TPTP Problem File: SWW615_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW615_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Linked list rev-T-WP parameter in place reverse
% 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 : linked_list_rev-T-WP_parameter_in_place_reverse [Fil14]
% Status : Theorem
% Rating : 0.25 v8.2.0, 0.38 v7.5.0, 0.40 v7.4.0, 0.38 v7.3.0, 0.33 v7.0.0, 0.29 v6.4.0, 0.00 v6.3.0, 0.57 v6.2.0, 0.62 v6.1.0
% Syntax : Number of formulae : 118 ( 37 unt; 48 typ; 0 def)
% Number of atoms : 147 ( 67 equ)
% Maximal formula atoms : 15 ( 1 avg)
% Number of connectives : 89 ( 12 ~; 5 |; 27 &)
% ( 5 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 16 ( 4 atm; 4 fun; 5 num; 3 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 69 ( 31 >; 38 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 0 prp; 2-4 aty)
% Number of functors : 40 ( 36 usr; 12 con; 0-5 aty)
% Number of variables : 217 ( 209 !; 8 ?; 217 :)
% 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(list,type,
list: ty > ty ).
tff(nil,type,
nil: ty > uni ).
tff(nil_sort,axiom,
! [A: ty] : sort(list(A),nil(A)) ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff(cons_sort,axiom,
! [A: ty,X: uni,X1: uni] : sort(list(A),cons(A,X,X1)) ).
tff(match_list,type,
match_list: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_list_sort,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort(A1,match_list(A1,A,X,X1,X2)) ).
tff(match_list_Nil,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort(A1,Z)
=> ( match_list(A1,A,nil(A),Z,Z1) = Z ) ) ).
tff(match_list_Cons,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni,U1: uni] :
( sort(A1,Z1)
=> ( match_list(A1,A,cons(A,U,U1),Z,Z1) = Z1 ) ) ).
tff(nil_Cons,axiom,
! [A: ty,V: uni,V1: uni] : nil(A) != cons(A,V,V1) ).
tff(cons_proj_1,type,
cons_proj_1: ( ty * uni ) > uni ).
tff(cons_proj_1_sort,axiom,
! [A: ty,X: uni] : sort(A,cons_proj_1(A,X)) ).
tff(cons_proj_1_def,axiom,
! [A: ty,U: uni,U1: uni] :
( sort(A,U)
=> ( cons_proj_1(A,cons(A,U,U1)) = U ) ) ).
tff(cons_proj_2,type,
cons_proj_2: ( ty * uni ) > uni ).
tff(cons_proj_2_sort,axiom,
! [A: ty,X: uni] : sort(list(A),cons_proj_2(A,X)) ).
tff(cons_proj_2_def,axiom,
! [A: ty,U: uni,U1: uni] : cons_proj_2(A,cons(A,U,U1)) = U1 ).
tff(list_inversion,axiom,
! [A: ty,U: uni] :
( ( U = nil(A) )
| ( U = cons(A,cons_proj_1(A,U),cons_proj_2(A,U)) ) ) ).
tff(head,type,
head: ( ty * uni ) > uni ).
tff(head_sort,axiom,
! [A: ty,X: uni] : sort(A,head(A,X)) ).
tff(head_cons,axiom,
! [A: ty,X: uni,L: uni] :
( sort(A,X)
=> ( head(A,cons(A,X,L)) = X ) ) ).
tff(tail,type,
tail: ( ty * uni ) > uni ).
tff(tail_sort,axiom,
! [A: ty,X: uni] : sort(list(A),tail(A,X)) ).
tff(tail_cons,axiom,
! [A: ty,X: uni,L: uni] : tail(A,cons(A,X,L)) = L ).
tff(mem,type,
mem: ( ty * uni * uni ) > $o ).
tff(mem_def,axiom,
! [A: ty,X: uni] :
( sort(A,X)
=> ( ~ mem(A,X,nil(A))
& ! [X1: uni,X2: uni] :
( sort(A,X1)
=> ( mem(A,X,cons(A,X1,X2))
<=> ( ( X = X1 )
| mem(A,X,X2) ) ) ) ) ) ).
tff(disjoint,type,
disjoint: ( ty * uni * uni ) > $o ).
tff(disjoint_def,axiom,
! [A: ty,L1: uni,L2: uni] :
( ( disjoint(A,L1,L2)
=> ! [X: uni] :
~ ( mem(A,X,L1)
& mem(A,X,L2) ) )
& ( ! [X: uni] :
( sort(A,X)
=> ~ ( mem(A,X,L1)
& mem(A,X,L2) ) )
=> disjoint(A,L1,L2) ) ) ).
tff(no_repet,type,
no_repet: ( ty * uni ) > $o ).
tff(no_repet_def,axiom,
! [A: ty] :
( no_repet(A,nil(A))
& ! [X: uni,X1: uni] :
( no_repet(A,cons(A,X,X1))
<=> ( ~ mem(A,X,X1)
& no_repet(A,X1) ) ) ) ).
tff(infix_plpl,type,
infix_plpl: ( ty * uni * uni ) > uni ).
tff(infix_plpl_sort,axiom,
! [A: ty,X: uni,X1: uni] : sort(list(A),infix_plpl(A,X,X1)) ).
tff(infix_plpl_def,axiom,
! [A: ty,L2: uni] :
( ( infix_plpl(A,nil(A),L2) = L2 )
& ! [X: uni,X1: uni] : infix_plpl(A,cons(A,X,X1),L2) = cons(A,X,infix_plpl(A,X1,L2)) ) ).
tff(append_assoc,axiom,
! [A: ty,L1: uni,L2: uni,L3: uni] : infix_plpl(A,L1,infix_plpl(A,L2,L3)) = infix_plpl(A,infix_plpl(A,L1,L2),L3) ).
tff(append_l_nil,axiom,
! [A: ty,L: uni] : infix_plpl(A,L,nil(A)) = L ).
tff(length,type,
length: ( ty * uni ) > $int ).
tff(length_def,axiom,
! [A: ty] :
( ( length(A,nil(A)) = 0 )
& ! [X: uni,X1: uni] : length(A,cons(A,X,X1)) = $sum(1,length(A,X1)) ) ).
tff(length_nonnegative,axiom,
! [A: ty,L: uni] : $lesseq(0,length(A,L)) ).
tff(length_nil,axiom,
! [A: ty,L: uni] :
( ( length(A,L) = 0 )
<=> ( L = nil(A) ) ) ).
tff(append_length,axiom,
! [A: ty,L1: uni,L2: uni] : length(A,infix_plpl(A,L1,L2)) = $sum(length(A,L1),length(A,L2)) ).
tff(mem_append,axiom,
! [A: ty,X: uni,L1: uni,L2: uni] :
( mem(A,X,infix_plpl(A,L1,L2))
<=> ( mem(A,X,L1)
| mem(A,X,L2) ) ) ).
tff(mem_decomp,axiom,
! [A: ty,X: uni,L: uni] :
( mem(A,X,L)
=> ? [L1: uni,L2: uni] :
( sort(list(A),L1)
& sort(list(A),L2)
& ( L = infix_plpl(A,L1,cons(A,X,L2)) ) ) ) ).
tff(reverse,type,
reverse: ( ty * uni ) > uni ).
tff(reverse_sort,axiom,
! [A: ty,X: uni] : sort(list(A),reverse(A,X)) ).
tff(reverse_def,axiom,
! [A: ty] :
( ( reverse(A,nil(A)) = nil(A) )
& ! [X: uni,X1: uni] : reverse(A,cons(A,X,X1)) = infix_plpl(A,reverse(A,X1),cons(A,X,nil(A))) ) ).
tff(reverse_append,axiom,
! [A: ty,L1: uni,L2: uni,X: uni] : infix_plpl(A,reverse(A,cons(A,X,L1)),L2) = infix_plpl(A,reverse(A,L1),cons(A,X,L2)) ).
tff(reverse_cons,axiom,
! [A: ty,L: uni,X: uni] : reverse(A,cons(A,X,L)) = infix_plpl(A,reverse(A,L),cons(A,X,nil(A))) ).
tff(reverse_reverse,axiom,
! [A: ty,L: uni] : reverse(A,reverse(A,L)) = L ).
tff(reverse_mem,axiom,
! [A: ty,L: uni,X: uni] :
( mem(A,X,L)
<=> mem(A,X,reverse(A,L)) ) ).
tff(reverse_length,axiom,
! [A: ty,L: uni] : length(A,reverse(A,L)) = length(A,L) ).
tff(map,type,
map: ( ty * ty ) > ty ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(get_sort,axiom,
! [A: ty,B: ty,X: uni,X1: uni] : sort(B,get(B,A,X,X1)) ).
tff(set,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(set_sort,axiom,
! [A: ty,B: ty,X: uni,X1: uni,X2: uni] : sort(map(A,B),set(B,A,X,X1,X2)) ).
tff(select_eq,axiom,
! [A: ty,B: ty,M: uni,A1: uni,A2: uni,B1: uni] :
( sort(B,B1)
=> ( ( A1 = A2 )
=> ( get(B,A,set(B,A,M,A1,B1),A2) = B1 ) ) ) ).
tff(select_neq,axiom,
! [A: ty,B: ty,M: uni,A1: uni,A2: uni] :
( sort(A,A1)
=> ( sort(A,A2)
=> ! [B1: uni] :
( ( A1 != A2 )
=> ( get(B,A,set(B,A,M,A1,B1),A2) = get(B,A,M,A2) ) ) ) ) ).
tff(const,type,
const: ( ty * ty * uni ) > uni ).
tff(const_sort,axiom,
! [A: ty,B: ty,X: uni] : sort(map(A,B),const(B,A,X)) ).
tff(const1,axiom,
! [A: ty,B: ty,B1: uni,A1: uni] :
( sort(B,B1)
=> ( get(B,A,const(B,A,B1),A1) = B1 ) ) ).
tff(loc,type,
loc: $tType ).
tff(loc1,type,
loc1: ty ).
tff(null,type,
null: loc ).
tff(list_loc,type,
list_loc: $tType ).
tff(map_loc_loc,type,
map_loc_loc: $tType ).
tff(list_seg,type,
list_seg: ( loc * map_loc_loc * list_loc * loc ) > $o ).
tff(t2tb,type,
t2tb: list_loc > uni ).
tff(t2tb_sort,axiom,
! [X: list_loc] : sort(list(loc1),t2tb(X)) ).
tff(tb2t,type,
tb2t: uni > list_loc ).
tff(bridgeL,axiom,
! [I: list_loc] : tb2t(t2tb(I)) = I ).
tff(bridgeR,axiom,
! [J: uni] : t2tb(tb2t(J)) = J ).
tff(list_seg_nil,axiom,
! [P: loc,Next: map_loc_loc] : list_seg(P,Next,tb2t(nil(loc1)),P) ).
tff(t2tb1,type,
t2tb1: map_loc_loc > uni ).
tff(t2tb_sort1,axiom,
! [X: map_loc_loc] : sort(map(loc1,loc1),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > map_loc_loc ).
tff(bridgeL1,axiom,
! [I: map_loc_loc] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] :
( sort(map(loc1,loc1),J)
=> ( t2tb1(tb2t1(J)) = J ) ) ).
tff(t2tb2,type,
t2tb2: loc > uni ).
tff(t2tb_sort2,axiom,
! [X: loc] : sort(loc1,t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > loc ).
tff(bridgeL2,axiom,
! [I: loc] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] :
( sort(loc1,J)
=> ( t2tb2(tb2t2(J)) = J ) ) ).
tff(list_seg_cons,axiom,
! [P: loc,Q: loc,Next: map_loc_loc,L: list_loc] :
( ( ( P != null )
& list_seg(tb2t2(get(loc1,loc1,t2tb1(Next),t2tb2(P))),Next,L,Q) )
=> list_seg(P,Next,tb2t(cons(loc1,t2tb2(P),t2tb(L))),Q) ) ).
tff(list_seg_inversion,axiom,
! [Z: loc,Z1: map_loc_loc,Z2: list_loc,Z3: loc] :
( list_seg(Z,Z1,Z2,Z3)
=> ( ? [P: loc,Next: map_loc_loc] :
( ( Z = P )
& ( Z1 = Next )
& ( Z2 = tb2t(nil(loc1)) )
& ( Z3 = P ) )
| ? [P: loc,Q: loc,Next: map_loc_loc,L: list_loc] :
( ( P != null )
& list_seg(tb2t2(get(loc1,loc1,t2tb1(Next),t2tb2(P))),Next,L,Q)
& ( Z = P )
& ( Z1 = Next )
& ( Z2 = tb2t(cons(loc1,t2tb2(P),t2tb(L))) )
& ( Z3 = Q ) ) ) ) ).
tff(list_seg_frame,axiom,
! [Next1: map_loc_loc,Next2: map_loc_loc,P: loc,Q: loc,V: loc,PM: list_loc] :
( ( list_seg(P,Next1,PM,null)
& ( Next2 = tb2t1(set(loc1,loc1,t2tb1(Next1),t2tb2(Q),t2tb2(V))) )
& ~ mem(loc1,t2tb2(Q),t2tb(PM)) )
=> list_seg(P,Next2,PM,null) ) ).
tff(list_seg_functional,axiom,
! [Next: map_loc_loc,L1: list_loc,L2: list_loc,P: loc] :
( ( list_seg(P,Next,L1,null)
& list_seg(P,Next,L2,null) )
=> ( L1 = L2 ) ) ).
tff(list_seg_sublistl,axiom,
! [Next: map_loc_loc,L1: list_loc,L2: list_loc,P: loc,Q: loc] :
( list_seg(P,Next,tb2t(infix_plpl(loc1,t2tb(L1),cons(loc1,t2tb2(Q),t2tb(L2)))),null)
=> list_seg(Q,Next,tb2t(cons(loc1,t2tb2(Q),t2tb(L2))),null) ) ).
tff(list_seg_no_repet,axiom,
! [Next: map_loc_loc,PM: list_loc,P: loc] :
( list_seg(P,Next,PM,null)
=> no_repet(loc1,t2tb(PM)) ) ).
tff(ref,type,
ref: ty > ty ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(mk_ref_sort,axiom,
! [A: ty,X: uni] : sort(ref(A),mk_ref(A,X)) ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(contents_sort,axiom,
! [A: ty,X: uni] : sort(A,contents(A,X)) ).
tff(contents_def,axiom,
! [A: ty,U: uni] :
( sort(A,U)
=> ( contents(A,mk_ref(A,U)) = U ) ) ).
tff(ref_inversion,axiom,
! [A: ty,U: uni] :
( sort(ref(A),U)
=> ( U = mk_ref(A,contents(A,U)) ) ) ).
tff(wP_parameter_in_place_reverse,conjecture,
! [L: loc,LM: list_loc,Next: map_loc_loc] :
( list_seg(L,Next,LM,null)
=> ! [RM: list_loc,R: loc,PM: list_loc,P: loc,Next1: map_loc_loc] :
( ( list_seg(P,Next1,PM,null)
& list_seg(R,Next1,RM,null)
& disjoint(loc1,t2tb(PM),t2tb(RM))
& ( tb2t(infix_plpl(loc1,reverse(loc1,t2tb(PM)),t2tb(RM))) = tb2t(reverse(loc1,t2tb(LM))) ) )
=> ( ( P != null )
=> ! [Next2: map_loc_loc] :
( ( Next2 = tb2t1(set(loc1,loc1,t2tb1(Next1),t2tb2(P),t2tb2(R))) )
=> ( list_seg(R,Next2,RM,null)
=> ! [R1: loc] :
( ( R1 = P )
=> ! [P1: loc] :
( ( P1 = tb2t2(get(loc1,loc1,t2tb1(Next1),t2tb2(P))) )
=> ! [RM1: list_loc] :
( ( RM1 = tb2t(cons(loc1,head(loc1,t2tb(PM)),t2tb(RM))) )
=> ! [PM1: list_loc] :
( ( PM1 = tb2t(tail(loc1,t2tb(PM))) )
=> ( ( PM != tb2t(nil(loc1)) )
& ! [X: loc,X1: list_loc] :
( ( PM = tb2t(cons(loc1,t2tb2(X),t2tb(X1))) )
=> ( X1 = PM1 ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------