TPTP Problem File: SWV036+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV036+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Domain : Software Verification
% Problem : Unsimplified proof obligation gauss_init_0057
% 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_0057 [Fis04]
% Status : Theorem
% Rating : 0.56 v8.2.0, 0.53 v8.1.0, 0.50 v7.5.0, 0.56 v7.4.0, 0.47 v7.3.0, 0.55 v7.2.0, 0.52 v7.1.0, 0.57 v7.0.0, 0.60 v6.4.0, 0.62 v6.2.0, 0.64 v6.1.0, 0.67 v6.0.0, 0.61 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0, 0.75 v5.1.0, 0.81 v5.0.0, 0.79 v4.1.0, 0.78 v4.0.1, 0.87 v4.0.0, 0.88 v3.7.0, 0.80 v3.5.0, 0.79 v3.3.0
% Syntax : Number of formulae : 85 ( 49 unt; 0 def)
% Number of atoms : 389 ( 137 equ)
% Maximal formula atoms : 140 ( 4 avg)
% Number of connectives : 312 ( 8 ~; 17 |; 199 &)
% ( 5 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 4 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 44 ( 44 usr; 26 con; 0-4 aty)
% Number of variables : 188 ( 188 !; 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_0057,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(n2,pv1388)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1388,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 )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init ) ) )
=> ( init = init
& s_best7_init = init
& a_select2(s_values7_init,s_best7) = init
& a_select2(s_values7_init,pv1388) = init
& ( ~ gt(a_select2(s_values7,pv1388),a_select2(s_values7,s_best7))
=> ( init = init
& s_worst7_init = init
& a_select2(s_values7_init,s_worst7) = init
& a_select2(s_values7_init,pv1388) = init
& ( ~ leq(a_select2(s_values7,pv1388),a_select2(s_values7,s_worst7))
=> ( init = init
& s_sworst7_init = init
& a_select2(s_values7_init,s_sworst7) = init
& a_select2(s_values7_init,pv1388) = init
& ( ~ leq(a_select2(s_values7,pv1388),a_select2(s_values7,s_sworst7))
=> ( 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)
& ! [E] :
( ( leq(n0,E)
& leq(E,n2) )
=> ! [F] :
( ( leq(n0,F)
& leq(F,n3) )
=> a_select3(simplex7_init,F,E) = init ) )
& ! [G] :
( ( leq(n0,G)
& leq(G,n3) )
=> a_select2(s_values7_init,G) = init )
& ! [H] :
( ( leq(n0,H)
& leq(H,n2) )
=> a_select2(s_center7_init,H) = init )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init ) ) ) )
& ( leq(a_select2(s_values7,pv1388),a_select2(s_values7,s_sworst7))
=> ( init = init
& s_best7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_worst7)
& leq(n0,pv1388)
& leq(s_best7,n3)
& leq(s_worst7,n3)
& leq(pv1388,n3)
& ! [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 )
& ! [L] :
( ( leq(n0,L)
& leq(L,n2) )
=> a_select2(s_center7_init,L) = init )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init ) ) ) ) ) )
& ( leq(a_select2(s_values7,pv1388),a_select2(s_values7,s_worst7))
=> ( init = init
& s_best7_init = init
& s_worst7_init = init
& leq(n0,s_best7)
& leq(n0,s_worst7)
& leq(n0,pv1388)
& leq(s_best7,n3)
& leq(s_worst7,n3)
& leq(pv1388,n3)
& ! [M] :
( ( leq(n0,M)
& leq(M,n2) )
=> ! [N] :
( ( leq(n0,N)
& leq(N,n3) )
=> a_select3(simplex7_init,N,M) = init ) )
& ! [O] :
( ( leq(n0,O)
& leq(O,n3) )
=> a_select2(s_values7_init,O) = init )
& ! [P] :
( ( leq(n0,P)
& leq(P,n2) )
=> a_select2(s_center7_init,P) = init )
& ( gt(loopcounter,n1)
=> ( pvar1400_init = init
& pvar1401_init = init
& pvar1402_init = init ) ) ) ) ) )
& ( gt(a_select2(s_values7,pv1388),a_select2(s_values7,s_best7))
=> ( init = init
& s_sworst7_init = init
& s_worst7_init = init
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n0,pv1388)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1388,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 )
& ( 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_4_tptp_minus_1,axiom,
gt(n4,tptp_minus_1) ).
fof(gt_5_tptp_minus_1,axiom,
gt(n5,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_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_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_3_2,axiom,
gt(n3,n2) ).
fof(gt_4_3,axiom,
gt(n4,n3) ).
fof(gt_5_3,axiom,
gt(n5,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 ).
%------------------------------------------------------------------------------