TPTP Problem File: SWV221+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV221+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Domain : Software Verification
% Problem : Simplified proof obligation quaternion_ds1_symm_0401
% Version : [DFS04] axioms : Especial.
% English : Proof obligation emerging from the symm-safety verification for
% the quaternion_ds1 program. symmetry-safety ensures that certain
% two-dimensional arrays remain symmetric.
% Refs : [Fis04] Fischer (2004), Email to G. Sutcliffe
% : [DFS04] Denney et al. (2004), Using Automated Theorem Provers
% Source : [Fis04]
% Names : quaternion_ds1_symm_0401 [Fis04]
% Status : Theorem
% Rating : 0.14 v8.1.0, 0.19 v7.5.0, 0.25 v7.4.0, 0.13 v7.3.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.17 v6.4.0, 0.19 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.33 v6.0.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.33 v5.2.0, 0.20 v5.1.0, 0.24 v5.0.0, 0.25 v4.1.0, 0.26 v4.0.0, 0.29 v3.7.0, 0.25 v3.5.0, 0.32 v3.4.0, 0.37 v3.3.0
% Syntax : Number of formulae : 92 ( 56 unt; 0 def)
% Number of atoms : 303 ( 91 equ)
% Maximal formula atoms : 47 ( 3 avg)
% Number of connectives : 218 ( 7 ~; 17 |; 125 &)
% ( 5 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 18 con; 0-4 aty)
% Number of variables : 182 ( 182 !; 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(quaternion_ds1_symm_0401,conjecture,
( ( leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [A,B] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
& ! [C,D] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [E,F] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) )
& ! [G,H] :
( ( leq(n0,G)
& leq(n0,H)
& leq(G,n5)
& leq(H,n5) )
=> ( ( G = pv57
& gt(pv58,H) )
=> a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G) ) )
& ! [I,J] :
( ( leq(n0,I)
& leq(n0,J)
& leq(I,n5)
& leq(J,n5) )
=> ( gt(pv57,I)
=> a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I) ) )
& ! [K] :
( ( leq(n0,K)
& leq(K,pred(pv57)) )
=> ! [L] :
( ( leq(n0,L)
& leq(L,n5) )
=> a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K) ) ) )
=> ! [M] :
( ( leq(n0,M)
& leq(M,pred(pv57)) )
=> ! [N] :
( ( leq(n0,N)
& leq(N,n5) )
=> ( ( ~ ( pv57 = N
& N = M )
& pv57 != M )
=> a_select3(id_ds1_filter,M,N) = a_select3(id_ds1_filter,N,M) ) ) ) ) ).
%----Automatically generated axioms
fof(gt_5_4,axiom,
gt(n5,n4) ).
fof(gt_998_4,axiom,
gt(n998,n4) ).
fof(gt_998_5,axiom,
gt(n998,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_998_tptp_minus_1,axiom,
gt(n998,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_998_0,axiom,
gt(n998,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_998_1,axiom,
gt(n998,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_998_2,axiom,
gt(n998,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_998_3,axiom,
gt(n998,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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