TSTP Solution File: SWW634_2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW634_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:35:43 EDT 2024
% Result : Theorem 1.73s 0.60s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 104
% Syntax : Number of formulae : 197 ( 17 unt; 83 typ; 0 def)
% Number of atoms : 978 ( 162 equ)
% Maximal formula atoms : 110 ( 8 avg)
% Number of connectives : 1296 ( 432 ~; 346 |; 426 &)
% ( 46 <=>; 43 =>; 0 <=; 3 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 1156 ( 375 atm; 279 fun; 273 num; 229 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 119 ( 56 >; 63 *; 0 +; 0 <<)
% Number of predicates : 24 ( 20 usr; 9 prp; 0-4 aty)
% Number of functors : 68 ( 64 usr; 21 con; 0-5 aty)
% Number of variables : 367 ( 238 !; 129 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool1: $tType ).
tff(type_def_8,type,
tuple02: $tType ).
tff(type_def_9,type,
set_int: $tType ).
tff(type_def_10,type,
map_int_int: $tType ).
tff(type_def_11,type,
map_int_lpmap_int_intrp: $tType ).
tff(func_def_0,type,
witness1: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool: ty ).
tff(func_def_4,type,
true1: bool1 ).
tff(func_def_5,type,
false1: bool1 ).
tff(func_def_6,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(func_def_7,type,
tuple0: ty ).
tff(func_def_8,type,
tuple03: tuple02 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
set: ty > ty ).
tff(func_def_13,type,
empty: ty > uni ).
tff(func_def_14,type,
add: ( ty * uni * uni ) > uni ).
tff(func_def_15,type,
remove: ( ty * uni * uni ) > uni ).
tff(func_def_16,type,
union: ( ty * uni * uni ) > uni ).
tff(func_def_17,type,
inter: ( ty * uni * uni ) > uni ).
tff(func_def_18,type,
diff: ( ty * uni * uni ) > uni ).
tff(func_def_19,type,
choose: ( ty * uni ) > uni ).
tff(func_def_20,type,
cardinal1: ( ty * uni ) > $int ).
tff(func_def_23,type,
min_elt1: set_int > $int ).
tff(func_def_24,type,
t2tb: set_int > uni ).
tff(func_def_25,type,
tb2t: uni > set_int ).
tff(func_def_26,type,
t2tb1: $int > uni ).
tff(func_def_27,type,
tb2t1: uni > $int ).
tff(func_def_28,type,
max_elt1: set_int > $int ).
tff(func_def_29,type,
below1: $int > set_int ).
tff(func_def_30,type,
succ1: set_int > set_int ).
tff(func_def_32,type,
pred1: set_int > set_int ).
tff(func_def_33,type,
ref: ty > ty ).
tff(func_def_34,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_35,type,
contents: ( ty * uni ) > uni ).
tff(func_def_36,type,
map: ( ty * ty ) > ty ).
tff(func_def_37,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(func_def_38,type,
set1: ( ty * ty * uni * uni * uni ) > uni ).
tff(func_def_39,type,
const: ( ty * ty * uni ) > uni ).
tff(func_def_40,type,
n1: $int ).
tff(func_def_41,type,
t2tb2: map_int_int > uni ).
tff(func_def_42,type,
tb2t2: uni > map_int_int ).
tff(func_def_43,type,
t2tb3: map_int_lpmap_int_intrp > uni ).
tff(func_def_44,type,
tb2t3: uni > map_int_lpmap_int_intrp ).
tff(func_def_46,type,
sK3: ( $int * map_int_int * $int ) > $int ).
tff(func_def_47,type,
sK4: $int ).
tff(func_def_48,type,
sK5: $int ).
tff(func_def_49,type,
sK6: map_int_lpmap_int_intrp ).
tff(func_def_50,type,
sK7: $int ).
tff(func_def_51,type,
sK8: map_int_int ).
tff(func_def_52,type,
sK9: $int ).
tff(func_def_53,type,
sK10: map_int_lpmap_int_intrp ).
tff(func_def_54,type,
sK11: $int ).
tff(func_def_55,type,
sK12: map_int_int ).
tff(func_def_56,type,
sK13: map_int_int ).
tff(func_def_57,type,
sK14: $int ).
tff(func_def_58,type,
sK15: map_int_int > $int ).
tff(func_def_59,type,
sK16: $int > $int ).
tff(func_def_60,type,
sK17: $int > $int ).
tff(func_def_61,type,
sK18: ( ty * uni ) > uni ).
tff(func_def_62,type,
sK19: ( map_int_int * map_int_int ) > $int ).
tff(func_def_63,type,
sK20: ( map_int_int * $int ) > $int ).
tff(func_def_64,type,
sK21: ( $int * map_int_int ) > $int ).
tff(func_def_65,type,
sK22: ( ty * uni * uni ) > uni ).
tff(func_def_66,type,
sK23: ( ty * uni * uni ) > uni ).
tff(func_def_67,type,
sK24: ( map_int_lpmap_int_intrp * $int * $int ) > $int ).
tff(func_def_68,type,
sK25: ( map_int_lpmap_int_intrp * $int * $int ) > $int ).
tff(func_def_69,type,
sK26: ( ty * uni * uni * $int ) > $int ).
tff(pred_def_1,type,
sort1: ( ty * uni ) > $o ).
tff(pred_def_3,type,
mem: ( ty * uni * uni ) > $o ).
tff(pred_def_4,type,
infix_eqeq: ( ty * uni * uni ) > $o ).
tff(pred_def_5,type,
subset: ( ty * uni * uni ) > $o ).
tff(pred_def_6,type,
is_empty: ( ty * uni ) > $o ).
tff(pred_def_8,type,
eq_prefix1: ( ty * uni * uni * $int ) > $o ).
tff(pred_def_9,type,
partial_solution1: ( $int * map_int_int ) > $o ).
tff(pred_def_10,type,
lt_sol1: ( map_int_int * map_int_int ) > $o ).
tff(pred_def_11,type,
sorted1: ( map_int_lpmap_int_intrp * $int * $int ) > $o ).
tff(pred_def_12,type,
sP0: ( $int * map_int_int * $int ) > $o ).
tff(pred_def_13,type,
sP1: ( $int * map_int_int ) > $o ).
tff(pred_def_14,type,
sP2: ( map_int_int * $int ) > $o ).
tff(f4148,plain,
$false,
inference(avatar_sat_refutation,[],[f478,f483,f488,f493,f546,f567,f585,f652,f4145]) ).
tff(f4145,plain,
spl27_10,
inference(avatar_contradiction_clause,[],[f4144]) ).
tff(f4144,plain,
( $false
| spl27_10 ),
inference(subsumption_resolution,[],[f4139,f4105]) ).
tff(f4105,plain,
( ~ $less(sK26(int,t2tb2(sK12),t2tb2(sK13),0),0)
| spl27_10 ),
inference(resolution,[],[f439,f611]) ).
tff(f611,plain,
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(sK13),0)
| spl27_10 ),
inference(avatar_component_clause,[],[f609]) ).
tff(f609,plain,
( spl27_10
<=> eq_prefix1(int,t2tb2(sK12),t2tb2(sK13),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_10])]) ).
tff(f439,plain,
! [X2: uni,X3: $int,X0: ty,X1: uni] :
( eq_prefix1(X0,X1,X2,X3)
| ~ $less(sK26(X0,X1,X2,X3),0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: ty,X1: uni,X2: uni,X3: $int] :
( ( eq_prefix1(X0,X1,X2,X3)
| ( ( get(X0,int,X1,t2tb1(sK26(X0,X1,X2,X3))) != get(X0,int,X2,t2tb1(sK26(X0,X1,X2,X3))) )
& $less(sK26(X0,X1,X2,X3),X3)
& ~ $less(sK26(X0,X1,X2,X3),0) ) )
& ( ! [X5: $int] :
( ( get(X0,int,X1,t2tb1(X5)) = get(X0,int,X2,t2tb1(X5)) )
| ~ $less(X5,X3)
| $less(X5,0) )
| ~ eq_prefix1(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f281,f282]) ).
tff(f282,plain,
! [X0: ty,X1: uni,X2: uni,X3: $int] :
( ? [X4: $int] :
( ( get(X0,int,X1,t2tb1(X4)) != get(X0,int,X2,t2tb1(X4)) )
& $less(X4,X3)
& ~ $less(X4,0) )
=> ( ( get(X0,int,X1,t2tb1(sK26(X0,X1,X2,X3))) != get(X0,int,X2,t2tb1(sK26(X0,X1,X2,X3))) )
& $less(sK26(X0,X1,X2,X3),X3)
& ~ $less(sK26(X0,X1,X2,X3),0) ) ),
introduced(choice_axiom,[]) ).
tff(f281,plain,
! [X0: ty,X1: uni,X2: uni,X3: $int] :
( ( eq_prefix1(X0,X1,X2,X3)
| ? [X4: $int] :
( ( get(X0,int,X1,t2tb1(X4)) != get(X0,int,X2,t2tb1(X4)) )
& $less(X4,X3)
& ~ $less(X4,0) ) )
& ( ! [X5: $int] :
( ( get(X0,int,X1,t2tb1(X5)) = get(X0,int,X2,t2tb1(X5)) )
| ~ $less(X5,X3)
| $less(X5,0) )
| ~ eq_prefix1(X0,X1,X2,X3) ) ),
inference(rectify,[],[f280]) ).
tff(f280,plain,
! [X0: ty,X1: uni,X2: uni,X3: $int] :
( ( eq_prefix1(X0,X1,X2,X3)
| ? [X4: $int] :
( ( get(X0,int,X1,t2tb1(X4)) != get(X0,int,X2,t2tb1(X4)) )
& $less(X4,X3)
& ~ $less(X4,0) ) )
& ( ! [X4: $int] :
( ( get(X0,int,X1,t2tb1(X4)) = get(X0,int,X2,t2tb1(X4)) )
| ~ $less(X4,X3)
| $less(X4,0) )
| ~ eq_prefix1(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: ty,X1: uni,X2: uni,X3: $int] :
( eq_prefix1(X0,X1,X2,X3)
<=> ! [X4: $int] :
( ( get(X0,int,X1,t2tb1(X4)) = get(X0,int,X2,t2tb1(X4)) )
| ~ $less(X4,X3)
| $less(X4,0) ) ),
inference(flattening,[],[f217]) ).
tff(f217,plain,
! [X0: ty,X1: uni,X2: uni,X3: $int] :
( eq_prefix1(X0,X1,X2,X3)
<=> ! [X4: $int] :
( ( get(X0,int,X1,t2tb1(X4)) = get(X0,int,X2,t2tb1(X4)) )
| ~ $less(X4,X3)
| $less(X4,0) ) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: ty,X1: uni,X2: uni,X3: $int] :
( eq_prefix1(X0,X1,X2,X3)
<=> ! [X4: $int] :
( ( $less(X4,X3)
& ~ $less(X4,0) )
=> ( get(X0,int,X1,t2tb1(X4)) = get(X0,int,X2,t2tb1(X4)) ) ) ),
inference(rectify,[],[f92]) ).
tff(f92,plain,
! [X0: ty,X20: uni,X6: uni,X12: $int] :
( eq_prefix1(X0,X20,X6,X12)
<=> ! [X21: $int] :
( ( $less(X21,X12)
& ~ $less(X21,0) )
=> ( get(X0,int,X20,t2tb1(X21)) = get(X0,int,X6,t2tb1(X21)) ) ) ),
inference(theory_normalization,[],[f64]) ).
tff(f64,axiom,
! [X0: ty,X20: uni,X6: uni,X12: $int] :
( eq_prefix1(X0,X20,X6,X12)
<=> ! [X21: $int] :
( ( $less(X21,X12)
& $lesseq(0,X21) )
=> ( get(X0,int,X20,t2tb1(X21)) = get(X0,int,X6,t2tb1(X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq_prefix_def) ).
tff(f4139,plain,
( $less(sK26(int,t2tb2(sK12),t2tb2(sK13),0),0)
| spl27_10 ),
inference(resolution,[],[f440,f611]) ).
tff(f440,plain,
! [X2: uni,X3: $int,X0: ty,X1: uni] :
( eq_prefix1(X0,X1,X2,X3)
| $less(sK26(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f283]) ).
tff(f652,plain,
( ~ spl27_10
| ~ spl27_3
| ~ spl27_4 ),
inference(avatar_split_clause,[],[f651,f476,f472,f609]) ).
tff(f472,plain,
( spl27_3
<=> partial_solution1(n1,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_3])]) ).
tff(f476,plain,
( spl27_4
<=> ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),n1)
| $less(X10,0)
| ~ $less(X10,$sum(sK9,$uminus(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_4])]) ).
tff(f651,plain,
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(sK13),0)
| ~ spl27_3
| ~ spl27_4 ),
inference(subsumption_resolution,[],[f650,f591]) ).
tff(f591,plain,
( partial_solution1(sK4,sK13)
| ~ spl27_3 ),
inference(forward_demodulation,[],[f473,f297]) ).
tff(f297,plain,
n1 = sK4,
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
( ( ( ( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),n1)
| ~ $less(X10,$sum(sK9,$uminus(sK5)))
| $less(X10,0) )
| ~ partial_solution1(n1,sK13) )
& ( ( eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(sK14)),n1)
& $less(sK14,$sum(sK9,$uminus(sK5)))
& ~ $less(sK14,0) )
| partial_solution1(n1,sK13) ) )
| ~ sorted1(sK10,0,sK9)
| ( sK9 != $sum(sK9,$uminus(sK5)) ) )
& eq_prefix1(map(int,int),t2tb3(sK6),t2tb3(sK10),sK5)
& eq_prefix1(int,t2tb2(sK8),t2tb2(sK12),sK11)
& ! [X12: map_int_int] :
( ( ( eq_prefix1(int,t2tb2(sK12),t2tb2(X12),sK11)
& partial_solution1(n1,X12) )
| ! [X13: $int] :
( ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(X13)),n1)
| ~ $less(X13,sK9)
| $less(X13,sK5) ) )
& ( ( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(sK15(X12))),n1)
& $less(sK15(X12),sK9)
& ~ $less(sK15(X12),sK5) )
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),sK11)
| ~ partial_solution1(n1,X12) ) )
& sorted1(sK10,sK5,sK9)
& ( sK7 = sK11 )
& ~ $less($sum(sK9,$uminus(sK5)),0)
& partial_solution1(sK7,sK8)
& ! [X15: $int] :
( ( ( ~ mem(int,t2tb1(X15),empty(int))
| ( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(sK16(X15)))) = $sum($sum(X15,sK7),$uminus(sK16(X15))) )
& $less(sK16(X15),sK7)
& ~ $less(sK16(X15),0) ) )
& ( ! [X17: $int] :
( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(X17))) != $sum($sum(X15,sK7),$uminus(X17)) )
| ~ $less(X17,sK7)
| $less(X17,0) )
| mem(int,t2tb1(X15),empty(int)) ) )
| $less(X15,0) )
& ! [X18: $int] :
( ( ( ~ mem(int,t2tb1(X18),empty(int))
| ( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(sK17(X18)))) = $sum($sum(X18,sK17(X18)),$uminus(sK7)) )
& $less(sK17(X18),sK7)
& ~ $less(sK17(X18),0) ) )
& ( ! [X20: $int] :
( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(X20))) != $sum($sum(X18,X20),$uminus(sK7)) )
| ~ $less(X20,sK7)
| $less(X20,0) )
| mem(int,t2tb1(X18),empty(int)) ) )
| $less(X18,0) )
& ! [X21: $int] :
( ( mem(int,t2tb1(X21),t2tb(below1(sK4)))
| ~ sP0(X21,sK8,sK7) )
& ( sP0(X21,sK8,sK7)
| ~ mem(int,t2tb1(X21),t2tb(below1(sK4))) ) )
& ~ $less(sK5,0)
& ( n1 = $sum(sK7,cardinal1(int,t2tb(below1(sK4)))) )
& ~ $less(sK7,0)
& ( 0 = sK7 )
& ( 0 = sK5 )
& ( n1 = sK4 )
& ~ $less(sK4,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17])],[f235,f242,f241,f240,f239,f238,f237,f236]) ).
tff(f236,plain,
( ? [X0: $int,X1: $int,X2: map_int_lpmap_int_intrp,X3: $int,X4: map_int_int] :
( ? [X5: $int,X6: map_int_lpmap_int_intrp,X7: $int,X8: map_int_int] :
( ( ? [X9: map_int_int] :
( ( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(X6),t2tb1(X10)),n1)
| ~ $less(X10,$sum(X5,$uminus(X1)))
| $less(X10,0) )
| ~ partial_solution1(n1,X9) )
& ( ? [X11: $int] :
( eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(X6),t2tb1(X11)),n1)
& $less(X11,$sum(X5,$uminus(X1)))
& ~ $less(X11,0) )
| partial_solution1(n1,X9) ) )
| ~ sorted1(X6,0,X5)
| ( $sum(X5,$uminus(X1)) != X5 ) )
& eq_prefix1(map(int,int),t2tb3(X2),t2tb3(X6),X1)
& eq_prefix1(int,t2tb2(X4),t2tb2(X8),X7)
& ! [X12: map_int_int] :
( ( ( eq_prefix1(int,t2tb2(X8),t2tb2(X12),X7)
& partial_solution1(n1,X12) )
| ! [X13: $int] :
( ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(X6),t2tb1(X13)),n1)
| ~ $less(X13,X5)
| $less(X13,X1) ) )
& ( ? [X14: $int] :
( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(X6),t2tb1(X14)),n1)
& $less(X14,X5)
& ~ $less(X14,X1) )
| ~ eq_prefix1(int,t2tb2(X8),t2tb2(X12),X7)
| ~ partial_solution1(n1,X12) ) )
& sorted1(X6,X1,X5)
& ( X3 = X7 )
& ~ $less($sum(X5,$uminus(X1)),0) )
& partial_solution1(X3,X4)
& ! [X15: $int] :
( ( ( ~ mem(int,t2tb1(X15),empty(int))
| ? [X16: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X16))) = $sum($sum(X15,X3),$uminus(X16)) )
& $less(X16,X3)
& ~ $less(X16,0) ) )
& ( ! [X17: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X17))) != $sum($sum(X15,X3),$uminus(X17)) )
| ~ $less(X17,X3)
| $less(X17,0) )
| mem(int,t2tb1(X15),empty(int)) ) )
| $less(X15,0) )
& ! [X18: $int] :
( ( ( ~ mem(int,t2tb1(X18),empty(int))
| ? [X19: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X19))) = $sum($sum(X18,X19),$uminus(X3)) )
& $less(X19,X3)
& ~ $less(X19,0) ) )
& ( ! [X20: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X20))) != $sum($sum(X18,X20),$uminus(X3)) )
| ~ $less(X20,X3)
| $less(X20,0) )
| mem(int,t2tb1(X18),empty(int)) ) )
| $less(X18,0) )
& ! [X21: $int] :
( ( mem(int,t2tb1(X21),t2tb(below1(X0)))
| ~ sP0(X21,X4,X3) )
& ( sP0(X21,X4,X3)
| ~ mem(int,t2tb1(X21),t2tb(below1(X0))) ) )
& ~ $less(X1,0)
& ( n1 = $sum(X3,cardinal1(int,t2tb(below1(X0)))) )
& ~ $less(X3,0)
& ( 0 = X3 )
& ( 0 = X1 )
& ( n1 = X0 )
& ~ $less(X0,0) )
=> ( ? [X8: map_int_int,X7: $int,X6: map_int_lpmap_int_intrp,X5: $int] :
( ( ? [X9: map_int_int] :
( ( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(X6),t2tb1(X10)),n1)
| ~ $less(X10,$sum(X5,$uminus(sK5)))
| $less(X10,0) )
| ~ partial_solution1(n1,X9) )
& ( ? [X11: $int] :
( eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(X6),t2tb1(X11)),n1)
& $less(X11,$sum(X5,$uminus(sK5)))
& ~ $less(X11,0) )
| partial_solution1(n1,X9) ) )
| ~ sorted1(X6,0,X5)
| ( $sum(X5,$uminus(sK5)) != X5 ) )
& eq_prefix1(map(int,int),t2tb3(sK6),t2tb3(X6),sK5)
& eq_prefix1(int,t2tb2(sK8),t2tb2(X8),X7)
& ! [X12: map_int_int] :
( ( ( eq_prefix1(int,t2tb2(X8),t2tb2(X12),X7)
& partial_solution1(n1,X12) )
| ! [X13: $int] :
( ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(X6),t2tb1(X13)),n1)
| ~ $less(X13,X5)
| $less(X13,sK5) ) )
& ( ? [X14: $int] :
( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(X6),t2tb1(X14)),n1)
& $less(X14,X5)
& ~ $less(X14,sK5) )
| ~ eq_prefix1(int,t2tb2(X8),t2tb2(X12),X7)
| ~ partial_solution1(n1,X12) ) )
& sorted1(X6,sK5,X5)
& ( sK7 = X7 )
& ~ $less($sum(X5,$uminus(sK5)),0) )
& partial_solution1(sK7,sK8)
& ! [X15: $int] :
( ( ( ~ mem(int,t2tb1(X15),empty(int))
| ? [X16: $int] :
( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(X16))) = $sum($sum(X15,sK7),$uminus(X16)) )
& $less(X16,sK7)
& ~ $less(X16,0) ) )
& ( ! [X17: $int] :
( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(X17))) != $sum($sum(X15,sK7),$uminus(X17)) )
| ~ $less(X17,sK7)
| $less(X17,0) )
| mem(int,t2tb1(X15),empty(int)) ) )
| $less(X15,0) )
& ! [X18: $int] :
( ( ( ~ mem(int,t2tb1(X18),empty(int))
| ? [X19: $int] :
( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(X19))) = $sum($sum(X18,X19),$uminus(sK7)) )
& $less(X19,sK7)
& ~ $less(X19,0) ) )
& ( ! [X20: $int] :
( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(X20))) != $sum($sum(X18,X20),$uminus(sK7)) )
| ~ $less(X20,sK7)
| $less(X20,0) )
| mem(int,t2tb1(X18),empty(int)) ) )
| $less(X18,0) )
& ! [X21: $int] :
( ( mem(int,t2tb1(X21),t2tb(below1(sK4)))
| ~ sP0(X21,sK8,sK7) )
& ( sP0(X21,sK8,sK7)
| ~ mem(int,t2tb1(X21),t2tb(below1(sK4))) ) )
& ~ $less(sK5,0)
& ( n1 = $sum(sK7,cardinal1(int,t2tb(below1(sK4)))) )
& ~ $less(sK7,0)
& ( 0 = sK7 )
& ( 0 = sK5 )
& ( n1 = sK4 )
& ~ $less(sK4,0) ) ),
introduced(choice_axiom,[]) ).
tff(f237,plain,
( ? [X8: map_int_int,X7: $int,X6: map_int_lpmap_int_intrp,X5: $int] :
( ( ? [X9: map_int_int] :
( ( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(X6),t2tb1(X10)),n1)
| ~ $less(X10,$sum(X5,$uminus(sK5)))
| $less(X10,0) )
| ~ partial_solution1(n1,X9) )
& ( ? [X11: $int] :
( eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(X6),t2tb1(X11)),n1)
& $less(X11,$sum(X5,$uminus(sK5)))
& ~ $less(X11,0) )
| partial_solution1(n1,X9) ) )
| ~ sorted1(X6,0,X5)
| ( $sum(X5,$uminus(sK5)) != X5 ) )
& eq_prefix1(map(int,int),t2tb3(sK6),t2tb3(X6),sK5)
& eq_prefix1(int,t2tb2(sK8),t2tb2(X8),X7)
& ! [X12: map_int_int] :
( ( ( eq_prefix1(int,t2tb2(X8),t2tb2(X12),X7)
& partial_solution1(n1,X12) )
| ! [X13: $int] :
( ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(X6),t2tb1(X13)),n1)
| ~ $less(X13,X5)
| $less(X13,sK5) ) )
& ( ? [X14: $int] :
( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(X6),t2tb1(X14)),n1)
& $less(X14,X5)
& ~ $less(X14,sK5) )
| ~ eq_prefix1(int,t2tb2(X8),t2tb2(X12),X7)
| ~ partial_solution1(n1,X12) ) )
& sorted1(X6,sK5,X5)
& ( sK7 = X7 )
& ~ $less($sum(X5,$uminus(sK5)),0) )
=> ( ( ? [X9: map_int_int] :
( ( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),n1)
| ~ $less(X10,$sum(sK9,$uminus(sK5)))
| $less(X10,0) )
| ~ partial_solution1(n1,X9) )
& ( ? [X11: $int] :
( eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(sK10),t2tb1(X11)),n1)
& $less(X11,$sum(sK9,$uminus(sK5)))
& ~ $less(X11,0) )
| partial_solution1(n1,X9) ) )
| ~ sorted1(sK10,0,sK9)
| ( sK9 != $sum(sK9,$uminus(sK5)) ) )
& eq_prefix1(map(int,int),t2tb3(sK6),t2tb3(sK10),sK5)
& eq_prefix1(int,t2tb2(sK8),t2tb2(sK12),sK11)
& ! [X12: map_int_int] :
( ( ( eq_prefix1(int,t2tb2(sK12),t2tb2(X12),sK11)
& partial_solution1(n1,X12) )
| ! [X13: $int] :
( ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(X13)),n1)
| ~ $less(X13,sK9)
| $less(X13,sK5) ) )
& ( ? [X14: $int] :
( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(X14)),n1)
& $less(X14,sK9)
& ~ $less(X14,sK5) )
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),sK11)
| ~ partial_solution1(n1,X12) ) )
& sorted1(sK10,sK5,sK9)
& ( sK7 = sK11 )
& ~ $less($sum(sK9,$uminus(sK5)),0) ) ),
introduced(choice_axiom,[]) ).
tff(f238,plain,
( ? [X9: map_int_int] :
( ( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),n1)
| ~ $less(X10,$sum(sK9,$uminus(sK5)))
| $less(X10,0) )
| ~ partial_solution1(n1,X9) )
& ( ? [X11: $int] :
( eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(sK10),t2tb1(X11)),n1)
& $less(X11,$sum(sK9,$uminus(sK5)))
& ~ $less(X11,0) )
| partial_solution1(n1,X9) ) )
=> ( ( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),n1)
| ~ $less(X10,$sum(sK9,$uminus(sK5)))
| $less(X10,0) )
| ~ partial_solution1(n1,sK13) )
& ( ? [X11: $int] :
( eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X11)),n1)
& $less(X11,$sum(sK9,$uminus(sK5)))
& ~ $less(X11,0) )
| partial_solution1(n1,sK13) ) ) ),
introduced(choice_axiom,[]) ).
tff(f239,plain,
( ? [X11: $int] :
( eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X11)),n1)
& $less(X11,$sum(sK9,$uminus(sK5)))
& ~ $less(X11,0) )
=> ( eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(sK14)),n1)
& $less(sK14,$sum(sK9,$uminus(sK5)))
& ~ $less(sK14,0) ) ),
introduced(choice_axiom,[]) ).
tff(f240,plain,
! [X12: map_int_int] :
( ? [X14: $int] :
( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(X14)),n1)
& $less(X14,sK9)
& ~ $less(X14,sK5) )
=> ( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(sK15(X12))),n1)
& $less(sK15(X12),sK9)
& ~ $less(sK15(X12),sK5) ) ),
introduced(choice_axiom,[]) ).
tff(f241,plain,
! [X15: $int] :
( ? [X16: $int] :
( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(X16))) = $sum($sum(X15,sK7),$uminus(X16)) )
& $less(X16,sK7)
& ~ $less(X16,0) )
=> ( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(sK16(X15)))) = $sum($sum(X15,sK7),$uminus(sK16(X15))) )
& $less(sK16(X15),sK7)
& ~ $less(sK16(X15),0) ) ),
introduced(choice_axiom,[]) ).
tff(f242,plain,
! [X18: $int] :
( ? [X19: $int] :
( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(X19))) = $sum($sum(X18,X19),$uminus(sK7)) )
& $less(X19,sK7)
& ~ $less(X19,0) )
=> ( ( tb2t1(get(int,int,t2tb2(sK8),t2tb1(sK17(X18)))) = $sum($sum(X18,sK17(X18)),$uminus(sK7)) )
& $less(sK17(X18),sK7)
& ~ $less(sK17(X18),0) ) ),
introduced(choice_axiom,[]) ).
tff(f235,plain,
? [X0: $int,X1: $int,X2: map_int_lpmap_int_intrp,X3: $int,X4: map_int_int] :
( ? [X5: $int,X6: map_int_lpmap_int_intrp,X7: $int,X8: map_int_int] :
( ( ? [X9: map_int_int] :
( ( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(X6),t2tb1(X10)),n1)
| ~ $less(X10,$sum(X5,$uminus(X1)))
| $less(X10,0) )
| ~ partial_solution1(n1,X9) )
& ( ? [X11: $int] :
( eq_prefix1(int,t2tb2(X9),get(map(int,int),int,t2tb3(X6),t2tb1(X11)),n1)
& $less(X11,$sum(X5,$uminus(X1)))
& ~ $less(X11,0) )
| partial_solution1(n1,X9) ) )
| ~ sorted1(X6,0,X5)
| ( $sum(X5,$uminus(X1)) != X5 ) )
& eq_prefix1(map(int,int),t2tb3(X2),t2tb3(X6),X1)
& eq_prefix1(int,t2tb2(X4),t2tb2(X8),X7)
& ! [X12: map_int_int] :
( ( ( eq_prefix1(int,t2tb2(X8),t2tb2(X12),X7)
& partial_solution1(n1,X12) )
| ! [X13: $int] :
( ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(X6),t2tb1(X13)),n1)
| ~ $less(X13,X5)
| $less(X13,X1) ) )
& ( ? [X14: $int] :
( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(X6),t2tb1(X14)),n1)
& $less(X14,X5)
& ~ $less(X14,X1) )
| ~ eq_prefix1(int,t2tb2(X8),t2tb2(X12),X7)
| ~ partial_solution1(n1,X12) ) )
& sorted1(X6,X1,X5)
& ( X3 = X7 )
& ~ $less($sum(X5,$uminus(X1)),0) )
& partial_solution1(X3,X4)
& ! [X15: $int] :
( ( ( ~ mem(int,t2tb1(X15),empty(int))
| ? [X16: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X16))) = $sum($sum(X15,X3),$uminus(X16)) )
& $less(X16,X3)
& ~ $less(X16,0) ) )
& ( ! [X17: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X17))) != $sum($sum(X15,X3),$uminus(X17)) )
| ~ $less(X17,X3)
| $less(X17,0) )
| mem(int,t2tb1(X15),empty(int)) ) )
| $less(X15,0) )
& ! [X18: $int] :
( ( ( ~ mem(int,t2tb1(X18),empty(int))
| ? [X19: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X19))) = $sum($sum(X18,X19),$uminus(X3)) )
& $less(X19,X3)
& ~ $less(X19,0) ) )
& ( ! [X20: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X20))) != $sum($sum(X18,X20),$uminus(X3)) )
| ~ $less(X20,X3)
| $less(X20,0) )
| mem(int,t2tb1(X18),empty(int)) ) )
| $less(X18,0) )
& ! [X21: $int] :
( ( mem(int,t2tb1(X21),t2tb(below1(X0)))
| ~ sP0(X21,X4,X3) )
& ( sP0(X21,X4,X3)
| ~ mem(int,t2tb1(X21),t2tb(below1(X0))) ) )
& ~ $less(X1,0)
& ( n1 = $sum(X3,cardinal1(int,t2tb(below1(X0)))) )
& ~ $less(X3,0)
& ( 0 = X3 )
& ( 0 = X1 )
& ( n1 = X0 )
& ~ $less(X0,0) ),
inference(rectify,[],[f234]) ).
tff(f234,plain,
? [X0: $int,X1: $int,X2: map_int_lpmap_int_intrp,X3: $int,X4: map_int_int] :
( ? [X11: $int,X12: map_int_lpmap_int_intrp,X13: $int,X14: map_int_int] :
( ( ? [X17: map_int_int] :
( ( ! [X18: $int] :
( ~ eq_prefix1(int,t2tb2(X17),get(map(int,int),int,t2tb3(X12),t2tb1(X18)),n1)
| ~ $less(X18,$sum(X11,$uminus(X1)))
| $less(X18,0) )
| ~ partial_solution1(n1,X17) )
& ( ? [X18: $int] :
( eq_prefix1(int,t2tb2(X17),get(map(int,int),int,t2tb3(X12),t2tb1(X18)),n1)
& $less(X18,$sum(X11,$uminus(X1)))
& ~ $less(X18,0) )
| partial_solution1(n1,X17) ) )
| ~ sorted1(X12,0,X11)
| ( $sum(X11,$uminus(X1)) != X11 ) )
& eq_prefix1(map(int,int),t2tb3(X2),t2tb3(X12),X1)
& eq_prefix1(int,t2tb2(X4),t2tb2(X14),X13)
& ! [X15: map_int_int] :
( ( ( eq_prefix1(int,t2tb2(X14),t2tb2(X15),X13)
& partial_solution1(n1,X15) )
| ! [X16: $int] :
( ~ eq_prefix1(int,t2tb2(X15),get(map(int,int),int,t2tb3(X12),t2tb1(X16)),n1)
| ~ $less(X16,X11)
| $less(X16,X1) ) )
& ( ? [X16: $int] :
( eq_prefix1(int,t2tb2(X15),get(map(int,int),int,t2tb3(X12),t2tb1(X16)),n1)
& $less(X16,X11)
& ~ $less(X16,X1) )
| ~ eq_prefix1(int,t2tb2(X14),t2tb2(X15),X13)
| ~ partial_solution1(n1,X15) ) )
& sorted1(X12,X1,X11)
& ( X3 = X13 )
& ~ $less($sum(X11,$uminus(X1)),0) )
& partial_solution1(X3,X4)
& ! [X5: $int] :
( ( ( ~ mem(int,t2tb1(X5),empty(int))
| ? [X6: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X6))) = $sum($sum(X5,X3),$uminus(X6)) )
& $less(X6,X3)
& ~ $less(X6,0) ) )
& ( ! [X6: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X6))) != $sum($sum(X5,X3),$uminus(X6)) )
| ~ $less(X6,X3)
| $less(X6,0) )
| mem(int,t2tb1(X5),empty(int)) ) )
| $less(X5,0) )
& ! [X7: $int] :
( ( ( ~ mem(int,t2tb1(X7),empty(int))
| ? [X8: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X8))) = $sum($sum(X7,X8),$uminus(X3)) )
& $less(X8,X3)
& ~ $less(X8,0) ) )
& ( ! [X8: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X8))) != $sum($sum(X7,X8),$uminus(X3)) )
| ~ $less(X8,X3)
| $less(X8,0) )
| mem(int,t2tb1(X7),empty(int)) ) )
| $less(X7,0) )
& ! [X9: $int] :
( ( mem(int,t2tb1(X9),t2tb(below1(X0)))
| ~ sP0(X9,X4,X3) )
& ( sP0(X9,X4,X3)
| ~ mem(int,t2tb1(X9),t2tb(below1(X0))) ) )
& ~ $less(X1,0)
& ( n1 = $sum(X3,cardinal1(int,t2tb(below1(X0)))) )
& ~ $less(X3,0)
& ( 0 = X3 )
& ( 0 = X1 )
& ( n1 = X0 )
& ~ $less(X0,0) ),
inference(flattening,[],[f233]) ).
tff(f233,plain,
? [X0: $int,X1: $int,X2: map_int_lpmap_int_intrp,X3: $int,X4: map_int_int] :
( ? [X11: $int,X12: map_int_lpmap_int_intrp,X13: $int,X14: map_int_int] :
( ( ? [X17: map_int_int] :
( ( ! [X18: $int] :
( ~ eq_prefix1(int,t2tb2(X17),get(map(int,int),int,t2tb3(X12),t2tb1(X18)),n1)
| ~ $less(X18,$sum(X11,$uminus(X1)))
| $less(X18,0) )
| ~ partial_solution1(n1,X17) )
& ( ? [X18: $int] :
( eq_prefix1(int,t2tb2(X17),get(map(int,int),int,t2tb3(X12),t2tb1(X18)),n1)
& $less(X18,$sum(X11,$uminus(X1)))
& ~ $less(X18,0) )
| partial_solution1(n1,X17) ) )
| ~ sorted1(X12,0,X11)
| ( $sum(X11,$uminus(X1)) != X11 ) )
& eq_prefix1(map(int,int),t2tb3(X2),t2tb3(X12),X1)
& eq_prefix1(int,t2tb2(X4),t2tb2(X14),X13)
& ! [X15: map_int_int] :
( ( ( eq_prefix1(int,t2tb2(X14),t2tb2(X15),X13)
& partial_solution1(n1,X15) )
| ! [X16: $int] :
( ~ eq_prefix1(int,t2tb2(X15),get(map(int,int),int,t2tb3(X12),t2tb1(X16)),n1)
| ~ $less(X16,X11)
| $less(X16,X1) ) )
& ( ? [X16: $int] :
( eq_prefix1(int,t2tb2(X15),get(map(int,int),int,t2tb3(X12),t2tb1(X16)),n1)
& $less(X16,X11)
& ~ $less(X16,X1) )
| ~ eq_prefix1(int,t2tb2(X14),t2tb2(X15),X13)
| ~ partial_solution1(n1,X15) ) )
& sorted1(X12,X1,X11)
& ( X3 = X13 )
& ~ $less($sum(X11,$uminus(X1)),0) )
& partial_solution1(X3,X4)
& ! [X5: $int] :
( ( ( ~ mem(int,t2tb1(X5),empty(int))
| ? [X6: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X6))) = $sum($sum(X5,X3),$uminus(X6)) )
& $less(X6,X3)
& ~ $less(X6,0) ) )
& ( ! [X6: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X6))) != $sum($sum(X5,X3),$uminus(X6)) )
| ~ $less(X6,X3)
| $less(X6,0) )
| mem(int,t2tb1(X5),empty(int)) ) )
| $less(X5,0) )
& ! [X7: $int] :
( ( ( ~ mem(int,t2tb1(X7),empty(int))
| ? [X8: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X8))) = $sum($sum(X7,X8),$uminus(X3)) )
& $less(X8,X3)
& ~ $less(X8,0) ) )
& ( ! [X8: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X8))) != $sum($sum(X7,X8),$uminus(X3)) )
| ~ $less(X8,X3)
| $less(X8,0) )
| mem(int,t2tb1(X7),empty(int)) ) )
| $less(X7,0) )
& ! [X9: $int] :
( ( mem(int,t2tb1(X9),t2tb(below1(X0)))
| ~ sP0(X9,X4,X3) )
& ( sP0(X9,X4,X3)
| ~ mem(int,t2tb1(X9),t2tb(below1(X0))) ) )
& ~ $less(X1,0)
& ( n1 = $sum(X3,cardinal1(int,t2tb(below1(X0)))) )
& ~ $less(X3,0)
& ( 0 = X3 )
& ( 0 = X1 )
& ( n1 = X0 )
& ~ $less(X0,0) ),
inference(nnf_transformation,[],[f224]) ).
tff(f224,plain,
? [X0: $int,X1: $int,X2: map_int_lpmap_int_intrp,X3: $int,X4: map_int_int] :
( ? [X11: $int,X12: map_int_lpmap_int_intrp,X13: $int,X14: map_int_int] :
( ( ? [X17: map_int_int] :
( partial_solution1(n1,X17)
<~> ? [X18: $int] :
( eq_prefix1(int,t2tb2(X17),get(map(int,int),int,t2tb3(X12),t2tb1(X18)),n1)
& $less(X18,$sum(X11,$uminus(X1)))
& ~ $less(X18,0) ) )
| ~ sorted1(X12,0,X11)
| ( $sum(X11,$uminus(X1)) != X11 ) )
& eq_prefix1(map(int,int),t2tb3(X2),t2tb3(X12),X1)
& eq_prefix1(int,t2tb2(X4),t2tb2(X14),X13)
& ! [X15: map_int_int] :
( ( eq_prefix1(int,t2tb2(X14),t2tb2(X15),X13)
& partial_solution1(n1,X15) )
<=> ? [X16: $int] :
( eq_prefix1(int,t2tb2(X15),get(map(int,int),int,t2tb3(X12),t2tb1(X16)),n1)
& $less(X16,X11)
& ~ $less(X16,X1) ) )
& sorted1(X12,X1,X11)
& ( X3 = X13 )
& ~ $less($sum(X11,$uminus(X1)),0) )
& partial_solution1(X3,X4)
& ! [X5: $int] :
( ( ~ mem(int,t2tb1(X5),empty(int))
<=> ! [X6: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X6))) != $sum($sum(X5,X3),$uminus(X6)) )
| ~ $less(X6,X3)
| $less(X6,0) ) )
| $less(X5,0) )
& ! [X7: $int] :
( ( ~ mem(int,t2tb1(X7),empty(int))
<=> ! [X8: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X8))) != $sum($sum(X7,X8),$uminus(X3)) )
| ~ $less(X8,X3)
| $less(X8,0) ) )
| $less(X7,0) )
& ! [X9: $int] :
( mem(int,t2tb1(X9),t2tb(below1(X0)))
<=> sP0(X9,X4,X3) )
& ~ $less(X1,0)
& ( n1 = $sum(X3,cardinal1(int,t2tb(below1(X0)))) )
& ~ $less(X3,0)
& ( 0 = X3 )
& ( 0 = X1 )
& ( n1 = X0 )
& ~ $less(X0,0) ),
inference(definition_folding,[],[f176,f223]) ).
tff(f223,plain,
! [X9: $int,X4: map_int_int,X3: $int] :
( sP0(X9,X4,X3)
<=> ( ! [X10: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X10))) != X9 )
| ~ $less(X10,X3)
| $less(X10,0) )
& $less(X9,n1)
& ~ $less(X9,0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f176,plain,
? [X0: $int,X1: $int,X2: map_int_lpmap_int_intrp,X3: $int,X4: map_int_int] :
( ? [X11: $int,X12: map_int_lpmap_int_intrp,X13: $int,X14: map_int_int] :
( ( ? [X17: map_int_int] :
( partial_solution1(n1,X17)
<~> ? [X18: $int] :
( eq_prefix1(int,t2tb2(X17),get(map(int,int),int,t2tb3(X12),t2tb1(X18)),n1)
& $less(X18,$sum(X11,$uminus(X1)))
& ~ $less(X18,0) ) )
| ~ sorted1(X12,0,X11)
| ( $sum(X11,$uminus(X1)) != X11 ) )
& eq_prefix1(map(int,int),t2tb3(X2),t2tb3(X12),X1)
& eq_prefix1(int,t2tb2(X4),t2tb2(X14),X13)
& ! [X15: map_int_int] :
( ( eq_prefix1(int,t2tb2(X14),t2tb2(X15),X13)
& partial_solution1(n1,X15) )
<=> ? [X16: $int] :
( eq_prefix1(int,t2tb2(X15),get(map(int,int),int,t2tb3(X12),t2tb1(X16)),n1)
& $less(X16,X11)
& ~ $less(X16,X1) ) )
& sorted1(X12,X1,X11)
& ( X3 = X13 )
& ~ $less($sum(X11,$uminus(X1)),0) )
& partial_solution1(X3,X4)
& ! [X5: $int] :
( ( ~ mem(int,t2tb1(X5),empty(int))
<=> ! [X6: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X6))) != $sum($sum(X5,X3),$uminus(X6)) )
| ~ $less(X6,X3)
| $less(X6,0) ) )
| $less(X5,0) )
& ! [X7: $int] :
( ( ~ mem(int,t2tb1(X7),empty(int))
<=> ! [X8: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X8))) != $sum($sum(X7,X8),$uminus(X3)) )
| ~ $less(X8,X3)
| $less(X8,0) ) )
| $less(X7,0) )
& ! [X9: $int] :
( mem(int,t2tb1(X9),t2tb(below1(X0)))
<=> ( ! [X10: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X10))) != X9 )
| ~ $less(X10,X3)
| $less(X10,0) )
& $less(X9,n1)
& ~ $less(X9,0) ) )
& ~ $less(X1,0)
& ( n1 = $sum(X3,cardinal1(int,t2tb(below1(X0)))) )
& ~ $less(X3,0)
& ( 0 = X3 )
& ( 0 = X1 )
& ( n1 = X0 )
& ~ $less(X0,0) ),
inference(flattening,[],[f175]) ).
tff(f175,plain,
? [X0: $int,X1: $int,X2: map_int_lpmap_int_intrp,X3: $int,X4: map_int_int] :
( ? [X11: $int,X12: map_int_lpmap_int_intrp,X13: $int,X14: map_int_int] :
( ( ? [X17: map_int_int] :
( partial_solution1(n1,X17)
<~> ? [X18: $int] :
( eq_prefix1(int,t2tb2(X17),get(map(int,int),int,t2tb3(X12),t2tb1(X18)),n1)
& $less(X18,$sum(X11,$uminus(X1)))
& ~ $less(X18,0) ) )
| ~ sorted1(X12,0,X11)
| ( $sum(X11,$uminus(X1)) != X11 ) )
& eq_prefix1(map(int,int),t2tb3(X2),t2tb3(X12),X1)
& eq_prefix1(int,t2tb2(X4),t2tb2(X14),X13)
& ! [X15: map_int_int] :
( ( eq_prefix1(int,t2tb2(X14),t2tb2(X15),X13)
& partial_solution1(n1,X15) )
<=> ? [X16: $int] :
( eq_prefix1(int,t2tb2(X15),get(map(int,int),int,t2tb3(X12),t2tb1(X16)),n1)
& $less(X16,X11)
& ~ $less(X16,X1) ) )
& sorted1(X12,X1,X11)
& ( X3 = X13 )
& ~ $less($sum(X11,$uminus(X1)),0) )
& partial_solution1(X3,X4)
& ! [X5: $int] :
( ( ~ mem(int,t2tb1(X5),empty(int))
<=> ! [X6: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X6))) != $sum($sum(X5,X3),$uminus(X6)) )
| ~ $less(X6,X3)
| $less(X6,0) ) )
| $less(X5,0) )
& ! [X7: $int] :
( ( ~ mem(int,t2tb1(X7),empty(int))
<=> ! [X8: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X8))) != $sum($sum(X7,X8),$uminus(X3)) )
| ~ $less(X8,X3)
| $less(X8,0) ) )
| $less(X7,0) )
& ! [X9: $int] :
( mem(int,t2tb1(X9),t2tb(below1(X0)))
<=> ( ! [X10: $int] :
( ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X10))) != X9 )
| ~ $less(X10,X3)
| $less(X10,0) )
& $less(X9,n1)
& ~ $less(X9,0) ) )
& ~ $less(X1,0)
& ( n1 = $sum(X3,cardinal1(int,t2tb(below1(X0)))) )
& ~ $less(X3,0)
& ( 0 = X3 )
& ( 0 = X1 )
& ( n1 = X0 )
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f111]) ).
tff(f111,plain,
~ ! [X0: $int,X1: $int,X2: map_int_lpmap_int_intrp,X3: $int,X4: map_int_int] :
( ( ( 0 = X3 )
& ( 0 = X1 )
& ( n1 = X0 )
& ~ $less(X0,0) )
=> ( ( partial_solution1(X3,X4)
& ! [X5: $int] :
( ~ $less(X5,0)
=> ( ~ mem(int,t2tb1(X5),empty(int))
<=> ! [X6: $int] :
( ( $less(X6,X3)
& ~ $less(X6,0) )
=> ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X6))) != $sum($sum(X5,X3),$uminus(X6)) ) ) ) )
& ! [X7: $int] :
( ~ $less(X7,0)
=> ( ~ mem(int,t2tb1(X7),empty(int))
<=> ! [X8: $int] :
( ( $less(X8,X3)
& ~ $less(X8,0) )
=> ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X8))) != $sum($sum(X7,X8),$uminus(X3)) ) ) ) )
& ! [X9: $int] :
( mem(int,t2tb1(X9),t2tb(below1(X0)))
<=> ( ! [X10: $int] :
( ( $less(X10,X3)
& ~ $less(X10,0) )
=> ( tb2t1(get(int,int,t2tb2(X4),t2tb1(X10))) != X9 ) )
& $less(X9,n1)
& ~ $less(X9,0) ) )
& ~ $less(X1,0)
& ( n1 = $sum(X3,cardinal1(int,t2tb(below1(X0)))) )
& ~ $less(X3,0) )
=> ! [X11: $int,X12: map_int_lpmap_int_intrp,X13: $int,X14: map_int_int] :
( ( eq_prefix1(map(int,int),t2tb3(X2),t2tb3(X12),X1)
& eq_prefix1(int,t2tb2(X4),t2tb2(X14),X13)
& ! [X15: map_int_int] :
( ( eq_prefix1(int,t2tb2(X14),t2tb2(X15),X13)
& partial_solution1(n1,X15) )
<=> ? [X16: $int] :
( eq_prefix1(int,t2tb2(X15),get(map(int,int),int,t2tb3(X12),t2tb1(X16)),n1)
& $less(X16,X11)
& ~ $less(X16,X1) ) )
& sorted1(X12,X1,X11)
& ( X3 = X13 )
& ~ $less($sum(X11,$uminus(X1)),0) )
=> ( ! [X17: map_int_int] :
( partial_solution1(n1,X17)
<=> ? [X18: $int] :
( eq_prefix1(int,t2tb2(X17),get(map(int,int),int,t2tb3(X12),t2tb1(X18)),n1)
& $less(X18,$sum(X11,$uminus(X1)))
& ~ $less(X18,0) ) )
& sorted1(X12,0,X11)
& ( $sum(X11,$uminus(X1)) = X11 ) ) ) ) ),
inference(rectify,[],[f78]) ).
tff(f78,plain,
~ ! [X22: $int,X10: $int,X23: map_int_lpmap_int_intrp,X21: $int,X24: map_int_int] :
( ( ( 0 = X21 )
& ( 0 = X10 )
& ( n1 = X22 )
& ~ $less(X22,0) )
=> ( ( partial_solution1(X21,X24)
& ! [X12: $int] :
( ~ $less(X12,0)
=> ( ~ mem(int,t2tb1(X12),empty(int))
<=> ! [X13: $int] :
( ( $less(X13,X21)
& ~ $less(X13,0) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != $sum($sum(X12,X21),$uminus(X13)) ) ) ) )
& ! [X12: $int] :
( ~ $less(X12,0)
=> ( ~ mem(int,t2tb1(X12),empty(int))
<=> ! [X13: $int] :
( ( $less(X13,X21)
& ~ $less(X13,0) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != $sum($sum(X12,X13),$uminus(X21)) ) ) ) )
& ! [X12: $int] :
( mem(int,t2tb1(X12),t2tb(below1(X22)))
<=> ( ! [X13: $int] :
( ( $less(X13,X21)
& ~ $less(X13,0) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != X12 ) )
& $less(X12,n1)
& ~ $less(X12,0) ) )
& ~ $less(X10,0)
& ( n1 = $sum(X21,cardinal1(int,t2tb(below1(X22)))) )
& ~ $less(X21,0) )
=> ! [X8: $int,X25: map_int_lpmap_int_intrp,X26: $int,X27: map_int_int] :
( ( eq_prefix1(map(int,int),t2tb3(X23),t2tb3(X25),X10)
& eq_prefix1(int,t2tb2(X24),t2tb2(X27),X26)
& ! [X20: map_int_int] :
( ( eq_prefix1(int,t2tb2(X27),t2tb2(X20),X26)
& partial_solution1(n1,X20) )
<=> ? [X12: $int] :
( eq_prefix1(int,t2tb2(X20),get(map(int,int),int,t2tb3(X25),t2tb1(X12)),n1)
& $less(X12,X8)
& ~ $less(X12,X10) ) )
& sorted1(X25,X10,X8)
& ( X21 = X26 )
& ~ $less($sum(X8,$uminus(X10)),0) )
=> ( ! [X20: map_int_int] :
( partial_solution1(n1,X20)
<=> ? [X12: $int] :
( eq_prefix1(int,t2tb2(X20),get(map(int,int),int,t2tb3(X25),t2tb1(X12)),n1)
& $less(X12,$sum(X8,$uminus(X10)))
& ~ $less(X12,0) ) )
& sorted1(X25,0,X8)
& ( $sum(X8,$uminus(X10)) = X8 ) ) ) ) ),
inference(theory_normalization,[],[f77]) ).
tff(f77,negated_conjecture,
~ ! [X22: $int,X10: $int,X23: map_int_lpmap_int_intrp,X21: $int,X24: map_int_int] :
( ( ( 0 = X21 )
& ( 0 = X10 )
& ( n1 = X22 )
& $lesseq(0,X22) )
=> ( ( partial_solution1(X21,X24)
& ! [X12: $int] :
( $lesseq(0,X12)
=> ( ~ mem(int,t2tb1(X12),empty(int))
<=> ! [X13: $int] :
( ( $less(X13,X21)
& $lesseq(0,X13) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != $difference($sum(X12,X21),X13) ) ) ) )
& ! [X12: $int] :
( $lesseq(0,X12)
=> ( ~ mem(int,t2tb1(X12),empty(int))
<=> ! [X13: $int] :
( ( $less(X13,X21)
& $lesseq(0,X13) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != $difference($sum(X12,X13),X21) ) ) ) )
& ! [X12: $int] :
( mem(int,t2tb1(X12),t2tb(below1(X22)))
<=> ( ! [X13: $int] :
( ( $less(X13,X21)
& $lesseq(0,X13) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != X12 ) )
& $less(X12,n1)
& $lesseq(0,X12) ) )
& $lesseq(0,X10)
& ( n1 = $sum(X21,cardinal1(int,t2tb(below1(X22)))) )
& $lesseq(0,X21) )
=> ! [X8: $int,X25: map_int_lpmap_int_intrp,X26: $int,X27: map_int_int] :
( ( eq_prefix1(map(int,int),t2tb3(X23),t2tb3(X25),X10)
& eq_prefix1(int,t2tb2(X24),t2tb2(X27),X26)
& ! [X20: map_int_int] :
( ( eq_prefix1(int,t2tb2(X27),t2tb2(X20),X26)
& partial_solution1(n1,X20) )
<=> ? [X12: $int] :
( eq_prefix1(int,t2tb2(X20),get(map(int,int),int,t2tb3(X25),t2tb1(X12)),n1)
& $less(X12,X8)
& $lesseq(X10,X12) ) )
& sorted1(X25,X10,X8)
& ( X21 = X26 )
& $lesseq(0,$difference(X8,X10)) )
=> ( ! [X20: map_int_int] :
( partial_solution1(n1,X20)
<=> ? [X12: $int] :
( eq_prefix1(int,t2tb2(X20),get(map(int,int),int,t2tb3(X25),t2tb1(X12)),n1)
& $less(X12,$difference(X8,X10))
& $lesseq(0,X12) ) )
& sorted1(X25,0,X8)
& ( $difference(X8,X10) = X8 ) ) ) ) ),
inference(negated_conjecture,[],[f76]) ).
tff(f76,conjecture,
! [X22: $int,X10: $int,X23: map_int_lpmap_int_intrp,X21: $int,X24: map_int_int] :
( ( ( 0 = X21 )
& ( 0 = X10 )
& ( n1 = X22 )
& $lesseq(0,X22) )
=> ( ( partial_solution1(X21,X24)
& ! [X12: $int] :
( $lesseq(0,X12)
=> ( ~ mem(int,t2tb1(X12),empty(int))
<=> ! [X13: $int] :
( ( $less(X13,X21)
& $lesseq(0,X13) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != $difference($sum(X12,X21),X13) ) ) ) )
& ! [X12: $int] :
( $lesseq(0,X12)
=> ( ~ mem(int,t2tb1(X12),empty(int))
<=> ! [X13: $int] :
( ( $less(X13,X21)
& $lesseq(0,X13) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != $difference($sum(X12,X13),X21) ) ) ) )
& ! [X12: $int] :
( mem(int,t2tb1(X12),t2tb(below1(X22)))
<=> ( ! [X13: $int] :
( ( $less(X13,X21)
& $lesseq(0,X13) )
=> ( tb2t1(get(int,int,t2tb2(X24),t2tb1(X13))) != X12 ) )
& $less(X12,n1)
& $lesseq(0,X12) ) )
& $lesseq(0,X10)
& ( n1 = $sum(X21,cardinal1(int,t2tb(below1(X22)))) )
& $lesseq(0,X21) )
=> ! [X8: $int,X25: map_int_lpmap_int_intrp,X26: $int,X27: map_int_int] :
( ( eq_prefix1(map(int,int),t2tb3(X23),t2tb3(X25),X10)
& eq_prefix1(int,t2tb2(X24),t2tb2(X27),X26)
& ! [X20: map_int_int] :
( ( eq_prefix1(int,t2tb2(X27),t2tb2(X20),X26)
& partial_solution1(n1,X20) )
<=> ? [X12: $int] :
( eq_prefix1(int,t2tb2(X20),get(map(int,int),int,t2tb3(X25),t2tb1(X12)),n1)
& $less(X12,X8)
& $lesseq(X10,X12) ) )
& sorted1(X25,X10,X8)
& ( X21 = X26 )
& $lesseq(0,$difference(X8,X10)) )
=> ( ! [X20: map_int_int] :
( partial_solution1(n1,X20)
<=> ? [X12: $int] :
( eq_prefix1(int,t2tb2(X20),get(map(int,int),int,t2tb3(X25),t2tb1(X12)),n1)
& $less(X12,$difference(X8,X10))
& $lesseq(0,X12) ) )
& sorted1(X25,0,X8)
& ( $difference(X8,X10) = X8 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_queens3) ).
tff(f473,plain,
( partial_solution1(n1,sK13)
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f472]) ).
tff(f650,plain,
( ~ partial_solution1(sK4,sK13)
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(sK13),0)
| ~ spl27_4 ),
inference(forward_demodulation,[],[f649,f335]) ).
tff(f335,plain,
! [X0: map_int_int] : ( tb2t2(t2tb2(X0)) = X0 ),
inference(cnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: map_int_int] : ( tb2t2(t2tb2(X0)) = X0 ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X12: map_int_int] : ( tb2t2(t2tb2(X12)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeL2) ).
tff(f649,plain,
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(sK13),0)
| ~ partial_solution1(sK4,tb2t2(t2tb2(sK13)))
| ~ spl27_4 ),
inference(subsumption_resolution,[],[f648,f617]) ).
tff(f617,plain,
! [X0: uni] :
( ~ eq_prefix1(int,t2tb2(sK12),X0,0)
| ~ partial_solution1(sK4,tb2t2(X0))
| $less(sK15(tb2t2(X0)),sK9) ),
inference(superposition,[],[f551,f339]) ).
tff(f339,plain,
! [X0: uni] : ( t2tb2(tb2t2(X0)) = X0 ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: uni] : ( t2tb2(tb2t2(X0)) = X0 ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X13: uni] : ( t2tb2(tb2t2(X13)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeR2) ).
tff(f551,plain,
! [X12: map_int_int] :
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),0)
| ~ partial_solution1(sK4,X12)
| $less(sK15(X12),sK9) ),
inference(backward_demodulation,[],[f513,f297]) ).
tff(f513,plain,
! [X12: map_int_int] :
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),0)
| $less(sK15(X12),sK9)
| ~ partial_solution1(n1,X12) ),
inference(backward_demodulation,[],[f318,f511]) ).
tff(f511,plain,
0 = sK11,
inference(backward_demodulation,[],[f315,f299]) ).
tff(f299,plain,
0 = sK7,
inference(cnf_transformation,[],[f243]) ).
tff(f315,plain,
sK7 = sK11,
inference(cnf_transformation,[],[f243]) ).
tff(f318,plain,
! [X12: map_int_int] :
( $less(sK15(X12),sK9)
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),sK11)
| ~ partial_solution1(n1,X12) ),
inference(cnf_transformation,[],[f243]) ).
tff(f648,plain,
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(sK13),0)
| ~ partial_solution1(sK4,tb2t2(t2tb2(sK13)))
| ~ $less(sK15(tb2t2(t2tb2(sK13))),sK9)
| ~ spl27_4 ),
inference(subsumption_resolution,[],[f643,f616]) ).
tff(f616,plain,
! [X0: uni] :
( ~ eq_prefix1(int,t2tb2(sK12),X0,0)
| ~ $less(sK15(tb2t2(X0)),0)
| ~ partial_solution1(sK4,tb2t2(X0)) ),
inference(superposition,[],[f555,f339]) ).
tff(f555,plain,
! [X12: map_int_int] :
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),0)
| ~ $less(sK15(X12),0)
| ~ partial_solution1(sK4,X12) ),
inference(backward_demodulation,[],[f543,f297]) ).
tff(f543,plain,
! [X12: map_int_int] :
( ~ $less(sK15(X12),0)
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),0)
| ~ partial_solution1(n1,X12) ),
inference(backward_demodulation,[],[f512,f298]) ).
tff(f298,plain,
0 = sK5,
inference(cnf_transformation,[],[f243]) ).
tff(f512,plain,
! [X12: map_int_int] :
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),0)
| ~ $less(sK15(X12),sK5)
| ~ partial_solution1(n1,X12) ),
inference(backward_demodulation,[],[f317,f511]) ).
tff(f317,plain,
! [X12: map_int_int] :
( ~ $less(sK15(X12),sK5)
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),sK11)
| ~ partial_solution1(n1,X12) ),
inference(cnf_transformation,[],[f243]) ).
tff(f643,plain,
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(sK13),0)
| ~ partial_solution1(sK4,tb2t2(t2tb2(sK13)))
| ~ $less(sK15(tb2t2(t2tb2(sK13))),sK9)
| $less(sK15(tb2t2(t2tb2(sK13))),0)
| ~ spl27_4 ),
inference(resolution,[],[f618,f590]) ).
tff(f590,plain,
( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),sK4)
| ~ $less(X10,sK9)
| $less(X10,0) )
| ~ spl27_4 ),
inference(evaluation,[],[f589]) ).
tff(f589,plain,
( ! [X10: $int] :
( ~ $less(X10,$sum(sK9,$uminus(0)))
| ~ eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),sK4)
| $less(X10,0) )
| ~ spl27_4 ),
inference(forward_demodulation,[],[f588,f298]) ).
tff(f588,plain,
( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),sK4)
| $less(X10,0)
| ~ $less(X10,$sum(sK9,$uminus(sK5))) )
| ~ spl27_4 ),
inference(forward_demodulation,[],[f477,f297]) ).
tff(f477,plain,
( ! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),n1)
| $less(X10,0)
| ~ $less(X10,$sum(sK9,$uminus(sK5))) )
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f476]) ).
tff(f618,plain,
! [X0: uni] :
( eq_prefix1(int,X0,get(map(int,int),int,t2tb3(sK10),t2tb1(sK15(tb2t2(X0)))),sK4)
| ~ eq_prefix1(int,t2tb2(sK12),X0,0)
| ~ partial_solution1(sK4,tb2t2(X0)) ),
inference(forward_demodulation,[],[f613,f339]) ).
tff(f613,plain,
! [X0: uni] :
( eq_prefix1(int,X0,get(map(int,int),int,t2tb3(sK10),t2tb1(sK15(tb2t2(X0)))),sK4)
| ~ partial_solution1(sK4,tb2t2(X0))
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(tb2t2(X0)),0) ),
inference(superposition,[],[f557,f339]) ).
tff(f557,plain,
! [X12: map_int_int] :
( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(sK15(X12))),sK4)
| ~ partial_solution1(sK4,X12)
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),0) ),
inference(forward_demodulation,[],[f552,f297]) ).
tff(f552,plain,
! [X12: map_int_int] :
( ~ partial_solution1(sK4,X12)
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),0)
| eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(sK15(X12))),n1) ),
inference(backward_demodulation,[],[f514,f297]) ).
tff(f514,plain,
! [X12: map_int_int] :
( ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),0)
| eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(sK15(X12))),n1)
| ~ partial_solution1(n1,X12) ),
inference(backward_demodulation,[],[f319,f511]) ).
tff(f319,plain,
! [X12: map_int_int] :
( eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(sK15(X12))),n1)
| ~ eq_prefix1(int,t2tb2(sK12),t2tb2(X12),sK11)
| ~ partial_solution1(n1,X12) ),
inference(cnf_transformation,[],[f243]) ).
tff(f585,plain,
( spl27_3
| ~ spl27_5
| ~ spl27_6
| spl27_7 ),
inference(avatar_contradiction_clause,[],[f584]) ).
tff(f584,plain,
( $false
| spl27_3
| ~ spl27_5
| ~ spl27_6
| spl27_7 ),
inference(subsumption_resolution,[],[f583,f569]) ).
tff(f569,plain,
( $less(sK14,sK9)
| ~ spl27_6 ),
inference(evaluation,[],[f568]) ).
tff(f568,plain,
( $less(sK14,$sum(sK9,$uminus(0)))
| ~ spl27_6 ),
inference(forward_demodulation,[],[f487,f298]) ).
tff(f487,plain,
( $less(sK14,$sum(sK9,$uminus(sK5)))
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f485]) ).
tff(f485,plain,
( spl27_6
<=> $less(sK14,$sum(sK9,$uminus(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_6])]) ).
tff(f583,plain,
( ~ $less(sK14,sK9)
| spl27_3
| ~ spl27_5
| spl27_7 ),
inference(subsumption_resolution,[],[f582,f492]) ).
tff(f492,plain,
( ~ $less(sK14,0)
| spl27_7 ),
inference(avatar_component_clause,[],[f490]) ).
tff(f490,plain,
( spl27_7
<=> $less(sK14,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).
tff(f582,plain,
( $less(sK14,0)
| ~ $less(sK14,sK9)
| spl27_3
| ~ spl27_5 ),
inference(subsumption_resolution,[],[f581,f571]) ).
tff(f571,plain,
( ~ partial_solution1(sK4,sK13)
| spl27_3 ),
inference(forward_demodulation,[],[f474,f297]) ).
tff(f474,plain,
( ~ partial_solution1(n1,sK13)
| spl27_3 ),
inference(avatar_component_clause,[],[f472]) ).
tff(f581,plain,
( partial_solution1(sK4,sK13)
| $less(sK14,0)
| ~ $less(sK14,sK9)
| ~ spl27_5 ),
inference(resolution,[],[f558,f570]) ).
tff(f570,plain,
( eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(sK14)),sK4)
| ~ spl27_5 ),
inference(forward_demodulation,[],[f482,f297]) ).
tff(f482,plain,
( eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(sK14)),n1)
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f480]) ).
tff(f480,plain,
( spl27_5
<=> eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(sK14)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_5])]) ).
tff(f558,plain,
! [X12: map_int_int,X13: $int] :
( ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(X13)),sK4)
| partial_solution1(sK4,X12)
| $less(X13,0)
| ~ $less(X13,sK9) ),
inference(forward_demodulation,[],[f554,f297]) ).
tff(f554,plain,
! [X12: map_int_int,X13: $int] :
( partial_solution1(sK4,X12)
| $less(X13,0)
| ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(X13)),n1)
| ~ $less(X13,sK9) ),
inference(backward_demodulation,[],[f541,f297]) ).
tff(f541,plain,
! [X12: map_int_int,X13: $int] :
( $less(X13,0)
| partial_solution1(n1,X12)
| ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(X13)),n1)
| ~ $less(X13,sK9) ),
inference(backward_demodulation,[],[f320,f298]) ).
tff(f320,plain,
! [X12: map_int_int,X13: $int] :
( partial_solution1(n1,X12)
| ~ eq_prefix1(int,t2tb2(X12),get(map(int,int),int,t2tb3(sK10),t2tb1(X13)),n1)
| ~ $less(X13,sK9)
| $less(X13,sK5) ),
inference(cnf_transformation,[],[f243]) ).
tff(f567,plain,
spl27_1,
inference(avatar_contradiction_clause,[],[f566]) ).
tff(f566,plain,
( $false
| spl27_1 ),
inference(evaluation,[],[f565]) ).
tff(f565,plain,
( ( sK9 != $sum(sK9,$uminus(0)) )
| spl27_1 ),
inference(forward_demodulation,[],[f466,f298]) ).
tff(f466,plain,
( ( sK9 != $sum(sK9,$uminus(sK5)) )
| spl27_1 ),
inference(avatar_component_clause,[],[f464]) ).
tff(f464,plain,
( spl27_1
<=> ( sK9 = $sum(sK9,$uminus(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).
tff(f546,plain,
spl27_2,
inference(avatar_split_clause,[],[f540,f468]) ).
tff(f468,plain,
( spl27_2
<=> sorted1(sK10,0,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).
tff(f540,plain,
sorted1(sK10,0,sK9),
inference(backward_demodulation,[],[f316,f298]) ).
tff(f316,plain,
sorted1(sK10,sK5,sK9),
inference(cnf_transformation,[],[f243]) ).
tff(f493,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f324,f490,f472,f468,f464]) ).
tff(f324,plain,
( ~ $less(sK14,0)
| partial_solution1(n1,sK13)
| ~ sorted1(sK10,0,sK9)
| ( sK9 != $sum(sK9,$uminus(sK5)) ) ),
inference(cnf_transformation,[],[f243]) ).
tff(f488,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3
| spl27_6 ),
inference(avatar_split_clause,[],[f325,f485,f472,f468,f464]) ).
tff(f325,plain,
( $less(sK14,$sum(sK9,$uminus(sK5)))
| partial_solution1(n1,sK13)
| ~ sorted1(sK10,0,sK9)
| ( sK9 != $sum(sK9,$uminus(sK5)) ) ),
inference(cnf_transformation,[],[f243]) ).
tff(f483,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3
| spl27_5 ),
inference(avatar_split_clause,[],[f326,f480,f472,f468,f464]) ).
tff(f326,plain,
( eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(sK14)),n1)
| partial_solution1(n1,sK13)
| ~ sorted1(sK10,0,sK9)
| ( sK9 != $sum(sK9,$uminus(sK5)) ) ),
inference(cnf_transformation,[],[f243]) ).
tff(f478,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_3
| spl27_4 ),
inference(avatar_split_clause,[],[f327,f476,f472,f468,f464]) ).
tff(f327,plain,
! [X10: $int] :
( ~ eq_prefix1(int,t2tb2(sK13),get(map(int,int),int,t2tb3(sK10),t2tb1(X10)),n1)
| ~ $less(X10,$sum(sK9,$uminus(sK5)))
| $less(X10,0)
| ~ partial_solution1(n1,sK13)
| ~ sorted1(sK10,0,sK9)
| ( sK9 != $sum(sK9,$uminus(sK5)) ) ),
inference(cnf_transformation,[],[f243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW634_2 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 03:39:13 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (16972)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (16975)WARNING: value z3 for option sas not known
% 0.14/0.37 % (16976)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (16973)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (16974)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (16977)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (16978)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (16975)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (16979)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (16973)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (16974)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (16974)Terminated due to inappropriate strategy.
% 0.14/0.38 % (16974)------------------------------
% 0.14/0.38 % (16974)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (16974)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (16974)Memory used [KB]: 1101
% 0.14/0.38 % (16974)Time elapsed: 0.009 s
% 0.14/0.38 % (16974)Instructions burned: 16 (million)
% 0.14/0.38 % (16974)------------------------------
% 0.14/0.38 % (16974)------------------------------
% 0.14/0.38 % (16973)Terminated due to inappropriate strategy.
% 0.14/0.38 % (16973)------------------------------
% 0.14/0.38 % (16973)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (16976)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (16976)Terminated due to inappropriate strategy.
% 0.14/0.38 % (16976)------------------------------
% 0.14/0.38 % (16976)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (16973)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (16973)Memory used [KB]: 1101
% 0.14/0.38 % (16973)Time elapsed: 0.009 s
% 0.14/0.38 % (16973)Instructions burned: 17 (million)
% 0.14/0.38 % (16973)------------------------------
% 0.14/0.38 % (16973)------------------------------
% 0.14/0.38 % (16976)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (16976)Memory used [KB]: 1106
% 0.14/0.38 % (16976)Time elapsed: 0.009 s
% 0.14/0.38 % (16976)Instructions burned: 17 (million)
% 0.14/0.38 % (16976)------------------------------
% 0.14/0.38 % (16976)------------------------------
% 0.14/0.40 % (16980)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40 % (16981)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.14/0.40 % (16982)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.14/0.41 % (16980)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.41 % (16980)Terminated due to inappropriate strategy.
% 0.14/0.41 % (16980)------------------------------
% 0.14/0.41 % (16980)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.41 % (16980)Termination reason: Inappropriate
% 0.14/0.41
% 0.14/0.41 % (16980)Memory used [KB]: 1057
% 0.14/0.41 % (16980)Time elapsed: 0.008 s
% 0.14/0.41 % (16980)Instructions burned: 15 (million)
% 0.14/0.41 % (16980)------------------------------
% 0.14/0.41 % (16980)------------------------------
% 0.20/0.42 % (16983)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.73/0.59 % (16982)First to succeed.
% 1.73/0.60 % (16982)Refutation found. Thanks to Tanya!
% 1.73/0.60 % SZS status Theorem for theBenchmark
% 1.73/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.73/0.60 % (16982)------------------------------
% 1.73/0.60 % (16982)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.73/0.60 % (16982)Termination reason: Refutation
% 1.73/0.60
% 1.73/0.60 % (16982)Memory used [KB]: 2470
% 1.73/0.60 % (16982)Time elapsed: 0.217 s
% 1.73/0.60 % (16982)Instructions burned: 439 (million)
% 1.73/0.60 % (16982)------------------------------
% 1.73/0.60 % (16982)------------------------------
% 1.73/0.60 % (16972)Success in time 0.232 s
%------------------------------------------------------------------------------