TSTP Solution File: SWW619_2 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW619_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n005.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 : Mon Jun 24 18:35:15 EDT 2024
% Result : Theorem 0.24s 0.52s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 212 ( 24 equ)
% Maximal formula atoms : 30 ( 11 avg)
% Number of connectives : 279 ( 86 ~; 39 |; 122 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 456 ( 141 atm; 163 fun; 81 num; 71 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 14 usr; 1 prp; 0-7 aty)
% Number of functors : 59 ( 55 usr; 18 con; 0-7 aty)
% Number of variables : 101 ( 55 !; 46 ?; 101 :)
% 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,
elt4: $tType ).
tff(type_def_10,type,
array_elt2: $tType ).
tff(type_def_11,type,
map_int_elt2: $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,
map: ( ty * ty ) > ty ).
tff(func_def_13,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(func_def_14,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(func_def_15,type,
const: ( ty * ty * uni ) > uni ).
tff(func_def_16,type,
array: ty > ty ).
tff(func_def_17,type,
mk_array1: ( ty * $int * uni ) > uni ).
tff(func_def_18,type,
length1: ( ty * uni ) > $int ).
tff(func_def_19,type,
elts: ( ty * uni ) > uni ).
tff(func_def_20,type,
get2: ( ty * uni * $int ) > uni ).
tff(func_def_21,type,
t2tb: $int > uni ).
tff(func_def_22,type,
tb2t: uni > $int ).
tff(func_def_23,type,
set2: ( ty * uni * $int * uni ) > uni ).
tff(func_def_24,type,
make1: ( ty * $int * uni ) > uni ).
tff(func_def_25,type,
elt5: ty ).
tff(func_def_26,type,
t2tb7: elt4 > uni ).
tff(func_def_27,type,
tb2t7: uni > elt4 ).
tff(func_def_28,type,
t2tb8: array_elt2 > uni ).
tff(func_def_29,type,
tb2t8: uni > array_elt2 ).
tff(func_def_30,type,
ref: ty > ty ).
tff(func_def_31,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_32,type,
contents: ( ty * uni ) > uni ).
tff(func_def_33,type,
occ1: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_37,type,
abs: $int > $int ).
tff(func_def_39,type,
div: ( $int * $int ) > $int ).
tff(func_def_40,type,
mod: ( $int * $int ) > $int ).
tff(func_def_41,type,
min: ( $int * $int ) > $int ).
tff(func_def_42,type,
max: ( $int * $int ) > $int ).
tff(func_def_43,type,
t2tb9: map_int_elt2 > uni ).
tff(func_def_44,type,
tb2t9: uni > map_int_elt2 ).
tff(func_def_45,type,
sK1: ( ty * $int * $int * uni * uni ) > $int ).
tff(func_def_46,type,
sK2: ( ty * $int * uni * $int * uni ) > uni ).
tff(func_def_47,type,
sK3: $int ).
tff(func_def_48,type,
sK4: map_int_elt2 ).
tff(func_def_49,type,
sK5: map_int_elt2 ).
tff(func_def_50,type,
sK6: $int ).
tff(func_def_51,type,
sK7: map_int_elt2 ).
tff(func_def_52,type,
sK8: $int ).
tff(func_def_53,type,
sK9: $int ).
tff(func_def_54,type,
sK10: ( uni * $int * $int * uni * ty ) > $int ).
tff(func_def_55,type,
sK11: ( $int * $int * uni * ty * uni ) > $int ).
tff(func_def_56,type,
sK12: ( array_elt2 * $int * $int ) > $int ).
tff(func_def_57,type,
sK13: ( array_elt2 * $int * $int ) > $int ).
tff(func_def_58,type,
sK14: ( $int * uni * $int * ty * uni ) > $int ).
tff(func_def_59,type,
sK15: ( $int * $int * $int * uni * ty * uni ) > $int ).
tff(func_def_60,type,
sK16: ( $int * uni * ty * $int * uni * $int * $int ) > $int ).
tff(pred_def_1,type,
sort1: ( ty * uni ) > $o ).
tff(pred_def_3,type,
le3: ( elt4 * elt4 ) > $o ).
tff(pred_def_4,type,
sorted_sub3: ( array_elt2 * $int * $int ) > $o ).
tff(pred_def_6,type,
sorted3: array_elt2 > $o ).
tff(pred_def_7,type,
permut2: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_8,type,
map_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_9,type,
array_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_10,type,
array_eq: ( ty * uni * uni ) > $o ).
tff(pred_def_11,type,
exchange2: ( ty * uni * uni * $int * $int * $int * $int ) > $o ).
tff(pred_def_12,type,
exchange3: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_13,type,
permut3: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_14,type,
permut_sub1: ( ty * uni * uni * $int * $int ) > $o ).
tff(pred_def_15,type,
permut_all: ( ty * uni * uni ) > $o ).
tff(pred_def_16,type,
sP0: ( $int * uni * ty * $int * uni * $int * $int ) > $o ).
tff(f655,plain,
$false,
inference(subsumption_resolution,[],[f654,f461]) ).
tff(f461,plain,
$less($product(sK9,sK8),sK3),
inference(cnf_transformation,[],[f359]) ).
tff(f359,plain,
( ( sK3 = sK6 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(sK5),t2tb(X4))) )
| ~ $less(X4,sK6)
| $less(X4,0) )
& permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(sK7)))
& $less(sK8,sK3)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X7,sK8),min(sK3,$sum($product(X7,sK8),sK8)))
| $less($product(X7,sK8),0)
| ~ $less($product(X7,sK8),sK3) )
& ~ $less(sK8,1)
& ~ $less($product(sK9,sK8),0)
& $less($product(sK9,sK8),sK3)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(sK9,sK8),min(sK3,$sum($product(sK9,sK8),sK8)))
& ~ $less(sK6,0)
& ~ $less(sK3,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9])],[f354,f358,f357,f356,f355]) ).
tff(f355,plain,
( ? [X0: $int,X1: map_int_elt2] :
( ? [X2: map_int_elt2,X3: $int] :
( ( X0 = X3 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X2),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
| ~ $less(X4,X3)
| $less(X4,0) )
& ? [X5: map_int_elt2,X6: $int] :
( permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5)))
& $less(X6,X0)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X6),min(X0,$sum($product(X7,X6),X6)))
| $less($product(X7,X6),0)
| ~ $less($product(X7,X6),X0) )
& ~ $less(X6,1)
& ? [X8: $int] :
( ~ $less($product(X8,X6),0)
& $less($product(X8,X6),X0)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X8,X6),min(X0,$sum($product(X8,X6),X6))) ) )
& ~ $less(X3,0) )
& ~ $less(X0,0) )
=> ( ? [X3: $int,X2: map_int_elt2] :
( ( sK3 = X3 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X2),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X4))) )
| ~ $less(X4,X3)
| $less(X4,0) )
& ? [X6: $int,X5: map_int_elt2] :
( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(X5)))
& $less(X6,sK3)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X7,X6),min(sK3,$sum($product(X7,X6),X6)))
| $less($product(X7,X6),0)
| ~ $less($product(X7,X6),sK3) )
& ~ $less(X6,1)
& ? [X8: $int] :
( ~ $less($product(X8,X6),0)
& $less($product(X8,X6),sK3)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X8,X6),min(sK3,$sum($product(X8,X6),X6))) ) )
& ~ $less(X3,0) )
& ~ $less(sK3,0) ) ),
introduced(choice_axiom,[]) ).
tff(f356,plain,
( ? [X3: $int,X2: map_int_elt2] :
( ( sK3 = X3 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X2),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X4))) )
| ~ $less(X4,X3)
| $less(X4,0) )
& ? [X6: $int,X5: map_int_elt2] :
( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(X5)))
& $less(X6,sK3)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X7,X6),min(sK3,$sum($product(X7,X6),X6)))
| $less($product(X7,X6),0)
| ~ $less($product(X7,X6),sK3) )
& ~ $less(X6,1)
& ? [X8: $int] :
( ~ $less($product(X8,X6),0)
& $less($product(X8,X6),sK3)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X8,X6),min(sK3,$sum($product(X8,X6),X6))) ) )
& ~ $less(X3,0) )
=> ( ( sK3 = sK6 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(sK5),t2tb(X4))) )
| ~ $less(X4,sK6)
| $less(X4,0) )
& ? [X6: $int,X5: map_int_elt2] :
( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(X5)))
& $less(X6,sK3)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X7,X6),min(sK3,$sum($product(X7,X6),X6)))
| $less($product(X7,X6),0)
| ~ $less($product(X7,X6),sK3) )
& ~ $less(X6,1)
& ? [X8: $int] :
( ~ $less($product(X8,X6),0)
& $less($product(X8,X6),sK3)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X8,X6),min(sK3,$sum($product(X8,X6),X6))) ) )
& ~ $less(sK6,0) ) ),
introduced(choice_axiom,[]) ).
tff(f357,plain,
( ? [X6: $int,X5: map_int_elt2] :
( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(X5)))
& $less(X6,sK3)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X7,X6),min(sK3,$sum($product(X7,X6),X6)))
| $less($product(X7,X6),0)
| ~ $less($product(X7,X6),sK3) )
& ~ $less(X6,1)
& ? [X8: $int] :
( ~ $less($product(X8,X6),0)
& $less($product(X8,X6),sK3)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(X5))),$product(X8,X6),min(sK3,$sum($product(X8,X6),X6))) ) )
=> ( permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK4)),mk_array1(elt5,sK3,t2tb9(sK7)))
& $less(sK8,sK3)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X7,sK8),min(sK3,$sum($product(X7,sK8),sK8)))
| $less($product(X7,sK8),0)
| ~ $less($product(X7,sK8),sK3) )
& ~ $less(sK8,1)
& ? [X8: $int] :
( ~ $less($product(X8,sK8),0)
& $less($product(X8,sK8),sK3)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X8,sK8),min(sK3,$sum($product(X8,sK8),sK8))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f358,plain,
( ? [X8: $int] :
( ~ $less($product(X8,sK8),0)
& $less($product(X8,sK8),sK3)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X8,sK8),min(sK3,$sum($product(X8,sK8),sK8))) )
=> ( ~ $less($product(sK9,sK8),0)
& $less($product(sK9,sK8),sK3)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(sK9,sK8),min(sK3,$sum($product(sK9,sK8),sK8))) ) ),
introduced(choice_axiom,[]) ).
tff(f354,plain,
? [X0: $int,X1: map_int_elt2] :
( ? [X2: map_int_elt2,X3: $int] :
( ( X0 = X3 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X2),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
| ~ $less(X4,X3)
| $less(X4,0) )
& ? [X5: map_int_elt2,X6: $int] :
( permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5)))
& $less(X6,X0)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X6),min(X0,$sum($product(X7,X6),X6)))
| $less($product(X7,X6),0)
| ~ $less($product(X7,X6),X0) )
& ~ $less(X6,1)
& ? [X8: $int] :
( ~ $less($product(X8,X6),0)
& $less($product(X8,X6),X0)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X8,X6),min(X0,$sum($product(X8,X6),X6))) ) )
& ~ $less(X3,0) )
& ~ $less(X0,0) ),
inference(rectify,[],[f330]) ).
tff(f330,plain,
? [X1: $int,X0: map_int_elt2] :
( ? [X3: map_int_elt2,X2: $int] :
( ( X1 = X2 )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X0),t2tb(X4))) )
| ~ $less(X4,X2)
| $less(X4,0) )
& ? [X5: map_int_elt2,X6: $int] :
( permut_all(elt5,mk_array1(elt5,X1,t2tb9(X0)),mk_array1(elt5,X1,t2tb9(X5)))
& $less(X6,X1)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X7,X6),min(X1,$sum($product(X7,X6),X6)))
| $less($product(X7,X6),0)
| ~ $less($product(X7,X6),X1) )
& ~ $less(X6,1)
& ? [X8: $int] :
( ~ $less($product(X8,X6),0)
& $less($product(X8,X6),X1)
& ~ sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X8,X6),min(X1,$sum($product(X8,X6),X6))) ) )
& ~ $less(X2,0) )
& ~ $less(X1,0) ),
inference(flattening,[],[f329]) ).
tff(f329,plain,
? [X1: $int,X0: map_int_elt2] :
( ? [X2: $int,X3: map_int_elt2] :
( ? [X6: $int,X5: map_int_elt2] :
( ? [X8: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X8,X6),min(X1,$sum($product(X8,X6),X6)))
& ~ $less($product(X8,X6),0)
& $less($product(X8,X6),X1) )
& $less(X6,X1)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X7,X6),min(X1,$sum($product(X7,X6),X6)))
| ~ $less($product(X7,X6),X1)
| $less($product(X7,X6),0) )
& ~ $less(X6,1)
& permut_all(elt5,mk_array1(elt5,X1,t2tb9(X0)),mk_array1(elt5,X1,t2tb9(X5))) )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X0),t2tb(X4))) )
| $less(X4,0)
| ~ $less(X4,X2) )
& ( X1 = X2 )
& ~ $less(X2,0) )
& ~ $less(X1,0) ),
inference(ennf_transformation,[],[f242]) ).
tff(f242,plain,
~ ! [X1: $int,X0: map_int_elt2] :
( ~ $less(X1,0)
=> ! [X2: $int,X3: map_int_elt2] :
( ( ! [X4: $int] :
( ( ~ $less(X4,0)
& $less(X4,X2) )
=> ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X0),t2tb(X4))) ) )
& ( X1 = X2 )
& ~ $less(X2,0) )
=> ! [X6: $int,X5: map_int_elt2] :
( ( ! [X7: $int] :
( ( $less($product(X7,X6),X1)
& ~ $less($product(X7,X6),0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X7,X6),min(X1,$sum($product(X7,X6),X6))) )
& ~ $less(X6,1)
& permut_all(elt5,mk_array1(elt5,X1,t2tb9(X0)),mk_array1(elt5,X1,t2tb9(X5))) )
=> ( $less(X6,X1)
=> ! [X8: $int] :
( ( ~ $less($product(X8,X6),0)
& $less($product(X8,X6),X1) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X1,t2tb9(X5))),$product(X8,X6),min(X1,$sum($product(X8,X6),X6))) ) ) ) ) ),
inference(rectify,[],[f135]) ).
tff(f135,plain,
~ ! [X10: map_int_elt2,X0: $int] :
( ~ $less(X0,0)
=> ! [X29: $int,X30: map_int_elt2] :
( ( ( X0 = X29 )
& ~ $less(X29,0)
& ! [X14: $int] :
( ( ~ $less(X14,0)
& $less(X14,X29) )
=> ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) ) )
=> ! [X11: map_int_elt2,X31: $int] :
( ( ~ $less(X31,1)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
& ! [X25: $int] :
( ( ~ $less($product(X25,X31),0)
& $less($product(X25,X31),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) )
=> ( $less(X31,X0)
=> ! [X25: $int] :
( ( ~ $less($product(X25,X31),0)
& $less($product(X25,X31),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) ) ) ) ),
inference(theory_normalization,[],[f99]) ).
tff(f99,negated_conjecture,
~ ! [X10: map_int_elt2,X0: $int] :
( $lesseq(0,X0)
=> ! [X29: $int,X30: map_int_elt2] :
( ( ( X0 = X29 )
& $lesseq(0,X29)
& ! [X14: $int] :
( ( $lesseq(0,X14)
& $less(X14,X29) )
=> ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) ) )
=> ! [X11: map_int_elt2,X31: $int] :
( ( $lesseq(1,X31)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
& ! [X25: $int] :
( ( $lesseq(0,$product(X25,X31))
& $less($product(X25,X31),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) )
=> ( $less(X31,X0)
=> ! [X25: $int] :
( ( $lesseq(0,$product(X25,X31))
& $less($product(X25,X31),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) ) ) ) ),
inference(negated_conjecture,[],[f98]) ).
tff(f98,conjecture,
! [X10: map_int_elt2,X0: $int] :
( $lesseq(0,X0)
=> ! [X29: $int,X30: map_int_elt2] :
( ( ( X0 = X29 )
& $lesseq(0,X29)
& ! [X14: $int] :
( ( $lesseq(0,X14)
& $less(X14,X29) )
=> ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) ) )
=> ! [X11: map_int_elt2,X31: $int] :
( ( $lesseq(1,X31)
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
& ! [X25: $int] :
( ( $lesseq(0,$product(X25,X31))
& $less($product(X25,X31),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) )
=> ( $less(X31,X0)
=> ! [X25: $int] :
( ( $lesseq(0,$product(X25,X31))
& $less($product(X25,X31),X0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f654,plain,
~ $less($product(sK9,sK8),sK3),
inference(subsumption_resolution,[],[f645,f462]) ).
tff(f462,plain,
~ $less($product(sK9,sK8),0),
inference(cnf_transformation,[],[f359]) ).
tff(f645,plain,
( $less($product(sK9,sK8),0)
| ~ $less($product(sK9,sK8),sK3) ),
inference(resolution,[],[f464,f460]) ).
tff(f460,plain,
~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(sK9,sK8),min(sK3,$sum($product(sK9,sK8),sK8))),
inference(cnf_transformation,[],[f359]) ).
tff(f464,plain,
! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK7))),$product(X7,sK8),min(sK3,$sum($product(X7,sK8),sK8)))
| $less($product(X7,sK8),0)
| ~ $less($product(X7,sK8),sK3) ),
inference(cnf_transformation,[],[f359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW619_2 : TPTP v8.2.0. Released v6.1.0.
% 0.03/0.13 % Command : run_vampire %s %d THM
% 0.13/0.36 % Computer : n005.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Jun 19 06:08:09 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.23/0.38 This is a TF0_THM_EQU_ARI problem
% 0.23/0.38 Running first-order theorem proving
% 0.23/0.38 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.44 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44 % (1242)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/34Mi)
% 0.23/0.44 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44 % (1245)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.23/0.44 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44 % (1243)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/8Mi)
% 0.23/0.45 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45 % (1241)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59848Mi)
% 0.23/0.45 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45 % (1247)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/32Mi)
% 0.23/0.45 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45 % (1244)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.23/0.45 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45 % (1246)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/15Mi)
% 0.23/0.45 % (1244)Instruction limit reached!
% 0.23/0.45 % (1244)------------------------------
% 0.23/0.45 % (1244)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.23/0.45 % (1244)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.23/0.45 % (1244)Termination reason: Time limit
% 0.23/0.45 % (1244)Termination phase: shuffling
% 0.23/0.45
% 0.23/0.45 % (1244)Memory used [KB]: 857
% 0.23/0.45 % (1244)Time elapsed: 0.002 s
% 0.23/0.45 % (1244)Instructions burned: 2 (million)
% 0.23/0.45 % (1243)Instruction limit reached!
% 0.23/0.45 % (1243)------------------------------
% 0.23/0.45 % (1243)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.23/0.45 % (1243)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.23/0.45 % (1243)Termination reason: Time limit
% 0.23/0.45 % (1243)Termination phase: Preprocessing 3
% 0.23/0.45
% 0.23/0.45 % (1243)Memory used [KB]: 1091
% 0.23/0.45 % (1243)Time elapsed: 0.007 s
% 0.23/0.45 % (1243)Instructions burned: 8 (million)
% 0.24/0.45 % (1246)Instruction limit reached!
% 0.24/0.45 % (1246)------------------------------
% 0.24/0.45 % (1246)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.45 % (1246)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.45 % (1246)Termination reason: Time limit
% 0.24/0.45 % (1246)Termination phase: Saturation
% 0.24/0.45
% 0.24/0.45 % (1246)Memory used [KB]: 1136
% 0.24/0.45 % (1246)Time elapsed: 0.010 s
% 0.24/0.45 % (1246)Instructions burned: 16 (million)
% 0.24/0.46 % (1242)Instruction limit reached!
% 0.24/0.46 % (1242)------------------------------
% 0.24/0.46 % (1242)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.46 % (1242)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.46 % (1242)Termination reason: Time limit
% 0.24/0.46 % (1242)Termination phase: Saturation
% 0.24/0.46
% 0.24/0.46 % (1242)Memory used [KB]: 1497
% 0.24/0.46 % (1242)Time elapsed: 0.021 s
% 0.24/0.46 % (1242)Instructions burned: 34 (million)
% 0.24/0.47 % (1247)Instruction limit reached!
% 0.24/0.47 % (1247)------------------------------
% 0.24/0.47 % (1247)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.47 % (1247)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.47 % (1247)Termination reason: Time limit
% 0.24/0.47 % (1247)Termination phase: Saturation
% 0.24/0.47
% 0.24/0.47 % (1247)Memory used [KB]: 1382
% 0.24/0.47 % (1247)Time elapsed: 0.022 s
% 0.24/0.47 % (1247)Instructions burned: 33 (million)
% 0.24/0.47 % (1245)Instruction limit reached!
% 0.24/0.47 % (1245)------------------------------
% 0.24/0.47 % (1245)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.47 % (1245)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.47 % (1245)Termination reason: Time limit
% 0.24/0.47 % (1245)Termination phase: Saturation
% 0.24/0.47
% 0.24/0.47 % (1245)Memory used [KB]: 1543
% 0.24/0.47 % (1245)Time elapsed: 0.026 s
% 0.24/0.47 % (1245)Instructions burned: 37 (million)
% 0.24/0.51 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.51 % (1248)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 0.24/0.51 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.51 % (1249)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 0.24/0.51 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.51 % (1250)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.24/0.52 % (1250)Instruction limit reached!
% 0.24/0.52 % (1250)------------------------------
% 0.24/0.52 % (1250)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.52 % (1250)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.52 % (1250)Termination reason: Time limit
% 0.24/0.52 % (1250)Termination phase: Property scanning
% 0.24/0.52
% 0.24/0.52 % (1250)Memory used [KB]: 861
% 0.24/0.52 % (1250)Time elapsed: 0.003 s
% 0.24/0.52 % (1250)Instructions burned: 3 (million)
% 0.24/0.52 % (1248)First to succeed.
% 0.24/0.52 % (1248)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1240"
% 0.24/0.52 % (1240)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.52 % (1248)Refutation found. Thanks to Tanya!
% 0.24/0.52 % SZS status Theorem for theBenchmark
% 0.24/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.52 % (1248)------------------------------
% 0.24/0.52 % (1248)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.52 % (1248)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.52 % (1248)Termination reason: Refutation
% 0.24/0.52
% 0.24/0.52 % (1248)Memory used [KB]: 1343
% 0.24/0.52 % (1248)Time elapsed: 0.015 s
% 0.24/0.52 % (1248)Instructions burned: 23 (million)
% 0.24/0.52 % (1248)------------------------------
% 0.24/0.52 % (1248)------------------------------
% 0.24/0.52 % (1240)Success in time 0.128 s
%------------------------------------------------------------------------------