) )
=> a_select2(s_values7_init,K) = init )
& ( ~ geq(plus(abs(minus(a_select2(s_values7,s_best7),pv1400)),plus(abs(minus(a_select2(s_values7,s_sworst7),pv1401)),abs(minus(a_select2(s_values7,s_worst7),pv1402)))),tptp_float_0_001)
=> ( s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3) ) )
& ( gt(loopcounter,n0)
=> ( s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3) ) )
& ( gt(loopcounter,n0)
=> ( a_select2(s_values7_init,s_best7) = init
& a_select2(s_values7_init,s_sworst7) = init
& a_select2(s_values7_init,s_worst7) = init ) ) ) ) ) )
& ( leq(plus(log(n2),divide(minus(minus(minus(plus(log(n330),log(n410)),log(pv1410)),n1),log(n4)),n2)),a_select2(s_values7,s_sworst7))
=> ( s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& a_select2(s_values7_init,s_worst7) = init
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& ! [L] :
( ( leq(n0,L)
& leq(L,n2) )
=> ! [M] :
( ( leq(n0,M)
& leq(M,n3) )
=> a_select3(simplex7_init,M,L) = init ) )
& ! [N] :
( ( leq(n0,N)
& leq(N,n3) )
=> a_select2(s_values7_init,N) = init )
& ! [O] :
( ( leq(n0,O)
& leq(O,n2) )
=> a_select2(s_center7_init,O) = init )
& ! [P] :
( ( leq(n0,P)
& leq(P,minus(n3,n1)) )
=> a_select2(s_try7_init,P) = init )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init ) ) ) ) ) )
& ( geq(plus(log(n2),divide(minus(minus(minus(plus(log(n330),log(n410)),log(pv1410)),n1),log(n4)),n2)),a_select2(s_values7,s_best7))
=> ( s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& ! [Q] :
( ( leq(n0,Q)
& leq(Q,n2) )
=> ! [R] :
( ( leq(n0,R)
& leq(R,n3) )
=> a_select3(simplex7_init,R,Q) = init ) )
& ! [S] :
( ( leq(n0,S)
& leq(S,n3) )
=> a_select2(s_values7_init,S) = init )
& ! [T] :
( ( leq(n0,T)
& leq(T,n2) )
=> a_select2(s_center7_init,T) = init )
& ! [U] :
( ( leq(n0,U)
& leq(U,minus(n3,n1)) )
=> a_select2(s_try7_init,U) = init )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init ) ) ) ) ) )
& ( gt(plus(log(n2),divide(minus(minus(minus(plus(log(n330),log(n410)),log(pv1410)),n1),log(n4)),n2)),a_select2(s_values7,s_worst7))
=> ( init = init
& s_best7_init = init
& s_sworst7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& ! [V] :
( ( leq(n0,V)
& leq(V,n2) )
=> ! [W] :
( ( leq(n0,W)
& leq(W,n3) )
=> a_select3(simplex7_init,W,V) = init ) )
& ! [X] :
( ( leq(n0,X)
& leq(X,n3) )
=> a_select2(tptp_update2(s_values7_init,s_worst7,init),X) = init )
& ! [Y] :
( ( leq(n0,Y)
& leq(Y,n2) )
=> a_select2(s_center7_init,Y) = init )
& ! [Z] :
( ( leq(n0,Z)
& leq(Z,minus(n3,n1)) )
=> a_select2(s_try7_init,Z) = init )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init ) ) ) ) ) ) ).
%----Automatically generated axioms
fof(gt_5_4,axiom,
gt(n5,n4) ).
fof(gt_330_4,axiom,
gt(n330,n4) ).
fof(gt_410_4,axiom,
gt(n410,n4) ).
fof(gt_330_5,axiom,
gt(n330,n5) ).
fof(gt_410_5,axiom,
gt(n410,n5) ).
fof(gt_410_330,axiom,
gt(n410,n330) ).
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_330_tptp_minus_1,axiom,
gt(n330,tptp_minus_1) ).
fof(gt_410_tptp_minus_1,axiom,
gt(n410,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_0,axiom,
gt(n4,n0) ).
fof(gt_5_0,axiom,
gt(n5,n0) ).
fof(gt_330_0,axiom,
gt(n330,n0) ).
fof(gt_410_0,axiom,
gt(n410,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_330_1,axiom,
gt(n330,n1) ).
fof(gt_410_1,axiom,
gt(n410,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_330_2,axiom,
gt(n330,n2) ).
fof(gt_410_2,axiom,
gt(n410,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_330_3,axiom,
gt(n330,n3) ).
fof(gt_410_3,axiom,
gt(n410,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 ).
%------------------------------------------------------------------------------