TSTP Solution File: SWW616_2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SWW616_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n007.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 : Wed Aug 31 19:20:19 EDT 2022
% Result : Theorem 1.90s 0.63s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 85
% Syntax : Number of formulae : 132 ( 36 unt; 70 typ; 0 def)
% Number of atoms : 495 ( 130 equ)
% Maximal formula atoms : 52 ( 7 avg)
% Number of connectives : 697 ( 264 ~; 68 |; 299 &)
% ( 0 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 1859 ( 364 atm; 924 fun; 377 num; 194 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 70 ( 31 >; 39 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 67 ( 61 usr; 36 con; 0-5 aty)
% Number of variables : 203 ( 103 !; 100 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
tuple0: $tType ).
tff(type_def_9,type,
map_int_int: $tType ).
tff(type_def_10,type,
array_int: $tType ).
tff(func_def_0,type,
witness: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool1: ty ).
tff(func_def_4,type,
true: bool ).
tff(func_def_5,type,
false: bool ).
tff(func_def_6,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(func_def_7,type,
tuple01: ty ).
tff(func_def_8,type,
tuple02: tuple0 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
ref: ty > ty ).
tff(func_def_13,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_14,type,
contents: ( ty * uni ) > uni ).
tff(func_def_15,type,
abs: $int > $int ).
tff(func_def_17,type,
div: ( $int * $int ) > $int ).
tff(func_def_18,type,
mod: ( $int * $int ) > $int ).
tff(func_def_21,type,
map: ( ty * ty ) > ty ).
tff(func_def_22,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(func_def_23,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(func_def_24,type,
const: ( ty * ty * uni ) > uni ).
tff(func_def_25,type,
array: ty > ty ).
tff(func_def_26,type,
mk_array: ( ty * $int * uni ) > uni ).
tff(func_def_27,type,
length: ( ty * uni ) > $int ).
tff(func_def_28,type,
elts: ( ty * uni ) > uni ).
tff(func_def_29,type,
get1: ( ty * uni * $int ) > uni ).
tff(func_def_30,type,
t2tb: $int > uni ).
tff(func_def_31,type,
tb2t: uni > $int ).
tff(func_def_32,type,
set1: ( ty * uni * $int * uni ) > uni ).
tff(func_def_33,type,
make: ( ty * $int * uni ) > uni ).
tff(func_def_34,type,
sum: ( map_int_int * $int * $int ) > $int ).
tff(func_def_35,type,
t2tb1: map_int_int > uni ).
tff(func_def_36,type,
tb2t1: uni > map_int_int ).
tff(func_def_38,type,
sum1: ( array_int * $int * $int ) > $int ).
tff(func_def_39,type,
t2tb2: array_int > uni ).
tff(func_def_40,type,
tb2t2: uni > array_int ).
tff(func_def_42,type,
sK0: ( map_int_int * $int * map_int_int * $int ) > $int ).
tff(func_def_43,type,
sK1: $int ).
tff(func_def_44,type,
sK2: map_int_int ).
tff(func_def_45,type,
sK3: $int ).
tff(func_def_46,type,
sK4: $int ).
tff(func_def_47,type,
sK5: $int ).
tff(func_def_48,type,
sK6: $int ).
tff(func_def_49,type,
sK7: $int ).
tff(func_def_50,type,
sK8: $int ).
tff(func_def_51,type,
sK9: $int ).
tff(func_def_52,type,
sK10: $int ).
tff(func_def_53,type,
sK11: $int ).
tff(func_def_54,type,
sK12: $int ).
tff(func_def_55,type,
sF13: $int ).
tff(func_def_56,type,
sF14: $int ).
tff(func_def_57,type,
sF15: $int ).
tff(func_def_58,type,
sF16: $int ).
tff(func_def_59,type,
sF17: $int ).
tff(func_def_60,type,
sF18: $int ).
tff(func_def_61,type,
sF19: $int ).
tff(func_def_62,type,
sF20: $int ).
tff(func_def_63,type,
sF21: $int ).
tff(func_def_64,type,
sF22: $int ).
tff(func_def_65,type,
sF23: $int ).
tff(func_def_66,type,
sF24: $int ).
tff(func_def_67,type,
sF25: $int ).
tff(pred_def_1,type,
sort: ( ty * uni ) > $o ).
tff(pred_def_4,type,
maxsublo: ( array_int * $int * $int ) > $o ).
tff(pred_def_5,type,
maxsub: ( array_int * $int ) > $o ).
tff(f602,plain,
$false,
inference(subsumption_resolution,[],[f601,f355]) ).
tff(f355,plain,
$less(sK9,sF17),
inference(definition_folding,[],[f307,f354]) ).
tff(f354,plain,
sum(sK2,sK12,sK11) = sF17,
introduced(function_definition,[]) ).
tff(f307,plain,
$less(sK9,sum(sK2,sK12,sK11)),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
( ~ $less(sK4,sK3)
& ( sK3 != sK1 )
& ~ $less(sK3,sK1)
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = sK6 )
& $less(sK9,sum(sK2,sK12,sK11))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),sK12)
& ~ $less(sK11,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(sK12,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),sK11)
& ( sK9 = sK10 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ! [X12: $int] :
( ~ $less(sK9,sum(sK2,X12,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X12)
| ~ $less($sum(sK1,$uminus(1)),X12) )
& ~ $less(sK8,sK1)
& ( sK7 = sum(sK2,$sum($sum(sK1,$uminus(1)),1),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ( sK9 = sum(sK2,sK8,sK6) )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = sK6 )
& ! [X13: $int] :
( ~ $less(sum(sK2,sK8,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) )
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),sK8)
& ~ $less($sum($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),$uminus(1)),sK1)
& ( sK5 = $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) )
& ~ $less(sK4,0)
& ~ $less(sK1,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f227,f233,f232,f231,f230,f229,f228]) ).
tff(f228,plain,
( ? [X0: $int,X1: map_int_int,X2: $int,X3: $int] :
( ~ $less(X3,X2)
& ( X0 != X2 )
& ~ $less(X2,X0)
& ? [X4: $int] :
( ? [X5: $int] :
( ( $sum(X0,div($sum(X2,$uminus(X0)),2)) = X5 )
& ? [X6: $int,X7: $int,X8: $int] :
( ? [X9: $int] :
( ? [X10: $int,X11: $int] :
( $less(X8,sum(X1,X11,X10))
& ~ $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X11)
& ~ $less(X10,$sum(X0,div($sum(X2,$uminus(X0)),2)))
& ~ $less(X11,X0)
& ~ $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X10) )
& ( X8 = X9 )
& ~ $less($sum(X2,$uminus(1)),$sum(X0,div($sum(X2,$uminus(X0)),2))) )
& ! [X12: $int] :
( ~ $less(X8,sum(X1,X12,$sum(X0,div($sum(X2,$uminus(X0)),2))))
| $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X12)
| ~ $less($sum(X0,$uminus(1)),X12) )
& ~ $less(X7,X0)
& ( sum(X1,$sum($sum(X0,$uminus(1)),1),$sum(X0,div($sum(X2,$uminus(X0)),2))) = X6 )
& ( sum(X1,X7,X5) = X8 )
& ( $sum(X0,div($sum(X2,$uminus(X0)),2)) = X5 )
& ! [X13: $int] :
( ~ $less(sum(X1,X7,$sum(X0,div($sum(X2,$uminus(X0)),2))),sum(X1,X13,$sum(X0,div($sum(X2,$uminus(X0)),2))))
| $less(X13,X0)
| $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X13) )
& ~ $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X7) )
& ~ $less($sum($sum(X0,div($sum(X2,$uminus(X0)),2)),$uminus(1)),X0) )
& ( $sum(X0,div($sum(X2,$uminus(X0)),2)) = X4 ) )
& ~ $less(X3,0)
& ~ $less(X0,0) )
=> ( ~ $less(sK4,sK3)
& ( sK3 != sK1 )
& ~ $less(sK3,sK1)
& ? [X4: $int] :
( ? [X5: $int] :
( ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X5 )
& ? [X8: $int,X7: $int,X6: $int] :
( ? [X9: $int] :
( ? [X11: $int,X10: $int] :
( $less(X8,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( X8 = X9 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ! [X12: $int] :
( ~ $less(X8,sum(sK2,X12,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X12)
| ~ $less($sum(sK1,$uminus(1)),X12) )
& ~ $less(X7,sK1)
& ( sum(sK2,$sum($sum(sK1,$uminus(1)),1),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) = X6 )
& ( sum(sK2,X7,X5) = X8 )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X5 )
& ! [X13: $int] :
( ~ $less(sum(sK2,X7,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) )
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X7) )
& ~ $less($sum($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),$uminus(1)),sK1) )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X4 ) )
& ~ $less(sK4,0)
& ~ $less(sK1,0) ) ),
introduced(choice_axiom,[]) ).
tff(f229,plain,
( ? [X4: $int] :
( ? [X5: $int] :
( ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X5 )
& ? [X8: $int,X7: $int,X6: $int] :
( ? [X9: $int] :
( ? [X11: $int,X10: $int] :
( $less(X8,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( X8 = X9 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ! [X12: $int] :
( ~ $less(X8,sum(sK2,X12,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X12)
| ~ $less($sum(sK1,$uminus(1)),X12) )
& ~ $less(X7,sK1)
& ( sum(sK2,$sum($sum(sK1,$uminus(1)),1),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) = X6 )
& ( sum(sK2,X7,X5) = X8 )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X5 )
& ! [X13: $int] :
( ~ $less(sum(sK2,X7,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) )
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X7) )
& ~ $less($sum($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),$uminus(1)),sK1) )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X4 ) )
=> ( ? [X5: $int] :
( ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X5 )
& ? [X8: $int,X7: $int,X6: $int] :
( ? [X9: $int] :
( ? [X11: $int,X10: $int] :
( $less(X8,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( X8 = X9 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ! [X12: $int] :
( ~ $less(X8,sum(sK2,X12,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X12)
| ~ $less($sum(sK1,$uminus(1)),X12) )
& ~ $less(X7,sK1)
& ( sum(sK2,$sum($sum(sK1,$uminus(1)),1),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) = X6 )
& ( sum(sK2,X7,X5) = X8 )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X5 )
& ! [X13: $int] :
( ~ $less(sum(sK2,X7,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) )
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X7) )
& ~ $less($sum($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),$uminus(1)),sK1) )
& ( sK5 = $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f230,plain,
( ? [X5: $int] :
( ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X5 )
& ? [X8: $int,X7: $int,X6: $int] :
( ? [X9: $int] :
( ? [X11: $int,X10: $int] :
( $less(X8,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( X8 = X9 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ! [X12: $int] :
( ~ $less(X8,sum(sK2,X12,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X12)
| ~ $less($sum(sK1,$uminus(1)),X12) )
& ~ $less(X7,sK1)
& ( sum(sK2,$sum($sum(sK1,$uminus(1)),1),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) = X6 )
& ( sum(sK2,X7,X5) = X8 )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = X5 )
& ! [X13: $int] :
( ~ $less(sum(sK2,X7,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) )
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X7) )
& ~ $less($sum($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),$uminus(1)),sK1) )
=> ( ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = sK6 )
& ? [X8: $int,X7: $int,X6: $int] :
( ? [X9: $int] :
( ? [X11: $int,X10: $int] :
( $less(X8,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( X8 = X9 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ! [X12: $int] :
( ~ $less(X8,sum(sK2,X12,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X12)
| ~ $less($sum(sK1,$uminus(1)),X12) )
& ~ $less(X7,sK1)
& ( sum(sK2,$sum($sum(sK1,$uminus(1)),1),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) = X6 )
& ( sum(sK2,X7,sK6) = X8 )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = sK6 )
& ! [X13: $int] :
( ~ $less(sum(sK2,X7,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) )
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X7) )
& ~ $less($sum($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),$uminus(1)),sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f231,plain,
( ? [X8: $int,X7: $int,X6: $int] :
( ? [X9: $int] :
( ? [X11: $int,X10: $int] :
( $less(X8,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( X8 = X9 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ! [X12: $int] :
( ~ $less(X8,sum(sK2,X12,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X12)
| ~ $less($sum(sK1,$uminus(1)),X12) )
& ~ $less(X7,sK1)
& ( sum(sK2,$sum($sum(sK1,$uminus(1)),1),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) = X6 )
& ( sum(sK2,X7,sK6) = X8 )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = sK6 )
& ! [X13: $int] :
( ~ $less(sum(sK2,X7,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) )
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X7) )
=> ( ? [X9: $int] :
( ? [X11: $int,X10: $int] :
( $less(sK9,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( sK9 = X9 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ! [X12: $int] :
( ~ $less(sK9,sum(sK2,X12,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X12)
| ~ $less($sum(sK1,$uminus(1)),X12) )
& ~ $less(sK8,sK1)
& ( sK7 = sum(sK2,$sum($sum(sK1,$uminus(1)),1),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
& ( sK9 = sum(sK2,sK8,sK6) )
& ( $sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = sK6 )
& ! [X13: $int] :
( ~ $less(sum(sK2,sK8,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) )
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),sK8) ) ),
introduced(choice_axiom,[]) ).
tff(f232,plain,
( ? [X9: $int] :
( ? [X11: $int,X10: $int] :
( $less(sK9,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( sK9 = X9 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) )
=> ( ? [X11: $int,X10: $int] :
( $less(sK9,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
& ( sK9 = sK10 )
& ~ $less($sum(sK3,$uminus(1)),$sum(sK1,div($sum(sK3,$uminus(sK1)),2))) ) ),
introduced(choice_axiom,[]) ).
tff(f233,plain,
( ? [X11: $int,X10: $int] :
( $less(sK9,sum(sK2,X11,X10))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X11)
& ~ $less(X10,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(X11,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X10) )
=> ( $less(sK9,sum(sK2,sK12,sK11))
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),sK12)
& ~ $less(sK11,$sum(sK1,div($sum(sK3,$uminus(sK1)),2)))
& ~ $less(sK12,sK1)
& ~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),sK11) ) ),
introduced(choice_axiom,[]) ).
tff(f227,plain,
? [X0: $int,X1: map_int_int,X2: $int,X3: $int] :
( ~ $less(X3,X2)
& ( X0 != X2 )
& ~ $less(X2,X0)
& ? [X4: $int] :
( ? [X5: $int] :
( ( $sum(X0,div($sum(X2,$uminus(X0)),2)) = X5 )
& ? [X6: $int,X7: $int,X8: $int] :
( ? [X9: $int] :
( ? [X10: $int,X11: $int] :
( $less(X8,sum(X1,X11,X10))
& ~ $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X11)
& ~ $less(X10,$sum(X0,div($sum(X2,$uminus(X0)),2)))
& ~ $less(X11,X0)
& ~ $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X10) )
& ( X8 = X9 )
& ~ $less($sum(X2,$uminus(1)),$sum(X0,div($sum(X2,$uminus(X0)),2))) )
& ! [X12: $int] :
( ~ $less(X8,sum(X1,X12,$sum(X0,div($sum(X2,$uminus(X0)),2))))
| $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X12)
| ~ $less($sum(X0,$uminus(1)),X12) )
& ~ $less(X7,X0)
& ( sum(X1,$sum($sum(X0,$uminus(1)),1),$sum(X0,div($sum(X2,$uminus(X0)),2))) = X6 )
& ( sum(X1,X7,X5) = X8 )
& ( $sum(X0,div($sum(X2,$uminus(X0)),2)) = X5 )
& ! [X13: $int] :
( ~ $less(sum(X1,X7,$sum(X0,div($sum(X2,$uminus(X0)),2))),sum(X1,X13,$sum(X0,div($sum(X2,$uminus(X0)),2))))
| $less(X13,X0)
| $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X13) )
& ~ $less($sum(X0,div($sum(X2,$uminus(X0)),2)),X7) )
& ~ $less($sum($sum(X0,div($sum(X2,$uminus(X0)),2)),$uminus(1)),X0) )
& ( $sum(X0,div($sum(X2,$uminus(X0)),2)) = X4 ) )
& ~ $less(X3,0)
& ~ $less(X0,0) ),
inference(rectify,[],[f180]) ).
tff(f180,plain,
? [X2: $int,X1: map_int_int,X3: $int,X0: $int] :
( ~ $less(X0,X3)
& ( X2 != X3 )
& ~ $less(X3,X2)
& ? [X4: $int] :
( ? [X5: $int] :
( ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 )
& ? [X6: $int,X7: $int,X8: $int] :
( ? [X11: $int] :
( ? [X13: $int,X12: $int] :
( $less(X8,sum(X1,X12,X13))
& ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X12)
& ~ $less(X13,$sum(X2,div($sum(X3,$uminus(X2)),2)))
& ~ $less(X12,X2)
& ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X13) )
& ( X8 = X11 )
& ~ $less($sum(X3,$uminus(1)),$sum(X2,div($sum(X3,$uminus(X2)),2))) )
& ! [X9: $int] :
( ~ $less(X8,sum(X1,X9,$sum(X2,div($sum(X3,$uminus(X2)),2))))
| $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9)
| ~ $less($sum(X2,$uminus(1)),X9) )
& ~ $less(X7,X2)
& ( sum(X1,$sum($sum(X2,$uminus(1)),1),$sum(X2,div($sum(X3,$uminus(X2)),2))) = X6 )
& ( sum(X1,X7,X5) = X8 )
& ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 )
& ! [X10: $int] :
( ~ $less(sum(X1,X7,$sum(X2,div($sum(X3,$uminus(X2)),2))),sum(X1,X10,$sum(X2,div($sum(X3,$uminus(X2)),2))))
| $less(X10,X2)
| $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X10) )
& ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X7) )
& ~ $less($sum($sum(X2,div($sum(X3,$uminus(X2)),2)),$uminus(1)),X2) )
& ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X4 ) )
& ~ $less(X0,0)
& ~ $less(X2,0) ),
inference(flattening,[],[f179]) ).
tff(f179,plain,
? [X1: map_int_int,X3: $int,X2: $int,X0: $int] :
( ? [X4: $int] :
( ? [X5: $int] :
( ? [X8: $int,X7: $int,X6: $int] :
( ? [X11: $int] :
( ? [X13: $int,X12: $int] :
( $less(X8,sum(X1,X12,X13))
& ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X12)
& ~ $less(X12,X2)
& ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X13)
& ~ $less(X13,$sum(X2,div($sum(X3,$uminus(X2)),2))) )
& ~ $less($sum(X3,$uminus(1)),$sum(X2,div($sum(X3,$uminus(X2)),2)))
& ( X8 = X11 ) )
& ! [X10: $int] :
( ~ $less(sum(X1,X7,$sum(X2,div($sum(X3,$uminus(X2)),2))),sum(X1,X10,$sum(X2,div($sum(X3,$uminus(X2)),2))))
| $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X10)
| $less(X10,X2) )
& ( sum(X1,X7,X5) = X8 )
& ( sum(X1,$sum($sum(X2,$uminus(1)),1),$sum(X2,div($sum(X3,$uminus(X2)),2))) = X6 )
& ! [X9: $int] :
( ~ $less(X8,sum(X1,X9,$sum(X2,div($sum(X3,$uminus(X2)),2))))
| $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9)
| ~ $less($sum(X2,$uminus(1)),X9) )
& ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 )
& ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X7)
& ~ $less(X7,X2) )
& ~ $less($sum($sum(X2,div($sum(X3,$uminus(X2)),2)),$uminus(1)),X2)
& ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 ) )
& ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X4 ) )
& ( X2 != X3 )
& ~ $less(X2,0)
& ~ $less(X0,0)
& ~ $less(X3,X2)
& ~ $less(X0,X3) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
~ ! [X1: map_int_int,X3: $int,X2: $int,X0: $int] :
( ( ~ $less(X2,0)
& ~ $less(X0,0)
& ~ $less(X3,X2)
& ~ $less(X0,X3) )
=> ( ( X2 != X3 )
=> ! [X4: $int] :
( ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X4 )
=> ! [X5: $int] :
( ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 )
=> ( ~ $less($sum($sum(X2,div($sum(X3,$uminus(X2)),2)),$uminus(1)),X2)
=> ! [X8: $int,X7: $int,X6: $int] :
( ( ( sum(X1,X7,X5) = X8 )
& ( sum(X1,$sum($sum(X2,$uminus(1)),1),$sum(X2,div($sum(X3,$uminus(X2)),2))) = X6 )
& ! [X9: $int] :
( ( ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9)
& $less($sum(X2,$uminus(1)),X9) )
=> ~ $less(X8,sum(X1,X9,$sum(X2,div($sum(X3,$uminus(X2)),2)))) )
& ( $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 )
& ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X7)
& ~ $less(X7,X2) )
=> ( ! [X10: $int] :
( ( ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X10)
& ~ $less(X10,X2) )
=> ~ $less(sum(X1,X7,$sum(X2,div($sum(X3,$uminus(X2)),2))),sum(X1,X10,$sum(X2,div($sum(X3,$uminus(X2)),2)))) )
=> ! [X11: $int] :
( ( X8 = X11 )
=> ( ~ $less($sum(X3,$uminus(1)),$sum(X2,div($sum(X3,$uminus(X2)),2)))
=> ! [X13: $int,X12: $int] :
( ( ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X12)
& ~ $less(X12,X2)
& ~ $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X13)
& ~ $less(X13,$sum(X2,div($sum(X3,$uminus(X2)),2))) )
=> ~ $less(X8,sum(X1,X12,X13)) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f105]) ).
tff(f105,plain,
~ ! [X0: $int,X10: map_int_int,X22: $int,X23: $int] :
( ( ~ $less(X23,X22)
& ~ $less(X0,X23)
& ~ $less(X0,0)
& ~ $less(X22,0) )
=> ( ( X22 != X23 )
=> ! [X26: $int] :
( ( $sum(X22,div($sum(X23,$uminus(X22)),2)) = X26 )
=> ! [X27: $int] :
( ( $sum(X22,div($sum(X23,$uminus(X22)),2)) = X27 )
=> ( ~ $less($sum($sum(X22,div($sum(X23,$uminus(X22)),2)),$uminus(1)),X22)
=> ! [X25: $int,X29: $int,X28: $int] :
( ( ( sum(X10,X29,X27) = X28 )
& ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X29)
& ~ $less(X29,X22)
& ( sum(X10,$sum($sum(X22,$uminus(1)),1),$sum(X22,div($sum(X23,$uminus(X22)),2))) = X25 )
& ! [X30: $int] :
( ( $less($sum(X22,$uminus(1)),X30)
& ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X30) )
=> ~ $less(X28,sum(X10,X30,$sum(X22,div($sum(X23,$uminus(X22)),2)))) )
& ( $sum(X22,div($sum(X23,$uminus(X22)),2)) = X27 ) )
=> ( ! [X30: $int] :
( ( ~ $less(X30,X22)
& ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X30) )
=> ~ $less(sum(X10,X29,$sum(X22,div($sum(X23,$uminus(X22)),2))),sum(X10,X30,$sum(X22,div($sum(X23,$uminus(X22)),2)))) )
=> ! [X31: $int] :
( ( X28 = X31 )
=> ( ~ $less($sum(X23,$uminus(1)),$sum(X22,div($sum(X23,$uminus(X22)),2)))
=> ! [X30: $int,X32: $int] :
( ( ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X30)
& ~ $less(X32,$sum(X22,div($sum(X23,$uminus(X22)),2)))
& ~ $less(X30,X22)
& ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X32) )
=> ~ $less(X28,sum(X10,X30,X32)) ) ) ) ) ) ) ) ) ) ),
inference(theory_normalization,[],[f70]) ).
tff(f70,plain,
~ ! [X0: $int,X10: map_int_int,X22: $int,X23: $int] :
( ( ~ $less(X23,X22)
& ~ $less(X0,X23)
& ~ $less(X0,0)
& ~ $less(X22,0) )
=> ( ( X22 != X23 )
=> ! [X26: $int] :
( ( $sum(X22,div($sum(X23,$uminus(X22)),2)) = X26 )
=> ! [X27: $int] :
( ( $sum(X22,div($sum(X23,$uminus(X22)),2)) = X27 )
=> ( ~ $less($sum($sum(X22,div($difference(X23,X22),2)),$uminus(1)),X22)
=> ! [X25: $int,X29: $int,X28: $int] :
( ( ( sum(X10,X29,X27) = X28 )
& ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X29)
& ~ $less(X29,X22)
& ( sum(X10,$sum($sum(X22,$uminus(1)),1),$sum(X22,div($sum(X23,$uminus(X22)),2))) = X25 )
& ! [X30: $int] :
( ( $less($sum(X22,$uminus(1)),X30)
& ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X30) )
=> ~ $less(X28,sum(X10,X30,$sum(X22,div($sum(X23,$uminus(X22)),2)))) )
& ( $sum(X22,div($sum(X23,$uminus(X22)),2)) = X27 ) )
=> ( ! [X30: $int] :
( ( ~ $less(X30,X22)
& ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X30) )
=> ~ $less(sum(X10,X29,$sum(X22,div($sum(X23,$uminus(X22)),2))),sum(X10,X30,$sum(X22,div($sum(X23,$uminus(X22)),2)))) )
=> ! [X31: $int] :
( ( X28 = X31 )
=> ( ~ $less($sum(X23,$uminus(1)),$sum(X22,div($sum(X23,$uminus(X22)),2)))
=> ! [X30: $int,X32: $int] :
( ( ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X30)
& ~ $less(X32,$sum(X22,div($sum(X23,$uminus(X22)),2)))
& ~ $less(X30,X22)
& ~ $less($sum(X22,div($sum(X23,$uminus(X22)),2)),X32) )
=> ~ $less(X28,sum(X10,X30,X32)) ) ) ) ) ) ) ) ) ) ),
inference(theory_normalization,[],[f65]) ).
tff(f65,negated_conjecture,
~ ! [X0: $int,X10: map_int_int,X22: $int,X23: $int] :
( ( $lesseq(X22,X23)
& $lesseq(X23,X0)
& $lesseq(0,X0)
& $lesseq(0,X22) )
=> ( ( X22 != X23 )
=> ! [X26: $int] :
( ( $sum(X22,div($difference(X23,X22),2)) = X26 )
=> ! [X27: $int] :
( ( $sum(X22,div($difference(X23,X22),2)) = X27 )
=> ( $lesseq(X22,$difference($sum(X22,div($difference(X23,X22),2)),1))
=> ! [X25: $int,X29: $int,X28: $int] :
( ( ( sum(X10,X29,X27) = X28 )
& $lesseq(X29,$sum(X22,div($difference(X23,X22),2)))
& $lesseq(X22,X29)
& ( sum(X10,$sum($difference(X22,1),1),$sum(X22,div($difference(X23,X22),2))) = X25 )
& ! [X30: $int] :
( ( $less($difference(X22,1),X30)
& $lesseq(X30,$sum(X22,div($difference(X23,X22),2))) )
=> $lesseq(sum(X10,X30,$sum(X22,div($difference(X23,X22),2))),X28) )
& ( $sum(X22,div($difference(X23,X22),2)) = X27 ) )
=> ( ! [X30: $int] :
( ( $lesseq(X22,X30)
& $lesseq(X30,$sum(X22,div($difference(X23,X22),2))) )
=> $lesseq(sum(X10,X30,$sum(X22,div($difference(X23,X22),2))),sum(X10,X29,$sum(X22,div($difference(X23,X22),2)))) )
=> ! [X31: $int] :
( ( X28 = X31 )
=> ( $lesseq($sum(X22,div($difference(X23,X22),2)),$difference(X23,1))
=> ! [X30: $int,X32: $int] :
( ( $lesseq(X30,$sum(X22,div($difference(X23,X22),2)))
& $lesseq($sum(X22,div($difference(X23,X22),2)),X32)
& $lesseq(X22,X30)
& $lesseq(X32,$sum(X22,div($difference(X23,X22),2))) )
=> $lesseq(sum(X10,X30,X32),X28) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f64]) ).
tff(f64,conjecture,
! [X0: $int,X10: map_int_int,X22: $int,X23: $int] :
( ( $lesseq(X22,X23)
& $lesseq(X23,X0)
& $lesseq(0,X0)
& $lesseq(0,X22) )
=> ( ( X22 != X23 )
=> ! [X26: $int] :
( ( $sum(X22,div($difference(X23,X22),2)) = X26 )
=> ! [X27: $int] :
( ( $sum(X22,div($difference(X23,X22),2)) = X27 )
=> ( $lesseq(X22,$difference($sum(X22,div($difference(X23,X22),2)),1))
=> ! [X25: $int,X29: $int,X28: $int] :
( ( ( sum(X10,X29,X27) = X28 )
& $lesseq(X29,$sum(X22,div($difference(X23,X22),2)))
& $lesseq(X22,X29)
& ( sum(X10,$sum($difference(X22,1),1),$sum(X22,div($difference(X23,X22),2))) = X25 )
& ! [X30: $int] :
( ( $less($difference(X22,1),X30)
& $lesseq(X30,$sum(X22,div($difference(X23,X22),2))) )
=> $lesseq(sum(X10,X30,$sum(X22,div($difference(X23,X22),2))),X28) )
& ( $sum(X22,div($difference(X23,X22),2)) = X27 ) )
=> ( ! [X30: $int] :
( ( $lesseq(X22,X30)
& $lesseq(X30,$sum(X22,div($difference(X23,X22),2))) )
=> $lesseq(sum(X10,X30,$sum(X22,div($difference(X23,X22),2))),sum(X10,X29,$sum(X22,div($difference(X23,X22),2)))) )
=> ! [X31: $int] :
( ( X28 = X31 )
=> ( $lesseq($sum(X22,div($difference(X23,X22),2)),$difference(X23,1))
=> ! [X30: $int,X32: $int] :
( ( $lesseq(X30,$sum(X22,div($difference(X23,X22),2)))
& $lesseq($sum(X22,div($difference(X23,X22),2)),X32)
& $lesseq(X22,X30)
& $lesseq(X32,$sum(X22,div($difference(X23,X22),2))) )
=> $lesseq(sum(X10,X30,X32),X28) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_maximum_subarray_rec) ).
tff(f601,plain,
~ $less(sK9,sF17),
inference(subsumption_resolution,[],[f600,f402]) ).
tff(f402,plain,
~ $less(sK5,sK12),
inference(backward_demodulation,[],[f383,f399]) ).
tff(f399,plain,
sK5 = sK6,
inference(backward_demodulation,[],[f353,f375]) ).
tff(f375,plain,
sF16 = sK5,
inference(definition_folding,[],[f292,f352,f351,f350,f349]) ).
tff(f349,plain,
$uminus(sK1) = sF13,
introduced(function_definition,[]) ).
tff(f350,plain,
$sum(sK3,sF13) = sF14,
introduced(function_definition,[]) ).
tff(f351,plain,
div(sF14,2) = sF15,
introduced(function_definition,[]) ).
tff(f352,plain,
sF16 = $sum(sK1,sF15),
introduced(function_definition,[]) ).
tff(f292,plain,
sK5 = $sum(sK1,div($sum(sK3,$uminus(sK1)),2)),
inference(cnf_transformation,[],[f234]) ).
tff(f353,plain,
sF16 = sK6,
inference(definition_folding,[],[f308,f352,f351,f350,f349]) ).
tff(f308,plain,
$sum(sK1,div($sum(sK3,$uminus(sK1)),2)) = sK6,
inference(cnf_transformation,[],[f234]) ).
tff(f383,plain,
~ $less(sK6,sK12),
inference(backward_demodulation,[],[f356,f353]) ).
tff(f356,plain,
~ $less(sF16,sK12),
inference(definition_folding,[],[f306,f352,f351,f350,f349]) ).
tff(f306,plain,
~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),sK12),
inference(cnf_transformation,[],[f234]) ).
tff(f600,plain,
( $less(sK5,sK12)
| ~ $less(sK9,sF17) ),
inference(subsumption_resolution,[],[f599,f304]) ).
tff(f304,plain,
~ $less(sK12,sK1),
inference(cnf_transformation,[],[f234]) ).
tff(f599,plain,
( $less(sK12,sK1)
| ~ $less(sK9,sF17)
| $less(sK5,sK12) ),
inference(superposition,[],[f412,f598]) ).
tff(f598,plain,
sF17 = sum(sK2,sK12,sK5),
inference(backward_demodulation,[],[f354,f595]) ).
tff(f595,plain,
sK5 = sK11,
inference(subsumption_resolution,[],[f562,f408]) ).
tff(f408,plain,
~ $less(sK11,sK5),
inference(backward_demodulation,[],[f393,f399]) ).
tff(f393,plain,
~ $less(sK11,sK6),
inference(forward_demodulation,[],[f357,f353]) ).
tff(f357,plain,
~ $less(sK11,sF16),
inference(definition_folding,[],[f305,f352,f351,f350,f349]) ).
tff(f305,plain,
~ $less(sK11,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),
inference(cnf_transformation,[],[f234]) ).
tff(f562,plain,
( ( sK5 = sK11 )
| $less(sK11,sK5) ),
inference(resolution,[],[f94,f403]) ).
tff(f403,plain,
~ $less(sK5,sK11),
inference(backward_demodulation,[],[f384,f399]) ).
tff(f384,plain,
~ $less(sK6,sK11),
inference(backward_demodulation,[],[f358,f353]) ).
tff(f358,plain,
~ $less(sF16,sK11),
inference(definition_folding,[],[f303,f352,f351,f350,f349]) ).
tff(f303,plain,
~ $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),sK11),
inference(cnf_transformation,[],[f234]) ).
tff(f94,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_149,[]) ).
tff(f412,plain,
! [X13: $int] :
( ~ $less(sK9,sum(sK2,X13,sK5))
| $less(sK5,X13)
| $less(X13,sK1) ),
inference(forward_demodulation,[],[f410,f399]) ).
tff(f410,plain,
! [X13: $int] :
( $less(sK5,X13)
| ~ $less(sK9,sum(sK2,X13,sK6))
| $less(X13,sK1) ),
inference(backward_demodulation,[],[f398,f399]) ).
tff(f398,plain,
! [X13: $int] :
( ~ $less(sK9,sum(sK2,X13,sK6))
| $less(sK6,X13)
| $less(X13,sK1) ),
inference(forward_demodulation,[],[f397,f353]) ).
tff(f397,plain,
! [X13: $int] :
( $less(X13,sK1)
| ~ $less(sK9,sum(sK2,X13,sK6))
| $less(sF16,X13) ),
inference(forward_demodulation,[],[f396,f391]) ).
tff(f391,plain,
sK9 = sF24,
inference(forward_demodulation,[],[f387,f381]) ).
tff(f381,plain,
sK9 = sum(sK2,sK8,sK6),
inference(backward_demodulation,[],[f367,f368]) ).
tff(f368,plain,
sK9 = sF23,
inference(definition_folding,[],[f297,f367]) ).
tff(f297,plain,
sK9 = sum(sK2,sK8,sK6),
inference(cnf_transformation,[],[f234]) ).
tff(f367,plain,
sum(sK2,sK8,sK6) = sF23,
introduced(function_definition,[]) ).
tff(f387,plain,
sF24 = sum(sK2,sK8,sK6),
inference(backward_demodulation,[],[f370,f353]) ).
tff(f370,plain,
sF24 = sum(sK2,sK8,sF16),
introduced(function_definition,[]) ).
tff(f396,plain,
! [X13: $int] :
( $less(X13,sK1)
| ~ $less(sF24,sum(sK2,X13,sK6))
| $less(sF16,X13) ),
inference(forward_demodulation,[],[f371,f353]) ).
tff(f371,plain,
! [X13: $int] :
( ~ $less(sF24,sum(sK2,X13,sF16))
| $less(X13,sK1)
| $less(sF16,X13) ),
inference(definition_folding,[],[f295,f352,f351,f350,f349,f352,f351,f350,f349,f370,f352,f351,f350,f349]) ).
tff(f295,plain,
! [X13: $int] :
( ~ $less(sum(sK2,sK8,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))),sum(sK2,X13,$sum(sK1,div($sum(sK3,$uminus(sK1)),2))))
| $less(X13,sK1)
| $less($sum(sK1,div($sum(sK3,$uminus(sK1)),2)),X13) ),
inference(cnf_transformation,[],[f234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWW616=2 : TPTP v8.1.0. Released v6.1.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 20:41:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.54 % (14711)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.55 % (14711)Instruction limit reached!
% 0.19/0.55 % (14711)------------------------------
% 0.19/0.55 % (14711)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55 % (14727)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.55 % (14726)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.55 % (14719)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.56 % (14718)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.56 % (14710)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.56 % (14711)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56 % (14711)Termination reason: Unknown
% 0.19/0.56 % (14711)Termination phase: Preprocessing 3
% 0.19/0.56
% 0.19/0.56 % (14711)Memory used [KB]: 1151
% 0.19/0.56 % (14711)Time elapsed: 0.007 s
% 0.19/0.56 % (14711)Instructions burned: 7 (million)
% 0.19/0.56 % (14711)------------------------------
% 0.19/0.56 % (14711)------------------------------
% 0.19/0.56 % (14710)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.58 % (14710)Terminated due to inappropriate strategy.
% 0.19/0.58 % (14710)------------------------------
% 0.19/0.58 % (14710)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.58 % (14710)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.58 % (14710)Termination reason: Inappropriate
% 0.19/0.58
% 0.19/0.58 % (14710)Memory used [KB]: 1151
% 0.19/0.58 % (14710)Time elapsed: 0.009 s
% 0.19/0.58 % (14710)Instructions burned: 10 (million)
% 0.19/0.58 % (14710)------------------------------
% 0.19/0.58 % (14710)------------------------------
% 0.19/0.59 % (14713)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.60 % (14705)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.60 % (14714)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.61 % (14708)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.61 % (14729)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.61 % (14725)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.61 % (14728)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.61 % (14709)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.61 % (14732)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.61 % (14704)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.61 % (14721)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.62 % (14730)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.62 % (14733)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.19/0.62 % (14704)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.62 % (14704)Terminated due to inappropriate strategy.
% 0.19/0.62 % (14704)------------------------------
% 0.19/0.62 % (14704)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.62 % (14704)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.62 % (14704)Termination reason: Inappropriate
% 0.19/0.62
% 0.19/0.62 % (14704)Memory used [KB]: 1151
% 0.19/0.62 % (14704)Time elapsed: 0.008 s
% 0.19/0.62 % (14704)Instructions burned: 9 (million)
% 0.19/0.62 % (14704)------------------------------
% 0.19/0.62 % (14704)------------------------------
% 0.19/0.62 % (14716)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.62 % (14706)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.62 % (14720)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.90/0.62 % (14717)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.90/0.62 % (14719)First to succeed.
% 1.90/0.62 % (14724)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.90/0.63 % (14712)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.90/0.63 % (14712)Instruction limit reached!
% 1.90/0.63 % (14712)------------------------------
% 1.90/0.63 % (14712)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.90/0.63 % (14712)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.90/0.63 % (14712)Termination reason: Unknown
% 1.90/0.63 % (14712)Termination phase: Including theory axioms
% 1.90/0.63
% 1.90/0.63 % (14712)Memory used [KB]: 895
% 1.90/0.63 % (14712)Time elapsed: 0.003 s
% 1.90/0.63 % (14712)Instructions burned: 3 (million)
% 1.90/0.63 % (14712)------------------------------
% 1.90/0.63 % (14712)------------------------------
% 1.90/0.63 % (14719)Refutation found. Thanks to Tanya!
% 1.90/0.63 % SZS status Theorem for theBenchmark
% 1.90/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 1.90/0.63 % (14719)------------------------------
% 1.90/0.63 % (14719)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.90/0.63 % (14719)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.90/0.63 % (14719)Termination reason: Refutation
% 1.90/0.63
% 1.90/0.63 % (14719)Memory used [KB]: 1535
% 1.90/0.63 % (14719)Time elapsed: 0.210 s
% 1.90/0.63 % (14719)Instructions burned: 28 (million)
% 1.90/0.63 % (14719)------------------------------
% 1.90/0.63 % (14719)------------------------------
% 1.90/0.63 % (14703)Success in time 0.284 s
%------------------------------------------------------------------------------