TPTP Problem File: SWW652=2.p
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% File : SWW652=2 : TPTP v7.4.0. 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 : 0.80 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 unit; 32 type)
% Number of atoms : 68 ( 21 equality)
% Maximal formula depth : 15 ( 4 average)
% Number of connectives : 45 ( 1 ~; 3 |; 17 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% ( 0 ~|; 0 ~&)
% Number of type conns : 27 ( 14 >; 13 *; 0 +; 0 <<)
% Number of predicates : 43 ( 35 propositional; 0-3 arity)
% Number of functors : 16 ( 5 constant; 0-4 arity)
% Number of variables : 68 ( 0 sgn; 58 !; 10 ?)
% ( 68 :; 0 !>; 0 ?*)
% Maximal term depth : 3 ( 1 average)
% Arithmetic symbols : 38 ( 2 prd; 2 fun; 2 num; 32 var)
% 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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