TPTP Problem File: SWW652_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW652_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Vacid 0 build maze-T-Ineq1
% Version : Especial : Let and conditional terms encoded away.
% English :
% Refs : [Fil14] Filliatre (2014), Email to Geoff Sutcliffe
% : [BF+] Bobot et al. (URL), Toccata: Certified Programs and Cert
% Source : [Fil14]
% Names : vacid_0_build_maze-T-Ineq1 [Fil14]
% Status : Theorem
% Rating : 0.38 v8.2.0, 0.62 v7.5.0, 0.80 v7.4.0, 0.62 v7.3.0, 0.67 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.86 v6.2.0, 0.88 v6.1.0
% Syntax : Number of formulae : 56 ( 9 unt; 32 typ; 0 def)
% Number of atoms : 68 ( 21 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 45 ( 1 ~; 3 |; 17 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 66 ( 19 atm; 5 fun; 10 num; 32 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 27 ( 14 >; 13 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 0 prp; 2-3 aty)
% Number of functors : 24 ( 20 usr; 13 con; 0-4 aty)
% Number of variables : 68 ( 58 !; 10 ?; 68 :)
% SPC : TF0_THM_EQU_ARI
% Comments :
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tff(uni,type,
uni: $tType ).
tff(ty,type,
ty: $tType ).
tff(sort,type,
sort1: ( ty * uni ) > $o ).
tff(witness,type,
witness1: ty > uni ).
tff(witness_sort1,axiom,
! [A: ty] : sort1(A,witness1(A)) ).
tff(int,type,
int: ty ).
tff(real,type,
real: ty ).
tff(bool,type,
bool1: $tType ).
tff(bool1,type,
bool: ty ).
tff(true,type,
true1: bool1 ).
tff(false,type,
false1: bool1 ).
tff(match_bool,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(match_bool_sort1,axiom,
! [A: ty,X: bool1,X1: uni,X2: uni] : sort1(A,match_bool1(A,X,X1,X2)) ).
tff(match_bool_True,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort1(A,Z)
=> ( match_bool1(A,true1,Z,Z1) = Z ) ) ).
tff(match_bool_False,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort1(A,Z1)
=> ( match_bool1(A,false1,Z,Z1) = Z1 ) ) ).
tff(true_False,axiom,
true1 != false1 ).
tff(bool_inversion,axiom,
! [U: bool1] :
( ( U = true1 )
| ( U = false1 ) ) ).
tff(tuple0,type,
tuple02: $tType ).
tff(tuple01,type,
tuple0: ty ).
tff(tuple02,type,
tuple03: tuple02 ).
tff(tuple0_inversion,axiom,
! [U: tuple02] : U = tuple03 ).
tff(qtmark,type,
qtmark: ty ).
tff(compatOrderMult,axiom,
! [X: $int,Y: $int,Z: $int] :
( $lesseq(X,Y)
=> ( $lesseq(0,Z)
=> $lesseq($product(X,Z),$product(Y,Z)) ) ) ).
tff(ref,type,
ref: ty > ty ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(mk_ref_sort1,axiom,
! [A: ty,X: uni] : sort1(ref(A),mk_ref(A,X)) ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(contents_sort1,axiom,
! [A: ty,X: uni] : sort1(A,contents(A,X)) ).
tff(contents_def1,axiom,
! [A: ty,U: uni] :
( sort1(A,U)
=> ( contents(A,mk_ref(A,U)) = U ) ) ).
tff(ref_inversion1,axiom,
! [A: ty,U: uni] :
( sort1(ref(A),U)
=> ( U = mk_ref(A,contents(A,U)) ) ) ).
tff(uf_pure,type,
uf_pure1: $tType ).
tff(uf_pure1,type,
uf_pure: ty ).
tff(repr,type,
repr1: ( uf_pure1 * $int * $int ) > $o ).
tff(size,type,
size1: uf_pure1 > $int ).
tff(num,type,
num1: uf_pure1 > $int ).
tff(repr_function_1,axiom,
! [U: uf_pure1,X: $int] :
( ( $lesseq(0,X)
& $less(X,size1(U)) )
=> ? [Y: $int] :
( $lesseq(0,Y)
& $less(Y,size1(U))
& repr1(U,X,Y) ) ) ).
tff(repr_function_2,axiom,
! [U: uf_pure1,X: $int,Y: $int,Z: $int] :
( ( $lesseq(0,X)
& $less(X,size1(U)) )
=> ( repr1(U,X,Y)
=> ( repr1(U,X,Z)
=> ( Y = Z ) ) ) ) ).
tff(same,type,
same1: ( uf_pure1 * $int * $int ) > $o ).
tff(same_def,axiom,
! [U: uf_pure1,X: $int,Y: $int] :
( same1(U,X,Y)
<=> ! [R: $int] :
( repr1(U,X,R)
<=> repr1(U,Y,R) ) ) ).
tff(same_reprs,type,
same_reprs1: ( uf_pure1 * uf_pure1 ) > $o ).
tff(same_reprs_def,axiom,
! [U1: uf_pure1,U2: uf_pure1] :
( same_reprs1(U1,U2)
<=> ! [X: $int,R: $int] :
( repr1(U1,X,R)
<=> repr1(U2,X,R) ) ) ).
tff(oneClass,axiom,
! [U: uf_pure1] :
( ( num1(U) = 1 )
=> ! [X: $int,Y: $int] :
( ( $lesseq(0,X)
& $less(X,size1(U)) )
=> ( ( $lesseq(0,Y)
& $less(Y,size1(U)) )
=> same1(U,X,Y) ) ) ) ).
tff(uf,type,
uf1: $tType ).
tff(uf1,type,
uf: ty ).
tff(mk_uf,type,
mk_uf1: uf_pure1 > uf1 ).
tff(state,type,
state1: uf1 > uf_pure1 ).
tff(state_def1,axiom,
! [U: uf_pure1] : state1(mk_uf1(U)) = U ).
tff(uf_inversion1,axiom,
! [U: uf1] : U = mk_uf1(state1(U)) ).
tff(graph,type,
graph1: $tType ).
tff(graph1,type,
graph: ty ).
tff(path,type,
path1: ( graph1 * $int * $int ) > $o ).
tff(path_refl,axiom,
! [G: graph1,X: $int] : path1(G,X,X) ).
tff(path_sym,axiom,
! [G: graph1,X: $int,Y: $int] :
( path1(G,X,Y)
=> path1(G,Y,X) ) ).
tff(path_trans,axiom,
! [G: graph1,X: $int,Y: $int,Z: $int] :
( path1(G,X,Y)
=> ( path1(G,Y,Z)
=> path1(G,X,Z) ) ) ).
tff(path_inversion,axiom,
! [Z: graph1,Z1: $int,Z2: $int] :
( path1(Z,Z1,Z2)
=> ( ? [G: graph1,X: $int] :
( ( Z = G )
& ( Z1 = X )
& ( Z2 = X ) )
| ? [G: graph1,X: $int,Y: $int] :
( path1(G,X,Y)
& ( Z = G )
& ( Z1 = Y )
& ( Z2 = X ) )
| ? [G: graph1,X: $int,Y: $int,Z3: $int] :
( path1(G,X,Y)
& path1(G,Y,Z3)
& ( Z = G )
& ( Z1 = X )
& ( Z2 = Z3 ) ) ) ) ).
tff(ineq1,conjecture,
! [N: $int,X: $int,Y: $int] :
( $lesseq(0,N)
=> ( ( $lesseq(0,X)
& $less(X,N) )
=> ( ( $lesseq(0,Y)
& $less(Y,N) )
=> $less($sum($product(X,N),Y),$product(N,N)) ) ) ) ).
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