TPTP Problem File: SWW598_2.p
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%------------------------------------------------------------------------------
% File : SWW598_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Foveoos11 challenge2-T-WP parameter maximum
% 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 : foveoos11_challenge2-T-WP_parameter_maximum [Fil14]
% Status : Theorem
% Rating : 0.38 v8.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.00 v6.3.0, 0.71 v6.2.0, 0.75 v6.1.0
% Syntax : Number of formulae : 57 ( 10 unt; 27 typ; 0 def)
% Number of atoms : 98 ( 40 equ)
% Maximal formula atoms : 46 ( 1 avg)
% Number of connectives : 76 ( 8 ~; 6 |; 28 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 89 ( 30 atm; 4 fun; 8 num; 47 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 24 ( 12 >; 12 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 20 usr; 12 con; 0-4 aty)
% Number of variables : 95 ( 95 !; 0 ?; 95 :)
% SPC : TF0_THM_EQU_ARI
% Comments :
%------------------------------------------------------------------------------
tff(uni,type,
uni: $tType ).
tff(ty,type,
ty: $tType ).
tff(sort,type,
sort: ( ty * uni ) > $o ).
tff(witness,type,
witness: ty > uni ).
tff(witness_sort,axiom,
! [A: ty] : sort(A,witness(A)) ).
tff(int,type,
int: ty ).
tff(real,type,
real: ty ).
tff(bool,type,
bool: $tType ).
tff(bool1,type,
bool1: ty ).
tff(true,type,
true: bool ).
tff(false,type,
false: bool ).
tff(match_bool,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(match_bool_sort,axiom,
! [A: ty,X: bool,X1: uni,X2: uni] : sort(A,match_bool(A,X,X1,X2)) ).
tff(match_bool_True,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort(A,Z)
=> ( match_bool(A,true,Z,Z1) = Z ) ) ).
tff(match_bool_False,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort(A,Z1)
=> ( match_bool(A,false,Z,Z1) = Z1 ) ) ).
tff(true_False,axiom,
true != false ).
tff(bool_inversion,axiom,
! [U: bool] :
( ( U = true )
| ( U = false ) ) ).
tff(tuple0,type,
tuple0: $tType ).
tff(tuple01,type,
tuple01: ty ).
tff(tuple02,type,
tuple02: tuple0 ).
tff(tuple0_inversion,axiom,
! [U: tuple0] : U = tuple02 ).
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(min,type,
min: ( $int * $int ) > $int ).
tff(max,type,
max: ( $int * $int ) > $int ).
tff(max_is_ge,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,max(X,Y))
& $lesseq(Y,max(X,Y)) ) ).
tff(max_is_some,axiom,
! [X: $int,Y: $int] :
( ( max(X,Y) = X )
| ( max(X,Y) = Y ) ) ).
tff(min_is_le,axiom,
! [X: $int,Y: $int] :
( $lesseq(min(X,Y),X)
& $lesseq(min(X,Y),Y) ) ).
tff(min_is_some,axiom,
! [X: $int,Y: $int] :
( ( min(X,Y) = X )
| ( min(X,Y) = Y ) ) ).
tff(max_x,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( max(X,Y) = X ) ) ).
tff(max_y,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> ( max(X,Y) = Y ) ) ).
tff(min_x,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> ( min(X,Y) = X ) ) ).
tff(min_y,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( min(X,Y) = Y ) ) ).
tff(max_sym,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( max(X,Y) = max(Y,X) ) ) ).
tff(min_sym,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( min(X,Y) = min(Y,X) ) ) ).
tff(tree,type,
tree: $tType ).
tff(tree1,type,
tree1: ty ).
tff(empty,type,
empty: tree ).
tff(node,type,
node: ( tree * $int * tree ) > tree ).
tff(match_tree,type,
match_tree: ( ty * tree * uni * uni ) > uni ).
tff(match_tree_sort,axiom,
! [A: ty,X: tree,X1: uni,X2: uni] : sort(A,match_tree(A,X,X1,X2)) ).
tff(match_tree_Empty,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort(A,Z)
=> ( match_tree(A,empty,Z,Z1) = Z ) ) ).
tff(match_tree_Node,axiom,
! [A: ty,Z: uni,Z1: uni,U: tree,U1: $int,U2: tree] :
( sort(A,Z1)
=> ( match_tree(A,node(U,U1,U2),Z,Z1) = Z1 ) ) ).
tff(empty_Node,axiom,
! [V: tree,V1: $int,V2: tree] : empty != node(V,V1,V2) ).
tff(node_proj_1,type,
node_proj_1: tree > tree ).
tff(node_proj_1_def,axiom,
! [U: tree,U1: $int,U2: tree] : node_proj_1(node(U,U1,U2)) = U ).
tff(node_proj_2,type,
node_proj_2: tree > $int ).
tff(node_proj_2_def,axiom,
! [U: tree,U1: $int,U2: tree] : node_proj_2(node(U,U1,U2)) = U1 ).
tff(node_proj_3,type,
node_proj_3: tree > tree ).
tff(node_proj_3_def,axiom,
! [U: tree,U1: $int,U2: tree] : node_proj_3(node(U,U1,U2)) = U2 ).
tff(tree_inversion,axiom,
! [U: tree] :
( ( U = empty )
| ( U = node(node_proj_1(U),node_proj_2(U),node_proj_3(U)) ) ) ).
tff(size,type,
size: tree > $int ).
tff(size_def,axiom,
( ( size(empty) = 0 )
& ! [X: tree,X1: $int,X2: tree] : size(node(X,X1,X2)) = $sum($sum(1,size(X)),size(X2)) ) ).
tff(size_nonneg,axiom,
! [T: tree] : $lesseq(0,size(T)) ).
tff(mem,type,
mem: ( $int * tree ) > $o ).
tff(mem_def,axiom,
! [X: $int] :
( ~ mem(X,empty)
& ! [X1: tree,X2: $int,X3: tree] :
( mem(X,node(X1,X2,X3))
<=> ( mem(X,X1)
| ( X = X2 )
| mem(X,X3) ) ) ) ).
tff(wP_parameter_maximum,conjecture,
! [T: tree] :
( ( T != empty )
=> ( ( ( T = empty )
=> $false )
& ! [X: tree,X1: $int,X2: tree] :
( ( T = node(X,X1,X2) )
=> ( ( ( X2 = empty )
=> ( ( ( X = empty )
=> ( mem(X1,T)
& ! [X3: $int] :
( mem(X3,T)
=> $lesseq(X3,X1) ) ) )
& ! [W: tree,W1: $int,W2: tree] :
( ( X = node(W,W1,W2) )
=> ( $lesseq(0,size(T))
& $less(size(X),size(T))
& ( X != empty )
& ! [O: $int] :
( ( mem(O,X)
& ! [X3: $int] :
( mem(X3,X)
=> $lesseq(X3,O) ) )
=> ( mem(max(O,X1),T)
& ! [X3: $int] :
( mem(X3,T)
=> $lesseq(X3,max(O,X1)) ) ) ) ) ) ) )
& ! [W: tree,W1: $int,W2: tree] :
( ( X2 = node(W,W1,W2) )
=> ( ( ( X = empty )
=> ( $lesseq(0,size(T))
& $less(size(X2),size(T))
& ( X2 != empty )
& ! [O: $int] :
( ( mem(O,X2)
& ! [X3: $int] :
( mem(X3,X2)
=> $lesseq(X3,O) ) )
=> ( mem(max(O,X1),T)
& ! [X3: $int] :
( mem(X3,T)
=> $lesseq(X3,max(O,X1)) ) ) ) ) )
& ! [W3: tree,W4: $int,W5: tree] :
( ( X = node(W3,W4,W5) )
=> ( $lesseq(0,size(T))
& $less(size(X2),size(T))
& ( X2 != empty )
& ! [O: $int] :
( ( mem(O,X2)
& ! [X3: $int] :
( mem(X3,X2)
=> $lesseq(X3,O) ) )
=> ( $lesseq(0,size(T))
& $less(size(X),size(T))
& ( X != empty )
& ! [O1: $int] :
( ( mem(O1,X)
& ! [X3: $int] :
( mem(X3,X)
=> $lesseq(X3,O1) ) )
=> ( mem(max(O1,max(X1,O)),T)
& ! [X3: $int] :
( mem(X3,T)
=> $lesseq(X3,max(O1,max(X1,O))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------