TSTP Solution File: SWW619_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW619_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 May 21 07:27:32 EDT 2024
% Result : Theorem 0.11s 0.37s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 168
% Syntax : Number of formulae : 313 ( 137 unt; 76 typ; 0 def)
% Number of atoms : 554 ( 102 equ)
% Maximal formula atoms : 30 ( 2 avg)
% Number of connectives : 473 ( 156 ~; 87 |; 139 &)
% ( 53 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 753 ( 224 atm; 230 fun; 129 num; 170 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 166 ( 53 >; 113 *; 0 +; 0 <<)
% Number of predicates : 68 ( 64 usr; 51 prp; 0-7 aty)
% Number of functors : 60 ( 55 usr; 18 con; 0-7 aty)
% Number of variables : 315 ( 269 !; 46 ?; 315 :)
% 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: $int ).
tff(func_def_46,type,
sK2: map_int_elt2 ).
tff(func_def_47,type,
sK3: $int ).
tff(func_def_48,type,
sK4: map_int_elt2 ).
tff(func_def_49,type,
sK5: $int ).
tff(func_def_50,type,
sK6: map_int_elt2 ).
tff(func_def_51,type,
sK7: $int ).
tff(func_def_52,type,
sK8: ( array_elt2 * $int * $int ) > $int ).
tff(func_def_53,type,
sK9: ( array_elt2 * $int * $int ) > $int ).
tff(func_def_54,type,
sK10: ( ty * uni * uni * $int * $int ) > uni ).
tff(func_def_55,type,
sK11: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_56,type,
sK12: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_57,type,
sK13: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_58,type,
sK14: ( ty * uni * uni * $int * $int * $int ) > $int ).
tff(func_def_59,type,
sK15: ( ty * uni * uni * $int * $int ) > $int ).
tff(func_def_60,type,
sK16: ( uni * ty * uni * $int * $int * $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: ( uni * ty * uni * $int * $int * $int * $int ) > $o ).
tff(f762,plain,
$false,
inference(avatar_sat_refutation,[],[f547,f552,f557,f562,f567,f572,f576,f581,f585,f589,f594,f598,f602,f606,f610,f615,f619,f623,f627,f631,f635,f639,f643,f647,f651,f655,f659,f663,f667,f671,f675,f679,f683,f687,f693,f699,f703,f707,f711,f715,f719,f727,f732,f736,f740,f744,f748,f752,f756,f760,f761]) ).
tff(f761,plain,
( spl17_4
| ~ spl17_5
| spl17_16
| ~ spl17_42 ),
inference(avatar_split_clause,[],[f728,f725,f612,f564,f559]) ).
tff(f559,plain,
( spl17_4
<=> $less($product(sK7,sK5),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
tff(f564,plain,
( spl17_5
<=> $less($product(sK7,sK5),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
tff(f612,plain,
( spl17_16
<=> sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK6))),$product(sK7,sK5),min(sK3,$sum(sK5,$product(sK7,sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
tff(f725,plain,
( spl17_42
<=> ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK6))),$product(X7,sK5),min(sK3,$sum(sK5,$product(X7,sK5))))
| ~ $less($product(X7,sK5),sK3)
| $less($product(X7,sK5),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).
tff(f728,plain,
( ~ $less($product(sK7,sK5),sK3)
| $less($product(sK7,sK5),0)
| spl17_16
| ~ spl17_42 ),
inference(resolution,[],[f726,f614]) ).
tff(f614,plain,
( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK6))),$product(sK7,sK5),min(sK3,$sum(sK5,$product(sK7,sK5))))
| spl17_16 ),
inference(avatar_component_clause,[],[f612]) ).
tff(f726,plain,
( ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK6))),$product(X7,sK5),min(sK3,$sum(sK5,$product(X7,sK5))))
| ~ $less($product(X7,sK5),sK3)
| $less($product(X7,sK5),0) )
| ~ spl17_42 ),
inference(avatar_component_clause,[],[f725]) ).
tff(f760,plain,
spl17_50,
inference(avatar_split_clause,[],[f460,f758]) ).
tff(f758,plain,
( spl17_50
<=> ! [X0: ty,X3: uni,X2: uni,X1: ty] : sort1(X1,get(X1,X0,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).
tff(f460,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty] : sort1(X1,get(X1,X0,X2,X3)),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] : sort1(X1,get(X1,X0,X2,X3)),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: ty,X8: ty,X1: uni,X2: uni] : sort1(X8,get(X8,X0,X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',get_sort6) ).
tff(f756,plain,
spl17_49,
inference(avatar_split_clause,[],[f459,f754]) ).
tff(f754,plain,
( spl17_49
<=> ! [X0: ty,X3: uni,X2: uni,X1: bool1] : sort1(X0,match_bool1(X0,X1,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).
tff(f459,plain,
! [X2: uni,X3: uni,X0: ty,X1: bool1] : sort1(X0,match_bool1(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: ty,X1: bool1,X2: uni,X3: uni] : sort1(X0,match_bool1(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_bool_sort3) ).
tff(f752,plain,
spl17_48,
inference(avatar_split_clause,[],[f440,f750]) ).
tff(f750,plain,
( spl17_48
<=> ! [X2: uni,X0: ty,X1: $int] : sort1(array(X0),mk_array1(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
tff(f440,plain,
! [X2: uni,X0: ty,X1: $int] : sort1(array(X0),mk_array1(X0,X1,X2)),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
! [X0: ty,X1: $int,X2: uni] : sort1(array(X0),mk_array1(X0,X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mk_array_sort3) ).
tff(f748,plain,
spl17_47,
inference(avatar_split_clause,[],[f436,f746]) ).
tff(f746,plain,
( spl17_47
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
tff(f436,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,abs(X0)) ),
inference(cnf_transformation,[],[f342]) ).
tff(f342,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X1,abs(X0))
| $less(X1,X0)
| $less(X0,$uminus(X1)) )
& ( ( ~ $less(X1,X0)
& ~ $less(X0,$uminus(X1)) )
| $less(X1,abs(X0)) ) ),
inference(flattening,[],[f341]) ).
tff(f341,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X1,abs(X0))
| $less(X1,X0)
| $less(X0,$uminus(X1)) )
& ( ( ~ $less(X1,X0)
& ~ $less(X0,$uminus(X1)) )
| $less(X1,abs(X0)) ) ),
inference(nnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,abs(X0))
<=> ( ~ $less(X1,X0)
& ~ $less(X0,$uminus(X1)) ) ),
inference(rectify,[],[f120]) ).
tff(f120,plain,
! [X1: $int,X7: $int] :
( ~ $less(X7,abs(X1))
<=> ( ~ $less(X7,X1)
& ~ $less(X1,$uminus(X7)) ) ),
inference(theory_normalization,[],[f69]) ).
tff(f69,axiom,
! [X1: $int,X7: $int] :
( $lesseq(abs(X1),X7)
<=> ( $lesseq(X1,X7)
& $lesseq($uminus(X7),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_le) ).
tff(f744,plain,
spl17_46,
inference(avatar_split_clause,[],[f406,f742]) ).
tff(f742,plain,
( spl17_46
<=> ! [X0: ty,X1: uni] : sort1(map(int,X0),elts(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
tff(f406,plain,
! [X0: ty,X1: uni] : sort1(map(int,X0),elts(X0,X1)),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
! [X0: ty,X1: uni] : sort1(map(int,X0),elts(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',elts_sort3) ).
tff(f740,plain,
spl17_45,
inference(avatar_split_clause,[],[f399,f738]) ).
tff(f738,plain,
( spl17_45
<=> ! [X0: $int] :
( ( abs(X0) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
tff(f399,plain,
! [X0: $int] :
( ( abs(X0) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $int] :
( ( ( $uminus(X0) = abs(X0) )
| ~ $less(X0,0) )
& ( ( abs(X0) = X0 )
| $less(X0,0) ) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $int] :
( ( $less(X0,0)
=> ( $uminus(X0) = abs(X0) ) )
& ( ~ $less(X0,0)
=> ( abs(X0) = X0 ) ) ),
inference(rectify,[],[f102]) ).
tff(f102,plain,
! [X1: $int] :
( ( $less(X1,0)
=> ( abs(X1) = $uminus(X1) ) )
& ( ~ $less(X1,0)
=> ( abs(X1) = X1 ) ) ),
inference(theory_normalization,[],[f68]) ).
tff(f68,axiom,
! [X1: $int] :
( ( ~ $lesseq(0,X1)
=> ( abs(X1) = $uminus(X1) ) )
& ( $lesseq(0,X1)
=> ( abs(X1) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_def) ).
tff(f736,plain,
spl17_44,
inference(avatar_split_clause,[],[f153,f734]) ).
tff(f734,plain,
( spl17_44
<=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).
tff(f153,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f732,plain,
spl17_43,
inference(avatar_split_clause,[],[f142,f730]) ).
tff(f730,plain,
( spl17_43
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).
tff(f142,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f727,plain,
spl17_42,
inference(avatar_split_clause,[],[f541,f725]) ).
tff(f541,plain,
! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK6))),$product(X7,sK5),min(sK3,$sum(sK5,$product(X7,sK5))))
| ~ $less($product(X7,sK5),sK3)
| $less($product(X7,sK5),0) ),
inference(forward_demodulation,[],[f527,f142]) ).
tff(f527,plain,
! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK6))),$product(X7,sK5),min(sK3,$sum($product(X7,sK5),sK5)))
| ~ $less($product(X7,sK5),sK3)
| $less($product(X7,sK5),0) ),
inference(definition_unfolding,[],[f377,f373,f373,f373]) ).
tff(f373,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f340]) ).
tff(f340,plain,
( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(sK6))),$product(sK7,sK5),min(sK1,$sum($product(sK7,sK5),sK5)))
& $less($product(sK7,sK5),sK1)
& ~ $less($product(sK7,sK5),0)
& $less(sK5,sK1)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(sK6))),$product(X7,sK5),min(sK1,$sum($product(X7,sK5),sK5)))
| ~ $less($product(X7,sK5),sK1)
| $less($product(X7,sK5),0) )
& permut_all(elt5,mk_array1(elt5,sK1,t2tb9(sK2)),mk_array1(elt5,sK1,t2tb9(sK6)))
& ~ $less(sK5,1)
& ! [X8: $int] :
( ( tb2t7(get(elt5,int,t2tb9(sK2),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X8))) )
| ~ $less(X8,sK3)
| $less(X8,0) )
& ( sK1 = sK3 )
& ~ $less(sK3,0)
& ~ $less(sK1,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f335,f339,f338,f337,f336]) ).
tff(f336,plain,
( ? [X0: $int,X1: map_int_elt2] :
( ? [X2: $int,X3: map_int_elt2] :
( ? [X4: $int,X5: map_int_elt2] :
( ? [X6: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4)))
& $less($product(X6,X4),X0)
& ~ $less($product(X6,X4),0) )
& $less(X4,X0)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4)))
| ~ $less($product(X7,X4),X0)
| $less($product(X7,X4),0) )
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5)))
& ~ $less(X4,1) )
& ! [X8: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X8))) )
| ~ $less(X8,X2)
| $less(X8,0) )
& ( X0 = X2 )
& ~ $less(X2,0) )
& ~ $less(X0,0) )
=> ( ? [X3: map_int_elt2,X2: $int] :
( ? [X5: map_int_elt2,X4: $int] :
( ? [X6: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(X5))),$product(X6,X4),min(sK1,$sum($product(X6,X4),X4)))
& $less($product(X6,X4),sK1)
& ~ $less($product(X6,X4),0) )
& $less(X4,sK1)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(X5))),$product(X7,X4),min(sK1,$sum($product(X7,X4),X4)))
| ~ $less($product(X7,X4),sK1)
| $less($product(X7,X4),0) )
& permut_all(elt5,mk_array1(elt5,sK1,t2tb9(sK2)),mk_array1(elt5,sK1,t2tb9(X5)))
& ~ $less(X4,1) )
& ! [X8: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK2),t2tb(X8))) )
| ~ $less(X8,X2)
| $less(X8,0) )
& ( sK1 = X2 )
& ~ $less(X2,0) )
& ~ $less(sK1,0) ) ),
introduced(choice_axiom,[]) ).
tff(f337,plain,
( ? [X3: map_int_elt2,X2: $int] :
( ? [X5: map_int_elt2,X4: $int] :
( ? [X6: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(X5))),$product(X6,X4),min(sK1,$sum($product(X6,X4),X4)))
& $less($product(X6,X4),sK1)
& ~ $less($product(X6,X4),0) )
& $less(X4,sK1)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(X5))),$product(X7,X4),min(sK1,$sum($product(X7,X4),X4)))
| ~ $less($product(X7,X4),sK1)
| $less($product(X7,X4),0) )
& permut_all(elt5,mk_array1(elt5,sK1,t2tb9(sK2)),mk_array1(elt5,sK1,t2tb9(X5)))
& ~ $less(X4,1) )
& ! [X8: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK2),t2tb(X8))) )
| ~ $less(X8,X2)
| $less(X8,0) )
& ( sK1 = X2 )
& ~ $less(X2,0) )
=> ( ? [X5: map_int_elt2,X4: $int] :
( ? [X6: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(X5))),$product(X6,X4),min(sK1,$sum($product(X6,X4),X4)))
& $less($product(X6,X4),sK1)
& ~ $less($product(X6,X4),0) )
& $less(X4,sK1)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(X5))),$product(X7,X4),min(sK1,$sum($product(X7,X4),X4)))
| ~ $less($product(X7,X4),sK1)
| $less($product(X7,X4),0) )
& permut_all(elt5,mk_array1(elt5,sK1,t2tb9(sK2)),mk_array1(elt5,sK1,t2tb9(X5)))
& ~ $less(X4,1) )
& ! [X8: $int] :
( ( tb2t7(get(elt5,int,t2tb9(sK2),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X8))) )
| ~ $less(X8,sK3)
| $less(X8,0) )
& ( sK1 = sK3 )
& ~ $less(sK3,0) ) ),
introduced(choice_axiom,[]) ).
tff(f338,plain,
( ? [X5: map_int_elt2,X4: $int] :
( ? [X6: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(X5))),$product(X6,X4),min(sK1,$sum($product(X6,X4),X4)))
& $less($product(X6,X4),sK1)
& ~ $less($product(X6,X4),0) )
& $less(X4,sK1)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(X5))),$product(X7,X4),min(sK1,$sum($product(X7,X4),X4)))
| ~ $less($product(X7,X4),sK1)
| $less($product(X7,X4),0) )
& permut_all(elt5,mk_array1(elt5,sK1,t2tb9(sK2)),mk_array1(elt5,sK1,t2tb9(X5)))
& ~ $less(X4,1) )
=> ( ? [X6: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(sK6))),$product(X6,sK5),min(sK1,$sum($product(X6,sK5),sK5)))
& $less($product(X6,sK5),sK1)
& ~ $less($product(X6,sK5),0) )
& $less(sK5,sK1)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(sK6))),$product(X7,sK5),min(sK1,$sum($product(X7,sK5),sK5)))
| ~ $less($product(X7,sK5),sK1)
| $less($product(X7,sK5),0) )
& permut_all(elt5,mk_array1(elt5,sK1,t2tb9(sK2)),mk_array1(elt5,sK1,t2tb9(sK6)))
& ~ $less(sK5,1) ) ),
introduced(choice_axiom,[]) ).
tff(f339,plain,
( ? [X6: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(sK6))),$product(X6,sK5),min(sK1,$sum($product(X6,sK5),sK5)))
& $less($product(X6,sK5),sK1)
& ~ $less($product(X6,sK5),0) )
=> ( ~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(sK6))),$product(sK7,sK5),min(sK1,$sum($product(sK7,sK5),sK5)))
& $less($product(sK7,sK5),sK1)
& ~ $less($product(sK7,sK5),0) ) ),
introduced(choice_axiom,[]) ).
tff(f335,plain,
? [X0: $int,X1: map_int_elt2] :
( ? [X2: $int,X3: map_int_elt2] :
( ? [X4: $int,X5: map_int_elt2] :
( ? [X6: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4)))
& $less($product(X6,X4),X0)
& ~ $less($product(X6,X4),0) )
& $less(X4,X0)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4)))
| ~ $less($product(X7,X4),X0)
| $less($product(X7,X4),0) )
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5)))
& ~ $less(X4,1) )
& ! [X8: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X8))) )
| ~ $less(X8,X2)
| $less(X8,0) )
& ( X0 = X2 )
& ~ $less(X2,0) )
& ~ $less(X0,0) ),
inference(rectify,[],[f251]) ).
tff(f251,plain,
? [X0: $int,X1: map_int_elt2] :
( ? [X2: $int,X3: map_int_elt2] :
( ? [X5: $int,X6: map_int_elt2] :
( ? [X8: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5)))
& $less($product(X8,X5),X0)
& ~ $less($product(X8,X5),0) )
& $less(X5,X0)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5)))
| ~ $less($product(X7,X5),X0)
| $less($product(X7,X5),0) )
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ~ $less(X5,1) )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
| ~ $less(X4,X2)
| $less(X4,0) )
& ( X0 = X2 )
& ~ $less(X2,0) )
& ~ $less(X0,0) ),
inference(flattening,[],[f250]) ).
tff(f250,plain,
? [X0: $int,X1: map_int_elt2] :
( ? [X2: $int,X3: map_int_elt2] :
( ? [X5: $int,X6: map_int_elt2] :
( ? [X8: $int] :
( ~ sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5)))
& $less($product(X8,X5),X0)
& ~ $less($product(X8,X5),0) )
& $less(X5,X0)
& ! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5)))
| ~ $less($product(X7,X5),X0)
| $less($product(X7,X5),0) )
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ~ $less(X5,1) )
& ! [X4: $int] :
( ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) )
| ~ $less(X4,X2)
| $less(X4,0) )
& ( X0 = X2 )
& ~ $less(X2,0) )
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
~ ! [X0: $int,X1: map_int_elt2] :
( ~ $less(X0,0)
=> ! [X2: $int,X3: map_int_elt2] :
( ( ! [X4: $int] :
( ( $less(X4,X2)
& ~ $less(X4,0) )
=> ( tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) ) )
& ( X0 = X2 )
& ~ $less(X2,0) )
=> ! [X5: $int,X6: map_int_elt2] :
( ( ! [X7: $int] :
( ( $less($product(X7,X5),X0)
& ~ $less($product(X7,X5),0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) )
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6)))
& ~ $less(X5,1) )
=> ( $less(X5,X0)
=> ! [X8: $int] :
( ( $less($product(X8,X5),X0)
& ~ $less($product(X8,X5),0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5))) ) ) ) ) ),
inference(rectify,[],[f100]) ).
tff(f100,plain,
~ ! [X0: $int,X10: map_int_elt2] :
( ~ $less(X0,0)
=> ! [X29: $int,X30: map_int_elt2] :
( ( ! [X14: $int] :
( ( $less(X14,X29)
& ~ $less(X14,0) )
=> ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) )
& ( X0 = X29 )
& ~ $less(X29,0) )
=> ! [X31: $int,X11: map_int_elt2] :
( ( ! [X25: $int] :
( ( $less($product(X25,X31),X0)
& ~ $less($product(X25,X31),0) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) )
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
& ~ $less(X31,1) )
=> ( $less(X31,X0)
=> ! [X25: $int] :
( ( $less($product(X25,X31),X0)
& ~ $less($product(X25,X31),0) )
=> 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,
~ ! [X0: $int,X10: map_int_elt2] :
( $lesseq(0,X0)
=> ! [X29: $int,X30: map_int_elt2] :
( ( ! [X14: $int] :
( ( $less(X14,X29)
& $lesseq(0,X14) )
=> ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) )
& ( X0 = X29 )
& $lesseq(0,X29) )
=> ! [X31: $int,X11: map_int_elt2] :
( ( ! [X25: $int] :
( ( $less($product(X25,X31),X0)
& $lesseq(0,$product(X25,X31)) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) )
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
& $lesseq(1,X31) )
=> ( $less(X31,X0)
=> ! [X25: $int] :
( ( $less($product(X25,X31),X0)
& $lesseq(0,$product(X25,X31)) )
=> 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,
! [X0: $int,X10: map_int_elt2] :
( $lesseq(0,X0)
=> ! [X29: $int,X30: map_int_elt2] :
( ( ! [X14: $int] :
( ( $less(X14,X29)
& $lesseq(0,X14) )
=> ( tb2t7(get(elt5,int,t2tb9(X30),t2tb(X14))) = tb2t7(get(elt5,int,t2tb9(X10),t2tb(X14))) ) )
& ( X0 = X29 )
& $lesseq(0,X29) )
=> ! [X31: $int,X11: map_int_elt2] :
( ( ! [X25: $int] :
( ( $less($product(X25,X31),X0)
& $lesseq(0,$product(X25,X31)) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) )
& permut_all(elt5,mk_array1(elt5,X0,t2tb9(X10)),mk_array1(elt5,X0,t2tb9(X11)))
& $lesseq(1,X31) )
=> ( $less(X31,X0)
=> ! [X25: $int] :
( ( $less($product(X25,X31),X0)
& $lesseq(0,$product(X25,X31)) )
=> sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X11))),$product(X25,X31),min(X0,$sum($product(X25,X31),X31))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_bottom_up_mergesort) ).
tff(f377,plain,
! [X7: $int] :
( sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(sK6))),$product(X7,sK5),min(sK1,$sum($product(X7,sK5),sK5)))
| ~ $less($product(X7,sK5),sK1)
| $less($product(X7,sK5),0) ),
inference(cnf_transformation,[],[f340]) ).
tff(f719,plain,
spl17_41,
inference(avatar_split_clause,[],[f412,f717]) ).
tff(f717,plain,
( spl17_41
<=> ! [X0: elt4,X1: elt4] :
( le3(X1,X0)
| le3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).
tff(f412,plain,
! [X0: elt4,X1: elt4] :
( le3(X1,X0)
| le3(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: elt4,X1: elt4] :
( le3(X1,X0)
| le3(X0,X1) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X1: elt4,X7: elt4] :
( le3(X7,X1)
| le3(X1,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total3) ).
tff(f715,plain,
spl17_40,
inference(avatar_split_clause,[],[f405,f713]) ).
tff(f713,plain,
( spl17_40
<=> ! [X0: ty,X1: uni] : sort1(ref(X0),mk_ref(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).
tff(f405,plain,
! [X0: ty,X1: uni] : sort1(ref(X0),mk_ref(X0,X1)),
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
! [X0: ty,X1: uni] : sort1(ref(X0),mk_ref(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mk_ref_sort3) ).
tff(f711,plain,
spl17_39,
inference(avatar_split_clause,[],[f401,f709]) ).
tff(f709,plain,
( spl17_39
<=> ! [X0: bool1] :
( ( false1 = X0 )
| ( true1 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).
tff(f401,plain,
! [X0: bool1] :
( ( false1 = X0 )
| ( true1 = X0 ) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: bool1] :
( ( false1 = X0 )
| ( true1 = X0 ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X6: bool1] :
( ( false1 = X6 )
| ( true1 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bool_inversion) ).
tff(f707,plain,
spl17_38,
inference(avatar_split_clause,[],[f398,f705]) ).
tff(f705,plain,
( spl17_38
<=> ! [X0: map_int_elt2] : sort1(map(int,elt5),t2tb9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).
tff(f398,plain,
! [X0: map_int_elt2] : sort1(map(int,elt5),t2tb9(X0)),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: map_int_elt2] : sort1(map(int,elt5),t2tb9(X0)),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X1: map_int_elt2] : sort1(map(int,elt5),t2tb9(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2tb_sort11) ).
tff(f703,plain,
spl17_37,
inference(avatar_split_clause,[],[f146,f701]) ).
tff(f701,plain,
( spl17_37
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).
tff(f146,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f699,plain,
( spl17_36
| ~ spl17_13
| ~ spl17_27 ),
inference(avatar_split_clause,[],[f688,f657,f600,f697]) ).
tff(f697,plain,
( spl17_36
<=> ! [X0: uni] : sort1(int,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
tff(f600,plain,
( spl17_13
<=> ! [X0: $int] : sort1(int,t2tb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
tff(f657,plain,
( spl17_27
<=> ! [X0: uni] : ( t2tb(tb2t(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).
tff(f688,plain,
( ! [X0: uni] : sort1(int,X0)
| ~ spl17_13
| ~ spl17_27 ),
inference(superposition,[],[f601,f658]) ).
tff(f658,plain,
( ! [X0: uni] : ( t2tb(tb2t(X0)) = X0 )
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f657]) ).
tff(f601,plain,
( ! [X0: $int] : sort1(int,t2tb(X0))
| ~ spl17_13 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f693,plain,
spl17_35,
inference(avatar_split_clause,[],[f374,f691]) ).
tff(f691,plain,
( spl17_35
<=> ! [X8: $int] :
( ( tb2t7(get(elt5,int,t2tb9(sK2),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X8))) )
| ~ $less(X8,sK3)
| $less(X8,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
tff(f374,plain,
! [X8: $int] :
( ( tb2t7(get(elt5,int,t2tb9(sK2),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK4),t2tb(X8))) )
| ~ $less(X8,sK3)
| $less(X8,0) ),
inference(cnf_transformation,[],[f340]) ).
tff(f687,plain,
spl17_34,
inference(avatar_split_clause,[],[f411,f685]) ).
tff(f685,plain,
( spl17_34
<=> ! [X0: $int,X1: $int] : ~ $less(X1,min(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).
tff(f411,plain,
! [X0: $int,X1: $int] : ~ $less(X1,min(X0,X1)),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,min(X0,X1))
& ~ $less(X0,min(X0,X1)) ),
inference(rectify,[],[f105]) ).
tff(f105,plain,
! [X1: $int,X7: $int] :
( ~ $less(X7,min(X1,X7))
& ~ $less(X1,min(X1,X7)) ),
inference(theory_normalization,[],[f87]) ).
tff(f87,axiom,
! [X1: $int,X7: $int] :
( $lesseq(min(X1,X7),X7)
& $lesseq(min(X1,X7),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',min_is_le) ).
tff(f683,plain,
spl17_33,
inference(avatar_split_clause,[],[f410,f681]) ).
tff(f681,plain,
( spl17_33
<=> ! [X0: $int,X1: $int] : ~ $less(X0,min(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).
tff(f410,plain,
! [X0: $int,X1: $int] : ~ $less(X0,min(X0,X1)),
inference(cnf_transformation,[],[f183]) ).
tff(f679,plain,
spl17_32,
inference(avatar_split_clause,[],[f409,f677]) ).
tff(f677,plain,
( spl17_32
<=> ! [X0: $int,X1: $int] : ~ $less(max(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).
tff(f409,plain,
! [X0: $int,X1: $int] : ~ $less(max(X0,X1),X1),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $int,X1: $int] :
( ~ $less(max(X0,X1),X1)
& ~ $less(max(X0,X1),X0) ),
inference(rectify,[],[f104]) ).
tff(f104,plain,
! [X1: $int,X7: $int] :
( ~ $less(max(X1,X7),X7)
& ~ $less(max(X1,X7),X1) ),
inference(theory_normalization,[],[f85]) ).
tff(f85,axiom,
! [X1: $int,X7: $int] :
( $lesseq(X7,max(X1,X7))
& $lesseq(X1,max(X1,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_is_ge) ).
tff(f675,plain,
spl17_31,
inference(avatar_split_clause,[],[f408,f673]) ).
tff(f673,plain,
( spl17_31
<=> ! [X0: $int,X1: $int] : ~ $less(max(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).
tff(f408,plain,
! [X0: $int,X1: $int] : ~ $less(max(X0,X1),X0),
inference(cnf_transformation,[],[f182]) ).
tff(f671,plain,
spl17_30,
inference(avatar_split_clause,[],[f404,f669]) ).
tff(f669,plain,
( spl17_30
<=> ! [X0: ty,X1: uni] : sort1(X0,contents(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).
tff(f404,plain,
! [X0: ty,X1: uni] : sort1(X0,contents(X0,X1)),
inference(cnf_transformation,[],[f41]) ).
tff(f41,axiom,
! [X0: ty,X1: uni] : sort1(X0,contents(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contents_sort3) ).
tff(f667,plain,
spl17_29,
inference(avatar_split_clause,[],[f397,f665]) ).
tff(f665,plain,
( spl17_29
<=> ! [X0: array_elt2] : sort1(array(elt5),t2tb8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).
tff(f397,plain,
! [X0: array_elt2] : sort1(array(elt5),t2tb8(X0)),
inference(cnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: array_elt2] : sort1(array(elt5),t2tb8(X0)),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X1: array_elt2] : sort1(array(elt5),t2tb8(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2tb_sort10) ).
tff(f663,plain,
spl17_28,
inference(avatar_split_clause,[],[f396,f661]) ).
tff(f661,plain,
( spl17_28
<=> ! [X0: $int] : ( div(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).
tff(f396,plain,
! [X0: $int] : ( div(X0,1) = X0 ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $int] : ( div(X0,1) = X0 ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X1: $int] : ( div(X1,1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_1) ).
tff(f659,plain,
spl17_27,
inference(avatar_split_clause,[],[f395,f657]) ).
tff(f395,plain,
! [X0: uni] : ( t2tb(tb2t(X0)) = X0 ),
inference(cnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: uni] : ( t2tb(tb2t(X0)) = X0 ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X15: uni] : ( t2tb(tb2t(X15)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR) ).
tff(f655,plain,
spl17_26,
inference(avatar_split_clause,[],[f394,f653]) ).
tff(f653,plain,
( spl17_26
<=> ! [X0: uni] : ( t2tb8(tb2t8(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
tff(f394,plain,
! [X0: uni] : ( t2tb8(tb2t8(X0)) = X0 ),
inference(cnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: uni] : ( t2tb8(tb2t8(X0)) = X0 ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X15: uni] : ( t2tb8(tb2t8(X15)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR8) ).
tff(f651,plain,
spl17_25,
inference(avatar_split_clause,[],[f393,f649]) ).
tff(f649,plain,
( spl17_25
<=> ! [X0: elt4] : ( tb2t7(t2tb7(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
tff(f393,plain,
! [X0: elt4] : ( tb2t7(t2tb7(X0)) = X0 ),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: elt4] : ( tb2t7(t2tb7(X0)) = X0 ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X14: elt4] : ( tb2t7(t2tb7(X14)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL7) ).
tff(f647,plain,
spl17_24,
inference(avatar_split_clause,[],[f392,f645]) ).
tff(f645,plain,
( spl17_24
<=> ! [X0: array_elt2] : ( tb2t8(t2tb8(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).
tff(f392,plain,
! [X0: array_elt2] : ( tb2t8(t2tb8(X0)) = X0 ),
inference(cnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: array_elt2] : ( tb2t8(t2tb8(X0)) = X0 ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X14: array_elt2] : ( tb2t8(t2tb8(X14)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL8) ).
tff(f643,plain,
spl17_23,
inference(avatar_split_clause,[],[f391,f641]) ).
tff(f641,plain,
( spl17_23
<=> ! [X0: $int] : ( tb2t(t2tb(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
tff(f391,plain,
! [X0: $int] : ( tb2t(t2tb(X0)) = X0 ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $int] : ( tb2t(t2tb(X0)) = X0 ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X14: $int] : ( tb2t(t2tb(X14)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL) ).
tff(f639,plain,
spl17_22,
inference(avatar_split_clause,[],[f390,f637]) ).
tff(f637,plain,
( spl17_22
<=> ! [X0: map_int_elt2] : ( tb2t9(t2tb9(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).
tff(f390,plain,
! [X0: map_int_elt2] : ( tb2t9(t2tb9(X0)) = X0 ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: map_int_elt2] : ( tb2t9(t2tb9(X0)) = X0 ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X14: map_int_elt2] : ( tb2t9(t2tb9(X14)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL9) ).
tff(f635,plain,
spl17_21,
inference(avatar_split_clause,[],[f389,f633]) ).
tff(f633,plain,
( spl17_21
<=> ! [X0: $int] : ( 0 = mod(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).
tff(f389,plain,
! [X0: $int] : ( 0 = mod(X0,1) ),
inference(cnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $int] : ( 0 = mod(X0,1) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X1: $int] : ( 0 = mod(X1,1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_1) ).
tff(f631,plain,
spl17_20,
inference(avatar_split_clause,[],[f156,f629]) ).
tff(f629,plain,
( spl17_20
<=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
tff(f156,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_149,[]) ).
tff(f627,plain,
spl17_19,
inference(avatar_split_clause,[],[f155,f625]) ).
tff(f625,plain,
( spl17_19
<=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
tff(f155,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f623,plain,
spl17_18,
inference(avatar_split_clause,[],[f152,f621]) ).
tff(f621,plain,
( spl17_18
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
tff(f152,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f619,plain,
spl17_17,
inference(avatar_split_clause,[],[f144,f617]) ).
tff(f617,plain,
( spl17_17
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
tff(f144,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f615,plain,
~ spl17_16,
inference(avatar_split_clause,[],[f540,f612]) ).
tff(f540,plain,
~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK6))),$product(sK7,sK5),min(sK3,$sum(sK5,$product(sK7,sK5)))),
inference(forward_demodulation,[],[f524,f142]) ).
tff(f524,plain,
~ sorted_sub3(tb2t8(mk_array1(elt5,sK3,t2tb9(sK6))),$product(sK7,sK5),min(sK3,$sum($product(sK7,sK5),sK5))),
inference(definition_unfolding,[],[f381,f373,f373]) ).
tff(f381,plain,
~ sorted_sub3(tb2t8(mk_array1(elt5,sK1,t2tb9(sK6))),$product(sK7,sK5),min(sK1,$sum($product(sK7,sK5),sK5))),
inference(cnf_transformation,[],[f340]) ).
tff(f610,plain,
spl17_15,
inference(avatar_split_clause,[],[f388,f608]) ).
tff(f608,plain,
( spl17_15
<=> ! [X0: $int] : ~ $less(abs(X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
tff(f388,plain,
! [X0: $int] : ~ $less(abs(X0),0),
inference(cnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $int] : ~ $less(abs(X0),0),
inference(rectify,[],[f101]) ).
tff(f101,plain,
! [X1: $int] : ~ $less(abs(X1),0),
inference(theory_normalization,[],[f70]) ).
tff(f70,axiom,
! [X1: $int] : $lesseq(0,abs(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_pos) ).
tff(f606,plain,
( spl17_14
| ~ spl17_9 ),
inference(avatar_split_clause,[],[f590,f583,f604]) ).
tff(f604,plain,
( spl17_14
<=> ! [X0: tuple02,X1: tuple02] : ( X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
tff(f583,plain,
( spl17_9
<=> ! [X0: tuple02] : ( tuple03 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
tff(f590,plain,
( ! [X0: tuple02,X1: tuple02] : ( X0 = X1 )
| ~ spl17_9 ),
inference(superposition,[],[f584,f584]) ).
tff(f584,plain,
( ! [X0: tuple02] : ( tuple03 = X0 )
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f583]) ).
tff(f602,plain,
spl17_13,
inference(avatar_split_clause,[],[f387,f600]) ).
tff(f387,plain,
! [X0: $int] : sort1(int,t2tb(X0)),
inference(cnf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $int] : sort1(int,t2tb(X0)),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X1: $int] : sort1(int,t2tb(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2tb_sort8) ).
tff(f598,plain,
spl17_12,
inference(avatar_split_clause,[],[f386,f596]) ).
tff(f596,plain,
( spl17_12
<=> ! [X0: elt4] : sort1(elt5,t2tb7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
tff(f386,plain,
! [X0: elt4] : sort1(elt5,t2tb7(X0)),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: elt4] : sort1(elt5,t2tb7(X0)),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X1: elt4] : sort1(elt5,t2tb7(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2tb_sort9) ).
tff(f594,plain,
spl17_11,
inference(avatar_split_clause,[],[f385,f592]) ).
tff(f592,plain,
( spl17_11
<=> ! [X0: ty] : sort1(X0,witness1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
tff(f385,plain,
! [X0: ty] : sort1(X0,witness1(X0)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: ty] : sort1(X0,witness1(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',witness_sort1) ).
tff(f589,plain,
spl17_10,
inference(avatar_split_clause,[],[f384,f587]) ).
tff(f587,plain,
( spl17_10
<=> ! [X0: elt4] : le3(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
tff(f384,plain,
! [X0: elt4] : le3(X0,X0),
inference(cnf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: elt4] : le3(X0,X0),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X1: elt4] : le3(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl3) ).
tff(f585,plain,
spl17_9,
inference(avatar_split_clause,[],[f383,f583]) ).
tff(f383,plain,
! [X0: tuple02] : ( tuple03 = X0 ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: tuple02] : ( tuple03 = X0 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X6: tuple02] : ( tuple03 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tuple0_inversion) ).
tff(f581,plain,
~ spl17_8,
inference(avatar_split_clause,[],[f382,f578]) ).
tff(f578,plain,
( spl17_8
<=> ( true1 = false1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
tff(f382,plain,
true1 != false1,
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
true1 != false1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',true_False) ).
tff(f576,plain,
spl17_7,
inference(avatar_split_clause,[],[f147,f574]) ).
tff(f574,plain,
( spl17_7
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
tff(f147,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f572,plain,
spl17_6,
inference(avatar_split_clause,[],[f528,f569]) ).
tff(f569,plain,
( spl17_6
<=> permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK2)),mk_array1(elt5,sK3,t2tb9(sK6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
tff(f528,plain,
permut_all(elt5,mk_array1(elt5,sK3,t2tb9(sK2)),mk_array1(elt5,sK3,t2tb9(sK6))),
inference(definition_unfolding,[],[f376,f373,f373]) ).
tff(f376,plain,
permut_all(elt5,mk_array1(elt5,sK1,t2tb9(sK2)),mk_array1(elt5,sK1,t2tb9(sK6))),
inference(cnf_transformation,[],[f340]) ).
tff(f567,plain,
spl17_5,
inference(avatar_split_clause,[],[f525,f564]) ).
tff(f525,plain,
$less($product(sK7,sK5),sK3),
inference(definition_unfolding,[],[f380,f373]) ).
tff(f380,plain,
$less($product(sK7,sK5),sK1),
inference(cnf_transformation,[],[f340]) ).
tff(f562,plain,
~ spl17_4,
inference(avatar_split_clause,[],[f379,f559]) ).
tff(f379,plain,
~ $less($product(sK7,sK5),0),
inference(cnf_transformation,[],[f340]) ).
tff(f557,plain,
spl17_3,
inference(avatar_split_clause,[],[f526,f554]) ).
tff(f554,plain,
( spl17_3
<=> $less(sK5,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
tff(f526,plain,
$less(sK5,sK3),
inference(definition_unfolding,[],[f378,f373]) ).
tff(f378,plain,
$less(sK5,sK1),
inference(cnf_transformation,[],[f340]) ).
tff(f552,plain,
~ spl17_2,
inference(avatar_split_clause,[],[f375,f549]) ).
tff(f549,plain,
( spl17_2
<=> $less(sK5,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
tff(f375,plain,
~ $less(sK5,1),
inference(cnf_transformation,[],[f340]) ).
tff(f547,plain,
~ spl17_1,
inference(avatar_split_clause,[],[f372,f544]) ).
tff(f544,plain,
( spl17_1
<=> $less(sK3,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
tff(f372,plain,
~ $less(sK3,0),
inference(cnf_transformation,[],[f340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW619_2 : TPTP v8.2.0. Released v6.1.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat May 18 19:35:23 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (22439)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (22442)WARNING: value z3 for option sas not known
% 0.11/0.35 % (22442)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)
% 0.11/0.35 % (22443)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35 % (22440)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35 % (22446)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)
% 0.11/0.35 % (22441)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35 % (22445)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)
% 0.11/0.35 % (22444)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)
% 0.11/0.35 % (22440)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.11/0.35 % (22440)Terminated due to inappropriate strategy.
% 0.11/0.35 % (22440)------------------------------
% 0.11/0.35 % (22440)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35 % (22441)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.11/0.35 % (22441)Terminated due to inappropriate strategy.
% 0.11/0.35 % (22441)------------------------------
% 0.11/0.35 % (22441)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35 % (22441)Termination reason: Inappropriate
% 0.11/0.35
% 0.11/0.35 % (22440)Termination reason: Inappropriate
% 0.11/0.35
% 0.11/0.35 % (22441)Memory used [KB]: 1061
% 0.11/0.35 % (22440)Memory used [KB]: 1061
% 0.11/0.35 % (22441)Time elapsed: 0.008 s
% 0.11/0.35 % (22440)Time elapsed: 0.008 s
% 0.11/0.35 % (22441)Instructions burned: 16 (million)
% 0.11/0.35 % (22440)Instructions burned: 17 (million)
% 0.11/0.35 % (22443)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.11/0.35 % (22443)Terminated due to inappropriate strategy.
% 0.11/0.35 % (22443)------------------------------
% 0.11/0.35 % (22443)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35 % (22443)Termination reason: Inappropriate
% 0.11/0.35
% 0.11/0.35 % (22443)Memory used [KB]: 1063
% 0.11/0.35 % (22443)Time elapsed: 0.008 s
% 0.11/0.35 % (22443)Instructions burned: 17 (million)
% 0.11/0.35 % (22440)------------------------------
% 0.11/0.35 % (22440)------------------------------
% 0.11/0.35 % (22441)------------------------------
% 0.11/0.35 % (22441)------------------------------
% 0.11/0.35 % (22443)------------------------------
% 0.11/0.35 % (22443)------------------------------
% 0.11/0.36 % (22444)First to succeed.
% 0.11/0.36 % (22444)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22439"
% 0.11/0.37 % (22444)Refutation found. Thanks to Tanya!
% 0.11/0.37 % SZS status Theorem for theBenchmark
% 0.11/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.37 % (22444)------------------------------
% 0.11/0.37 % (22444)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.37 % (22444)Termination reason: Refutation
% 0.11/0.37
% 0.11/0.37 % (22444)Memory used [KB]: 1209
% 0.11/0.37 % (22444)Time elapsed: 0.018 s
% 0.11/0.37 % (22444)Instructions burned: 33 (million)
% 0.11/0.37 % (22439)Success in time 0.037 s
%------------------------------------------------------------------------------